Oct 15, 1976 - M.Sc,, U n i v e r s i t y o f B r i t i s h Columbia,. 1972 ... both as a sequence, of boundary points and as a region in a ...... FIGURE 1.3 (b) The integers in the squares form ...... to a goal by reading the angles and ranges to the edges of ...... current sguare can either be one up, one right; or diagonally up.
9t
REPRESENTING
S P A T I A L E X P E R I E N C E AND S O L V I N G S P A T I A L PROBLEMS I N A S I M U L A T E D ROBOT ENVIRONMENT by PETER
M.Sc,,
University
FORBES
SOWAT
of British
Columbia,
A T H E S I S SUBMITTED IN PARTIAL THE R E Q U I R E M E N T S FOR T H E DOCTOR O F
EULF.ILLMENT D E G R E E OF
PHILOSOPHY in
THE
FACULTY
{ Department
We
OF
GRADUATE
of Computer
STUDIES Science)
accept t h i s t h e s i s as conforming to the required standard- .
THE
UNIVERSITY
OF
October, ^
BRITISH
1972
COLUMBIA
1979
P e t e r Forbes Rowat , 1 9 7 9
OF
In presenting
this thesis in partial
fulfilment of the requirements for
an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t freely available for reference
and study.
I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives.
It is understood that copying or publication
of this thesis f o r financial gain shall not be allowed without my written permission.
Department of
CfriAA^u^V
SCL&AICI
The University of B r i t i s h Columbia 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5
Date
11
Abstract This t h e s i s i s concerned with s p a t i a l a s p e c t s of p e r c e p t i o n and a c t i o n i n a simple robot. To this end, the problem of designing a r o b o t - c o n t r o l l e r f o r a robot in a simulated robot-environment system i s considered* The environment i s a two-dimensional t a b l e t o p with movable p o l y g o n a l shapes on i t . The robot has an eye which 'saes' an area of the t a b l e t o p centred on itself, with a r e s o l u t i o n which decreases from the centre to the periphery. Algorithms are presented for s i m u l a t i n g the motion and c o l l i s i o n of two dimensional shapes i n t h i s environment. These a l g o r i t h m s use r e p r e s e n t a t i o n s of shape both as a sequence, of boundary p o i n t s and as a r e g i o n i n a d i g i t a l image. A method i s o u t l i n e d f o r c o n s t r u c t i n g and updating the world model of the robot as new v i s u a l i n p u t i s r e c e i v e d from the eye. I t i s proposed t h a t , i n the world model, the s p a t i a l problems o f p a t h - f i n d i n g and object-moving be based on a l g o r i t h m s t h a t f i n d the s k e l e t o n of the shape of empty space and of the shape of the moved o b j e c t . A new i t e r a t i v e a l g o r i t h m f o r f i n d i n g the s k e l e t o n , with the property that the s k e l e t o n of a connected shape i s connected, i s presented. . T h i s i s a p p l i e d to p a t h - f i n d i n g and simple object-moving problems. Fi.nally, d i r e c t i o n s f o r f u t u r e work, are o u t l i n e d .
iii TABLE OF CONTENTS I
Int rod u c t i o n .......................................... 1 1.1 Aims and motivation . . . . . . . . . . . . . . . . . . . a . . . . .!,».... .1 1.2 The a c t i o n c y c l e ............. * .............. , .6 1*3 System overview ................................. ,10 1.4 System s t a t u s ................................... 22 1.5 Reader's guide .................................. 23 XI Background Issues • • . . . . . . . . . . . . » . : < . . * > , • » . • '• . . . . i. * » • ' • • 25 II. 1 a r t i f i c i a l intelligence i s a science with g o a l s and paradigms 25 IX.1.1 The paradigms of A r t i f i c i a l I n t e l l i g e n c e ...26 IX. 1,. 2 AI has p o t e n t i a l l y rich relationships with many other f i e l d s 29 II.1.3 Understanding the world i s a p r e r e q u i s i t e to doing mathematics 4 . . . . . . . . . . . . . . . . . . . . . 34 IX. 1.4 A theory of intelligence w i l l be p r i m a r i l y concerned with representations of t h e world .............................. 36 II.1.5 A theory o f i n t e l l i g e n c e w i l l describe intelligent systems a t many different l e v e l s ,. . .. ....... . . . . . . . ...... ....... ......... .39 I I . 2 Simulating a robot i s a promising approach to A r t i f i c i a l Intelligence ........................ 41 11*3 The c u r r e n t AI t r a d i t i o n f o r t h e design of planning and problem s o l v i n g ' systems i s not e a s i l y adaptable t o my purpose . 4 . . . . 45 II.3. 1 An exegesis of some AI p l a n n i n g and problem-solving systems ................... .45 11.3.2 C r i t i c i s m s of the Fregean t r a d i t i o n i n planning and problem-solving ............... .55 I I . 4 A survey of c l o s e l y r e l a t e d t o p i c s ............. 58 II*4.1 Previous robot s i m u l a t i o n s ................ 59 IX. 4'. 2 Three a n a l y s e s of simple organisms ......... 62 11.4.3 S i m u l a t i o n s based on animal behaviour . .... 65 IX. 4*4 Robot s i m u l a t i o n s based on decision theory .................................... 67 11.4.5 C o g n i t i v e maps ............................ 69 11.4.6 S p a t i a l planning systems .................. 71 11*4.7 Systems f o r s i m u l a t i n g . the motion of r i g i d o b j e c t s ............................. 72 IX. 4. 8 Imagery ............ 76 I I . 4.9 B e h a v i o u r a l t h e o r i e s ...................... 77 III The s i m u l a t e d organism-environment system ........... 83 I I I . 1 The simulated environment, TABLETOP ............ 87 I I I . 1.1 An overview of the s i m u l a t i o n method ..... 87 III.1*2 The algorithms used i n the s i m u l a t i o n .... 97 III-1.2.1 The o v e r l a y problem 117 III.1.3 An example of TABLETOP performance 122 I I I . 2 The simulated organism Utak and h i s t a s k s 128 III.2.1 Design c o n s i d e r a t i o n s ......... .,128
iv
III.2.2 III,. 2.3
IV
V
The s e n s o r y - m o t o r c a p a b i l i t i e s o f Otak ..130 Examples of Utak's sensory-motor experience ... , , . .... , ..... ... ... .» ... . 132 I I I , 2. 4 Examples o f t a s k s f o r Utak 134 I I I . 3 An extension and two generalizations of TABLETOP ...... 135 Towards t h e d e s i g n o f a r o b o t - c o n t r o l l e r »I * . . . . . . . . 143 IV. 1 An a n a l o g y i . 143 IV,2 The p a r t s o f an o r g a n i s m - c o n t r o l l e r ...... .. ... 147 IV, 3 The g o a l b e h a v i o u r f o r an o r g a n i s m - c o n t r o l l e r .149 IV.4 A f i r s t approach t o implementation ............175 IV. 4.1 D e f i n i t i o n o f t h e w o r l d model ,.,.,......,..176 IV;l4>2 P e r c e p t i o n : accommodation to the first r e t i n a l impression . . . ^ , 1 7 8 IV, 4.2,1 Edge and r e g i o n f i n d i n g .............179 IV.4;2.2 Interpreting the first retinal impression . . . . . . . . . . . . . . . . . . . . . . . . . . 181 IV. 4.2.3 Accommodating the default world model to the first retinal impression 185 IV,4.3 P e r c e p t i o n : accommodation t o subsequent r e t i n a l impressions . . . . . . . . . . . . . . . . . . . . . . 187 IV;. 4.4 accommodation, a n o t h e r a p p r o a c h ..........190 IV. 4,5 The s p a t i a l p l a n n e r .,.,,.,.,,..,....,,.,,,192 IV.5 An a l t e r n a t i v e a p p r o a c h t o i m p l e m e n t a t i o n i . . . . . 1 9 3 IV. 6 Summary .................................194 P a t h - f i n d i n g and t h e s k e l e t o n o f a p l a n a r shape i..,,,196 V. I Introduction to path-finding algorithms . . . . . . . . 196 V.2 The s k e l e t o n 202 V, 2, 1 D e f i n i t i o n and p r o p e r t i e s ............. 203 V.2.2 Approximating the E u c l i d e a n plane ......... 206 V.2.3 Montanari's algorithm .....................210 V. 2. 4 The new a l g o r i t h m 214 V.2,5 Ridge-following .V, i . ^ > i .->. . 219 V.2.6 D s i n g p a r a l l e l i s m t o compute t h e s k e l e t o n .224 V,2.7 Paths between objects and superfluous branches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 V.3 Using the skeleton f o r p a t h - f i n d i n g . . . . . . . . . . . . 226 V,3-1 D e s c r i b i n g a s k e l e t a l path . . . . . . . . . . . . . . . . 228 V, 3. 2 O p t i m i z i n g a s k e l e t a l p a t h . . . . . . . . . . . •» . .. 230 V.3.3 C o m p a r i s o n o f s k e l e t a l and A* p a t h f i n d i n g 233 V.4 Other a p p l i c a t i o n s of the skeleton . . . . . . . . . . . . . 233 V, 4. 1 O b j e c t moving i . . . . . . . . . . . . 234 V. 4.1.1 C i r c u l a r s h a p e d o b j e c t o f r a d i u s r ... 234 V,4,1.2 Other o b j e c t shapes i , , ... . 234 V.4,1.3 An L - s h a p e d o b j e c t . . . . . . . . . . . . . . . . . . . 235 V.4.2 F i n d i n g empty s p a c e . . . . . . . . . . . . . . . . . . . . . . . 236 V.4.3 Finding t h e s h o r t e s t d i s t a n c e between two shapes 2 36 V,4.4 F i n d i n g nearest neighbourhood r e g i o n s ,.,..237 V. 5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
V
VI
Summary, c o n c l u s i o n ^ and f u t u r e work . . . . . . . . . . . . . . . 240 VI. 1 Summary ... .. ......... ............ . . 240 VI. 2 Conclusion 243 VI.3 Research problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 a p p e n d i c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....... . ......... .246 a.1 T a B L E T O P u s e r ' s manual .... . . ^ 2 4 6 A.2 A c o m b i n a t o r i a l lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 A.3 On F u n t ' s r i g i d shape r o t a t i o n a l g o r i t h m . . . . . . . . . 251 R e f e r e n c e s ........... . . . . . . . . . . . . . . . . . . ... .-M . . . . . . . . . . . . . . 258 v
vi L I S T OF FIGURES Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure
1.1 . . . . . . . . . . . . . 9 1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 13 I. 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.5 . . . . . . . . , . . . ; , . » . . . . . . . . , . . . , , . , . . . , , . , . . , . . . . ; . . . 20 1.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 III. 1 , ....... 91 III.2 93 III.3 , 96 III.4 99 I I I . 5 ...... .... . 103 III.6 105 III.7 107 111*8 109 III.9 110 III.10 112 III.11 116 III.12 120 III.13 121 I I I . 14 123 III.15 .................................... * ...133 IV.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 IV.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 IV. 3 . 178 IV.4 ..,.,.,,.....,...184 IV.5 185 V.I ,.. ,. 198 V.2 201 V.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... ....... 207 V.4 , 208 V.5 .,. 210 V.6 211 V.7 , 214 V. 8 .....................218 V. 9 . . . . . . . . . . . . . . . . . . . . . . . . . ,., 221 V.10 223 V.11 ........ 227 V.12 . . . . ....... 229 V.13 231 A3.1 , 252
vii
Oh t h e mind, mind h a s m o u n t a i n s ; c l i f f s F r i g h t f u l * sheer, no-man-fathomed.
of f a l l Gerard
Manley H o p k i n s
££k£2£i e l e m e n t s
I would l i k e t o acknowledge my enormous debt to Richard Rosenberg, who h a s s u p e r v i s e d me, and who has g i v e n me a d v i c e , encouragement and s u p p o r t beyond a l l expectations of duty throughout t h e many y e a r s I h a v e s p e n t on t h e Ph.D program. I w i s h t o t h a n k A l a n Mackworth f o r s e r v i n g on my t h e s i s committee and f o r a l w a y s b e i n g r e a d y t o l i s t e n and t o g i v e me a d v i c e and e n c o u r a g e m e n t ; H a r v e y Abramson* Ray R e i t e r , Bob Wpodham, and John Y u i l l e f o r s e r v i n g on my t h e s i s c o m m i t t e e ; Gordon M c C a l l a , B i l l Havens, R a c h e l G e l b a r t , B r i a n Funt, Mike • K u t t n e r , • Roger Browse, Jan Mulder, and Randy G o e b e l f o r many helpful d i s c u s s i o n s ; Nona and Gwen f o r d r a w i n g t h e d i a g r a m s ; and above all Nona, w i t h Ruby, L e n a and Taku, f o r s t a n d i n g by me t h r o u g h a l l t h e s e y e a r s , s u p p o r t i n g ma i n e v e r y i m a g i n a b l e way, and f o r b e i n g t h a i r own d e l i g h t f u l s e l v e s . .
1
CHAPTER I INTRODUCTION
1.1. Aims and
motivation
This t h e s i s i s animated connection simple
by
between p e r c e p t i o n
things
a
and
desire action.
to
understand
Every day
we
do
the such
as
a v o i d i n g a l l o b s t a c l e s i n c r o s s i n g a c l u t t e r e d room n a v i g a t i n g through an u n f a m i l i a r house making
and
executing
a mental plan to go to the. l o c a l shop
or c r o s s a campus moving an awkward piece of f u r n i t u r e around a house. Likewise
our pet dogs and
their spatial
c a t s are good
so
easily,
processes
which may The
navigating
through
world. For an organism to do
Here you
at
are
what
such
tasks -
computational
required?
w i l l f i n d the beginnings of an answer to t h i s be r e f i n e d i n any question
as
one
stated
question,
of a dozen d i r e c t i o n s ; is
too
meaningful answer; to d e l i n e a t e i t more
nebulous precisely
to be given I
opted
a to
Inlntroduction
2 proceed 1.
as f o l l o w s :
Design and implement a simulated robot world
which
reflects
to a c e r t a i n extent the s p a t i a l aspects of a c l u t t e r e d room or the f l o o r p l a n of a house. . 2.
Specify
a
class
of
tasks
of a s p a t i a l nature which the
robot might reasonably be expected 3..
Design handle
computational
processes
The a
simulated robot world
non-trivial
and a c t i o n .
treatment
The
world.
which enable the robot t o
these t a s k s i n a reasonably
T h i s , i n summary, has been my
t o solve i n t h i s
i n t e l l i g e n t manner.
research program. i s c a r e f u l l y designed to
enforce
of the i n t e r a c t i o n between p e r c e p t i o n
robot's sensory input from d i s t a n t p a r t s of the
environment i s e i t h e r non-existent or very i n e x a c t and f u z z y , i n accord with r e a l world organisms; actions
executed.
I
yet p l a n s have t o be made
am thus s q u a r e l y c o n f r o n t e d , a l b e i t
c r u d e l y , with the problem of a c t i n g i n the. face and
inexact
knowledge.
In
the
simulated
of
and very
incomplete
robot world i t i s
p o s s i b l e f o r the executed
a c t i o n s t o be inexact i n
fuzzy
i n the r e a l world.. So f a r , however, I
manner,
have suppressed of
the
just
as
t h i s f e a t u r e , i n order to ease
overriding
concern:
the
creation
of
a
similarly
the
achievement
a
functioning
robot-controller.
This t h e s i s i s a l s o animated by the b e l i e f t h a t fundamental importance
to understand
i n v o l v e d i n s p a t i a l problem s o l v i n g .
the computational
it
is
of
processes
There are s e v e r a l l i n e s of Inlntroduction
3 argument t o e n c o u r a g e t h i s First
of a l l , s p a t i a l
fundamental a b i l i t y and
i f we
bumping
couldn't into
instance, or and
solve
we c o n t r o l
since
spatial We
large
must be
we i n h a b i t
problems
are
also
rectangular
one
we
of
would
superbly
of a small
round
spatial
[Marr,1976]
object
reasoning
with
world
at i t .
winding
be For
roads
the v e l o c i t y
precision.
satisfies
to guide the choice
most
always
good
s h a p e s on
fine
the
a spatial
l o t mazes, and a b a l l - p l a y e r c o n t r o l s
Second* by
reasoning
we p o s s e s s ,
things!
i n parking spin
belief.
the c r i t e r i a
of a research
proposed
problem
i n AI.,
"If one b e l i e v e s t h a t t h e aim o f information-processing studies i s to formulate and understand particular information-processing problems, then i t i s the s t r u c t u r e o f those problems t h a t i s central, not the mechanisms through which they are implemented* T h e r e f o r e , t h e f i r s t t h i n g t o do i s to find problems that we c a n s o l v e w e l l , f i n d o u t how t o s o l v e them, and examine o u r performance in the light of that understanding* The most fruitful source of such p r o b l e m s i s o p e r a t i o n s t h a t we p e r f o r m well, fluently, reliably, (and hence unconsciously) , since i t is d i f f i c u l t t o s e e how r e l i a b i l i t y c o u l d be achieved i f t h e r e . w e r e no sound u n d e r l y i n g method." Spatial
reasoning
reliably"
and
worthwhile
branches; touching
largely
research
Third, crayfish
i s a problem
there
runs an
we
solve
unconsciously;
"well,
therefore
fluently, i t'i s
a
objective. i s
an
mazes; b i r d s orca
that
whale
evolutionary don't races
a s t a l k ; a mouse w i l l
bump
argument.
into
through
a
rarely f a i l
or
a dog i t s bone; t h e monkey s w i n g s from
as
"ontegeny
r e c a p i t u l a t e s phylogeny",
forest
simple
leaves
and
kelp
bed w i t h o u t
to reach
i t s cheese
branch
one
The
t o b r a n c h . . So,
might
well
expect
Ialntroduction
4 s p a t i a l reasoning t o underly our higher mental f a c u l t i e s . aside,
the
minuscule
devastating flowers,
of
the
hummingbird
solves
an a
s p a t i a l problem: given a meadow with a p r o f u s i o n of
each
variety
propertias,
the
i n p u t while
foraging
expended
brain
As
having
humming
[Sass
bird
and
et
different appears
to maximize net energy
simultaneously
a l , , 1976/].
A
nectar-producing
minimizes
truly
the
amazing
piece
time of
computation by a very s m a l l brains Fourth,
there i s a developmental
argument.
Young c h i l d r e n
s o l v e s p a t i a l problems such as the c l a s s i c a l monkey and problem hours
before old,
flinching
they can t a l k , and the newborn babe, only a
will if
bananas
it
react
appropriately
comes
dangerously
to
a
close,
f o l l o w i t with eye-movements i f i t passes
moving and
behind
few
object,
c o n t i n u i n g to a
stationary
spatial
metaphors.
o b j e c t [ Bower, 1974 ]. Fifth, Consider
our language
the
word
is
permeated
"permeate"
by
j u s t used.
Does i t not evoke a
v i s u a l image c o n s i s t i n g of " s p a t i a l metaphors", "permeating", a
very p h y s i c a l sense, "our language"?
accompany every sentence type
of
language
uses
one u t t e r s ? spatial
in
Does not a v i s u a l image Even
metaphors.
the
most
abstract
For i n s t a n c e , one
" b u i l d s " an argument "on" a f i r m "foundation"; one
"arrives
at"
a conclusion; S i x t h , there are spatial
reasoning
scientific
many
and
discoveries.
anecdotes
visual For
imagery instance,
concerning in the
the
use
of
making fundamental paper
models
of
I•Introduction
5 Pauling f o r t h e a l p h a - h e l i x , and of Watson and C r i c k f o r the DNA molecule; Faraday's v i s u a l i z a t i o n o f magnetic l i n e s of f o r c e narrow
tubes
curving
as
through space; Kekule's d i s c o v e r y of the
s t r u c t u r e of the benzene molecule by h i s v i s u a l i z a t i o n of a r i n g of
snake-like,
tail;
writhing,
chains, each s e i z i n g i t s neighbour's
and i n mathematics, Hadamard has documented many i n s t a n c e s
where a problem was apparently These arguments i n favour lead
solved by v i s u a l imagery.. of s p a t i a l
one to propose the hypothesis
f o r s p a t i a l reasoning developed
reasoning
t h a t the mechanisms r e q u i r e d
may well underly
other a b i l i t i e s t h a t have
l a t e r i n e v o l u t i o n , f o r i n s t a n c e the use of language..
The o v e r a l l s t r u c t u r e of my t h e s i s may now I
functioning
summarized..
The o v e r a l l implementation g o a l i s t o
robot-controller
f o r the
simulated
implemented p a r t s are d e s c r i b e d i n d e t a i l . implemented,
their
theory
only
be
build
robot..
For those
parts
cases,
further
Intelligence,
intellectual disciplines:
feature
that
a The
not
i n some progress
made through an attempt a t implementation.
a l l i s s a i d and done, t h i s i s the Artificial
made on
and design i s sketched
depth, to the point a t which, i n some can
be
l a y o u t a r e s e a r c h program and d e s c r i b e the progress
several fronts.
yet
inexorably
After
distinguishes
as a c t u a l l y p r a c t i s e d , from a l l other the
development
of
theory
through
program implementation.
Iaintroduction
6
1,2
The a c t i o n
The
cycle
information-processing
p h y s i c a l l y i n t e r a c t s with the three
distinct
interest
of
p a r t s : sensory r e c e p t o r s , a c t i o n e f f e c t o r s ,
and
which
in
is
outside
world
r e l a t e s the senses
must
and
the
this
thesis
will
be
referred
in
intermediary, requirement behaviour;
to
as
My
the
The i n t e r m e d i a r y could of course be n u l l
t h a t r e s u l t s i n a very u n i n t e r e s t i n g organism survive
actions..
i n a s u f f i c i e n t design f o r the i n t e r m e d i a r y ,
robot-controller.
long
that
consist
an i n t e r m e d i a r y t h a t main
component of any organism
its
the
world.
In
my
robot-controller,
that
the
organism
which
not
case, the design of the is
constrained
e x h i b i t reasonably
( I n t e l l i g e n t behaviour
could
but
by
the
intelligent
w i l l be taken as a
primitive
judgment and analyzed no f u r t h e r . ) The the
major task of a r o b o t - c o n t r o l l e r , i n order
organism's
survival
chances,
to
improve
i s to b u i l d a world model: a
model of the o u t s i d e world.. In i n f o r m a t i o n - p r o c e s s i n g terms, world
model
interpretive sensory
is
a
data
procedures,
input.
base
of
enables
Eguivalently,
it
facts the
procedures f o r making p r e d i c t i o n s about good
world
The purpose plans and
model
makes
which, together with
prediction
is
a the
a
data
of
future
structure
outside
world*
and A
c o r r e c t p r e d i c t i o n s most of the time.
of a world model i s to
allow
the
thus to b e t t e r achieve the organism's
construction goals.
of
Building
a world model i s an i n d u c t i v e task, using sensory i n p u t s as
the
I•Introduction
7
primitive organism
items
evidence.
i s a f u n c t i o n of
furthermore o f the
of
can
outside
n e v e r be world
organisms
octopus,
for instance,
surface
texture
by
effectors, as
an
one
may
the
and
argue
whereas
there
design
of
receptors,
As
true
a
world
an and
nature
consequence, models.
To
only
an
touch
can
smooth
perspex sphere i s
o r g a n i s m and sensory
fact,
a
certainly
the
case of the i n a l a r g e or
an
may
the
a t any
signal
be
outside
amount o f
world
unbounded
potentially world*
n a t u r a l sensory
of
may
the
be
sense-able
of
by
outside
that
a
side finite
i f
one
world
are
or both,
finite
neither contain
information
nor
available
argument: by
receptors,
input
is
then
This i s
small
A more p r a c t i c a l a l l
the
information
information.
could
taken
information,
moreover,
the
is
action
sensory
of
is infinite,
fact
world
the
amount
and
sense-able
more g e n e r a l
On
and
supported
amount
time
features
This
world
moment i n t i m e a
unbounded
one
outside
receptors
or
finite
a t any
that
infinite
outside
First,
receive
detected
r e c e i v e a l l the the
of
smooth p e r s p e x c y l i n d e r h a v i n g
obvious
or t h a t the
i s an
organism
is
either
continuous*
a special
of
a small
organism's
follows.
only
which c o u l d be believes
model
c o r r e c t - the
i s n e c e s s a r i l y always sloppy.
as
can
from
a long
its
i n f o r m a t i o n - t h e o r e t i c arguments.
organism
there
curvature,
intuitively
following
of
different
whose s e n s e
from
world
unknowable.
very
i n t e r f a c e between an
defined
design
assumed t o be
build
and
the
[Wells,1978].
same c u r v a t u r e The
the
i s forever
different
indistinguishable
Thus
the
very
digitized,
Inlntreduction
8
hence i s an a p p r o x i m a t i o n to
be
the
statement
action
that
side,
the r e s u l t
implies
the
standard
of comparison
existence
points
percent
here* .
supposing
But
taken,
so
First,
so
mistakes
discussion
repetition perception,
While introduce
is
p l a n n i n g , and
taken
they
am
following
i n the
world
model which
incorrect,
may
be
very
or sloppy,
was
model i s n e v e r
outcome
used
as a
There
are
one
hundred
simply
wrong.
model i s e x a c t , t h e : c o m p u t a t i o n
of
require
of
life
an
unbounded
goes on and
in
amount
actions
must
amount
be of
I n our
in serial
are presumably
performed in
in
three
parts:
in
these most
parallel.
general,
i n p u t a t any
tactile*
the p e r p e t u a l
o r d e r , whereas
organisms
Our
robot-controller
terminology: the t o t a l
(visual,
by
a loop containing
action.
1.1.
figure
a t the top l e v e l *
a u d i t o r y , .,.)
a sensory,
summary,
was
world
cycle,
discussing
olfactory,
impression,
position
I
action
The
inevitable.
performed
the f o l l o w i n g
called
In
are
of t h e : a c t i o n
as f o l l o w s . .
must be c u t o f f i n a f i x e d
functions,
organisms
tactile,
may
argue
s o f a r i s summarized
p r o c e s s e s are
living
a
the world
may
outcome o f the a c t i o n .
predicted
the computation
robot-controller
three
a
i n the o u t s i d e world
- and The
o f an of
t h e outcome o f an a c t i o n time..
one
f o r the
e x a c t , so t h e
Second,
time
that are generally
continuous. On
two
to q u a n t i t i e s
sensory instant
let
me
(visual, of
time
olfactory,, auditory,,...)
D a v i d Hume*
then, the a c t i o n
cycle
information-processing
of
occupies a any
fundamental
organism.. ImIntroduction
The
PLAN MODEL
-MOTZG&_ OUTPUT
S L 0 P I N
P
r tr k r
y ACE
fe I Gr-LLfLE EJL
THE ACTION CYC
10
elucidation main t a s k chapters
I-3
o f my r e s e a r c h
The
the outside
is
i s the
described
in
world;
main p r o g r a m s : TABLETOP,
OTAK, t h a t
simulates
that
t h e r o b o t ; and
t h e r o b o t - c o n t r o l l i n g program.
restraining the
boundary later.
that
some
the o b j e c t s will
There
this
a frictionless
b o u n d a r y ; . T h e r e may
tabletop,
constitute
be
of
the
outside
another
object
standstill
t o a s t h e verc[e t o a v o i d
confusion
i n a fixed
offending
obstruction.
a
small
The c o n c e p t s
so.
Consequently there
times
associated
object
collides
with with
robot an
object.
laws o f p h y s i c s
remains i n v a r i a n t
gap
during
comes
between
o f mass and
to
an
have
difficulty in "slow
down"
movements, and when a wide
moving
obstacle
near
up" o r
by
i t and t h e
momentum
would be l i t t l e
a r e no " s t a r t
hold:
i s obstructed
t h e moving o b j e c t
been i m p l e m e n t e d , t h o u g h t h e r e
doing
o r movable
o f a moving o b j e c t
with
shapes
tabletop
or t h e verge then
immediate
shapes
These
world*
t a b l e t o p the everyday
path
polygonal
The
a r e n e v e r any h o l e s
i f the
a
polygonal
and some movable.
i s t o s a y , t h e shape o f an o b j e c t and
t a b l e t o p with
be a r b i t r a r y
fixed
referred
simulated
motion,
not
robot,
overview
TABLETOP s i m u l a t e s
On
My p r o g r e s s
program
system c o n s i s t s of t h r e e
simulates
on
the simulated
I V and V.
System
PPA,
i t s structure, for
of
one: o f
its
lateral
Inlntroduction
11
extremities
no
t e r m i n a l r o t a t i o n of any kind i s s i m u l a t e d : t h e
o b j e c t simply comes t o an immediate UTAK
simulates
dimensionless space.
the
robot, Utak*, who i s r e p r e s e n t e d
p o i n t and i s f r e e t o move anywhere t h e r e i s
Though
dimensionless,
adjacent o b j e c t s which have edge-to-edge
halt.
contact*
and can move with
he: cannot
point-to-point,
slip
as a empty
between
point-to-edge,
two or
He can grasp an a d j a c e n t movable o b j e c t ,
and r e l e a s e such a o b j e c t .
An
example,
task
environment i n c l u d i n g Utak i s shown i n f i g u r e 1.2... Utak senses h i s environment with an eye field
of
view
centre
(the "fovea")
periphery,* . at
having and
a
progressively
sticking
pointing directly
limited
a v a r i a b l e r e s o l u t i o n : f i n e i n the coarser
towards
The eye may be thought of as a TV camera,
the top of a s t a l k
camera of
and
having
the
suspended
v e r t i c a l l y up from Utak, with the
downwards a t the t a b l e t o p and i t s f i e l d
view c e n t e r e d on Utak.. Thus the eye gets
a
two-dimensional
view o f p a r t o f the t a b l e t o p and an image of Utak always appears at
the c e n t r e of the f i e l d The
r e t i n a l geometry
Each l i t t l e certain
of view* of the eye i s shown i n f i g u r e I * 3 ( a ) .
square c o n s t i t u t e s a r e t i n a l
area
of
the
task
environment
field*
a
n
^
covers
a
depending upon Utak's
iRather than always r e f e r r i n g t o the "robot" and using the pronoun " i t " , I w i l l u s u a l l y r e f e r to "Utak", who may be l i k e n e d to a semi-intelligent dog, and use the pronoun "him". Of course, no s e x u a l discrimination i s intended.^ Likewise no p h y l o g e n e t i c d i s c r i m i n a t i o n i s intended e i t h e r : "Utak" and "him" are simply more pleasant ways t o r e f e r t o what i s merely an abstract device embodied i n a computer program used to probe very g i n g e r l y i n t o the p r i n c i p l e s o f c o g n i t i v e s c i e n c e . I«Introduction
12
Fix
ED
PART
ITION
MOVABLE 08J-6CT
U T A K
A
Fl&VRE
I.Z.
A
TASK
ENVIRONMENT.
FIGURE 1.3
(a) The r e t i n a l
geometry.
0
o
O
o o
O
O
6
0
o
O
o
O
o
6
1
6 6 6
7
/
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
o
X
o
%
2,
V
©
o
O
o o
o
o
O
o
o o
o
O
O
o o
©
• • • • E D E E • • • • • • B E • • • • F J E E E E G 1 E O E E O E
• • • • • • E E • • • • • • • • O
o
o
o
o
o
O
o
O
©
©
o
o
o
o
o
o
6
(o
(o
(o
6
FIGURE 1.3
2,
z
I
o
1
0
O
O
O
o
»•>
4
(b) The i n t e g e r s i n t h e squares form the r e i t i n a l i m p r e s s i o n c o r r e s p o n d i n g to, Utak's p o s i t i o n i n F i g u r e 1.2.
14
position. retinal range
Corresponding cell,
which
to
each
registers
retinal
field
there
a gray_level, or i n t e g e r i n the
0 - 7 , t h a t depends on the r a t i o of o b j e c t t o
of the task environment
total
covered by the r e t i n a l f i e l d .
retinal
cells
at
one
particular
r e t i n a l impression r e c e i v e d by Utak when figure
1.2
"tactile"
i s shown
i n figure
r e c e p t o r s , one i n each
directions,
which
immediately
adjacent
structured
allow
s e t of
him
object.. eight
i n time* .. The
i n the
situation
of
the
to
sense
colors
by a l l
instant
1.3(b).
A
area
A retinal
impression i s the s t r u c t u r e d s e t of g r a y l e v e l s r e g i s t e r e d the
is a
of
Utak a l s o has e i g h t eight
basic
the
tactile-
compass
colour
impression
registered
by
of
an
i s the
the
tactile
r e c e p t o r s at one p a r t i c u l a r i n s t a n t of time*'. In
sum,
then, Utak i n h a b i t s an o u t s i d e world which may be
l i k e n e d t o a t a b l e t o p with c o n f i n i n g verges, where he can wander around
and move o b j e c t s , and where h i s sensory c o n t a c t with
world c o n s i s t s of a s e r i e s of r e t i n a l and It
i s h i s problem
(James' "blooming, model"
to
make
buzzing
f o r planning
sense
impressions.
of a l l t h i s sensory i n p u t
confusion")
purposes.
tactile
this
That
and
create
a
"world
i s a major problem f o r
Utak's b r a i n , the r o b o t - c o n t r o l l i n g program. The
class
of t a s k s given to Utak c o n s i s t s of path
("Go t o t h e n o r t h - e a s t corner") and o b j e c t moving the
square
of a task may model.,
tasks
finding ("Push
movable o b j e c t i n t o the next room").. The statement require
Consider,
considerable
f o r instance,
changes
the
to
Utak's
object-moving
task
world just
Inlntroduction
15
mentioned. has
only
his
world
a
room
I f Otak has so f a r seen a square explored
one
"understanding" an
but
what he t h i n k s i s one end of a s i n g l e room,
model before t h e task statement with
movable o b j e c t
square
movable
the task statement
w i l l simply c o n s i s t of
object
i n i t ; but
h i s world model w i l l
after
include
e x t r a room with a doorway which connects i t t o the room he's
currently
i n at
a
position
consistent
with
h i s accumulated
sensory experience t o date. PPA, ACCOM, act;
the r o b o t - c o n t r o l l e r , i s d i v i d e d
SPLAN,
and
ACT.
the three p a r t s o f
the a c t i o n
cycle..
to
ACCOM
accepts
SPLAN
i s the
task
a
spatial
i s r e s p o n s i b l e f o r always maintaining a v a l i d
achieve the c u r r e n t
updating
parts:
(accommodates) the c u r r e n t world
model i n the l i g h t of t h i s new evidence; and
three
PPA i s an acronym f o r p_erceive, p_lan,
r e t i n a l impression and m o d i f i e s
planner
into
by
creating
a
new
plan
plan
or by
an o l d one; while ACT simply computes from the c u r r e n t
plan t h e next a c t i o n t o be executed. . A in
world
model, a t a s k , and a plan a r e d e f i n e d at a l l times
PPA, whatever Utak's a c t u a l s i t u a t i o n ,
before
Utak
"opens
h i s eye" and
including
the moment
receives his f i r s t
retinal
impression. . So far,; the f o l l o w i n g d e f a u l t s have been used. world
model
i s taken
Utak's i n i t i a l assumed
world,
to
position. which
be
a l a r g e empty square
The d e f a u l t task means
"collect
input) t o confirm the c u r r e n t world results
i n the s p e c i f i c
task
i s to
evidence:
The
centred on
explore
the
( i ; e . sensory
model".. I f the d e f a u l t task
o f , say, "go t o t h e . n o r t h - e a s t Ialntroduction
16
c o r n e r " , then the c u r r e n t plan would c o n s i s t of walk a c t i o n s the
hypothesized
position
of
the
north-east
p o s s i b l e d e f a u l t s are " s l e e p " o r " f i n d I
have
not
considered
These are c l e a r l y rewards. for
The a r c h e t y p a l problem
food i n an environment
are
partly
known.
is
a
involve
decision-making
whose f o o d - s u p p l y i n g
i s the
There
of motivation or d r i v e .
c o n s i s t s of an organism
The organism
running low); what organism?
and
survival
large s c i e n t i f i c
hunting
(food or f u e l
strategy
for
me,
these problems are secondary
sensory
ACC-INIT
the very f i r s t
all
problems.
program, r e s p o n s i b l e f o r understanding
impressions,
ACC-SOB. to
ACCOM
theory.
to the b a s i c q u e s t i o n s of
r e p r e s e n t i n g the s p a t i a l world and s o l v i n q s p a t i a l The
subsequent
divides
into
this
l i t e r a t u r e devoted to
such problems i n the f i e l d s of d e c i s i o n theory and game For
and
characteristics
i s g e t t i n g hungry
best
Other
food". ,
problems
important
corner.
to
two
parts,
incoming
ACC-INIT
and
accomodates the i n i t i a l d e f a u l t world model
r e t i n a l impression while ACC-SOB accomodations
of
the
carries
out
world model to incominq
sensory i m p r e s s i o n s . The
spatial
planner
SPL&N
depends on a subsystem
SHAPE to solve p a t h - f i n d i n g and object-moving makes is of
extensive
maintained Cartesian
the C a r t e s i a n SHAPE
use of the world model.
problems...
world
functions
model
SHAPE
The:basic world model
i n a format o f p o i n t s and l i n e s s p e c i f i e d coordinates
called
by means
and w i l l sometimes be r e f e r r e d t o as or
the
Cartesian
represent a t i o n .
by p r o j e c t i n g and r e - p r o j e c t i n g a l l or p a r t o f I«Introduction
17
the
Cartesian
world
Path-finding c a s e s from require
and
one
p r o j e c t i o n on
representation to
The
as
most
algorithms
an
this
image
important
shape.
i t i s the of
what
the
was
reasons
algorithms
totally the all
is of
of
will
of
the
the
Cartesian
sometimes
be
collection
of
object-moving
the
skeleton
of
for
devised in
which I
a
two
more cumbersome
term
a shape l o o k s
chapter
was
V,
i t .
the
to
an
examine
the
found
that
problems
derive
that,
skeleton
these a
would
out
published of
the
provided
I t turned
L u c k i l y , one
able
get
p r o b l e m s , and
object^moving t o compute
To
like,
I
for path-finding
problems., of
a shape;
drawn i n f i g u r e 1.4.
a
nice
mathematical
Consider
the
shape
is
then defined
maximal c i r c l e s has
very
a shape;;
within
skeleton
skeleton
cases
provided
satisfactory
algorithm.
There skeleton
of
were u n s a t i s f a c t o r y .
a good b a s e from skeleton
be
given
more i n t e r e s t i n g
is
and
axis transform
heuristic
could
simple
array
SHAPE
concept
a useful tool
useful
algorithms for
of
skeleton
skeleton
solved
projection
digital
part
symmetric
i t s skeleton
a
A
screen). in
A more d e s c r i p t i v e b u t
shape and
be
screen;
are
(the
representation.
b a s e d upon the
dimensional
idea
the
projections. onto
array
problems
for solving path-finding
These are
for
digital
object-moving
several
referred
model onto a
and
in this
associated
with
the
set of a l l c i r c l e s
partially
set.
t o be In
i t the
definition
order the
them
locus
by
of
radius
the
that l i e
inclusion;
the
a d d i t i o n , each
of
centre
point
of t h e : m a x i m a l
of
of the
circle
I•Introduction
F.I
&UR
£
X.4-,
_/_We_4.K.£4ETOH
OF
A SHAPE.
19
with c e n t r e at that p o i n t ; t h i s i s known as the guench f u n c t i o n . However,
the
skeleton
algorithm
that
e x a c t l y the s k e l e t o n as I have j u s t the
metric
points
in
a plane,
metric
to
approximate
quasi-Euclidean "local"
d e f i n e d i t . . . T h i s i s because
Euclidean The planner. solve
between
and
the
I t has
the s k e l e t o n can I
two
Dsing
this
be computed i n a very
shall,
computed
two
can
by
than
when . necessary,
can
also
be
as
and
can
the be
spatial
following
find§E§S§
problem
shape t h a t you
s u r f a c e , where do you
to
problems.
s o l v e . the
the
the 1.5.
used
object-moving
to
dimensional
want
place i t ?
to The
concerned with the s k e l e t o n of a shape are V.
To complete t h i s overview ACT,
used
known
cluttered
algorithms
is
idea behind
and The
on the d i g i t a l s k e l e t o n of f i g u r e
Given a two a
algorithm*.
be observed by o v e r l a y i n g
j u s t p a t h - f i n d i n g and
otherwise
on
my
a very i n t u i t i v e appeal
worked out i n chapter
component
between
distance. .
s k e l e t o n of a shape i s the key
[Sussman,1973J.
theory
Euclidean
as
s k e l e t o n of 1.4
For i n s t a n c e , i t
down
distance
a l g o r i t h m uses a q u a s i - E u c l i d e a n
Consequently
skeleton,
more
problem,
the
the
using
between a E u c l i d e a n s k e l e t o n , as d e f i n e d above,
digital
difference
for
whereas my
metric,
manner.
distinguish
put
compute
c i r c l e s used i n the mathematical d e f i n i t i o n are drawn
the.familiar Euclidean
the
I use does not
of
PPA,
the
third
and
the e x e c u t i v e program that computes the
a c t i o n f o r Utak from a completed p l a n .
This
is
not
final next
entirely
t r i v i a l because the s i z e of the next a c t i o n has to be a f u n c t i o n I«Introduction
pi
lc h i
;
»
(A \
X I
P! 2 .
*
*
21
of
t h e c o n f i d e n c e Otak has
the
vicinity
which he
can
of
i n the d e t a i l s
h i s current position
execute
an
action*
through
a room c l u t t e r e d
one
can
register
can
c o n t r o l o n e ' s movements.
the
To summarize
shape. stage of
elaboration
I.4
design,
of the
items
and
have
outlined
and
on
figure
1*6,
be
cycle
with
one on
how
runs
how
well
well
one
the
major
I have p r e s e n t e d
of f i g u r e
as
an
dimensional
which i l l u s t r a t e s
regarded
in
a
first
this order
1.1.
System s t a t u s All
degrees
parts of
produce and
the and
system
and
some p a r t s have
retinal
described
in
in f u l l
ACC-SOB h a s
major
A full
SHAPE
IV.
while
but is
the
The
ACCOM,
implemented.,
been
SPLAN,
Of t h e two
of the
overall
complete*,
to varying The
a c t i o n s and implemented
current status of
ACC-INIT has
implementation
been a t t e m p t e d , subpart
namely
i n chapter
been d e s i g n e d
implemented. not
been
i m p r e s s i o n s , have
chapter I I I .
o t h e r p a r t s o f the system, described
h a v e been d e s i g n e d ,
OTAK s i m u l a t i o n p r o g r a m s , which e x e c u t e
tactile
are
of
detail,
TABLETOP and
has
which
t h e s k e l e t o n o f a two
may
action
at
model
accuracy
depends b o t h
the r o b o t - c o n t r o l l e r ,
accompanying
PPA's
I
world
of t h e
speed
of the
section:
u n d e r l y i n g concept, The
and
furniture
positions
this
components o f PPA, important
with
The
of the
and
ACT,
the is
s u b p a r t s o f ACCOM, been
spatial
design SHAPE'S
designed planner
of SPLAN and most
and SPLAN its
fundamental
^Introduction
22
TlirT/NAL.
Ac c o ^
UTAK
SPLAN
T*€
O 0 T S \ & £
WORL\>
/
j
V / STRUCTURE
f«\oTtof\ O OTPyT
ACT
PLAN
F l GURE
I. 6
23
o p e r a t i o n , the s k e l e t o n - f i n d i n g computation, implemented;
that
is
complete
and
i s the main a l g o r i t h m i c c o n t r i b u t i o n of t h i s
thesis. Taking
the
engineering
view
towards
Al,
contributions in this thesis.
One
i s an
s i m u l a t i n g the motion of r i g i d
two
dimensional
i s the design and p a r t i a l implementation that
finds
I
efficient
of
make
two
system
for
shapes, the other
a
spatial
paths and produces plans f o r moving two
planner
dimensional
shapes around on a f l a t s u r f a c e .
1.5 Reader's guide Chapter background
I I , c o n s i s t i n g of issues.
The
two
first
parts,
is
numerous
pieces
of
work
from
d i s c i p l i n e s t h a t are c l o s e l y r e l a t e d to describes
the
the
Al
my
second
and
own.,
robot-controller
part sister
Chapter
design.,
I
IV
covers
III
to
be.
able
theory and a l g o r i t h m s
for
the
whole
i n c l u d e i n chapter IV a number of
task s c e n a r i o s t h a t my r o b o t - c o n t r o l l e r , when f u l l y designed
its
an
design c o n s i d e r a t i o n s and a l g o r i t h m i c d e t a i l s of
the simulated robot world, while chapter
is
with
p a r t concentrates on g i v i n g
o v e r a l l view of the whole A l e n t e r p r i s e : w h i l e reviews
concerned
to execute. . Chapter computing
the
implemented,
V d e s c r i b e s the
skeleton
of
a
two
dimensional shape, and i t s u s e f u l n e s s f o r p a t h f i n d i n g and o b j e c t moving problems. foregoing,
The
discusses
c o n c l u d i n g chapter my
VI
recapitulates
the
c o n t r i b u t i o n t o the A l e n t e r p r i s e , and I"Introduction
24 d e s c r i b e s f u t u r e d i r e c t i o n s of The
appendices
research.
include
a
user's manual f o r the TABLETOP
s i m u l a t i o n , a c o m b i n a t o r i a l lemma r e q u i r e d some
proofs
concerning
the
in
simulation
chapter
V,
and
system of Funt [1976]
r e q u i r e d i n s e c t i o n 11*4.7* If
you want to see a new
i t e r a t i v e a l g o r i t h m f o r computing
the s k e l e t o n read s e c t i o n V.2.4.
For a new
application
skeleton,
to p a t h f i n d i n g , read s e c t i o n 7,3.
I f you
algorithms
f o r s i m u l a t i n g the TABLETOP world read
of
want to
the see
section III.1.
The.
o v e r a l l design of a r o b o t - c o n t r o l l e r i s o u t l i n e d i n chapter
IV.
Finally,
Intelligence,
if
you
want
read the f i r s t
a
general
review
of
three s e c t i o n s of chapter
Artificial I I . . The
l a s t s e c t i o n of chapter I I contains a l i t e r a t u r e review.„
I"Introduction
25
CHAPTER-II BACKGROUND-ISSUES
In of
this
chapter
Artificial
Artificial
II.J
my p u r p o s e
Intelligence
Intelligence
Artificial
i s to briefly
and t h e n
and o t h e r
Intelligence^
t o review
sketch the nature related
work
in
fields.
i s a s c i e n c e - w i t h g o a l s and
para diqms Artificial man's
eternal
urge,
Less p o e t i c a l l y , to
Intelligence to
i s t h e computer age
understand
i t i s a scientific
make c o m p u t e r s more u s e f u l
computational intelligence, displayed
by man, a n i m a l ,
schizophrenic engineering
discipline
h i s mind and c o n s c i o u s n e s s . discipline.whose
of
and
here: -
principles
whether
o r computer.
tendency
of
goals
are
and t o d i s c o v e r and u n d e r s t a n d i n
terms t h e t h e o r i e s irrespective
expression
on
[Michie,1978]
underly
the: intelligence
The r e a d e r the
that
will
one: hand defines
is
note
a
i t is
an
i t as
"the
!The name i s u n f o r t u n a t e , f o r i t i s n o t t h e c u r r e n t e n d - p o i n t i n a p r o g r e s s i o n t h a t g o e s a n i m a l i n t e l l i g e n c e * human i n t e l l i g e n c e , a r t i f i c i a l i n t e l l i g e n c e , ...!*! .... as many a layman seems t o think on f i r s t h e a r i n g t h e name. N e i t h e r i s i t concerned with c o m p u t e r based s u p p o r t s y s t e m s f o r men i n s p a c e , a s one s c h o l a r seemed to think. (How about computer c o g n o l o g y ? ) Also, since one cannot denote a practitioner by t h e u s u a l scheme o f appending "-ist" t o t h e s u b j e c t ' s name, one i s f o r c e d t o u s e cumbersome terms such as "researcher in Artificial Intelligence". IlaBackground
Issues
26
pursuit
of
engineering
goals
through
machine
p r o c e s s i n g of
complex i n f o r m a t i o n i n t e r m s o f human c o n c e p t s " -
while
on
the
other
concerned
with
hand
i t
understanding is
areas of
study.
The
If
used
more
the
as
a
word
"paradigm"
a social
sense*
subject what
psychology
the
than
what
i n many d i f f e r e n t
senses,
h a r d l y one
understanding computational
of
we
Intelligence
held
on
the
has
shall
been
around
workers s i n c e a
subject
i s a young s c i e n c e and
except
for
intelligence
Symbol
System H y p o t h e s i s
symbol
system
the
Kuhn
in
10
1955. .
perhaps
So
still
a
result.
studies.,
has
its
necessary.
in scientific
at a l l
other
are
so
existence of a g e n e r a l l y accepted
overthrown
so
[ Masterman, 1970 i] p o i n t e d o u t ,
view o f
the
these
are
( m e t a p h y s i c a l paradigms or "Weltanschauung";
get
and
Intelligence :
d e f i n e d group o f communicating
Intelligence
for
As
terms,
i s a s c i e n c e then
Artificial
s e l f - c o n s c i o u s as a As
was
as
summer s c h o o l was
Artificial bit
computational
Intelligence
sense
discipline,
t o p h i l o s o p h y and
J. Kuhn, 1962 i]?
clearly
person
in
paradigms of A r t i f i c i a l
i n t r o d u c e : each In
intellectual
akin
Artificial
paradigms
an
intelligence
perhaps
I I . J..J.
is
T h i s has
the
basic
would now
by [ N e w e l l
necessary
revolutions) i n i t i a l l y
and
be
belief
and
that
achieved
been s t a t e d
there an
through
as t h e
Physical
Simon* 1 976 i}: "a
physical
sufficient
means f o r g e n e r a l
II«Background
Issues
27 i n t e l l i g e n t action". was
Very
soon the c e n t r a l importance
g e n e r a l l y accepted, and
Newell
and
Simon
as
this
the
too
has
Heuristic
been
Search
symbol
problem-solving progressively
system by
search
modifying
solution structure." Artificial
exercises
Now
Intelligence
-
that
symbol
its is,
enshrined
Hypothesis:
s o l u t i o n s to problems are represented as symbol physical
of s e a r c h by "The
structures.
A
intelligence
in
by • generating
and
s t r u c t u r e s u n t i l i t produces a
the g e n e r a l l y accepted core t o p i c s can
be
of
summarized as [Nilsson,1974 ]:
r e p r e s e n t a t i o n of knowledge, s e a r c h , common-sense:reasoning deduction,
and
computer
languages and systems a p p r o p r i a t e f o r
i n v e s t i g a t i n g the f i r s t three Going
down
paradigms,
one
or
Intelligence?
some
more
t o o l k i t . . One design.
A
what are some of the i n s t r u m e n t a l accepted
computer
course, the s i n e g j i a npn however
topics..
level*
generally The
and
tools
of
Artificial
programming languages are, of
of A r t i f i c i a l
specific,
Intelligence*
There
are
widely used, t o o l s i n the A l ' e r s
such i s the p r o d u c t i o n production
and
system
system
consists
style
of
a
s i t u a t i o n - a c t i o n r u l e s p l u s a scheme f o r choosing
of
program
collection
of
which r u l e
to
( apply
next.
Any|
g e n e r a l i z a t i o n of Another as a data together
a
production
behaviouristic
i s the semantic structure with
system
of
can
be
vxewed
stimulus-response
as
a
system.
net approach; here a system i s designed labelled
arc-traversal
nodes
algorithms.
h i s t o r i c a l l y , d i r e c t l y d e r i v e d from
and
connecting
This
approach
arcs is,
a s s o c i a tHaBackground ionist psychology. Issues
28
The
last
tool
we w i l l mention i s the most w e l l e s t a b l i s h e d of
them a l l , with a long i n t e l l e c t u a l h i s t o r y behind object
of
some
controversy:
first
i t , and t h e
order p r e d i c a t e
calculus,
which i s taken d i r e c t l y from t r a d i t i o n a l mathematical l o g i c . . What
are
Intelligence? attempting
As
or
Artificial What
of
the
examples,
defining anyone
problems
who
uses
of A r t i f i c i a l a
computer
in
t o : understand n a t u r a l language, play games such as
chess, c o n t r o l scene,
some
a robot, understand a TV image o f
understand
speech,
is
a
real
world
considered t o be working i n
Intelligence. are
Intelligence?
some
of
the c u r r e n t hot problems i n A r t i f i c i a l
Here i s a l i s t ,
culled
from
[ M c C a r t h y , 1 9 7 7 3 and
[ Simon, 1977 J . •
the problem
of c o o p e r a t i n g with others* or
opposition
-
this
overcoming
their
i s a task which even the youngest
infant
handles very w e l l [Donaldson,1978 ] . . •
the a c q u i s i t i o n of knowledge [ Winston, 1970 i], [ Winston* 1 978 g.
•
r e a s o n i n g about concurrent events and a c t i o n s . ,
B
expressing
knowledge
about space, and the l o c a t i o n s ,
shapes
and l a y o u t s of o b j e c t s i n space. a
the
r e l a t i o n between a scene and i t s two d i m e n s i o n a l image -
t h i s i s the v i s i o n
problem, c u r r e n t l y being attacked by
many
workers, f o r i n s t a n c e , [Barrow and Tenenbaum,1 9 7 8 J . . B
r e a s o n i n g with concepts of cause and can*
a
finally,
the
problem
of
representation
-
what knowledge
enables a system to c r e a t e a r e p r e s e n t a t i o n and o p e r a t o r s f o r IlaBackground Issues
29 a
new
is
to
and be
unfamiliar
problem?
distinguished
from
This
representation
knowledge
of
how
knowledge
to
solve
a
problem. In
summary, I h a v e o u t l i n e d
"Artificial
Intelligence"
by
this scientific
describing
field
i t from
known
several
as
Kuhnian
viewpoints*
I I . J_. 2 AI
has
potentially rich - relationships
with
many, o t h e r
fields There are and
other
work on
many r e l a t i o n s
fields
getting
subfield
of
research
has
study.
a
acrimonious
have
This
debate
advocates
to
Intelligence [ M i n s k y and community
research
i s of
simply
reasons f o r t h i s schism methodology
In
relationship i s the
example research
and
whereas
ignored seem t o
order
of
Artificial
an
programs.
relationship.
most
of
competing
Artificial
believe
with
topic
of
Intelligence The
more
that
monumental i m p o r t a n c e
[Miller,1978J
paradigms.
of
Intelligence
Papert,1972J, has
whereas i n f a c t t h i s f i e l d
differing
a somewhat l o p s i d e d
of A r t i f i c i a l
a
an
would
that
form
relationship -
Intelligence
might e x p e c t
language
contentious
a n o t h e r example, p s y c h o l o g y
enjoyed
research
example, one
proper,
linguistics*
Artificial
understand
somewhat
p a r a d i g m s , a l a Kuhn, due As
For
a machine t o
linguistics
traditional enduring,
of
between
the
vocal
Artificial
for
psychology
psychological
Intelligence* .
stem l a r g e l y f r o m
differences
-
another
example:
of
to
keep h i s
science
well
The in
competing
IIoBackground
founded Issues
30
on
f a c t s , and hence s c i e n t i f i c a l l y
is
concerned
with
t o produce f a l s i f i a b l e
demonstrably
true
hand, t h e A r t i f i c i a l produce
computations with
empirical are of
i s that
the latter
taken
as i n t u i t i v e l y
computation.
For
a
intolerably
obvious,
instance
unacceptable.
on
Thus
any
concerned
and
e m p i r i c a l consequences.
The
which
by
proposed
after
To c o n c l u d e :
explosion
actual
Artificial
a l l - i t i s grounded
and
large
or that
facts
mechanism
or
which
otherwise
potential
runs
computer
i s exponentially
domain o f i n t e r e s t i s u n l i k e l y t o be a c c e p t a b l e
run..
with t h e
but with t h e e m p i r i c a l
any
an a l g o r i t h m
to
mechanisms
i s n o t s o much c o n c e r n e d
combinatorial
slowly
theories
On t h e o t h e r
is
theories,
f a c t s o f human m e n t a l a b i l i t i e s ,
encounters
the
researcher
true
is,
consequences.
comp_utational
demonstrably
the psychologist
theories, that
empirical
Intelligence
falsifiable
difference
respectable,
is
slow i n
i n the
long
I n t e l l i g e n c e i s n o t so a r t i f i c i a l
on t h e e m p i r i c a l , n a t u r a l ,
facts
of
computation. One might
expect
behaviour
studies
reasons.
First
therefore to
is B
and
the
behaviour
i t should
of B d u p l i c a t e s
no s i g n i f i c a n t of
A,
operationalisra.)
t o be some
and A r t i f i c i a l
the c o n s t r u c t i o n
duplicate
behaviour
there
contact
animal
I n t e l l i g e n c e , f o r a t l e a s t two of
animals
of computational be
between
easier..
is
simpler
processes
(When
I
say
and
sufficient that
t h e b e h a v i o u r o f A, I mean t h a t
the there
o b s e r v a b l e d i f f e r e n c e between t h e b e h a v i o u r o f as
in
the
Turing
Second, t h e e v o l u t i o n
test
or
in
Bridgeman's
o f human b e h a v i o u r ( i * e . IIsBackground
Issues
31 intelligence)
can
be
traced
J e r i s o n , 1973 3-
behaviour subsystems
that
had
through
Consequently
a l r e a d y been
many one
grades might
shown t o d u p l i c a t e
behaviour occurring
earlier
could
be
blocks i n the c o n s t r u c t i o n
that
duplicate
a v e r y few contact
between t h e
A
animal
hungry
two
problem
monkey
later,
fields;
is and
get
his
T h i s problem
a box
typically
i n t h e c o r n e r ; how was
way
outdated
from
Artificial
More
algorithms;
facts
"Intrinsic
similar
t o the
bananas
problem.
does
about
the
visual
chimpanzees
and
or
four
have
are simply
into
also,
a t present.„
another
based
on
off
automata t h e o r y .
is clearly
the
the
branched
related aspects
Tenenbaum, 1978 ] a r e
of the columns i n
To
work on n e u r a l
c o r t e x , w h i l e some
Images" o f [ B a r r o w structure
vision
monkey
bananas.
which was
developed
hanging
the
up t h r e e
M c C u l i o c h - P i t t s model o f t h e n e u r o n , I n t e l l i g e n c e and
a
does come
Some v e r y e a r l y
[ M o o r e , 1956 ],
no
that
relationship
r e c e n t work by [ M a r r , 1976 fj on
the.known the
no
from
describe
neurophysiology
r e s e a r c h e r s , neurons
n e t s by [ K l e e n e , 1956 j} and now
piled
t o get the
and
almost
Intelligence
of implementing
systems
essentially
s o l v e d by K o h l e r ' s
t h e chimpanzee
Intelligence
surprisingly,
Artificial
monkey and
of
apart
In p a s s i n g , l e t me
boxes i n a m a r g i n a l l y s t a b l e p i l e
perhaps
been
record
i n a room w i t h a bunch o f b a n a n a s
the c e i l i n g
Artificial
t h e r e has
s t u d i e s - the
from
[ K o h l e r , 1 9 2 5 ];
In f a c t ,
that
aspects of
evolutionary
f o r p r o b l e m - s o l v i n g systems
behaviour
food?
the
a s p e c t s o f human b e h a v i o u r . .
s t u d i e s reviewed
traditional from
as b u i l d i n g
in
animal
expect
animal
used
of
visual
IlaBackground
to of
very
cortex. Issues
32 The
n e u r a l net
idea
has
been d e v e l o p e d
[ B r i n d l e y , 1969 ij
and
lErmentrout
Cowan, 1 9 7 8 .
also
and
paragraph
with neurophysiology On
a
deeper
relationship its
very
vision,
then
is
is
example,
is It
the
the
human
a r e found
CNS
decrease
has
in
being
computing
a
t o be
out
system
in
the
i s found
Artificial
for and
CNS?"
Intelligence As
another
Habituation i s
or p r o b a b i l i t y
of a
stimulus.
response
Habituation
i s the s i m p l e s t type of o t h e r k i n d s of
of
t o compute
these f u n c t i o n s ? "
i n the amplitude
and
the case
sufficient
phenomenon of h a b i t u a t i o n .
nature
two-way
neurophysiology
Take
carried
visual
f e a t u r e s i n common w i t h
sometimes
rich
n e u r o p h y s i o l o g y i s "Where
r e p e a t e d p r e s e n t a t i o n of a p a r t i c u l a r ubiquitous
word f o r word,
a
and
neurobiology.
in
throughout.
expect
Intelligence
the question f a c i n g
consider the
a gradual to
i f
over almost
might
computations
functions,
"Why
the
of behaviour
level
computations
e.g.
evolution
f o r behaviour
cousin,
physiologist
has
taken
one
a
S i n c e human n e u r o p h y s i o l o g y
the q u e s t i o n f a c i n g
are these
certain
be
by
biologists,
substituted
close
If certain
Conversely,
can
between A r t i f i c i a l
vision.
how
mathematical
e v o l v e d , t h e comments a b o u t
preceeding
or
by
further
learning.
learning
component o f more complex l e a r n i n g . ,
and
is
Consequently,
an
u n d e r s t a n d i n g o f t h e mechanisms of h a b i t u a t i o n
c o u l d be
to
build
Its biological
mechanisms f o r o t h e r t y p e s o f l e a r n i n g .
mechanisms
are
I K a n d e l , 1 978 i]. Intelligence
being On
slowly
t h e one
teased
out
hand, i t i s e a s y
viewpoint t o propose
by
neurobiologists
from
many methods
used
of
the
Artificial
implementing
II*Background
Issues
33 habituation;
the
obverse
of
I n t e l l i g e n c e one should p r e f e r some
this
i s that
a learning
in
Artificial
mechanism
which,
at
l e v e l o f d e s c r i p t i o n , i s consonant with the known f a c t s o f
habituation. There and
i s a strong
philosophy.
Artificial
This
r e l a t i o n between A r t i f i c i a l
i s not s u r p r i s i n g i n view of the f a c t
Intelligence
has
t r a d i t i o n a l problems of Artificial the
Intelligence
to
consider
philosphy.,
In
some, of
designing
the major
almost
any
I n t e l l i g e n c e system commitments have t o be made about
nature of knowledge, how knowledge i s o b t a i n e d ,
represented action.
that
and
The
used,
and
connection
how
i t is
the r e l a t i o n between knowledge and
between
philosophy
and
Artificial
Intelligence
i s considered
[Burks,1978J,
and o t h e r s * . [McCarthy e t al.,1978] have
a
f o r e x p r e s s i n g "knowing t h a t " and used i t t o s o l v e
formalism
two
riddles involving
some
recent
philosophy problems
papers by
knowledge : about knowledge. [McCarthy,1977a,b,c],
approaching
from
by [ Sloman, 1 978 s], [Dennett,1978a],
the
many
an
the
Artificial
enormous i n f l u e n c e I
have
sketched
between A r t i f i c i a l animal
Intelligence
philosophical viewpoint. . In
of
philosophy
is
viewpoint promises t o have
on p h i l o s o p h y . the
actual
Intelligence
or
and
potential
interactions
linguistics,
psychology,
behaviour* the n e u r o s c i e n c e s , and philosophy.
Artificial
in
has made i n r o a d s on
Intelligence
summary, i t seems t h a t whereas the i n f l u e n c e slight,
McCarthy,
traditional
Artificial
described
I n t e l l i g e n c e tread
i t s own w e l l - d e f i n e d
path
Thus does through
!!•Background Issues
34
the
maze o f modern s c i e n c e ,
being
enriched
by
with
many o t h e r
II> 1> 3 Oa der s t and i n g the
the
fields
world
potential for enriching o f the
scientific
i s a - p r e r e q u i s i t e -to
and
endeavour.
doing
mathematics An to
e a r l y dream o f
prove
significant
seemed, a p e r f e c t calculus, and
i n which p r o o f s
and the
run! i t
rules. The
ensuing
is
now
traditional
failure. to
Intelligence
mathematical
tool
a formal
deduction it
Artificial
just
system proceed
by
Put
formal
the
the
combinatorial
c l e a r t h a t any manner
M o r a l - a new
of tool
theorems;
waiting
which can
researchers
to
be.
There used:
express a l l of mechanical
system
use
mathematical i s useless
was,
was
mathematics,
application
until
one
of let
uncontrollable,
of a f o r m a l logic
it
predicate
i n a c o m p u t e r , and
explosion
direct
was
system
in
is
doomed
to
has
learnt
how
use i t . In
t o expect Hilbert,
retrospect,
one
s u c h a scheme who
formalizations
was
can to
say
that
succeed..
personally
i t was
quite
Consider
responsible
unreasonable
the
words
for
of
several
of m a t h e m a t i c s [ H i l b e r t , 1927 ij:
No more than any o t h e r s c i e n c e can m a t h e m a t i c s be f o u n d e d by l o q i c a l o n e ; r a t h e r , a s a condition for t h e use o f l o g i c a l i n f e r e n c e s and t h e p e r f o r m a n c e o f l o g i c a l o p e r a t i o n s , s o m e t h i n g must a l r e a d y be given to us in our faculty of r e p r e s e n t a t i o n , c e r t a i n e x t r a l o g i c a l concrete objects that are: i n t u i t i v e l y present as immediate experience prior to a l l thought. I f l o g i c a l i n f e r e n c e i s t o be r e l i a b l e , i t must be p o s s i b l e t o s u r v e y t h e s e o b j e c t s c o m p l e t e l y i n a l l t h e i r p a r t s , and t h e f a c t that they differ from one a n o t h e r * and t h a t t h e y f o l l o w e a c h o t h e r , IIoBackground
Issues
35
or are concatenated, is immediately given i n t u i t i v e l y , together with the o b j e c t s * as something t h a t can n e i t h e r be reduced to anything e l s e nor requires reduction. C l e a r l y H i l b e r t had no i l l u s i o n s system
about
the
use: of
a
formal
f o r d i s c o v e r i n q mathematical theorems., My own i n t u i t i o n
i s that the o b j e c t s o f one's thought - noesgs - which a r e "surveyed"
when proving a mathematical theorem, are e s s e n t i a l l y
the same as the noeses i n v o l v e d i n manipulating o b j e c t s external world.
being
world,
or
in
i n the
making mundane plans f o r a c t i o n i n the
T h i s i s s a i d by [Kleene,1952, p.51, using a
quote
from
Heyting j]: "There remains f o r mathematics no other source than an intuition, which places i t s concepts and i n f e r e n c e s before our eyes as immediately clear.. T h i s i n t u i t i o n i s nothing other than the f a c u l t y of considering separately particular concepts and inferences which occur regularly i n ordinary thinking." Consequently my guess i s that no r e a l l y i n mechanical theorem how t o get machines
system
achievements
proving a r e l i k e l y to occur u n t i l we
to
model
there
are
problems
with
truth*
One
mathematical
approach might be t o use two f o r m a l systems, each of r e f e r to and hence leads to problem
a
approximate the other.
reconsideration
fMinsky,1969,p.4263,
proposals
f o r representation
suggests
how
an
know
t o handle the r e a l world.
I t i s w e l l known that formal
significant
of
using
a
possible which
can
In o n e . d i r e c t i o n
this
Minsky's
"models
of
models"
i n another d i r e c t i o n t o p r a c t i c a l theory.,
approximating
[McCarthy,1977a,p.5 ]
formal
system
might
II»Background
be
Issues
36
constructed.
II..1.4 A theory o f i n t e l l i g e n c e w i l l be p r i m a r i l y - concerned
with
r e p r e s e n t a t i o n s of the-world As i s a l r e a d y c l e a r , any theory all
be
concerned with r e p r e s e n t a t i o n s .
[McCarthy and Hayes,1969$ c l a s s i f y by
their
adequacy.
facts
of
the
a
giant
aspect
quantum
book
is
of
reality
mechanical
metaphysically
t h a t i n t e r e s t us. For
wave
red".
A
a
First
order
epistemologically propositional knowledge,
as
practical
But
fact
but
notions
of
h e u r i s t i c a l l y adequate are I n t e l l i g e n c e , and henceforth The
practical
facts
about
fails
on
of
cause
It
some
can
on
the
express
other
and
kinds
of
ability.^
A
adequate i f i t represents the
the of
world
direct
that interest
I consider only
are to
problems. potentially Artificial
these.
amount o f search i n v o l v e d i n s o l v i n g a problem
critically
as
i s epistemologically.
representation*
i s heuristically
representations
such a
such
p r a c t i c a l f a c t s and can be used t o compute answers t o Only
i t
- a formal system - i s a candidate
adequate
knowledqe
such
representation
logic
represent
equation..
representation
adequate i f i t can express a l l the world.
world
could have t h a t form without c o n t r a d i c t i n g
r e p r e s e n t a t i o n cannot even express "this
level,
r e p r e s e n t a t i o n s of the
i n s t a n c e , a quantum t h e o r i s t c o u l d , i n p r i n c i p l e , by
above
At a very gross
A representation i s called
adequate i f the world the
of i n t e l l i g e n c e w i l l
depends
the r e p r e s e n t a t i o n of t h a t problem.. For example II»Background
Issues
37 [ A m a r e l , 1 968 (J c o n s i d e r e d [MSG]
t h e M i s s i o n a r i e s and C a n n i b a l s
and worked t h r o u g h s e v e r a l d i f f e r e n t
most p o w e r f u l . r e p r e s e n t a t i o n general
problem
the
simplest
at
a l l .
to find
M&C
new
solution
will
problem
that
finding
this
a
is
solution
with
only
eons-long Any
of
an
problem
world
be as
problem
many
T h i s i s what I t could
to
different
many
repairing
a
through
parts
cortex
devoted
f o r these
be
us:
the
other
viewpoints
as
f o r the
result
have a c c e s s
f o r a p r o b l e m . , J. Minsky , 19751] c i t e s
of
a
good r e p r e s e n t a t i o n
solver will
outside
evidence
to
applicable
surrounding
of the
representations
the
of
an
search.
endowed,
the
search?
which
However, t h e a d v a n t a g e o f a good
i t may
representations of
in
good
auto-mechanic
also
be programmed
finding
the
c a r , who
m e c h a n i c a l , and v i s u a l r e p r e s e n t a t i o n s are
search
of
evolutionary
representations
problem,
no
from
develop
competent
a system
a little
Humans have a r e m a r k a b l y
three-dimensional
a
almost
of the search
i s that
possible*
more
m e r e l y moving t h e f o c u s
representation
-
considerably
the s o l u t i o n t o a problem.
o f t h e problem._
Moral
The
p r o b l e m , and t h e s o l u t i o n t o
for
representation
problems;.
a
how c o u l d
representation be f o u n d
representations._
dropped o u t o f i t with arises,
h a p p e n s when one " s e e s " said
solve
than the o r i g i n a l
The q u e s t i o n
a
could
problem
the
world*
multiple
to solve
a
witness
to visual, There
the
uses
evolution,
world,
to several example
electrical,
problem.,
We
with
several
the
different
a u d i t o r y , and t a c t i l e
is
also
representations.
psychological For instance,
!!•Background
Issues
38 I Posner,1 972g
presents
evidence
experiments
f o r the
existence
corresponding
to d i f f e r e n t
that
an
infant
distinct
the: q u e s t i o n different
of
i s born
reaction
distinct
time
representations
[Bower,1974]
suggests
with an w h o l i s t i c , multimodal o b j e c t of development
representations. i s , what
on
modalities..
concept which i n the course many
based
into
For a problem s o l v i n g system,
interactions
representations?
differentiates
This
should
is
occur
largely
an
between unexplored
question* Minsky suggested t h a t an i n t e l l i g e n t system be organized as a c o l l e c t i o n o f i n t e r a c t i n g schemata ., A schema c o n s i s t s 2
bundle
of
"slots , 1 1
one
closely related features.
f o r each
member
In the absence
of
a
of a c o l l e c t i o n o f
of
evidence
to the
c o n t r a r y , the s l o t s of a schema assume d e f a u l t v a l u e s . . A schema i s a l s o l i k e n e d t o a mini-theory If
one
f o r a s m a l l p a r t of the
wishes t o handle schema theory
in f i r s t
world.
order l o g i c , i t
might be worth p o i n t i n g out t h a t the r e l a t i o n between
a
and
between a
i t s default
values
i s s i m i l a r to the r e l a t i o n
formal system and i t s standard integers
are
the
standard
model model
in
logic,
f o r any
just
schema
as t h e
formalization
of
arithmetic* In
view of the requirement of m u l t i p l e r e p r e s e n t a t i o n s f o r
zMinsky used 'frame', but I p r e f e r to f o l l o w [ Simon, 19771], who pointed out t h a t 'schema' i s a more a p p r o p r i a t e term, l o r two s u b s t a n t i a l reasons. . F i r s t , the term has been widely used i n the A l and p s y c h o l o g i c a l l i t e r a t u r e i n the sense with which i t was i n t r o d u c e d by B a r t l e t t i n 1932; second, 'frame' already has a w e l l - d e f i n e d t e c h n i c a l meaning i n the A l l i t e r a t u r e . II»Background
Issues
39 a problem s o l v e r , augmented
by
allowing
representations* aspect
Ninsky's
schema
every
schema
T h i s might be done
o f the world
schema,
to as
may have d i s t i n c t
t a c t i l e o r o l f a c t o r y schema. verbal
theory
between
There
visual
have
perhaps
Each
verbal, visual, are
be
many d i f f e r e n t
follows.
schema,
v e r b a l schema f o r one s m a l l aspect
should
small
auditory,
associations
between
e t c . ; i n a d d i t i o n the
of the world
may
evoke i t s
v i s u a l schema, which may evoke i t s a u d i t o r y schema, e t c . To summarize t h i s s e c t i o n : any f u n c t i o n i n g r o b o t - c o n t r o l l e r must
use
a heuristically
adequate r e p r e s e n t a t i o n
t h a t i s , a world model which reduces to time
required
to
produce
a plan
a
of the world,
minimum
the
or to s o l v e other
search
frequently
encountered problems.
I I . 1> 5 A theory
of i n t e l l i g e n c e w i l l d e s c r i b e
intelligent
systems at many d i f f e r e n t l e v e l s
A
c l o s e l y r e l a t e d i s s u e concerns how t o d e s c r i b e
information the
processinq
information
system.
processing
a complex
Marr and Poggio[1976] argue that of
a
system
such as the c e n t r a l
nervous system needs t o be understood a t four n e a r l y
independent
l e v e l s of d e s c r i p t i o n : (1)
that
(2)
that are
(3)
that
at which the nature of a computation i s expressed; at
which the algorithms
t h a t implement a computation
characterized; at
which
an
algorithm
i s committed t o p a r t i c u l a r HaBackground
Issues
40 mechanisms; and (4)
that
at which the mechanisms are r e a l i z e d
In g e n e r a l , the nature of a computation problem
to
i s determined
by the
be s o l v e d , the mechanisms t h a t are used depend upon
the a v a i l a b l e hardware, depend
i n hardware.
upon
both
and
the
the
nature
particular of
the
algorithms
chosen
computation and on the
a v a i l a b l e mechanisms; For example, c o n s i d e r the F o u r i e r transform.. The theory of the F o u r i e r t r a n s f o r m independently One it.
of
i s well
the
understood,
particular
and
i s expressed
way i n which i t i s computed.
l e v e l down, there are s e v e r a l
algorithms
f o r implementing
F o r i n s t a n c e , the Fast F o u r i e r Transform* which i s a s e r i a l
algorithm based upon the mechanisms of the d i g i t a l computer, and the
algorithms
of
holography,
which
are p a r a l l e l a l g o r i t h m s
based on the mechanisms of l a s e r o p t i c s , can implement
the
Fourier
about d e s c r i b i n g a details the
of
transform.,
complex
algorithms
essential
thing
system,
The
both
be
used
to
meta p o i n t to be made
i s that
while
the
gory
and mechanisms are of great importance,
i s to
understand
computation enforced by the problem
+
+
the
nature
of
the
t h a t i s being s o l v e d . .
+
To summarize t h i s s e c t i o n , I have: briefly
outlined
Artificial
I n t e l l i g e n c e by examining i t from l i s Background
Issues
41
s e v e r a l Kuhnian •
argued world
that
viewpoints;
i t i s necessary
before
one
can
hope
t o know how t o understand t h e to
know
how
to
do
more
s o p h i s t i c a t e d t a s k s such as mathematics; •
pointed out that any theory concerned
of i n t e l l i g e n c e
must be p r i m a r i l y
with r e p r e s e n t a t i o n s of the world, and s e c o n d a r i l y
w i l l d e s c r i b e any i n t e l l i g e n t system i n many d i f f e r e n t
I I . 2 S i m u l a t i n g a robot i s a promising
ways.
aEjiroach t o A r t i f i c i a l
Intelligence A l o t of work i n A r t i f i c i a l problems
which people f i n d
problems
which
reasoning
require
i s devoted
to
i n t e l l e c t u a l l y challenging* that i s ,
extensive
by
one's
are
t h a t people s o l v e e a s i l y and unconsciously
the
s o l u t i o n of these
has
the
problems
that
conscious
of i n t e l l i g e n c e .
paradoxical
c o n c l u s i o n t h a t only
are: intellectually
uninteresting . to
awareness
Intelligence* then
somewhat
are
lying
"easy" problems which are of most
fundamental i n t e r e s t t o any budding theory
for
every
- and t h e r e f o r e s o l v e well - and i t i s the p r i n c i p l e s
behind
one
definition
conscious
problems t h a t people are not i n g e n e r a l good a t . . But there
day
almost
of
are
problems
Thus
use
they
many
abilities.
Intelligence
So those one's
of fundamental i n t e r e s t to A r t i f i c i a l
But t h e r e i n l i e s the g r e a t e s t hope f o r optimism,
i t i s much e a s i e r t o be o b j e c t i v e about the s u b j e c t !!•Background
Issues
42 matter and not be functioning source
of
led
astray
one's
of guidance.
own
about
which are now Since
the.greatest s c i e n t i f i c
progress
examples
matter.
human
mind
Vision
been
devoted
how
is
such
an impressive
Intelligence
involved
the v a r i o u s aspects, e*g.„perception, memory, p l a n n i n g ,
reasonably
be expected
together..
Further*
these
Thus the complete s i m u l a t i o n of some very simple
would
be
instance,
a
worthwhile,
study
is
a
put
crayfish,
together
many
different
notably
investigated
A p l y s i a , or sea hare, by
turtle.
organisms,
a l l the i n f o r m a t i o n about one
organism.. I t should be added that there are most
or
problem here, i n t h a t even though a great
d e a l i s known about many aspects of has
organism
in A r t i f i c i a l Intelligence, for
a s i m u l a t i o n of a s t a r f i s h , or there
might
t o appear i n s i m p l e r organisms i n s i m p l e r
form.
no-one
and
to some s m a l l aspect of i t . , But i t i s q u i t e
a c t i o n , or speech, are woven
However
and
Intelligence.
l i k e l y t h a t there are b a s i c p r i n c i p l e s of i n t e l l i g e n c e in
be
of " u n i n t e r e s t i n g " problems
unfathomable a phenomenon, most work i n A r t i f i c i a l has
the
fallible
subject
are
whole
about
a devilishly
major s u b f i e l d s of A r t i f i c i a l
the
ideas
s c i e n c e s , where i t i s very easy to
the
speech-understanding
intuitive
consciousness,
After a l l *
has occurred i n the "hard" objective
by
neurobiologists
simple
single
creatures,
which have been e x t e n s i v e l y [Kandel,1976 ]
and
would
t h e r e f o r e be good candidates f o r the f i r s t s e r i o u s s i m u l a t i o n of a complete l i v i n g c r e a t u r e . some
s i m p l e r world
The
other suggestion
and organism and
is
to
invent
work out a l l the d e t a i l s of IlaBackground
Issues
43 the
organism-controlling
from
the
psychologist's
Dennettf1978J
suggested
critique
of
Artificial
followed,
with
point
make
simulation
Intelligence.
satisfy
and
the
the
on
and
cheap
the
other
the
and
of
analysis in
animal
from
provided
introspection,
the by to
robot
"naturalness"
extensive
while
program
and
should
from
on
criteria
of
of
on
actual
both
the
In
the
on t h e one hand
"animal-like-ness", feasible
t o simulate
c a n be
bug
done
using
design the
one hand
creatures,
the
intuition other
based
hand i t c a n n o t
used t o c o n s t r u c t
f o r the robot
reflect
and
based
proceed
on
with
the
studies
one's avoid
own being
i t ; namely
be c o m p u t a t i o n a l l y
world
the
from
on
to
various of
t h e . most one c a n do i s t o s e t t l e
"naturalness"
but
One has t o
o f t h e machine i n which t h e : p r o g r a m
fact
design
should
The
the concern that i t , t o o , should
arbitrary
control
program.
or
the
programs.
by t h e m a t e r i a l b e i n g
In
I have
b y p s y c h o l o g y , as f a r a s i t g o e s , f r o m
architecture
run.
recently
philosphical
constructing
experimentation of
observation
behaviour,
constrained
the
performance
organism-controlling derived
in
organism-controlling
organism-controlling
ideas
a
problems*
hand be c o m p u t a t i o n a l l y
enough t h a t
observe
of
more
out
representation.
decisions
world
some c r i t e r i a
and
and
this
T h i s i s the path
involves methodological
arbitrary
simulation,
view,
e m p h a s i s n o t so much on p r o b l e m s o f
approach
many
of
t h i s i n the context
r a t h e r on p r o b l e m s o f s p a t i a l This
TodaJ. 1 9 6 2 3 c a r r i e d
program.
r u n s , and feasible upon
some
some
unstated
the design
of the
HaBackground
Issues
44 controlling And
when
judged? world
program.
Again, this
nothing
that
is
given
an
is*
of
position
would be
the an
the
robot
world
performance
And
of
made.
seriously
finally,
even
in
always
the
i f
course
programs the
principle
some
of
used
human/environment
are
that
to the
and
much
t h a t no
o f the
a
with
road t o
a
designs
with
an
compared
potholes;
are of there
simulated
the
whole
principle worlds
robot but
the
discontinuity
human/environment via
then
with
worlds,
than
robot
actual
series
t h a t the
interesting
least
principles
robot
simpler
at
for
above, f o r
whole
roughly
This
better i f the
qualitative:
methodological
p r o m i s e s t o l e a d t o new
even
c o u l d be
knowledge
intuitive
f o r then
proposed
simulated
h i g h l y complex
In c o n c l u s i o n , t h e s t u d i e s i s strewn
so
system
of complexity
t o c a r r y over
Or
f o r various simulated
possibility
on
compared
building
robot
"elegance".
interesting
i s a t work which would say
worlds
level
the: c o n t r o l l e r organism*
controlling
obvious
be
or
be
since there i s
rely
were b u i l t *
c o u l d be
could
simulated
task
to
i s i t to
o r more d i f f e r e n t
program
of a r e a l
uncovered
robot
has
"interest", i f two
how
designed
i n i t s n a t u r a l environment, as
behaviour
the
improved
built,;
impossible One
"naturalness",
i n t e r - d e s i g n comparison
organism
an
with.
organism-controlling
simulated
is
it
and
arbitrarily
strictly,
t o compare
notions
designed
true
is
at
going
system. simulation
the
route
is
vistas!
IlaBackground
Issues
45 II.3
The
current Al t r a d i t i o n
f o r the d e s i g n of p l a n n i n g
problem s o l v i n g - systems i s not
easily
adaptable
and
to
my
purpose
My
research i s , i n part, a reaction
approach
to the d e s i g n of p l a n n i n g
T h i s a p p r o a c h i s so w i d e s p r e a d a
tradition.
call
i t the
[Newell,
Extending Freqean
Shaw,
&
and
the
Simon,1957]
[ Sussman, 1975 i]
Sussman,1977] epitomizes
The -
series
GPS
s y s t e m s say
about a c t i o n , section
is
remedy, and
I I , 3 . J An
nothing
amplify
show why,
exegesis
of
[Newell
systems. be
called we
programs
LT
& Simon,1963] -
H a r t , & N i l s s o n * 1972 ]
One's
t o one's o n g o i n g
-
a
everyday
p e r c e p t i o n and
and
plan. ,
justify
The
this
of some A l p l a n n i n g and
behaviour
is
actions,
yet
o n l y very purpose
complaint,
t e m p o r a r i l y , I shun t h i s
S
[ D o y l e , 1 978 i]
TMS
a b o u t p e r c e p t i o n and
i . e .. executing to
Al
of i S l o m a n , 1 9 7 1 g ,
[ McDermott, 1 978 ]
tradition..
related
usual
- NOAH [ S a c e r d o t i , 1977 9 - EL [ S t a l l m a n
DESI
this
intimately these
-
justifiably
terminology
tradition.
the
problem-solving
t h a t i t may
BLOCKS [ W i n o g r a d , 1 9 7 2 ] - STRIPS [ F i k e s , HACKER
against
little
of
this
suggest
a
tradition..
problem-solving
systems LT, first
52
the l o g i c
theorist,
theorems
was
given
i n the P r i n c i p j a
Russell.
A l l these
generate
subproblems
the t a s k
used
proving
the
M a t h e m a t i c a - o f Whitehead
are theorems i n the i t
of
sentential
substitutions,
calculus.,
detachment*
IlaBackground
& To
and
Issues
46
forward size
and b a c k w a r d c h a i n i n g , and t o r e d u c e
i t used
matching
and s i m i l a r i t y
52 t h e o r e m s and f a i l e d to
time
and space
on 1 4 .
Al
space
38 o f t h e
I t proved
Most o f t h e s e f a i l u r e s
very
important
i n L T a r e w i d e l y used
most modern
tests.
search
were
programming
i n A l . . The
techniques
i n A l and a r e i n c o r p o r a t e d i n t o
languages.
Its
importance
lies,
however, n o t s o much i n t h e t e c h n i q u e s i n v e n t e d by N e w e l l , and
Simon,
-
contributions in
t h e type
terms, followed which
verbally
and be
constructing airport. learning
believe system. being advice
which
shadow
accept
to
considered
a p l a n t o g e t from
something like
idea
i t must f i r s t
i t i s not q u i t e t h e r i g h t One o f t e n
about
i t .
To
illustrate type
i n one's
be c a p a b l e o f
was and
way t o d e v e l o p
i t i n words o r b e i n g
problem home
to
being
of the
told i t .
are reasons t o an
intelligent
a t some s k i l l able t o accept
Verbal expression of a s k i l l
i t s
t o be c a p a b l e o f
but there
becomes v e r y c o m p e t e n t
able t o express
of a decade,
f o r a program
a respectable basis,
which
was t o be a b l e t o r e a s o n
everyday
t h e desk
was t h a t
Kuhnian
published a proposal f o r
advice*
the
In
and
i n the c u r r e n t A l scene* .
year [McCarthy,1958J
able
technical
a paradigm
A l f o r the greater part
Shaw,
attempted,
acceptable*
established
T h i s program
he
important
o f problem
was f o u n d
program.
The b a s i c
may seem
i n the type
a significant
following Taker
undeniably
Shaw, and Simon
casts
functioning
That
- but r a t h e r
by m a i n s t r e a m
Advice
are
of s o l u t i o n
still The
an
these
Newell*
due
limitations.,
LT i s , h i s t o r i c a l l y , introduced
the
without verbal
comes a f t e r , n o t
II«Background
Issues
47 b e f o r e , t h e a c q u i s i t i o n of competence at the s k i l l .
To
give
a
very personal example^ I have two daughters aged 6 and 8 who can now s k i p r o f i c i e n t l y
-
yet they
nothing about technique; having
have
been
told,
verbally,
t h e i r only i n s t r u c t i o n has c o n s i s t e d o f
t h e i r hands held f o r s e v e r a l hours on beginners'
The
Advice
programs.
Taker
The program
proposal
of
influenced
[ Black, 1964 3,
the
slopes.
several program
later QA3
of
[ Green, 19 6 9 §, the MICROPLANNER language of [ Sussman, Winograd, & Charniak,1971J, and STRIPS a l l Taker.
Indeed
leaned
heavily
on
the
Advice
the f u n c t i o n i n g of MICROPLANNER c l o s e l y
follows
the o u t l i n e on pp. 406-409 o f [ McCarthy, 1 9583. GPS,
another
landmark
i n A r t i f i c i a l I n t e l l i g e n c e [Newell
and Simon,1963], i s a program whose design goal was t o human thought. as
the
I t handled
missionaries
problems,
proving
and
simulate
a v a r i e t y of i n t e l l e c t u a l t a s k s , such cannibals
theorems
in
task, the
some
integration
first-order
predicate
c a l c u l u s , and the monkey and bananas problem*. GPS deals with task
environment c o n s i s t i n g o f o b j e c t s which can be transformed
by v a r i o u s operators; and
i t detects
differences
between
objects;
i t o r g a n i z e s the i n f o r m a t i o n about the task environment i n t o
goals. what
a
Each g o a l i s a c o l l e c t i o n o f constitutes
goal
attainment,
information
that
defines
makes a v a i l a b l e the v a r i o u s
kinds of i n f o r m a t i o n r e l e v a n t to a t t a i n i n g t h e : g o a l , and r e l a t e s the i n f o r m a t i o n t o other g o a l s . . There are three types of g o a l s :
IIoBackground
Issues
48
Transform
object
A into object
B,
Reduce d i f f e r e n c e between o b j e c t Apply - o p e r a t o r Basically,
GPS
Q to
achieved
to
recursively
the
attainment
of the
Meanwhile
there
studies
in
set
the
a goal
up
initial was
principle
says
deduce BvC.
BvC
resolution principle
this
example
and
predicate
calculus,
arguments
of
algorithm
the
so
variables
such
become i d e n t i c a l
with
the
this
the
resolution principle,
formed
contributions
from
may
[ D a v i s , 1 9 6 3 ],
order
formula
This
and
was
two
logic,
clauses
others, a l l
consolidated
resolvent be
of
and
AvB
and
by
i t
by
that
variables
free
A,
B,
arguments
of
arguments of
can
may The
i n terms
allowing
may
order
appear
as
matching
substitutions
A i n the
A i n the
first
second
for
clause clause,
The
r e s u l t i n g r u l e of deduction
can
be
is
be:
complete
for
c a l c u l u s - t h a t i s , any
provable
well
be
proved to
of
extra
first
Introduce a
- t o compute
one
-iAvC.
i t t o the
C,....
resolution -IAVC
s u c c i n t l y described
lift
and
the
AvB
s y m b o l s and
predicate (wff)
effort
Generalize
i s possible.at a l l .
first
to
The
the
the
if
the
lead
logic.,
unification
that
would
from
symbols
- known as
heuristic
o f work e m a n a t i n g
follows.
predicate
means-ends
line
from t h e
full
disjunction
a
propositional
i s called
as
using
of I R o b i n s o n , 1 965 i ] .
in
that
A.
another
mechanize mathematics*
i t s simplest,
B,
goal. .
[ P r a w i t z , 1 9 6 0 ],
resolution principle At
by
object
s u b g o a l s whose a t t a i n m e n t
mathematical
[ G i l m o r e , 1960 ] , aimed t o
object
A and
deduced
by
sufficiently IIsBackground
many Issues
49 a p p l i c a t i o n s o f the r e s o l u t i o n The
resolution
theorem-proving mathematically matching,
principle.
principle
thus
reduces
to one r u l e o f i n f e r e n c e which subsumes, by the elegant u n i f i c a t i o n a l g o r i t h m , the s u b s t i t u t i o n s ,
and
similarity
t e s t s of LT.
However,
c o n s i d e r a b l e c h o i c e i n d e c i d i n g what p a i r of pair
of
predicate
together.
The
symbols
question
[Kowalski,1969]..
He
that
the
generalized
Raphael,19683,
and
of
derived A*
independent
of
search
strategies. search
reduced
of
QA4
that,
semantics
under
trying
this f a c i l i t y
the search. prover
to
by
which
In to
&
these
However, h i s s t r a t e g i e s
of the c l a u s e s and l i t e r a l s the search
control
these*
space
the: s i z e
i s not of the o f the
MICRO-PLANNER,
it is
possible
prove a wff of a c e r t a i n
other f a c t s of c e r t a i n r e s t r i c t e d type should However
studied
d e s p i t e the mathematical elegance
appeared. in
what
Nilsson,
rose when the programming languages
CONNIVER, and recommend
was
[Hart,
conditions
Hopes o f being a b l e t o
space
and
search s t r a t e g i e s f o r r e s o l u t i o n
under c o n s i d e r a t i o n * and conseguently significantly
clauses
strategy
algorithm
stated
the
there:remains
(technically, l i t e r a l s ) to resolve
s t r a t e g i e s were a d m i s s i b l e and optimal. are
mechanical
be
tried
does not* i n g e n e r a l , s u f f i c i e n t l y
to
type, first. reduce
[ R e i t e r , 1 9 7 2 J proposed the use of models i n theorem help
c o n t r o l the search, basing h i s approach on the
theorem
proving
machine
proposal
was
present
to the theorem prover a model of the
axiomatic
system i n v o l v e d .
to
of
I G e l e r n t e r , 1959t]. ,. H i s
geometry
In a d d i t i o n he
proposed
a
HaBackground
set of Issues
50 procedures required
for by
interface
extracting
the
theorem
between
such
syntactic
l o g i c a l system.
startling
breakthrough.
accepted way search
space
p r i n c i p l e may exposing in
information prover,
a
There
of using semantics in
and
semantic So f a r ,
about a
still
model when
flexible,
subsystem
this
to
the
has
general,
and the p u r e l y
not
led
to
any
seems t o be no g e n e r a l l y
control
the
size
of
the.
a theorem prover., In summary, the r e s o l u t i o n
be somewhat n e g a t i v e l y c h a r a c t e r i z e d
as
elegantly
the c o m b i n a t o r i a l e x p l o s i o n which seems t o be i n h e r e n t
any s t r a i g h t - f o r w a r d attempt
to
do
mechanical
mathematics
based on Fregean formalisms. The frame - problem a r i s e s whenever a theorem to the a
reason about a c t i o n s . QA3 program, system
This was f i r s t
a r e s o l u t i o n theorem
For
example,
(ON A B) and
(ABOVE A C ) .
some
facts
i f A, B, and C are b l o c k s , two
(ON B C ) ,
and
an
obvious
this axioms
deduction
is
I f the e f f e c t of an a c t i o n i s modelled by changing
which
which are now
of
false.
the previous deductions are s t i l l One
seems
c e r t a i n f a c t s remain unchanged modelled.
have
about
system of axioms then a f t e r the a c t i o n one cannot
formally,
an
Suppose you
of axioms that d e s c r i b e s a s i t u a t i o n i n the world - a
situation..
the
used
done by [Green,1969] i n
prover.
world model - and perhaps have deduced
might be
prover i s
to
need
axioms
be
sure,
t r u e and
saying
that
when the e f f e c t s of an a c t i o n are
T h i s i s e x a c t l y what Green d i d .
Every p r e d i c a t e
had
e x t r a argument p o s i t i o n f o r a s t a t e - v a r i a b l e - a s i t u a t i o n a l
f l u e n t i n the terminology of [McCarthy
&
Hayes,1969]
-
II«Background
which Issues
51
assumed a new value whenever an a c t i o n
was executed i n the world
model;
least
An a c t i o n was modelled by
axiom
described
said,
loosely,
objects
that
those
action, are s t i l l
true
multiplicity
axioms
the
was only the
of
axioms
able
most
languages.
describing
t o handle the s i m p l e s t
trivial
tasks,
attributes
However,
between
in
us c a l l
of each a c t i o n *
and
of problems..
In
any but
MICROPLANNEE, CONNIVER, and QA4 the p r o c e d u r a l
They r e p r e s e n t an advance over QA3 as follows._
as
describes
They
I n CONNIVER and QA4 each c o l l e c t i o n
a p a r t i c u l a r s i t u a t i o n i n the world
is
a c o n t e x t , and whenever the e f f e c t s of an a c t i o n So f a r ,
d e v i c e s used f o r modellinq the e f f e c t s of an a c t i o n -
other words, f o r s p r o u t i n g
addition
the
the world model, the axioms
are modelled, a new context i s sprouted from the o l d * . only
by t h e
explosion.
of axioms that
the
of
i t would be q u i c k l y overcome by t h e
do not use s t a t e v a r i a b l e s .
maintained
and the others
are not d i r e c t l y a f f e c t e d
a f t e r the action*
One
i n e f f i c i e n c i e s o f a r e s o l u t i o n theorem prover, QA3
combinatorial Let
axioms.
describing
both the e f f e c t s and n o n - e f f e c t s
inherent
two
the d i r e c t e f f e c t s of an a c t i o n
o f the world model that
describing
at
and
deletion
of
a new facts
though more powerful methods are
context
-
have
been
the
(axioms) from a context, even available
in
the
procedural
languages. STRIPS [ F i k e s and N i l s s o n * 1971g can successful The
marriage
of
GPS
be
described
as the
and the theorem proving approach.
problem space c o n s i s t s of an i n i t i a l world model, a HaBackground
s e t of Issues
52
operators
which
STRIPS attempts
affect to f i n d
transform
the i n i t i a l
statement
i s true.
wffs
the
in
the world a
sequence
of
operators
A world model i s represented
first-order
predicate was
initially
a
which must be s a t i s f i e d
wff,
world.
An
operator
the o p e r a t o r t o be a p p l i c a b l e , and a world
will
set
model
is
to
be
an
operator
This function i s s p e c i f i e d
and
delete
The
changes
consists
of
i n a world model f o r
function
which
describes
by two
effect
lists,
the add
list
of a p p l y i n g an a p p l i c a b l e
operator t o a given world model i s t o d e l e t e from the model those
a
changed when the operator i s
applied.
list.
of
the robot
t o an a c t i o n r o u t i n e whose execution causes
precondition
the
which
In
applied,
real
the
statement.
as
calculus*
i n the surrounding
how
a goal
world model i n t o a model i n which the g o a l
problems to which STRIPS corresponds
model, and
c l a u s e s s p e c i f i e d by the d e l e t e l i s t
all
and to add a l l those
c l a u s e s s p e c i f i e d by the add l i s t . , STRIPS attempt
begins
a p p l y i n g a r e s o l u t i o n theorem prover to
t o prove t h a t the goal wff GO
world model MO. in
by
the i n i t a l
f o l l o w s from
I f the proof succeeds
world model.
Otherwise
then GO
the
is trivially
the uncompleted
taken to be the " d i f f e r e n c e " between MO
and GO.
initial
proof
are
the . o p e r a t o r s
allow the proof t o
whose
continue.
a p p l i e d r e c u r s i v e l y t o these.
sought.
e f f e c t s on world models would
The
precondition
r e l e v a n t o p e r a t o r s are then taken to be new is
is
Next, o p e r a t o r s
t h a t might be r e l e v a n t t o " r e d u c i n g " t h i s d i f f e r e n c e are These
true
wffs
of
subgoals, and
A search s t r a t e g y i s
STRIPS
used
!!•Background
the
to
Issues
53 control
the
order
in
which
relevant
o p e r a t o r s are a p p l i e d .
STRIPS t e r m i n a t e s when a sequence o f o p e r a t o r s
has
been
found
which t r a n s f o r m s MO i n t o a world model i n which GO i s t r u e . STRIPS was l a t e r extended triangle in
by s t o r i n g g e n e r a l i z e d plans i n a
t a b l e format { F i k e s , Hart, N i l s s o n , 1972 [J. . T h i s was used
two ways: t o allow s i m i l a r
re-planning,
and
to
problems
assist
to
be. s o l v e d
without
i n monitoring the progress o f the
robot i n the course of e x e c u t i n g the plan. in
i n t e r e s t i n g guestion a r i s e s concerning t h e a b i l i t i e s of
STRIPS.
There a r e problems STRIPS can s o l v e and there are
similar
problems
has
a
STRIPS
perspicuous
very
cannot s o l v e ; at the.same time STRIPS
structure.
This
naturally
suggests
the
q u e s t i o n : i s there an i n t e r e s t i n g and u s e f u l way t o c h a r a c t e r i z e those problems - world model p l u s goal wff -
actually
solvable
by STRIPS? HACKER [Sussman,1975J
is
also
concerned
plans but works by a process of debugging skill
almost
One
contains
a l l the
BLOCKS
right plans, or
world
r e q u i r e d i n the course of s o l v i n g a BLOCKS type
of
producing
a c q u i s i t i o n . . HACKER i s endowed with s e v e r a l databases
assertions.
others
with
contain
bugs,
i n f o r m a t i o n about
types
summarizing
of
bugs.
patches HACKER
knowledge
problem,
starts
with
and a
techniques
for
dumb i n i t i a l
trial
procedure
f o r the t a s k .
fails
"process model" of t h e s t a t e o f the computation
a
point of f a i l u r e
i s constructed.
while
programming techniques, types
f o r bugs,
The t r i a l
of
procedure executes, and i f i t
HACKER then examines
a t the
this
IIoBackground
to
Issues
54
discover
why
the
procedure. f a i l e d .
attempts
to classify
If
attempt
the
about
bug-types
procedure; repeated,
i s used
If
process
an
procedure
that
until
a
a
known
and
to
patch
knowledge the
a bug f a i l s ,
of
i s then
then
is
HACKER
debugged
any o f a c e r t a i n
L o o s e l y s p e a k i n g , HACKER
database
trial
procedure
HACKER ends w i t h a f u l l y solve
types.
bug"
satisfactory
can s u c c e s s f u l l y
from
several
a modification
to c l a s s i f y
tasks.
i s t o s a y , HACKER
t h e n HACKER*s b u i l t - i n
"trial
Otherwise,
o f b l o c k s world
procedure
of
attempt
resigns;
one o f
t o propose
iteratively*
basically
a
i s successful
The
obtained.
class
t h e bug i n t o
That
general compiles
a l l t h e n e c e s s a r y f a c t s and
advice. The ability was
important
- i t wasn't good
of
a
retaining a
contribution
distinctly the reasons
o f HACKER was n o t i t s p l a n n i n g
- n o r even new
type
-
why a c e r t a i n
EL
of
[ Stallman
the
TMS s y s t e m Neither
and
which
the t e c h n i c a l
idea of
action
was p e r f o r m e d
or
why
This i s the idea
back-tracking of
the
& Sussman,1977], and was d e v e l o p e d
STRIPS n o r HACKER
and
-
system
further i n
of [Doyle,1978J.
the f o l l o w i n g
tabletop
ability
but
new p i e c e o f c o d e was added t o a p r o c e d u r e . .
underlying the dependency-directed
to
i t s learning
problem
three
C l i e s on A,
C
on
the table.
as
(AND (ON A B)
in
could the
obtain
BLOCKS
b l o c k s A, B, C.
The g o a l i s t o b u i l d These
systems
fail
the o p t i m a l world..
A and B r e s t a tower because
solution
There
is
a
on t h e t a b l e
A on B on C, w i t h the goal i s stated
(ON B C) ) , and b o t h STRIPS and
HACKER
IIoBackground
proceed Issues
55
to
attack
each subgoal independently.
Achieving e i t h e r o f the
ON subgoals
i n t e r f e r e s with a c h i e v i n g the other;
put A on B
you can't put B on C; i f you f i r s t
r
i s on A), you interacting
can't
put
to
Sacerdoti's subgoals*
on
B.
This
handle
r
put B on C
(which
i s an
example
[ T a t e 1 975 ], and [Warren,1975 ] a l l
of
system..
problems; I w i l l b r i e f l y
NOAH
builds
as
a
a
i s imposed
network
only
in a
when
sketch NOAH,
of
p r o c e d u r a l network.
r e g u i r e d t o achieve a goal are s t o r e d order
wrote
r
such
represented
temporal
first
subgoals;
[Sacerdoti*1975 J systems
A
I f you
goals
The subgoals
partial
necessary
order;
a
to resolve a
conflict
between brother subgoals.,
achieve
a g o a l i n a l a y e r e d f a s h i o n by expanding one subgoal at
a time* keeping primitive
NOAH c o n s t r u c t s
and
a
plan
a c a r e f u l watch f o r p o s s i b l e i n t e r a c t i o n s ,
actions
are reached*
In t h i s way a f u l l y
re-planning
to
achieve t h e f a i l e d
handled
subgoal and p a t c h i n g the
new plan i n t o the o r i g i n a l p r o c e d u r a l net. is
until
detailed
plan i s c o n s t r u c t e d before e x e c u t i o n begins; e r r o r s are by
to
To
summarize:
NOAH
a very e l e g a n t system which r e p r e s e n t s a c u r r e n t peak i n the
technology
of p l a n n i n g systems f o r a BLOCKS type
world*
II*3.2 C r i t i c i s m s of - the Fregean t r a d i t i o n - i n p l a n n i n g and problem-solving The
AI t r a d i t i o n , based upon
criticised
on two l e v e l s :
Fregean
formalisms,
can be
one i s p u r e l y t e c h n i c a l , the other i s
p h i l o s o p h i c a l . . On the t e c h n i c a l l e v e l there a r e a t l e a s t II"Background
three Issues
56 criticisms. reasoning
First,
about
previously.. handling facts,
actions*
Second,
a continual
an
ability
i n p u t from the
there
there
a changing
apply
to
static
interested
stream
axiom
well
numbers. trying
Lastly, to
knowledge On Fregean
more
formula
concerned
with
"dimension"
of
about
demands t h a t
well
accommodate
sensory
be
termed
a database
the
of
perpetually
Tarski-Kripke: In
addition*
the n a t u r a l
capture many
semantics
numbers
t o automate
the
i f
one
is
which
is
mathematics
that
concept
difficulties
only
no
Fregean
of the
natural
encountered
and
--
knowledge
in
about
formalism.
of
an the
action
and
attempt
as
in
the act of w r i t i n g to
yet
change., formula
- just
the dimension
level,
world;
Fregean
being tackled
to
contradictory
receives
might
causes, a b i l i t i e s *
implies
a
This
that
in
t h e r e i s no known s e m a n t i c s f o r
-
philosophical
aspect
organism
in
described
encountered
possibly
the well-known f a c t
fully
i n a Fregean a
of
i s trying
there are
reason
actionless
problem
to r e c a l l can
difficulty
systems*
it
encountered
problem,
o f e v i d e n c e about
o f axioms
t h e c a s e i f one
system
stream
Third,
presumably
formal
the
how
i n r e a s o n i n g about
would be
i s the frame
of any
problem:
database
difficulty
outside world.
o u t s i d e world.
a changing
the
is
incoming
a x i o m s t o an i n c o m i n g changing
This
required
accommodation
is
capture i n A l one
It's
as
a
by
timeless,
i s above a l l though
the
i s o f the wrong t y p e f o r t h e physics,
dimension
t y p e o f a f o r m u l a match t h e
t y p e o f t h e phenomenon d e s c r i b e d
down a
the
theory
dimension
formula. IlnBackground
Issues
57 At
this
p o i n t I must c a l l a h a l t .
l i n e of argument l e a d s t o deeper w a t e r s t h i s p o i n t , and,
developing
concerned
a
evidence;
than I care to e n t e r at
the
about
world
and
thesis.
r o b o t - c o n t r o l l e r one
with reasoning
accommodating
this
to do i t j u s t i c e , would t a k e . f a r more space
time than can be a f f o r d e d i n t h i s In
3
A c o n t i n u a t i o n of
actions
model
and
is, with
primarily, continually
t o the sensory i n p u t stream
s e c o n d a r i l y one d e s i r e s computationally
efficient,
at l e a s t t r a c t a b l e , algorithms f o r c a r r y i n g out these
of or
processes.
Throughout the exegesis I pointed out t h a t , i n e f f e c t ,
the
c o m b i n a t o r i a l e x p l o s i o n has not been brought under c o n t r o l .
For
some
and
special
proof
[Tseitin,1968J
procedures,
have
given
Without i n t r o d u c i n g any theorem
10
in
J.Cook
this
special &
"Cook a
&
Reckow, 1974 ij
more
precise
terminology,
Reckow, 1974 ] -
statement.
their
can
result
be r e - s t a t e d as
follows: For
infinitely
many n, there e x i s t s a theorem with n
c l a u s e s f o r which the number of steps i n i t s proof i s at l e a s t e x p o n e n t i a l i n (log(n) Thus one
may
complexity
conclude suqgests
shortest
squared).
t h a t the evidence, so f a r , from s t u d i e s of that
the
computational
reguirements
of
^Because i t l e a d s to the c o n c l u s i o n t h a t the metaphysics of Platonism, as found i n the p h i l o s o p h i c a l t r a d i t i o n which s t a r t s with P l a t o and continues with Descartes, Kant* Frege, Russell, and modern a n a l y t i c p h i l o s o p h e r s , i s suspect. A new metaphysics can be based on the notion of " p r o c e s s " as i n Whitehead's Process and reality: T h i s i s part of another great t r a d i t i o n , l a r g e l y i g n o r e d by modern p h i l o s o p h e r s , which can be t r a c e d from Aristotle through medieval p h i l o s o p h e r s to Bergson, Whitehead, H u s s e r l , and o t h e r s . II«Background
Issues
58 r e s o l u t i o n theorem-proving There already
is,
however,
an
important
i Kowalski, 1969 jj
mentioned,
algorithms
are of an i n t r a c t a b l e nature.
f o r theorem-proving
open problem
derived
it
was
open
improvement
case
n**2, a s i g n i f i c a n t
question
of
A*
be
is:
can
carried
of
improvement;
to
A*. A*,
a l g o r i t h m B whose
Martelli's
over
As
search
behaviour
2**n, and r e p l a c e d A* by a new
worst case behaviour was obvious
heuristic
t h a t were g e n e r a l i z a t i o n s of
But [ Mart e l l i , 19771] analyzed the worst found
here.
The
analysis
Kowalski's
and
search
algorithms? In c o n c l u s i o n , I hope t h a t some
notion
of
why
I
feel
the
knowledgeable
and
have chosen
consequently can understand to take another
has
t h a t the Fregean t r a d i t i o n i n Al
planning and problem-solving systems i s , perhaps, tracks,
reader
why,
on
the
wrong
i n my r e s e a r c h , I
approach.
II.4 A survey of c l o s e l y r e l a t e d t o p i c s The
purpose
comprehensive description
of
this
survey of
two
of
section closely
related
is
to
provide
related
topics,
work,
namely
a
and
fairly a brief
imagery
and
behavioural theories.. I s t a r t with the l i t e r a t u r e on a n a l y s e s and s i m u l a t i o n s organisms.
There
independent,
and each with i t s own
have
are
many
such
studies, particular
of
a l l more or l e s s orientation.
I
t r i e d to c l a s s i f y them a c c o r d i n g to t h e i r emphasis, but no IIoBackground
Issues
59 mutually e x c l u s i v e c l a s s i f i c a t i o n seems p o s s i b l e .
The
headings
I have chosen a r e : •
f u n c t i o n i n g robot
•
analyses
*
s t u d i e s based on animal behaviour;
•
a p p l i c a t i o n s of d e c i s i o n
•
c o g n i t i v e maps.
The
simulations;
o f simple organisms, without
inclusion
of
theory;
c o g n i t i v e maps here may seem a l i t t l e
p l a c e , but a moment's c o n s i d e r a t i o n * studies
are
simulation;
concerned
of the f a c t t h a t
reasoning*
•
s p a t i a l planners and
•
representation
T h i s f a l l s e a s i l y i n t o two c l a s s i f i c a t i o n s : conceived
as p o t e n t i a l t o o l s f o r a r c h i t e c t s
others;
systems f o r s i m u l a t i n g the motion of r i g i d
There
appropriate.
then proceed t o the . l i t e r a t u r e on s p a t i a l
and
a l l such
with how an animal or man f i n d s i t s way
around i t s environment, shows that i t i s q u i t e I
out o f
i s , in
addition,
one p u b l i s h e d
system f o r p a t h - f i n d i n g
[ Thomson, 1977i], which I do not i n c l u d e here appropriately Similarly
covered
in
my
bodies.
section
since
V.I
I do not review the l i t e r a t u r e on
on
the
i t is
more
path-finding. skeleton
here
s i n c e t h a t i s done i n s e c t i o n V. 1.
I i * 4 . 1 Previous [Nilsson environment
robot &
simulations
Raphael, 19671]
i n order
simulated
a
robot
and
its
to study the key problems i n designing and II«Background
Issues
60 controlling robot,
a robot.
was
simulated
based
robot
containing
Their l a t e r on
r e s i d e s on
both
the
simulated
features
that
system
any r e a l
f o roverall
by u s i n g
immediately
and
sensory
information. by
The
pushing
contained
robot
problem-solving
" g o t o " and " p u s h t o " p r o b l e m s .
of l o c a t i o n s .
i t s
Plans
front
could
richer
model o f i t s
f o r communicating
program, and a r o b o t The t a s k s
to solve
Moore's m a z e - s o l v i n g
The r o b o t
in
control.
several
i n a much
These i n c l u d e t h e r o b o t ' s
a heuristic
program
constructed
uses
a p r o b l e m - s p e c i f i c a t i o n language
the robot,
executive
the: location
changes to i t s environment
the
would n e e d .
environment, with
of
basic
environment
about
into"
movable o b j e c t s .
design
important
information
c o r r e c t , or update t h i s
c a n make s p e c i f i e d
The
Their
and s e n s e when i t "bumps
i n i t s e n v i r o n m e n t and
establish,
appropriate
arbitrarily
or l e f t ,
stores
properties of objects
robot
exploration.
SHI
The r o b o t c a n
It
an
the
movable and nonmovable o b j e c t s . .
an
to
preliminary
Shakey,
checkerboard
turn r i g h t
inputs
of
large
move f o r w a r d , object.,
this
design
these
algorithm
sense the contents
consisted of tasks
were
on t h e a r r a y
o f the
square
o f i t , and use t h i s t o c o r r e c t t h e w o r l d
model* Of closest my
the
published
studies
that
t o mine i n t e r m s o f o v e r a l l
simulated
world,
robot-controller corresponding
are
Utak's a l l
parts of their
I know o f , t h e i r s
a i m s and
sensory more:
design..
equipment,
sophisticated
i s the
However,
and than
Utak's the
system* II^Background
Issues
61 Becker and Merriam I Merriam, 1975 fj) world
([ Becker, 1972 ], [Becker
simulated
a
robot
cart
which used a s o p h i s t i c a t e d eye with
information
about
i t s surroundings.
This
eye
i n a two a
fovea
a "Martian"
could e i t h e r gather
coarse
eye for
a
landscape
detailed
and f o c u s s i n g down on one.object
information..
eye-controlling
This
conflict
scene.
a The
unfortunately
natural-looking design not
o b j e c t when the environment
took
of
robot
the
into
a ' lookout t o get more
resolved
by
the
and
which
when l o o k i n g at a s t r e e t program
was
The eye could a l s o track a f i x e d
the v i s u a l
by Martian
path
effort...,
eye-controlling
acount
The
later
the
finite
occlusion
mountains.
simulation size
of the
of the robot
of, f o r instance,
A long term memory was used
information.
i s a more s o p h i s t i c a t e d s i m u l a t i o n of the world and
a d i f f e r e n t eye, but no design of
scan
moved*
which s t o r e d no s p a t i a l Theirs
progress,
specified.
c h a s s i s and simulated Martian h i l l s
Thus the
program which took i n t o account such f a c t o r s as
d r i v e , s a l i e n c e of an o b j e c t , produced
was
was
information
small area, and could change i t s f o c a l p o i n t .
objects,
up
i n f o r m a t i o n from a
could be used f o r two c o n f l i c t i n g t a s k s : keeping new
pick
a city street
l a r g e area or could "zoom" down and o b t a i n d e t a i l e d from
dimensional
to
Initially
environment was used but subsequently used.
& Merriam,1973],
the simulated
of the robot executive*
robot executing
or r e p o r t
a goto o r pushto task, appears
to have been p u b l i s h e d .
IlaBackground
Issues
62 II.4.2 Three analyses of simple organisms Each organism
of
these
from
theoretic
analyses
a distinct
analysis
approach
environment;
of
the
Toda's
survival
paper
d e c i s i o n theory; while Becker a
representation
should develop
for
over
of
is
in
of
events
organism relating
the
i s concerned
external
an
equation
an
in
an
organism
same vein but
uses
with the s t r u c t u r e of and how
this structure
time.
[Simon,1956] considered a s i m p l i f i e d v i s i o n , with a s i n g l e need - food activity:
behaviour
point of view.. Simon's paper i s a game
environment i n which he d e r i v e s one to
the
resting,
organism
and
only
with
three
e x p l o r a t i o n , and o b t a i n i n g food.
of
I t has to
point
derived
the chances of s u r v i v a l of the
organism
depended
environment organism that
equation showinq how
and
on two
four
parameters,
describinq
the
two
of
kinds
s u r v i v e on a plane with i s o l a t e d an
sources
circular
orqanism,
organism
and
extended could
to
assure
be. s a t i s f i e d
decision
achieved
theory.
a
behaviour
found
i t s several
high p r o b a b i l i t y of i t s s u r v i v a l He a l s o
showed
how
multiple
with a very simple choice mechanism.
over qoals This
without the use of u t i l i t y f u n c t i o n s as i n
Simon's a n a l y s i s c a s t s e r i o u s doubts upon the
u s e f u l n e s s of then c u r r e n t economic and rational
he
the
i n i t s n a t u r a l environment r e q u i r e s only very
p e r i o d s of time.
a n a l y s i s was
the
assuming
behaved i n the obvious " r a t i o n a l " way.„ Thus
an
He
describinq
simple p e r c e p t u a l and choice mechanisms t o s a t i s f y needs
food*
s t a t i s t i c a l theories
as bases f o r e x p l a i n i n g the
of
characteristics
IIoBackground
Issues
63 o f human and
other
dissatisfaction As views
sprang
a device to man
planet. distributed eating
a
u n i f y the
s t u d i e d the The on
surface*
The
program
were
amount of
job
design*
to t r a v e l
uranium The
are
representation
i n at
collected effect
also
]
terms.
then
to induce,
such
function
a
distant
uranium
obtains
randomly
energy
program,
each moment* ,
i n the
of p r o c e s s e s experience world
b l o c k s may
given
and
and
from
a
the
to
Extending on
The
Simon's
choice
robot
choose
maximizing
choice
the
strategy
strategy
uses
the
choice
c o u l d reduce the c o m p u t a t i o n a l
a simple
robot
be
future,.
(My
style.),
He
by
which the
i t gained
c o n s i s t s of placed
and
world
events
i n t r u e Baconian
a system
e n v i r o n m e n t . . The
on
c h o i c e program has
robot observes
"Popperian"
coloured
robot
psychology
no
and
effort stored
environment.
The
events
the
this
emotion, . . . ) ,
robot
collect
o f o b s t a c l e s on
in
manipulate
The
is
analyzed
"Baconian"
predict
the
considered.
of t h e
[ B e c k e r , 1973
tries
to
perceiving
a l l considered.
various approximations
required
motivation,
of a s o l i t a r y is
which
a d e c i s i o n - t h e o r e t i c a n a l y s i s based
specified.
and
design
from
f u n g u s t h a t grows a t random l o c a t i o n s on
bodily
what d i r e c t i o n approach,
v a r i o u s ways i n
s u r f a c e , and
certain
(And
& GPS?)
learning,
robot's the
rationality. .
f o r t h LT
(perception,
[ T o d a , 1 9 6 2J
how
organismic
a
as they
style,
call
happen
and
r e p r e s e n t a t i o n s to
system proposed robot
through
i n what I
may
be
said
a representation could
store
interacting
smooth
manipulated,
to
shelf
and
with i t s on
a simple
li«Background
which movable Issues
64
square eye with 9 square in
the
eye
retinal
A h i s t o r y i s kept
commands
with the
their
robot
representation,
and a hand t h a t
a 1 X 1 r e d s q u a r e . . The w o r l d
as
physics.
record
fields,
of
sensory tries
which
motor
to
obeys t h e laws o f
commands
answers.
and
From
induce
appears
of
this
a
query
historical
semantic-net-like
i t u s e s t o p r e d i c t t h e outcome o f f u t u r e
actions. Becker's followed so
approach
is
A i n the past,
that
the
Becker's
with
a Baconian
his
analysis.
i tclearly approach*
input),
deciding
which
attempted
a t t o o low a l e v e l
are
B e c k e r d o e s , i t e n d s up b e i n g as a h y p o t h e t i c a l
observations must
decide
supposing problem relation part
in
a
by
which
the
'event'. large
there
is
on g u i t e
that
kernel
of
the
start
problem
one and s h o u l d
as,
I
claim,
criteria.
make a
million
i s not f e a s i b l e , Second,
have
therefore
a
i s the causal
be s t o r e d
What i f two c a u s a l l y r e l a t e d k e r n e l s periods
o f t i m e , a s might
of
decision i s
interest.)
may
of
of kernels
has been c h o s e n , t h e r e kernels
fact,
associated
arbitrary
but since are
i fB
succeeds,
the
If this
could
ones
i t
stream
scientist
how many n e a r b y chosen
continual
representation,
based
Baconian
significant
of deciding to
of
that
the d i f f i c u l t i e s
significant.
situation,
somehow
of t h i s
separated
a
the
that
A i n the future.
These a p p e a r r i g h t a t given
kernels
remember
B to follow
illustrates
First,
idea:
i n t e r e s t i n g n o t because
(motor commands and s e n s o r y
(Just
should
can expect
approach i s very
because
on one s i m p l e
an o r q a n i s m
organism
but
based
as are
occur i n object
II«Background
Issues
65
occlusion
problems?
problem,
which
might
several numerical hoc
basis
etc.,
B e c k e r has be
are
generalized,
termed
used t o e n a b l e
or
numerical
feature;
In
sum,
a very
its
and
not
Simulations
simulate
based
aphid
alternations e.g. model
is
based
reciprocal is
on
a separate
centre
sufficiently
strong
the at
centre a time
active system persist
This
is
a
be
These
mainly
of
for
even
of
with
behaviour,
wingspreading.
The and
For each
activity
there
each
other.
inhibition
one
several
When
from
equally stimulated
a system only
a
concerned
drives,
the
such
designed
centres,
active
such
was
types
flying,
i t i s possible for
period
but
model i s o n l y
inhibit
centre
i t
rival;
a is but
i s active to
be
configuration i s unstable)..
The
e x h i b i t s h y s t e r e s i s : once an for
to
unsatisfactory
proposal,
centres
t o s u p p r e s s an
concurrently,
ad
cost
subrules.
a very
different
concepts
The
f a t i g u e s ; . In (although
s c a l e s are
between c e n t r e s . .
centre*
particular
into distinct
probing,
the
inhibition
an
confidence,
a model a n i m a l which
several
feeding,
on
on a n i m a l - b e h a v i o u r
behaviour.
between
walking,
manipulated
successes.
[Ludlow,1976J d e s c r i b e s to
and
this
Third,
( d e r i v e d from events)
interesting
for i t s
s o l u t i o n to
'windowing' p r o b l e m .
rules
differentiated
arbitrary
I I . 4._3
a
measures o f c r i t i c a l i t y ,
apparently
faults
satisfactory
s c a l e s are introduced
to provide
which
no
activity
when t h e
centres
i s started i t
drive l e v e l
will
necessary
IlaBackground
to
Issues
66
e l i c i t the a c t i v i t y has been reduced would
seem
t o be a necessary
execute many d i f f e r e n t approach
might
controlling
by the
f e a t u r e of any organism
behaviours, to prevent
usefully
be
several different
incorporated
Releaser
Mechanisms"
with
an
a
control
program
the e x e c u t i v e c o n t r o l h i e r a r c h y .
The
(ADROIT) t h a t moves
The
along
the
in
a
programmed,
lines
of
the
ADROIT avoids o b s t a c l e s when en route
a goal by r e a d i n g the angles
cylinders.
system
of
designed
theory, .
AI
the Lorenz - Tinbergen
with a small number of c i r c u l a r o b s t a c l e s was
afore-mentioned to
in
This
"Selection
computer s i m u l a t i o n of a small animal plane
which can
thrashing.
animal behaviour by adding to
This
behaviours.
[ F r i e d m a n , 1 9 6 7 J analyzes and extends theory of i n s t i n c t i v e
performance..
and
ranges
to
the
edges
of
s t r u c t u r e of the " B e h a v i o u r a l U n i t " to c a r r y out
a "go t o " command was
exhibited.
No r e p r e s e n t a t i o n of the world
was i n v o l v e d . [ A r b i b & L i e b l i c h , 19771] are concerned
to
bridge
the
gap
between human memory s t u d i e s and the p s y c h o l o g i c a l l i t e r a t u r e animal l e a r n i n g and c o n d i t i o n i n g . . The research
effort
on
Pavlov - Bitterman learning
are
animal theory
the
that
same
They propose
major reason f o r the huge
behaviour has been the Thorndike the
in
[ Bitterman, 1975 ]; consequently research..
this
underlying
a l l animals,
processes including
i s an important d i r e c t i o n
a theory of how
an orqanism
in
its
spatial
environment
of
man of
couples i t s
memory s t r u c t u r e to i t s s p e c i f i c a c t i o n r o u t i n e s so t h a t i t operate
on
may
i n an i n t e l l i g e n t manner. II»Background Issues
67
They
adopt a world
model i n t h e
containing
drive-related
sensorimotor
features.
dynamics,
the
theory
learning
•LI'H'H
The t h e o r y
of
environment, An
approach
from
particular
robot
where e a c h
decision
edges
nodes
containing
general
drive
in
the
world.
results that relate r a t
that
d e c i s i o n - theory consider
operates
t h e . decision-making
in
i s
a
poorly
known
a c t i o n may have many p o s s i b l e o u t c o m e s .
b a s e d on m a x i m i z i n g t h e e x p e c t e d
each
with
behaviour*
Kiefer,1973]
a
and
where t o move n e x t
Robot - s i m u l a t i o n s based - on &
graph
model i s u p d a t e d , and t h e
e x p l a i n s some e x p e r i m e n t a l
[Jacobs
a
specifies the
way i n which t h e w o r l d
and s p a t i a l
component
of
information
way i n which t h e r a t d e c i d e s Their
form
developed.
utility
resulting
The d e c i s i o n t o e x e c u t e
a c t i o n i s viewed as a move
in
a
game
against
a
the
environment;
t h e outcome o f an a c t i o n i s t h e e n v i r o n m e n t ' s move
in
t h e game*
The e s t i m a t e d
by
backing
that
the u t i l i t y
expected the
up from
value
expected
task
assigned of their
utility
to
f o r a nest,
i s to build
the robot
eating,
is
utilities.
evaluated
using
the f a c t
The d e c i s i o n t h a t
chosen,
insect-like
This
robot
and may be s t u n g
a nest.
of a plan,
i s
t o a s e t o f u n c e r t a i n outcomes i s t h e
The t a s k
but i s s p e c i f i e d
adding
of a d e c i s i o n
the t e r m i n a l stages
c o n t r o l a simulated material
utility
approach
which s e e k s
i s
by an enemy.
m a t e r i a l t o the nest,
the u t i l i t y finding
used
food, The
i s not e x p l i c i t l y
through
maximizes to
collects robot's
represented
functions
for
m a t e r i a l , and b e i n g IlaBackground
Issues
68
stung.
Likewise,
through eating
its will
exceeds
a
utility
No
decision
(negative)
et
a
positive
and
false
the
tradeoffs
goals,
taking of
It i s also acguire
w o r t h w h i l e , and Feldman
not
of
&
among
used t o a
i n the
whether v e r i f i c a t i o n
Sproull
discuss
and
provided
give
a
are
the
-
have
used
utility function for
and
function is
used
achieving
value
be
of
problems
much p l a n n i n g
possible
to
reliability,
the
t e s t s should
false
of
suitability
s o l u t i o n s t o the
many o t h e r
the
actions
strategies
how
under
distance.
may
theory
strategy,
model,
this
a
such f a c t o r s a s
formulate
world
from
a
In
monkey i s
utility
as
problem.
the
apply
stated
the
sensing
various
starve.
respective
pushed
using
The
ever
represented
be
decision
i n t o account steps
be
bananas
All
strategy,
not
can
reliable
answers.
will
S p r o u l l , 19771]
"suitability"
is
technigues
robot
used
meal
solving.. Their
to
pushing, climbing,
solution
complexity
to
sensinq
except
utility
previous
is
&
s u i t a b l e , and
i n t e r m s of e n e r g y c o s t .
reveal
goal.
are
goal
environment i s used.
and
available
negative
The
best
problem
monkey and
device
- walking*
various
how
for the
energy c o s t s .
the
all
the
equivalent
the
the
starvation of
a
with the
poor
[Feldman
symbolic
of
not
Unfortunately
defined
and
s e v e r a l boxes are
device
to
to
version
with
of
the
representation
essentially
but
find
-
goal
a l . , 19753
bananas
monkey
bound
as
in fact
so
examples are
version
and
certain
theory
modified
function
represented
time s i n c e
stored
[Coles
i s not
never o c c u r i f the
However, t h e either.
eating
effort
the of is
performed.
applications
IIsBackground
of
Issues
69 d e c i s i o n theory i n robot problem s o l v e r s . Feldman and S p r o u l l ' s paper supports t h e i r c l a i m t h a t "a combination
of
d e c i s i o n - t h e o r e t i c and
symbolic
artificial
i n t e l l i g e n c e paradigms o f f e r s advantages not a v a i l a b l e to e i t h e r individually".
However,
although
I
can't
yet pinpoint i t
e x a c t l y , I confess t o a gueasy f e e l i n g when a p p l y i n g p r o b a b i l i t y theory to symbolic theory
reasoning.
The
basic
i s the p r o b a b i l i t y of an event,
value o f the r e l a t i v e frequency
definition
of the
defined as "the l i m i t i n g
of occurrence
o f the event
in a
long sequence of o b s e r v a t i o n s of randomly s e l e c t e d s i t u a t i o n s i n which the event is
very
may occur" [ Parzen, 1960 i]. . P h i l o s o p h i c a l l y
u n s a t i s f a c t o r y . . Bayes' theorem, an important
computing
conditional
unsatisfactory..
The
probabilities, task
of
clearly
difficulties
and proposing a new d e f i n i t i o n
beyond
scope o f t h i s t h e s i s .
the
is
rule:for
even
delineating of
this
more these
probability
is
A l l t h a t can be s a i d i s t h a t
t h e r e are many i n k l i n g s around, and i n chapter
IV
I
will
give
These s i m u l a t i o n s serve to confirm Simon's c o n c l u s i o n
that
some i n d i c a t i o n o f the d i r e c t i o n r e q u i r e d *
traditional of
decision
theory i s not a p p r o p r i a t e t o the a n a l y s i s
b e h a v i o u r a l systems.
I I . 4. 5_ C o g n i t i v e maps
A
traditional
cognitive
maps
field
of
psychology
([ Trowbridge , 1913 ],
i s concerned
[ Tolman, 1948 ],
with
[Moore
IIsBackground
&
Issues
70 Golledge, 1976 ], j_ K u i p e r s , 19781]) . the
knowledge
a
person
l a r g e - s c a l e space.
has
A person's about
cognitive
map i s
the s p a t i a l s t r u c t u r e of
Thus the t o p i c of cognitive:maps
i s relevant
to my work. The
f u n c t i o n s of a c o g n i t i v e
information position,
about
and
problems.. through
to
map
assimilate
new
the environment, t o r e p r e s e n t one's c u r r e n t answer
route-finding
and
relative-position
I t i s b u i l t up from o b s e r v a t i o n s made:as one t r a v e l s the
environment.
computational
model
[ K u i p e r s , 1978 ]
presents
a
(the TOUR model) of the c o g n i t i v e map t h a t
uses m u l t i p l e (5) r e p r e s e n t a t i o n s f o r builds
are t o
the c o g n i t i v e
map,
and
up knowledge by o b s e r v a t i o n s and by i n t e r a c t i o n s between
the separate r e p r e s e n t a t i o n s .
Whereas TODR gains new
knowledge
by d i s c r e t e o b s e r v a t i o n s at a s m a l l number of f i x e d p l a c e s , Utak gains new knowledge by r e c e i v i n g a new r e t i n a l impression new
position
impression
and
r e s o l v i n g the d i f f e r e n c e s between the a c t u a l
and the p r e d i c t e d r e t i n a l impression by modifying the
hypothesized
shape
environmental
empty space i s very s i m i l a r t o K u i p e r ' s
map
when regarded
concerned PPA
at a
of the environment*
as a network of r o u t e s .
Utak's s k e l e t o n o f the
Whereas TOUR i s only
with c i t y - s t r e e t networks and not at a l l
explicitly
environmental
represents space.
In
the two sum,
dimensional
Kuiper's
cognitive
work
with
shape,
shape o f the is
somewhat
complementary t o mine.
IIsBackground
Issues
71 II.4.6
Spatial
planning
systems
[ Eastman, 1973 i] r e v i e w s c u r r e n t program, tasks.
GSP,
for
rectangular
computer),
edge-adjacency
overall
the design
Various
the
proposer
DDs i n
consistent in are
which
S which
satisfies
are
described
S,
which,
proposes
with the arrangement
several
DDs
(e.g..an
reguirement f o r the of
the
a l lthe S-relations. depth-first improve
a
made;
t h e s i d e s o f t h e DUs a r e a l i g n e d
with
search.
o f GSP
new
The
the search,
an a r r a n g e m e n t
for
already
room),
the
An i m p o r t a n t p a r t
locations
arrangement
an a r r a n g e m e n t
which
when g i v e n
a new
(e.g. the p a r t s o f a
between
i s to f i n d
i s the
o f some o f
DU
which
are
Only
arrangements
the
sides
of
S
considered. f P f e f f e r k o r n , 1975 |J d e s c r i b e d
which
relaxed
the r e s t r i c t i o n
a l l o w i n g non-convex p o l y g o n a l type of s p a t i a l
constraint
which
a l l t h e empty
says that
connected. arrangement are
(DOs)
or a sight-line
from t h e S - r e l a t i o n s .
location
rectangular
o f GSP i s as a b a c k t r a c k i n g
heuristics
derived
S-relations
t h e problem
space
a large units
reguirement
operator's desk), in
design
and s e v e r a l
and d e s c r i b e s
two d i m e n s i o n a l s p a t i a l
Given a space S (e.g.
smaller
DUs
solving
programs
marked
DPS
that
convex and
planner,
DPS,
a l l s h a p e s b e : r e c t a n g u l a r by
s h a p e s , and which
on an a r r a n g e m e n t :
allowed
a path
a
must
o f space occupancy
polygons are the
primitives;
some a r e marked o c c u p i e d .
new
constraint,
space i n the arrangement
uses a representation
i n which empty
another s p a t i a l
be
o f an Some
These
convex
IlnBackground
Issues
72
polygons are c a l l e d represented
Each space block
as a set of s i d e s , and
When a new
by
a
side
of
space b l o c k s and
location
the
in
turn
new
every
space
block
shape i s broken i n t o
the occupancy marked a c c o r d i n g l y .
proposer e s s e n t i a l l y
space b l o c k s . . As i n GSP
is
each s i d e as a set of p o i n t s .
shape i s added t o an arrangement
intersected separate
space b l o c k s .
proposes a l l the c o r n e r s
the c o n s t r a i n t s are used to
two The
of empty
guide-
the
search* . Both systems explore the
branching
proposer and try
concerned
where
f a c t o r at each node i s c o n t r o l l e d by the l o c a t i o n
new
shapes.. The
convex polygon represented fault
t r e e of space . l a y o u t s
by other h e u r i s t i c s which decide
fitting
main
a search
from
my
order
to
p r i m i t i v e shape concept used i s a
as a l i s t
point
i n what
of
of boundary p o i n t s .
Their
view i s that these systems are
only with o b j e c t placement, not
with
path-finding
or
o b j e c t moving,.
II.4.7
Systems f o r s i m u l a t i n g the motion of r i g i d
[Baker,1973J, spatial
dissatified
simulation,
desired
with one
objects
conventional in
r e l a t i o n s h i p s of p o i n t s were e x p l i c i t . .
which To t h i s end
methods f o r the
spatial
he
presented
the design
of an i t e r a t i v e array of l o g i c c i r c u i t s
which
simulate
the
or
rotation
of
this
arbitrary The
continuous
shapes, and
rigid
translation
implemented a s i m u l a t i o n
system c o n s i s t s of a r e c t a n g u l a r a r r a y of l o g i c a l
could of
array.
circuits,
II«Background
Issues
73
each
representing
coordinate
a unit
system
the
square.
On
reaching
t o keep t r a c k
the
side
of the point
An
is
object
greater
than
of
stability
o f a s q u a r e , c o n t r o l and m o d i f i e d
local
are passed t o the neighbouring as a c o l l e c t i o n
root
of
of points
between
square. (where f o r
points
2 (root2)) ,
from
that
a
must
be
and i t s m o t i o n points.
can
derive
t h e u s e o f a n a l o g u e s i n t h e same way t h a t
people
e n d , he i m p l e m e n t e d
system
was
to
computer
a system
solve
two
program
WHISPER.. The
dimensional
comment
on
h i s arguments c o n c e r n i n g
from
my p o i n t
o f view WHISPER was i n t e n d e d
f o r simulating
rigid
object
motion
the:use t o be
purpose
blocks
p r o b l e m s by t h e use o f a s o - c a l l e d a n a l o g u e .
not
system
as i t c r o s s e s
was n o t d e v e l o p e d t o h a n d l e c o l l i s i o n s . „
To t h i s this
local
arc.
square
[Funt,1976] argues
do..
a
or a c i r c u l a r
represented
the
has
by f o l l o w i n g t h e p a t h s o f a l l t h e c o n s t i t u e n t
system
benefits
circuit
of a single point
r e a s o n s t h e minimum d i s t a n c e
simulated The
Each
I t s p a t h may be a s t r a i g h t l i n e
coordinates
technical
square.
I
world will
of analogues; a
performance
under t h e i n f l u e n c e o f
gravity. The
input
t o WHISPER i s a two d i m e n s i o n a l
s q u a r e s on which t h e s i d e view coloured, the
arbitrarily
corresponding
instabilities immediately interactions:
and
of a configuration
shaped, b l o c k s real
world
under
collapse, i n
the a
array
rotation, collision,
has been drawn. situation
influence
flurry
of
of
sliding,
of
block
of colored distinctly Typically
contains
many
gravity
would
motions
and f r e e
and
fall*
II»Background
Issues
74
WHISPER s i m u l a t e s produces
as
output
this
t h e same a r r a y
updated t o d i s p l a y t h e i r simulation
makes
human r e t i n a program
in
which
collapse
predicted
extensive some
the
retina,
contacts
about
symmetry;
The
non-overlapping size
circular
increases
with
parallel Funt's array
of
as
a
fixed
retina
is
o f automata.
similar
in this
properties
r e s i d e i n t h e diagram;
simulated
program,
movement
motions t h e
disintegrates
into
a
while
an
conclusion
the s i m u l a t i o n
WHISPER i s n o t s u i t a b l e f o r my H Howden, 1969 i]
considers
fact
and
finding finding array
an
c e n t r e . . Each
neighbours. iterative
becomes known t o shape
and
other
and a f t e r on
small i s o l a t e d
a few
the
array
pieces.
a p p e a r s i n a p p e n d i x A.3. of r i g i d
is
operating i n
to Baker's
object
of
The b u b b l e
immediate
are simple
of
of t h i s
that
circular
object's
of
multitude
area,
processors
their
primitives
depiction
main
operations
or bubbles.
respect
precise demonstration is
a
O n l y t h e c o l o r o f an o b j e c t
main
the
motions
the r e t i n a l
of
with
WHISPER'S
WHISPER'S
block
of
The
s o t h a t t h e whole r e t i n a
number only
of
o f r o t a t i o n , and
fields,
processor,
positions
resembles t h e
control
of
and
places..
which
centre
consists
and c o m m u n i c a t i n g
the block
the
d i s t a n c e . from
b u b b l e h a s an a s s o c i a t e d conceived
finding
retinal
array
t h e use o f s e v e r a l
visualization
retina
input
resting
Under
gravity,
including
between b l o c k s ,
but with
use of a r e t i n a
i n t e r a c t i o n s a r e computed t h r o u g h on
the
final
respects.
knows
on
motion p r o v i d e d
A The by
purpose.. the
sofa-moving
task;
that i s ,
II*Background
Issues
75 produce a plan f o r moving a two
dimensional
to
to
another
when
surrounding, The
and
constrained
shape from one.place
remain w i t h i n the w a l l s of a
i n general non-convex, two
edges of the w a l l s and
of the
of p o i n t s using chain-encoding i s easy t o simulate
dimensional
s o f a are represented
[Freeman,1974];
r i g i d o b j e c t motion.
used
In a pre-execution an
be extended to do so.
such an extension*
array
since.he
the
walls.
Presumably the
reported
I am
on a running
f o r every point on the perimeter
2 *
of the
program. into
must
sofa* ,
At
any
(integral)
point
within
plan the
i s a s m a l l number of p o s s i b l e a c t i o n s of t r a n s l a t i o n
or r o t a t i o n which may actions
So
(length of s o f a perimeter)
produced as f o l l o w s .
w a l l s there
be
referenced
times f o r every i n t e r s e c t i o n t e s t performed*. A sofa-moving is
will
author
step, the p o i n t s of the wall are sorted
the w a l l array i s u s u a l l y
it
i n t h i s paper
of buckets, which, i n the extended a l g o r i t h m ,
probed twice
lists
I t i s not, however, so
that the a l g o r i t h m as described
work, though i t can
as
conseguently
easy to detect the i n t e r s e c t i o n of the s o f a and not convinced
shape.
are
those
be a p p l i e d to the f o r which the
sofa;
the
permissible
intersection test f a i l s .
The
plan i s produced by executing
an u n d i r e c t e d , l o o k i n g
heuristic
s t a t e space e n t a i l e d by the s e t of
search through the
p e r m i s s i b l e a c t i o n s at each p o i n t . , That t h i s at
all
is
somewhat
surprising
-
scheme
apparently
backwards,
performed
i t d i d , on some
poorly s p e c i f i e d examples.
I t would perform p a r t i c u l a r l y
in
a
the
simplest
case
-
small
sofa
badly
w i t h i n a l a r g e empty II«Background
Issues
76 containing
space.
I I . 4; 8 Imagery
Mental imagery i s r e l e v a n t PPA
because the SHAPE
subsystem
of
can be viewed as a model of mental imagery even though t h a t
was not t h e goal of SHAPE'S design., discussed
in
the
[Piaget,1954 §,
This
Shepard,
presents
the c u r r e n t
imagery
has
been
p s y c h o l o g i c a l l i t e r a t u r e by \_ B a r t l e t t , 1932 i ] ,
[ Hebb, 196 8 ], i s how
Mental
iShepard,19783
iii the c o n c l u s i o n
and
many
of h i s recent
others. review,
s t a t u s of mental imagery i n psychology:
I submit t h a t there are both l o g i c a l and a n a l o g i c a l processes o f thought, and t h a t processes of the l a t t e r type, though often neglected i n p s y c h o l o g i c a l r e s e a r c h , may be comparable i n importance to the former. By an a n a l o g i c a l or analog process I mean j u s t t h i s : a process i n which the i n t e r n a l s t a t e s have . a natural one-to-one correspondence to appropriate intermediate states i n the e x t e r n a l world. . Thus, t o imagine an o b j e c t such as a complex molecule r o t a t e d i n t o a d i f f e r e n t o r i e n t a t i o n i s to perform an analog process i n t h a t h a l f way through the process, the i n t e r n a l s t a t e corresponds t o the external object i n an o r i e n t a t i o n h a l f way between the initial and f i n a l orientations. And this correspondence has the very r e a l meaning t h a t , a t t h i s half-way p o i n t * the. person c a r r y i n g out the process w i l l be e s p e c i a l l y f a s t i n d i s c r i m i n a t i v e l y responding t o the e x t e r n a l presentation of the corresponding external structure i n e x a c t l y that s p a t i a l o r i e n t a t i o n . The i n t e r m e d i a t e s t a t e s of a logical computation do not i n g e n e r a l have t h i s property. Thus, a d i g i t a l computer may c a l c u l a t e the c o o r d i n a t e s of a r o t a t e d s t r u c t u r e by performing a matrix multiplication. But the intermediate states of t h i s row-into-column c a l c u l a t i o n w i l l at no point correspond t o - o r p l a c e t h e . machine i n readiness f o r - an intermediate o r i e n t a t i o n o f the external object. !!•Background
Issues
77 To
summarize: thanks to the s e a r c h i n g r e a c t i o n time experiments
of Shepard and process now
h i s c o l l e a g u e s , the n o t i o n of a n a l o g i c a l
has
a f i r m p i e c e o f evidence
I have already imagery
in
could
34)
as v i s u a l
justifiably
and
i n t e r p r e t H i l b e r t ' s "concrete
can
be
used
construct.
[ Pylyshynj 1 9 7 3 , 1976?}
The
and
review, i s provided
Behavioural
In
The
others. He
to
a scientifically
main
protagonists
of
been
latest
design
of
a t t e n t i o n and
neurology.
"tridimensional
respectable have
been
Pomerantz, 1977 ij.
This
word i n t h i s debate, and
a
a
robot
controller
Hebb
one
is,
a b e h a v i o u r a l theory* . Thus i t i s worth
extended
I t i s intended
of
and
area.
developed a c e l l - a s s e m b l y theory
approaches h i s theory
facts
notion
the
[Anderson,1978J.
developing
[Hebb,1949]
whether
as
t a k i n g a b r i e f look at work i n t h i s
which has
(p.
theories
attempting
essentially,
by
over
[Kosslyn
cannot be d i s c u s s e d here..
II.4.9
objects"
imagery.
imagery
explanatory
mental
mathematical d i s c o v e r y ; i n a d d i t i o n
There i s c u r r e n t l y a debate mental
on.
mentioned the apparent importance of
scientific
one
to rest
thought
by
[Good, 1965 ],
of
[ B i n d r a , 1976 ],
t o be a p h y s i o l o g i c a l theory from two
and
of thought.
d i r e c t i o n s : the: p s y c h o l o g i c a l
o r i e n t a t i o n , and describes
lattice-like
behaviour,
a
assembly
the then
current
cell-assembly of
cells,
supposed to be the b a s i s of p e r c e p t u a l i n t e g r a t i o n . "
facts as
a
that I have Again,
HaBackground
he
Issues
78
writes,
assemblies
structures that only
by
may e n t e r any be
"diffuse,
function briefly
virtue
constituent
are
of
cells...
the
time
theory
and
underlies
the
relation
a
to
(subjective stimulus theory
a
new
stimulus
entity."
fault
as
described
Though
of
the
unit
times...,
At to
cell-assembly A pexgo
distinctive
neural
well
r e s p o n s e made i n
as
the
the
awareness
o r image) o f t h a t cell-assembly/pexgo
p r e c i s e stage
directly
s t r u c t u r e , which
SHRDLU d i r e c t l y
of d e v e l o p m e n t t o
wonderful
i s perhaps t h i s : i t
i n terms o f (the p o o r l y
might be l i k e n e d t o t r y i n g t o
such
a s an
operating
i n t e r m s o f machine c o d e ,
m e n t i o n o f PLANNER, PROGRAMMER,
LISP, stacks,
descriptive
In other
words, t h e d i f f e r e n c e i n
the
between n e u r o n and t h o u g h t , i s t o o g r e a t reductionist
theory.
system
by-passing
o f computer
descriptive
Artificial
or
a s s e m b l e r s and
vocabulary
science*
one s i n g l e
of
pexgp.
t h e Hebb-Bindra theory
a b i g c o m p u t e r program
by
firing
benefit.
explain
gap
so
considered
the
as p e r c e p t
suggestive,
neuronal
other
may be
identifying
entity,
known)
the
do
transmission
diversifies
the
t o e x p l a i n human t h o u g h t
Winograd's
and
the
at d i f f e r e n t
concept,
i s a t an i n s u f f i c i e n t l y
The
all
or
excited,
underlies
experience
o f any d i r e c t
tries
and
"currently
that
in
irregular
b a s i s " [ p. 196-7iJ. .
introduces
organization
all
cell
one moment, t h e a c t i o n o f an a s s e m b l y on an a l l - o r - n o n e
systems,
relations
one a s s e m b l y ,
[ Bindra,1976J extends
be
as c l o s e d
An i n d i v i d u a l
i n t o more t h a n
anatomically
level,
t o be b r i d g e d Intelligence,
IIsBackground
Issues
79 using to
the
build
language
of computer
the r e q u i s i t e
[Miller, i d e a s on
of
"TOTE"
executing
plans.
The
(fixed
describe
action
animal
most
units
specific
(test;
TOTE c o n c e p t p_attern) ,
behaviour
sketched
suggestion
operate,
i s related
which
and
ideal
position
theories.
P r i b r a m , 1960 ] a l s o
their
importance
FAP
intermediate
G a l a n t e r and
behaviour;
s c i e n c e , i s i n an
t o the
i s used
to
trace
test,
by
the
out
some
was
the
exit)
in
notion of
a
ethologists
to
evolution
of
behaviour. In p o n d e r i n g carrying
out
concluded,
best
c o m p u t e r s have had
that
theory
the
of the
direction
of M i l l e r ' s
reason
physical
I will
start
positive
can
world.
second
direction.
look s u p e r f i c i a l l y content
from
"don't"s..
success
in
our
First
viewpoint*
My
there
a theory
is
no
second,
that
to handle
the
work i s a s m a l l s t e p i n
+
the
+
from
negative
similar
Here t h e y
because
conclusion.
I conclude
with the
is
i s to develop
+
what
little
o f c o g n i t i v e o r g a n i z a t i o n , and
hope f o r p r o g r e s s
structure
So
so
human i n f o r m a t i o n p r o c e s s i n g t a s k s , [ M i l l e r , 1 9 7 4 ]
first,
satisfactory the
why
of
our
survey
conclusions all,
t o our The
though
project,
of the
literature?
and
proceed
in
many o f
these
studies
few
l e s s o n s t o be
have any learnt
a
positive
are
mainly
HaBackground
Issues
are.
80
• Hebb - Bindra
-
• Jacobs & K i e f e r
don't t r y t o do too much with one theory -
don't
try to
apply
decision
theory
d i r e c t l y to behaviour a C o l e s , Feldman & S p r o u l l decision
theory
I n t e l l i g e n c e don't • Ludlow, Friedman
-
irrelevant
and really
Artificial
mesh together
because they model
behaviour
without a world model a Becker
& Merriam
-
they
get
bogged
down
d e t a i l s ; no f u n c t i o n a l
i n simulation robot-controller
designed or implemented, a "Baconian"
Becker
* Simon* Toda
-
-
don't
use
the
Baconian
representing
experience.
interesting
high
rational
level
behaviour,
but
approach
to
analyses
of
irrelevant at
our l e v e l o f s y n t h e s i s * m Imagery
-
this of
i s an acceptable n o t i o n ; any model
i t i s of i n t e r e s t . .
arises
as
designed Of Baker's
the
three
studies
i s promising
simulation
but
side
tool.
model
effect
of a system
on the s i m u l a t i o n o f r i g i d not
of i t
f o r s p a t i a l reasoning.
carried
f a r enough,
i s not s a t i s f a c t o r y a f t e r the f i r s t
Howden's i s c o m p u t a t i o n a l l y experimental
a
My
rather
expensive
motion. Funt's
few moves, while f o r use
as
an
When i t comes t o s p a t i a l planning, Eastman
and P f e f f e r k o r n get bogged
down
in
heuristic
search
HaBackground
because Issues
81
their
underlying
representation
Howden's approach r e s u l t s i n a positively, precursor
Nilsson
of my
common-sense Lieblich,
own
&
Kuipers
space
combinatorial
work.
of
large-scale
model a r a t ' s c o g n i t i v e showed how
space,
The
model and
a r e s u l t of i n n a t e d r i v e s and
of a graph i s a promising of PPA
and
in
the
More
models Arbib
&
about
course
of
Arbib & L i e b l i c h
showed how
l e s s o n to be l e a r n t here i s t h a t a world
design
and
map.
to form a g r a p h - l i k e c o g n i t i v e map..
as
who
fragmentary p i e c e s of i n f o r m a t i o n
used a graph f o r t h e i r world modified
explosion.
T h i s leaves only K u i p e r s ,
one's s p a t i a l environment can be i n t e g r a t e d experience
i s inadeguate,
Raphael's i s i n t e r e s t i n g , but only as a
knowledge
who
of
it
could
be
of e x t e r n a l rewards. model i n
the
form
idea* * T h i s i s not i n c o r p o r a t e d i n the
but o b v i o u s l y
should
be
taken
up
as
soon
as
possible*
I will first
now
summarize t h i s chapter
delineated
Intelligence; interaction
the nature
then
I
of t h i s modern s c i e n c e .
described
next
the
between, r e p r e s e n t a t i o n and
i n t e l l i g e n c e ; then I presented The
on background i s s u e s . ,
section
my own
sketched
I n t e l l i g e n c e approach t o planning
importance search i n any
approach to
the
the
traditional
and
problem-solving,
I
Artificial of,
and
theory
of
subject. Artificial and
II«Background
found Issues
82
it
to
be
reviewed be
a
wanting f o r my
purposes;
while i n the l a s t s e c t i o n I
the l i t e r a t u r e on s i m i l a r p r o j e c t s but found
notable
A l l told, background
to
l a c k of p o s i t i v e content, only c a u t i o n a r y t a l e s .
the reader should now to
there
my
work;
let
have me
a now
good
feeling
advance
to
for
the
the
first
IlaBackground
Issues
embattlement.
83 CHAPTER I I I THE SIMULATED ORGANISM-ENVIRONMENT SYSTEM
T h i s system i s the b a s i c experimental It
provides
simulated
sensory input f o r , and accepts organism
that
I
call
input-output
characteristics
relevant
to
the
only read
t h e . r e s t of
this
111*2.2,
and
the
III.2.3,
The aim o f t h i s chapter
this
peruse
examples
planar
that
object
an
in
section
shapes.
competent
(a)
section
III.1.3 the
and
simulated
organism
controlling
be expected t o s o l v e . . I t simulates
the
physical
which have the form of
The t a b l e t o p i s bounded by a verge
can never f a l l o f f .
The p h y s i c s
and
sections
An o b j e c t moves only
Utak i s both h o l d i n g t h i s o b j e c t and executing command*
directly
For t h i s purpose you need
smooth t a b l e t o p o f o b j e c t s
polygonal
the f u n c t i o n a l are
i s to d e s c r i b e
system i s c a l l e d TABLETOP. a
Only
a
system and to d e s c r i b e the t a s k s t h a t such
program, might reasonably
on
research.
motor output from,
system
introductory
an organism, i f endowed with a
motion
of
r e s t o f my t h e s i s .
organism-environment
The
Utak.
t o o l f o r my
involved i s e s s e n t i a l l y
a pushto or
so when turn
trivial:
The shape of an o b j e c t i s i n v a r i a n t under t r a n s l a t i o n
and
rotation. (b)
I f a motor command
t o go a c e r t a i n d i s t a n c e : i n
d i r e c t i o n would r e s u l t i n Utak c o l l i d i n g the
with
a
an o b j e c t or
verge, then he h a l t s a s h o r t d i s t a n c e before IIIaThe simulated
certain
the f i r s t
organism-environment system
84 i n t e r s e c t i o n of h i s path with such an o b s t a c l e * (c)
S i m i l a r l y , i f Utak i s g r a s p i n g a
push
command
colliding
with
come
an
to
that
an o b j e c t and
would r e s u l t
some o b s t a c l e , then immediate
halt
When
Utak
is
temporarily, (e)
Utak
can
grasping
considered
minimum
as one
new
the
occurred.
the o b j e c t
are,
object..
neighbouring
o b j e c t s only i f the
between them i s greater
than
a
certain
experimental
the;
permanence
and
of the shape.of p h y s i c a l o b j e c t s .
In b u i l d i n g the TABLETOP tool
that
system
was
I
aimed
inexpensive
to
concerned to f i n d exact s o l u t i o n s to c o l l i s i o n approximate
solutions
to
collision
III.3.1
I
sketch
one
way
to
produce
an
I was
not
use.
problems.
problems
TABLETOP system computes are q u i t e s u f f i c i e n t section
object
value.
impermeability
In
the
would have
To put i t i n a n u t s h e l l , TABLETOP s i m u l a t e s
the
object or Utak
and
an o b j e c t he and
go between two
width of the gap
Utak
executing
a s m a l l d i s t a n c e before
p o i n t at which the t h i s c o l l i s i o n (d)
i n the
is
for
my
Thus,
that
the
purposes.
that TABLETOP c o u l d
be
extended to compute exact s o l u t i o n s * Previous shapes
simulations
(reviewed
incorrect, TABLETOP
or system
of
the
p h y s i c s of p l a n a r
i n 11*4.7 above) have e i t h e r computationally is
complete,
expensive correct'
l i m i t a t i o n s which I s p e c i f y l a t e r , and mean that both motion and
to to
been
whereas
within
c o l l i s i o n s are handled* _
III«The simulated
incomplete,
use,
efficient.
polygonal
my
certain
By complete I TABLETOP
is
organism-environment system
85
cheap
to use,
has
been used e x t e n s i v e l y , and has
v i a b l e experimental The
design
tool*
of
TABLETOP
is
based
on
the
r e p r e s e n t a t i o n s f o r o b j e c t s , the C a r t e s i a n and Cartesian
on the
two
r e p r e s e n t a t i o n of an o b j e c t s p e c i f i e s the shape of
the
of p o i n t s where each p o i n t i s s p e c i f i e d by
r e a l numbers. boundary
of of
himself
position,
consisting
a d d i t i o n , Utak has to
the
p o i n t s are t h e . p o i n t s
shape.,
An
edge
in
has
of
a
a
Cartesian
two
of
inflection
the
Cartesian
an o b j e c t i s a p a i r of consecutive
Utak
referring
The
the
the l i s t .
points in
representation*
or
s i n g l e p a i r of p o s i t i v e r e a l s . ,
an absolute
orientation*
Note that I am
In
here
s i m u l a t i o n of Utak, not the r o b o t - c o n t r o l l e r
Utak. The
TABLE
is
a
two
dimensional
corresponds t o a square i n a two
an a s s o c i a t e d c o l o u r , one objects colour
may
the
grid
tabletop.
letters
have the same c o l o u r , and
of
entry
squares
Each o b j e c t
A,B,
...
Z.
the verge always has
has Two the
'B'.
Now colour
of
array where each
dimensional
c o v e r i n g the s u r f a c e of the:simulated
imagine t h e . C a r t e s i a n c
superimposed
representation
on
the
representation TABLE
of the o b j e c t i s defined
of an o b j e c t
grid.. to be the
of TABLE t h a t l i e w i t h i n , or are i n t e r s e c t e d by the
of
The
representation
for
use
the d i g i t a l . .
o b j e c t by a l i s t positive
proved to be a
Cartesian representation
of the o b j e c t .
d i g i t a l r e p r e s e n t a t i o n of an o b j e c t are IIIaThe simulated
The
with
digital
set of squares the
edges
of,
A l l sguares i n the
assigned
the
object's
organism-environment system
86
colour
c.
The
digital
representation
of
an o b j e c t i s a l s o
c a l l e d the p r o j e c t i o n of the o b j e c t onto the TABLE. digital
r e p r e s e n t a t i o n , or p r o j e c t i o n ; c o n s i s t i n g of the
of TABLE t h a t c o n t a i n s h i s p o s i t i o n . this
square
TABLE.
is
His
the
of
position
all
p r o j e c t i o n , a l s o , i s outside
of
all
lies
outside
a l l the d i g i t a l
currently
be d i s p l a y e d on a screen Utak
described This
the
does
not
"see"
i n subsection
the
Cartesian Normally
representations the
or
has
onto
the
TABLE array
can
chapter
is
this
to
organized
of
as
follows.
system.
and
shown t h a t an
Section I I I . 2
III.1
Section
This
includes
discusses
and
includes
In
the
final
the
examples
section
design of
adapted
part
of
the
TABLETOP
f o r p a r a l l e l computation, and
method g e n e r a l i z e s to three
an
It is
simulation
is
that the TABLETOP
(or more) dimensions.
III«The simulated
his
(III.3)
g e n e r a l i z a t i o n s of TABLETOP are c o n s i d e r e d . . important
the
t h e . s p e c i f i c a t i o n of
Dtak,
sensory-motor experience. extension
Remember
display; h i s v i s u a l input i s
used* the problems encountered, and
capabilities
watch.
III.2.2.
the r e q u i s i t e algorithms..
easily
d i s p l a y of
verge are p r o j e c t e d
f o r a human user
d e s c r i b e s the TABLETOP s i m u l a t i o n
and
to
CRT
grasping
array when TABLETOP i s i n o p e r a t i o n . . The
method
assigned
letgo.
Utak, a l l the o b j e c t s , and
that
a
square
o b j e c t s , but i t can happen that i t l i e s w i t h i n
p r o j e c t i o n of an o b j e c t t h a t he i s recently
colour
the o b j e c t s on the t a b l e t o p .
his
the
The
BUGMARK, an a s t e r i s k on the
Cartesian
representations
TABLE
Utak has
Also,
it
is
organism-environment system
87
shown
how
answers
to
This i s an independent system that simulates the e f f e c t
of
collision
III.1
to
extend
TABLETOP
to
obtain
exact
problems.
The simulated environment, TABLETOP -
motor
commands i s s u e d by Utak.
It i s instructive
s i t down with TABLETOP and attempt a task such an 'L* shaped o b j e c t through a narrow The L-shaped o b j e c t problem Otak.
Indeed,
in
Kuhnian
as
or
i f ,
is
the
archetypal
terminology,
progress
organism-controlling where
Otak
is
program
able
in
the
task
intelligence.
construction
of
to the
t o s o l v e t h i s problem autonomously will
for
t h i s i s the paradigm
f o r Otak has advanced
b e l i e v e t h a t n o n - t r i v i a l advances been
manipulating
doorway..
problem f o r t h i s approach to understanding s p a t i a l When,
f o r a user to
almost
the point then I
certainly
have
made towards understanding the nature of some computations
t h a t are o f fundamental importance f o r s u c c e s s f u l organisms., At that
point
i t w i l l be o f great i n t e r e s t
facts
about b i o l o g i c a l b r a i n s i n terms of
to i n t e r p r e t
the known
these„computations.
111*1^1 A.D. overview of the - s i m u l a t i o n - method A
slide
is
the
simplest
movement of Otak along a sequentially
checking
i n t e r s e c t e d by Otak's
line each
action segment,
square
position
as
of he
of It
Otak. is
T h i s i s the simulated
by
the TABLE g r i d t h a t i s moves
along
the
III«The simulated organism-environment
line system
88
segment.
If
a
non-empty
(coloured)
sguare
of
encountered before the end of the l i n e segment, then point
of
intersection
with
the
from
this
point.
first
This
by
backing
neighbouring lies
If
the
Cartesian
point
representations
of
of two
o b j e c t s are so c l o s e t h a t no empty sguare o f
between
off
i s done by t a k i n g a p o i n t a
s m a l l d i s t a n c e € back along the l i n e segment from the intersection.
the
o b s t r u c t i n g sguare i s found,
second the h a l t i n g p o s i t i o n of Utak i s obtained slightly
TABLE i s
TABLE
t h e i r d i g i t a l r e p r e s e n t a t i o n s then Utak i s unable
t o s l i d e between the two objects* When
Utak
i s not g r a s p i n g
an o b j e c t he can only execute a
s l i d e a c t i o n o r a grasp a c t i o n . is
not
already
representation
grasping
i s adjacent
representation.
Two
Utak can grasp an o b j e c t i f
some
object
t o a square i n the
squares
are
horizontally,
v e r t i c a l l y , or d i a q o n a l l y
are:
TABLE
eight
and
squares
adjacent
i f his object's
adjacent
to
digital digital
i f they
adjacent.
Thus
Utak's
he
are there
diqital
representation* When Utak i s qrasping t u r n , or l e t g o a c t i o n s . Utak's
Cartesian
representation pushto
In t h i s s t a t e the r e l a t i v e p o s i t i o n
representation
and
the o b j e c t ' s
remains i n v a r i a n t under t r a n s l a t i o n —
actions
However, whereas single
an o b j e c t he can only execute pushto,
—
and
Utak's
rotations digital
--
of
Cartesian caused
by
caused by turn a c t i o n s .
representation
i s always
a
sguare, an o b j e c t ' s d i g i t a l r e p r e s e n t a t i o n may appear t o
change r a t h e r d r a s t i c a l l y i f the s i z e of the TABLE squares i s o f IIIaThe simulated
orqanism-environment system
89
the
same
simplest
order
of
magnitude
as the s i z e of the object*
example of t h i s e f f e c t i s
Cartesian
given
by
an
object
The whose
r e p r e s e n t a t i o n i s a square of e x a c t l y the same s i z e
as
the TABLE squares.
I f t h i s object's Cartesian representation i s
exactly
with
aligned
representation moved
TABLE
square
then
its
i s j u s t t h a t TABLE square, but i f the
diagonally
representation
a
a
small
distance
then
diqital
object
its
is
digital
becomes a l a r g e r square c o n s i s t i n g of f o u r
TABLE
squares. Suppose t h a t the user of TABLETOP requests whose
intent
is
from
some
if
the achieved of
any,
d»
occurs,
distance.
actually
d i s the
9
is
measured
f o l l o w i n g method i s traversed
intended
before
The
d i s t a n c e to the nearest
determines the achieved
area
object
are erased.
representations
Then the achieved The
for
as
the
grasped
object
o b s t a c l e found, i f
distance.
computed, j u s t as f o r the s l i d e a c t i o n . is
computed
of
Dtak
and
the
normal has
edges
of
the
a direction
Cartesian in
the
achieved follows*
distance First
the
These
r e p r e s e n t a t i o n whose outward
range
III»The simulated
of
d i s t a n c e f o r Utak i s
l e a d i n g edges r e l a t i v e t o the d i r e c t i o n 9 are determined. are
a
d i s t a n c e , d' i s
B a s i c a l l y the method i s t o scan the
F i r s t the c u r r e n t d i g i t a l the
angle
line
TABLE t h a t would be swept out by the o b j e c t i n the course of
the t r a n s l a t i o n . any,
The
f i x e d d i r e c t i o n * , The
used to compute the d i s t a n c e collision,
action
t o move the grasped object i n a s t r a i g h t
through d i s t a n c e d i n d i r e c t i o n 8. clockwise
a pushto
(6-90°, e+ 9 0 ° ) . .
As
the
organism-environment system
90 object
is
moved,
each,
l e a d i n g edge sweeps out
shape of a parallelogram* . Each imagined for
such
are
parallelogram
as superimposed on the TABLE g r i d .
an L-shaped o b j e c t subjected shown
in figure:III*1.
any
or
intersect
to a p a r t i c u l a r
distance
non-empty
or e l s e to be the minimum over the square.
The
lie
PE generated by E.
For
TABLE
the
minimum
point of the subpart of Then
the o b j e c t *
distance
i s returned
distances
DE
Utak
and
distances
is
scan,
for
each
f o r each l e a d i n g edge
as the
F i n a l l y the o v e r a l l achieved
minimum o f the a c h i e v a b l e both
minimum
minimum of the DE's
E, l e s s a small q u a n t i t y 6,
Then
action
to be d, i f no non-empty squares are found i n the
scanned
be
that
the square l y i n g w i t h i n PE i s computed*
for
pushto
(coloured),
from the edge E to the nearest
defined
to
For each leading edge E a scanning
the p a r a l l e l o g r a m
scanned square t h a t i s
is
the
The:parallelograms
process i s s t a r t e d t h a t scans those squares of within
an area i n
achieved
distance
d i s t a n c e d' i s the
f o r the o b j e c t and
the o b j e c t are r e - p r o j e c t e d
f o r Otak.
onto the
TABLE
g r i d at the computed f i n a l p o s i t i o n * . By c o n s t r u c t i o n , these p r o j e c t i o n s never o v e r l a p Now whose
the p r o j e c t i o n of an
is
to
rotate
the
radians about Utak's p o s i t i o n U. for if
computing the angle any,
obstacle.
suppose that the TABLETOP user requests intent
occurs.
rotation.
Both
Two
would be swept out by the
a turn
scan
methods w i l l
£
be
described
a
collision,
r o t a t i o n , ' i s the
for
action,
grasped by Utak by
a c t u a l l y r o t a t e d before
(J> i s the intended methods
object
new
achieved
o b s t a c l e s i n the area
that
o b j e c t i n the course of r o t a t i o n *
The
IIIaThe simulated
organism-environment system
FIGURE T I I . 1
91
Direction of movement
6
The four parallelograms form an L-shaped object subject to a p a r t i c u l a r PUSHTO action. Also shown are the Cartesian and d i g i t a l representations of the L-shape. Left constrainin edge Destination edge
Original leading edge
Right constraining edge
b)
Features of a p a r a l l e l o gram generated by an edge during a PUSHTO action.
92 angle
to
the nearest
rotation.. second one the
The
may
i f any,
miss a small one.,
method
the
Since
motion
computation. object,
for
obstacles
method, s i n c e i t and
may
be
the
parallels
of independent
of Utak and
the grasped o b j e c t
Utak's p o s i t i o n does not change: i n not
directly
Then the l e a d i n g
relative
whereas
first.
projections
does
achieved
Although the second method i s the
translation
i s described
First erased;
used
determines the
method f i n d s a l l the
c u r r e n t l y implemented, the f i r s t
interest,
his
first
obstacle,
to
the
contribute
segments
a
rotation,
the
collision
the
edges
of
rotation
U,
must
be
r o t a t i o n of an o b j e c t about U,
the
centre
of
to
are
of
the
determined. Definition.
For
a clockwise
l e a d i n g segment of an edge E i s found as f o l l o w s . . line
L
collinear
with
point N t o the centre to
E.
Compute on the
of r o t a t i o n U and
E at the p o i n t N.
Now
l i n e L the
draw an
of
it
may
normal
take the s e m i - i n f i n i t e h a l f - l i n e of L
with E.
l e a d i n g segment of E.
the
nearest
outward
t h a t l i e s t o the l e f t of the outward normal at N, intersection
Consider
The
and
form
the
r e s u l t i n g segment of E i s the
Note that the l e a d i n g segment of an
c o n s i s t of a l l or p a r t of the edge, or be n u l l .
segments f o r a s p e c i f i c t r i a n g l e
and
points
of
The
edge
leading
rotation
are
shown i n f i g u r e I I I . 2 . Lemma.
For
a clockwise
rotation
of
an
l e a d i n g segment of an edge E of the o b j e c t any
point
x on the i n t e r i o r of the
object has
the
about
the
property:
l e a d i n g segment, there
IIIaThe simulated
U,
is
for a
organism-environment system
FIGURE I I I . 2
Outward normal
6 AN^, = l e a d i n g segment of edge AB. BNp = l e a d i n g segment of edge BC. CNg = l e a d i n g segment of edge CA. Thus f o r r o t a t i o n c l o c k w i s e about P t h e r e a r e 3 l e a d i n g segments. CLOCKWISE ROTATION
For c l o c k w i s e r o t a t i o n about Q t h e r e i s o n l y 1 l e a d i n g segment: BC.
T h i s f i g u r e shows t h e l e a d i n g segments o f t h e t r i a n g l e ABC f o r two p o i n t s o f r o t a t i o n . I f a c l o c k w i s e r o t a t i o n about P i s i n t e n d e d , then t h e l e a d i n g segments a r e AN , BN^, CN^. I f an a n t i - c l o c k w i s e r o t a t i o n about P i s i n t e n d e d , then t h e l e a d i n g segments a r e N^B, N^C, and N^A. I f a c l o c k w i s e r o t a t i o n about Q i s i n t e n d e d , t h e r e i s o n l y one l e a d i n g segment: BC. I f an a n t i - c l o c k w i s e r o t a t i o n about Q i s i n t e n d e d , t h e r e a r e two l e a d i n g segments: CA and AB.
94
rotation
about
U such t h a t i f x* i s the new
p o s i t i o n of x, the
arc xx' l i e s i n the e x t e r i o r of the o b j e c t . Proof. other
Pick a disc centre
x, small enough that i t i n t e r s e c t s no
edge of the o b j e c t , and so t h a t i t does not c o n t a i n
p o i n t of the l e a d i n g segment* the new
Consider a r o t a t i o n so small
p o s i t i o n x' of x l i e s w i t h i n
Because
x
lies
to
the
left
the
of
disc
exterior
of
the
shape.
centred
that
on
x.
the outward normal to E the
d i r e c t i o n of motion of x i s p e r p e n d i c u l a r the
an end
Thus,
to Ox and p o i n t s
into
t h e . a r c xx' l i e s i n the
e x t e r i o r of the object* . QED. In
other
words
out
a new
area of
Depending
on
Cartesian
shape
considerable
the l e a d i n g segment of an edge E always sweeps t h e . TABLE
the
angle of
overlap
in
of
the
the
course: of
rotation
object,
and
there:
a
rotation.
the. exact o v e r a l l
will
in
general
be
between the areas swept out by each l e a d i n g
segment., I have ignored
the
problem
of
eliminating
multiple
scanning o f areas o f TABLE i n a turn a c t i o n . As t h e o b j e c t r o t a t e s each l e a d i n g four-sided
area
of space,
The s i d e s d i s t a l
point of r o t a t i o n are c i r c u l a r straight lines. that i f A
#
B are
segment
and
A',
0.
a r c s , the
sweeps
the
original
other
end-positions
B' are the f i n a l
two
Each doughnut
upon the TABLE g r i d *
slice
of
end-positions
and A'B'O
differ
out
a
and proximal to the
Hence I c a l l t h i s shape a doughnut
segment, then t r i a n g l e s ABO about
segment
only
sides
are
slice.,
Note
the
leading
of the l e a d i n g by a
rotation
i s t o be imagined as superimposed
The doughnut
s l i c e s f o r the r o t a t i o n of an
III»The simulated
organism-environment system
9 5
L-shaped
o b j e c t subjected
i n figure III*3. that
lie
of
For each l e a d i n g segment S the
within
are scanned;
to a p a r t i c u l a r t u r n a c t i o n are shown
between the l e a d i n g
{This i s
not
a
trivial
For each l e a d i n g segment S, the minimum i s taken
over the angles computed f o r each o b s t r u c t i n g square, minimum
slice
square the.minimum angle
r o t a t i o n s u f f i c i e n t t o cause a c o l l i s i o n
segment S and the square i s computed,
the
squares
or i n t e r s e c t the corresponding doughnut
For any non-empty scanned
computation;}
TABLE
of
a l l these
minimums,
taken
and
then
over a l l l e a d i n g
segments, g i v e s the achieved r o t a t i o n '•
Finally,
and
onto the TABLE g r i d .
the
rotated
object
are r e - p r o j e c t e d
That* i n o u t l i n e , i s the s i m u l a t i o n The
basic
problems
faced
both
Utak
method used i n TABLETOP.,
in
an
implementation
of this
s i m u l a t i o n method are as f o l l o w s . . •Tracing
a line
-- the intended path i n a s l i d e a c t —
the s i d e s of a p a r a l l e l o g r a m
in a
pushto
action —
the
straight
and
curved
sides
of
a
of
an
doughnut s l i c e i n a t u r n a c t i o n
•Scanning
a shape
-- the
Cartesian
object, f o r
representation
projecting
object's d i g i t a l
or
erasing
the
representation
the p a r a l l e l o g r a m
swept out by a
leading
edge i n a pushto a c t i o n -- the doughnut s l i c e
swept out by a l e a d i n g
IIInThe s i m u l a t e d organism-environment
system
FIGURE III.3
6
Rotation about U.
An L-shaped object showing i t s Cartesian and d i g i t a l representations. For the centre of r o t a t i o n , U, there are 5 leading segments (CB, BA, AN, FE, EM) and 5 doughnut s l i c e s swept out during the action (BCC'B', ABB'A', NAA'N', EFF'E', MEE'M'). N i s the point on AF closest to U, M i s the point on ED closest to U.
leading segment outer constraining arc
6' destination segment Features of the doughnut s l i c e generated by rotating the leading segment AB about the centre of rotation U by angle 0 .
97
segment i n a t u r n a c t i o n
•Computing
minimum
distance
from a l e a d i n g edge t o (a subpart
of) an o b s t r u c t i n g sguare
•Computing minimum angle
from a l e a d i n g segment
to
(a
subpart
of) an o b s t r u c t i n g sguare.
III>1.2 The a l g o r i t h m s
used i n - the
simulation
In t h i s s u b s e c t i o n I d e s c r i b e the:algorithms the. problems two
specified
line-tracing
circular
arcs.
i n the previous
subsection.
a l g o r i t h m s , one f o r s t r a i g h t I first
qrid
containing
the
squares
process
correctly.
This
as
has
tracing
seemingly innocuous reguirement i s a
alignment
c o i n c i d e n c e of the l i n e with tracing
o f the
the
t r i c k y t o program because of the s p e c i a l cases such
line.
i n i t i a l and t e r m i n a l p o i n t s of the
l i n e i n order t o i n i t i a l i z e and terminate
occur
There a r e
d e s c r i b e how t o t r a c e a s t r a i g h t
straight
little
solve
l i n e s and one f o r
As a p r e r e q u i s i t e f o r t h i s one has t o know the TABLE
used to
of
the
the
grid
t o handle four cases, I
can and
with
the
axes
lines..
The
code f o r
one f o r each guadrant of the
direction
o f the
line;
guadrant
case.
L e t the c u r r e n t sguare-be the square c u r r e n t l y
under c o n s i d e r a t i o n i n the c u r r e n t sguare can e i t h e r and
right
from the c u r r e n t
will
line
that
only
describe
line-tracing
the
procedure.
northeast
The
next
be one up, one r i g h t ; or d i a g o n a l l y up square.
IIInThe simulated
This
choice
i s made
by
organism-environment system
98 computing
whether the northeast corner of the c u r r e n t square i s k comparison of
l e f t o f , r i g h t o f , or on the l i n e . of
SP and SD,
suffices A
the
i n v o l v i n g two m u l t i p l i c a t i o n s and one
slopes
comparison,
( f i g u r e I I I . 4). circular
arc i s t r a c e d i n a s i m i l a r manner.
I f the a r c
t r a v e r s e s more than one quadrant i t i s broken i n t o subarcs traversing subarc
a l l or
traverses
procedure
is
part of a s i n g l e quadrant; the
northwest
next
When the a r c or
almost
the
current
(figure III.4).
square
is
As f o r the l i n e case,
e i t h e r one up, one r i g h t , or one
d i a g o n a l l y up and r i g h t from the c u r r e n t square, and t h i s is
same
used as f o r the case:of a l i n e whose d i r e c t i o n i s
in the northeast quadrant the
quadrant
each
made by computing
choice
whether the northeast c o r n e r of the c u r r e n t
square i s i n s i d e , o u t s i d e , or on the
arc.
This
requires
two
m u l t i p l i c a t i o n s , an a d d i t i o n , and a comparison; There are s e v e r a l o p e r a t i o n s which may squares
t h a t a l i n e passes through.
be added to a scan t a b l e f o r square
is
non-empty
and
a
i n t e r s e c t i o n computation may
applied
to
The square c o o r d i n a t e s
scanninq
hence
be
routine
or,
if
the may the
r e p r e s e n t s an o b s t r u c t i o n , an
be -executed
and
the
line-tracinq
procedure.abandoned. For the purpose of p r o j e c t i n g the C a r t e s i a n
representation
of a concave o b j e c t i n t o i t s d i g i t a l r e p r e s e n t a t i o n on the TABLE (briefly,
drawing
the
Cartesian
representation
object), is
and
erasing
decomposed
i t
later,
the
i n t o convex subparts.
T h i s i s done manually when the o b j e c t i s f i r s t
specified.
When
III«The simulated organism-environment
system
FIGURE
III.4
T r a c i n g an a r c i n the north-west quadrant.
100
the
object
erased
is
drawn or erased
each convex subpart i s drawn or
separately.
The
digital
representation
object i s constructed Cartesian
row
representation
by
of
a
row..
convex
First
are t r a c e d , and
(subpart
the
edges
of in
the c o o r d i n a t e s
the c o o r d i n a t e s o f each row.
of the squares at the l e f t
Since
cover only the
the s i z e of the
v e r t i c a l extent
p a i r of
( l e f t and
row
I f the o b j e c t
I f the o b j e c t for
turn action.
of TABLE t h a t corresponds
digital
The
representation
scan t a b l e s and
when, or i f , the A new
scan t a b l e i s s u f f i c i e n t
to
to scan
row
by
i s f i x e d the scan t a b l e s are then, d i s c a r d e d .
i s movable, the
l a t e r use
records
extremities
r i g h t ) scan t a b l e e n t r i e s .
t a b l e i s then used to draw the row.
right
the
of the convex shape, an o f f s e t i s
a l s o s t o r e d t h a t s p e c i f i e s the the f i r s t
and
the
of
squares encountered are used t o update a scan t a b l e t h a t
an)
o f f s e t s are
o b j e c t i s erased
scan t a b l e has
to be
stored
f o r a pushto or
constructed
for
each
convex subpart every time the o b j e c t i s redrawn. The action
parallelogram is
III.1).
scanned
The
sequence:
swept out by
in
almost
a l e a d i n g edge i n
identical
fashion
edges of such a p a r a l l e l o g r a m
leading
edge
AB,
left
are
d e s t i n a t i o n edge: A' B'.,
square can
the edge AB.
encountered* distance nearest
in
while
tracing
the
the
direction
e
p a r t of the
obstructing
(see f i g u r e
traced
in
No
the right
obstructing
I f an o b s t r u c t i n g square i s
edge
AA',
from the square
IIInThe simulated
pushto
c o n s t r a i n i n g edge AA',
c o n s t r a i n i n g edge BB', occur along
a
then
the
minimum
l e a d i n g edge AB to that
lies
within
the the
organism-environment system
101 parallelogram
i s computed.
T h i s i s taken as the new
the amount of the t r a n s l a t i o n . , encountered while t r a c i n g BB'.,
Similarly
if
an
value
of
obstacle
d, is
I f e i t h e r or both of these cases
occur then the
p o s i t i o n of the d e s t i n a t i o n edge
is
effectively
moved
to the
the
destination
closer
o r i g i n a l p o s i t i o n AB.
edge, at i t s p o s s i b l y new
p o s i t i o n , i s traced and
f o r the p a r a l l e l o g r a m
i s complete.. The
parallelogram
scanned and
found
the
distance
to the nearest The
one
obstructing
is
of the o b s t a c l e i s computed. a l e a d i n g segment i n a turn
concave bounding l i n e —
figure
the
the
arc does not c r o s s
p o i n t of r o t a t i o n .
doughnut s l i c e
inner
constraining
III.3)
i s cut along t h i s and
segment
AN,
the
vertical
vertical
in
each part formed i s scanned s e p a r a t e l y . .
The
the
inner c o n s t r a i n i n g arc NN',
(line
the
UU'
d e s t i n a t i o n segment A'N'.
line
no
line
I f t h i s c o n d i t i o n holds then
edges of a doughnut s l i c e are t r a c e d i n
sequence:
leading
outer c o n s t r a i n i n g
No o b s t r u c t i n g
square can
arc
occur
AN. . I f an o b s t r u c t i n g square i s encountered while t r a c i n g
the arc NN* nearest
then the
p a r t of the
i s computed. rotation., AA'.
square
However, s i n c e : a shape i s scanned row-by-row t h i s i s of
through the
along
the
from the l e a d i n g edge AB i n the d i r e c t i o n 9
corner
consequence provided
AA',
the scan t a b l e
TABLE sguares within
i f an
doughnut s l i c e swept out by
a c t i o n has arc.
are now
Now
minimum angle of r o t a t i o n about obstructing
square within the
T h i s i s taken as the new
S i m i l a r l y i f an o b s t a c l e
value of
to
doughnut the
the slice
intended
i s encountered while t r a c i n g
I f e i t h e r or both of these cases occur then III»The simulated
0*
the
position
organism-environment system
102
o f the d e s t i n a t i o n segment i s e f f e c t i v e l y r o t a t e d the o r i g i n a l p o s i t i o n AN. possibly
new
position
doughnut s l i c e doughnut out
Now the d e s t i n a t i o n i s traced
i s complete.
slice
are
and
The
back c l o s e r t o
segment
at i t s
the scan t a b l e f o r the
TABLE
squares
within
the
scanned and c o l l i s i o n computations c a r r i e d
i f any o b s t r u c t i n g squares are found. F i n a l l y I must s p e c i f y the c o l l i s i o n computations.. F i r s t I
d e s c r i b e them f o r a pushto a c t i o n , then f o r a t u r n The
simplest
swept out by
a
case i s t h i s :
leading
edge
encountered.
The
amount
c o l l i d e s with
the
nearest
calculated
(figure
f o r t h i s edge. corners
of
The nearest
o f the square.
when scanning the p a r a l l e l o g r a m AB,
an
obstructing
square
movement of the o b j e c t before
point
III.5).
action.
P
of
the
square
i t * . For
p o i n t of a
T h i s nearest
instance, corner
southeast
Let
the outward normal to direction
of
motion,
be
square
corner
is
one
of the
depends only
on the
i s used to
f o r a l e a d i n g edge.in the northeast
guadrant the nearest corner.
AB
This i s the d i s t a n c e to c o l l i s i o n
quadrant of the l e a d i n g edge so a simple t a b l e . l o o k u p find
must
is
of
an
obstructing
sguare
i s the
n be a u n i t v e c t o r i n the d i r e c t i o n o f
AB, and
let d let p
d i s t a n c e t o c o l l i s i o n i s given
(E-n)
be
a
unit
vector
be the vector
AP.
i n the Then the
by the formula
/ (i-n)
If an o b s t r u c t i n g sguare i s encountered III»The simulated
0 from AB to P = p_.n
l
C
O
104 constraining
edge
of a p a r a l l e l o g r a m ,
f i n d the d i s t a n c e to obstructing
collision.
square may
The
the
cases a r i s e
(1)
left (figure
c o n s t r a i n i n g edge of the p a r a l l e l o g r a m ,
four
between
and
the
left
of
collision
of
the
leading
the
obstructing
right is
square
constraining
the
same
as
edges.
before,
corner
lies
The
corner
c o n s t r a i n i n g edge* from
lies
The
s i d e of the
The
nearest
the
to
the
distance
to
left
of
collision
the
left
is
the
c o n s t r a i n i n g edge: i n t e r s e c t s
the the
square.
corner
c o n s t r a i n i n g edge. distance
to
A along the l e f t c o n s t r a i n i n g edge to
p o i n t P where the l e f t
(4)
using
corner.
nearest
distance
The
on the l e f t c o n s t r a i n i n g edge.
The d i s t a n c e t o c o l l i s i o n i s the d i s t a n c e from A
(3)
lies
(A) .
nearest
nearest
the
When
P
The
of
III.6).
distance to
(2)
corner
edge. ,
The nearest corner
equation
nearest
to
l i e o u t s i d e the p a r a l l e l o g r a m or even on
the o p p o s i t e s i d e of an extension tracing
more c a r e : i s r e q u i r e d
lies The
to
the
distance
right to
of
collision
the is
right the
from B along the r i g h t c o n s t r a i n i n g edge to the
p o i n t Q where the r i g h t c o n s t r a i n i n g edge i n t e r s e c t s III»The simulated
the
organism-environment system
105
FIGURE I I I . 6
,3'
Cases i n computing d i s t a n c e t o c o l l i s i o n a l o n g a c o n s t r a i n i n g edge. AB = l e a d i n g edge. NC = n e a r e s t c o r n e r of o b s t r u c t i n g square. P = n e a r e s t p o i n t of o b s t r u c t i n g square.
106 side
of
the
square.
There
are
really
i n v o l v e d here depending on whether P and
l i e on
the
edges of the square.. However, i t i s not
necessary to go
to
BQ
the
since
trouble
of
figuring
s u f f i c e s t o return the distance Notice (4)
out the
t h i s w i l l be computed under case (3)
when the r i g h t c o n s t r a i n i n g edge i s being
traced.
So i t
AP.
t h a t , when t r a c i n g the r i g h t c o n s t r a i n i n g edge [with
right
( f i g u r e 111.6(5)). been
Q
same or adjacent
distance
case
two subcases
returned
and
left
transposed]
T h i s i s because the d i s t a n c e
from
an occurrence of case
BB',
could not occur AP
would
have
(3) when t r a c i n g the
l e f t c o n s t r a i n i n g edge, and so the r i g h t c o n s t r a i n i n g edge would only be t r a c e d
as f a r as B''.
There are four cases when edge*
tracing
the
left
constraining
t h r e e cases when t r a c i n g the r i g h t c o n s t r a i n i n g edge, and
these are a l l repeated f o r each of the other three which
the
l e a d i n g edge may l i e .
by one 2 x 4 x 4
decision
table
quadrants
in
These 28 cases can be handled with
one
row
of
four
null
for a
turn
entries. Now I action.
describe
the
collision
computations
Suppose t h a t an o b s t r u c t i n g square i s encountered when
scanning the doughnut s l i c e swept out by a l e a d i n g segment.. The amount
of
r o t a t i o n of the object
before
of an edge AB c o l l i d e s with some point of calculated
(figure
III.7).
t h i s edge.
The p o i n t of
the
the l e a d i n g segment AN the
square
T h i s i s the angle-to square
IIIaThe simulated
at
which
must
be
collision for the
collision
organism-environment system
107
FIGURE I I I . 7
AB
= object's
edge.
AN = l e a d i n g segment. U
= centre
of r o t a t i o n .
P
= obstructing
point.
P' = p o i n t which c o i n c i d e s w i t h P a t the n e a r e s t moment of collision.
(-o)
= UP = UP' .
of
= angle t o c o l l i s i o n .
_ n — = - u n i t outward normal to AB.
u cos
r
x
= d i s t a n c e UN.
-- - C P. •«.)/£
cos V s * / r
« j - cos"'
FIGURE I I I . 7 .
-
cs'
[*/r}
The diagram shows the p o i n t P', on the edge AB, which c o i n c i d e s w i t h the p o i n t P a t the moment of c o l l i s i o n . The formula shows how to compute PUP', the angle t o c o l l i s i o n .
108
occurs
is
the c o l l i s i o n p o i n t .
I a l s o c a l l t h i s the
corner s i n c e i t i s c l e a r that the corner
of
the
obstructing
t r i v i a l t o determine
collision
square.
point
collision
must
Unfortunately
which" corner of the square; i s the
be
a
i t i s not collision
c o r n e r . . For i n s t a n c e , as the o b s t r u c t i n g square v a r i e s over
the
squares w i t h i n a doughnut s l i c e the c o l l i s i o n c o r n e r v a r i e s too. I f the r o t a t i o n i s c l o c k w i s e and the o b s t r u c t i n g square i s moved c l o c k w i s e then the c o l l i s i o n c o r n e r of moves
in
a
clockwise
o b s t r u c t i n q square.. collision
collision
c o n t a i n s e i t h e r two centre
d i r e c t i o n r e l a t i v e to the centre of the
the
collision
obstructing
corners
for
a
or three c o r n e r s .
sguare*.
specific
corners
instance,
if
and
the if
axes
there
0
lies
in
corners,
and i f 0 l i e s on the south v e r t i c a l
collision
corners III.9
determined
are
shows
the
southwest
occurrences
to
collision
with
of
and
of
each
an
at
grid
candidate
between the axes
( f i g u r e 111*8).
northwest,
c o r n e r s , f o r 0 i n the southwest anqle
two
the southwest guadrant
c o r n e r s are the southwest,
The
set
l e a d i n g segment
are
U i s i n a quadrant
collision
collision
The
Suppose axes are taken
there are t h r e e candidate c o l l i s i o n c o r n e r s
,
s e t s of candidate
of the o b s t r u c t i n g square and a l i q n e d with the
I f 0 i s on one of
Figure
square
c o r n e r s as a f u n c t i o n of the p o s i t i o n of the c e n t r e of
candidate
lines.
obstructinq
I t i s possible to specify
r o t a t i o n 0 r e l a t i v e to
the
the
the and
For
candidate northeast
a x i s the
candidate
northwest
corners.
of
the
candidate
guadrant. obstructing
by f i n d i n g the angle to c o l l i s i o n with
each
sguare i s of
the
III«The simulated organism-environment system
109
FIGURE I I I . 8
MW.Nt.SE.
—p w
S6.
This shows, for a clockwise rotation, how the set of candidate c o l l i s i o n corners of an obstructing square varies as a function of the p o s i t i o n of the centre of rotation r e l a t i v e to the axes of the square. This i s the set of c o l l i s i o n corners that must be considered i f the obstructing square i s encountered during the scan of the doughnut s l i c e . Along the arcs are shown the edges or corner that may be involved i f the obstructing square i s encountered when tracing a constraining arc.
FIGURE III.9
For a clockwise rotation about the point U i n the southwest quadrant r e l a t i v e to the axes of an obstructing square, this shows how each of the candidate c o l l i s i o n corners could actually occur. Leading segment AB c o l l i d e s with the southwest corner, CD c o l l i d e s with the northwest corner, and EF c o l l i d e s with the northeast corner. A'B', C'D', and E'F' are the positions of AB, CD, and EF, respectively, at the moment of c o l l i s i o n .
111
collision (or
corners
two) angles.
i s the corner
s e p a r a t e l y and t a k i n g the minimum of the three The c o l l i s i o n
corner
an
edge
a p o i n t U, the angle to c o l l i s i o n
as f o l l o w s .
L e t n be the u n i t vector
AB
being
i n the
direction
collision
on
of the from 0"
distance
to AB, l e t r be the r a d i u s UP, l e t £ be the v e c t o r point
rotated
with a p o i n t P i s found
outward normal to AB, l e t x be the p e r p e n d i c u l a r
the
square
with the s m a l l e s t a n q l e - t o - c o l l i s i o n .
Given a l e a d i n q segment AN of about
of the o b s t r u c t i n g
UP, l e t P' be
AN which c o i n c i d e s with P at t h e moment when the
occurs,
(figure I I I . 8 ) .
and
l e t alpha
be
to
collision
alpha = arcos[ - (p. n ) / r ] - a r c o s [ x / r ]
(B)
Then the f o l l o w i n g alpha = /PUN
-
the
angle
holds. /P«UN
cos (/PUN) = (p_/r) . (-n) = - ( p . n ) / r cos(/P«UN) = x/r
I f an o b s t r u c t i n g square i s encountered while inner
or
slightly corner
oufter
simpler.
Instead
of r o t a t i n g the
the
computation i s
candidate
collision
backwards to whe^re i t s a r c i n t e r s e c t s t h e l e a d i n g segment
as i n the:usual leading the
c o n s t r a i n i n g a r c , the c o l l i s i o n
tracinq
segment
case, here one has to r o t a t e the endpoint o f the forwards to where i t s a r c i n t e r s e c t s a s i d e o f
o b s t r u c t i n g square.
The computation i s simpler
s i d e s o f the square are a l i g n e d with the c o o r d i n a t e I describe t h i s c o l l i s i o n involving the p o i n t
the
outer
because
the
axes..
computation only f o r an
example
constraining arc (figure I I I . 1 0 ) . .
Suppose
of r o t a t i o n U l i e s i n the southwest guadrant IIIoThe simulated
relative
organism-environment system
FIGURE I I I . 1 0
112
AB = o b j e c t ' s
edge.
AN = l e a d i n g segment. U
= centre
of r o t a t i o n .
A' = p o i n t of c o l l i s i o n w i t h o b s t r u c t i n g r
= UA = UA'.
a.
' vector
°f
= angle t o c o l l i s i o n = ^ A
square,
UA.
UW = p e r p e n d i c u l a r
UA'.
from U t o c o l l i s i o n
ri
= u n i t outward normal from c o l l i s i o n
x
= distance
s i d e of square, side,
UV^
COSft:(SL).(-rs)* , t o i ,
(-Vr)/l.)
FIGURE I I I . 1 0 - The diagram shows the i n t e r s e c t i o n A' o f an outer c o n s t r a i n i n g a r c w i t h an o b s t r u c t i n g square. The formula shows how t o compute the angle of c o l l i s i o n . '
113 to
the
axes of symmetry of the square, and the endpoint A of a
l e a d i n g segment AN c o l l i d e s with a s i d e of the square. involved
is
the
collision
tracinq routine. west
side
of
from 0 to AN, from
0
to
side,
collision
one
drops
s i d e , meeting
p e r p e n d i c u l a r p r o j e c t i o n of A onto OW.. collision,
s i d e i s the
Instead of dropping a p e r p e n d i c u l a r
f o r t h i s computation the
side
and i s s p e c i f i e d by the a r c
In the example shown the c o l l i s i o n the square.
The
a
perpendicular
i t at W.
Let V be the
Then alpha, the angle to
i s given by alpha = arcos[-UV/r] - arcos[ UW/r]
The
arc
tracing
routine
may,
instead,
s p e c i f y that the a r c
e n t e r s the o b s t r u c t i n g square at the c o r n e r P., are
known so the angle t o c o l l i s i o n
(C)
The coords of
i s then simply given by
alpha = 2 * arcosj AP/ (2*r) i] When most
tracing
two
found.
routine
squares is
are
abandoned
encountered, as
soon
with
different
the.square.
ways
four
distinct
A
4x3
in
which
the
arc
may
Each of these twelve cases reduces
to one or other of the computations (D).
an
p o s i t i o n s of the c e n t r e of r o t a t i o n 0, and f o r each of
these t h e r e are t h r e e intersect
since
as an o b s t a c l e i s
For such an o b s t r u c t i n g square t h e r e are
relative
and
(D)
the c o n s t r a i n i n g a r c s of a doughnut s l i c e at
obstructing
arc-tracing
P
decision
s p e c i f i e d by
table
specifies
equations the
procedure.
(C)
correct .,
+
+
+
IIIaThe s i m u l a t e d organism-environment
system
,11 4
To
sum
up t h i s s e c t i o n so f a r , I have guided you
c o l l e c t i o n of algorithms involved
in
algorithms
an
sufficient
implementation
f o r scanning an
parallelograms pushto and
and
turn actions
the exact
d i s t a n c e to c o l l i s i o n *
these two
basic
former
inverse
scanning
algorithms
c i r c u l a r a r c s , and
cosines
not
or
and
for
algorithms
angle
to
time-consuming
quicker*
but d i r t i e r
and
implementation;
cheap*
coding.
10°,
This
is
i s erased, the
and
obstructing
its
squares
representation). i s encountered
the
the
new
latter
This or
the
requires I
used
more expensive,
is
to
Cartesian
projection
(without
TABLETOP
be
rotated
the The
representation onto
actually
TABLE
drawing
on
turn
digital rotated
scanned the
a
method
second method r e f e r r e d t o
for
digital
i s repeated u n t i l an o b s t r u c t i n g
square
intended
If
anqle
o b s t r u c t i n g square i s found, a b i n a r y the
for
a n a l y s i s . . The
procedure: a c t u a l l y implemented does the f o l l o w i n g .
by
tracing
f o r computing
Conseguently
computationally
Namely, when an o b j e c t
representation
the
collision*
extensive . case
computationally
and
page 92.
for
include
given above f o r the t u r n a c t i o n i n
careful
of
shape,
These
actions.
algorithms
are
TABLETOP..
respectively,
lines
requires
of
problems
s l i c e s swept out i n the course of
straight
The
and
to solve the b a s i c
object's
doughnut
through a
is
achieved.
search i s c a r r i e d out
l a s t sub-angle of r o t a t i o n u n t i l the
achieved
an over
position
is
l o c a t e d t o w i t h i n 2° accuracy. This
method l e a v e s open the
possibility
III«The simulated
that
some
small
organism-environment system
115 obstacle
may
be
jumped
over
between the 10° t e s t p o s i t i o n s .
T h i s has not y e t happened i n p r a c t i c e , p a r t l y because only simple
TABLETOP environments have been used t h a t do not c o n t a i n
s m a l l i s o l a t e d o b s t a c l e s , and p a r t l y because movable
o b j e c t s has not been s u f f i c i e n t l y
the
which
such an i n c i d e n t could
occur
size
configuration
digital
representation
occupies
an
obstacle
a s i n g l e sguare of TABLE
at a d i s t a n c e of about 13.5 from Utak, and Utak executing a c t i o n of more than 10° towards the o b s t a c l e An important implementation many
pushto
o b j e c t , the deformed
and
Cartesian
due
to
what was o r i g i n a l l y
turn
in
would have Utak grasping the
narrow edge o f a 1 x 14 movable o b j e c t or " s t i c k " , whose
of the
l a r g e f o r an o b s t a c l e
to be missed i n a 10° r o t a t i o n * . The simplest
When
very
problem
actions
a turn
(figure III.11).
arises
i n practice.
are a p p l i e d t o a movable
representation
of
the
object
becomes
cumulative f l o a t i n g point i n a c c u r a c i e s . a sguare may a t some l a t e r
time
look
Thus like
the end view o f a squashed cardboard box. To
overcome
representations
this
problem
three
Cartesian
are used f o r an o b j e c t , not j u s t
one;
style When the
o b j e c t i s f i r s t s p e c i f i e d a base r e p r e s e n t a t i o n i s s e t up.. T h i s is
i t s o r i g i n a l Cartesian representation.
sequence o f a c t i o n s the c u r r e n t
Cartesian
always
rotation
applied
be to
relatively
represented
as
one
t h e base
representation.
uncommon*
and
A f t e r any a r b i t r a r y representation and
Since
a r e computationally
r o t a t e d base r e p r e s e n t a t i o n i s a l s o used. III»The simulated
can
one t r a n s l a t i o n rotations
are
expensive,
a
This c o n s i s t s of the
orqanism-environment system
FIGURE I I I . 1 1
A T h i s shows the s i m p l e s t k i n d of s i t u a t i o n i n which a p o t e n t i a l o b s t a c l e (marked 'B') c o u l d be missed by the a l g o r i t h m a c t u a l l y implemented. Utak i s h o l d i n g a long s t i c k and when he executes a t u r n a c t i o n t o the r i g h t of a t l e a s t 10°, the o b s t a c l e i s missed by the a l g o r i t h m .
117
base
representation
current
Cartesian
rotated
by
the angle between i t and the
representation;
During
a
sequence
t r a n s l a t i o n s between two r o t a t i o n s , the C a r t e s i a n at
the end o f each t r a n s l a t i o n
representation
that
i s derived
r o t a t i o n occurs a new r o t a t e d base directly
from
representation from
base
r o t a t i o n . . When a
representation
the base r e p r e s e n t a t i o n .
i s computed
The c u r r e n t
Cartesian
a t t h i s point i s then obtained by one t r a n s l a t i o n
the new
rotated
base
representation.
implemented the C a r t e s i a n r e p r e s e n t a t i o n cannot
representation
from the r o t a t e d
was computed at t h e l a s t
of
of
With t h i s scheme a
movable
object
deform* however many pushto and t u r n a c t i o n s are a p p l i e d
to the o b j e c t . One
final
problem remains t o be c o n s i d e r e d .
I l l * ! . 2; 1. The o v e r l a y problem
A digital
problem
involving
representations
the crops
h o l d i n g and moving an o b j e c t .
interaction up
occasionally
contiguous
with
representation
and
when
and
Otak i s
formed
When he f i r s t
i s necessarily
the o b j e c t ' s d i g i t a l
time, the E u c l i d e a n
Cartesian
I r e f e r t o the system
Utak and a held o b j e c t as a sum o b j e c t . object h i s d i g i t a l
of
grasps an
outside
representation;
by
and
At t h a t
d i s t a n c e d between h i s C a r t e s i a n p o s i t i o n
the n e a r e s t point N on the o b j e c t ' s C a r t e s i a n
U
representation
must have a value s t r i c t l y between 0 and 2 * r o o t 2 . . The
distance
III«The s i m u l a t e d organism-environment system
118
d remains until
i n v a r i a n t over
Utak e x e c u t e s
When d < r o o t 2 such that lie
in
i ti sclearly
the d i g i t a l
in
the
held
concern while not
affect
U and N i n
representation object's
Utak
go o f t h e o b j e c t . .
to execute a s l i d e point
representation are
empty
procedure
situation
action.
within
o f an o b s t a c l e ,
representations
Consequently
the object
i ti s possible with
a square
This
i s o f no
since
i t does
i n p u s h t o and t u r n occurs
routine
a square
before
go and t h e n f i n d s that
belonging
and t h e r e f o r e
actions.
immediately
Suppose he l e t s
a c t i o n , . . The s l i d e
lies
Cartesian
representation..
the computations involved arises i fthis
starting
the
t o hold
The-problem lets
slide
o f Utak t o c o i n c i d e
digital
Utak c o n t i n u e s
by a
p o s s i b l e t o p o s i t i o n t h e sum o b j e c t
same s q u a r e o f TABLE.
for
movements o f t h e sum o b j e c t
a letgo action followed
the points the
a l l further
Utak's
to the d i g i t a l
fails!
TABLE s q u a r e s n e x t t o U t a k ' s s q u a r e t h e n
tries
If
there
the f o l l o w i n g
h a n d l e s the problem.
1.
L e t t h e v a l u e o f BUGSQUARE be t h e c o o r d i n a t e s o f t h e TABLE s q u a r e c u r r e n t l y o c c u p i e d by U t a k , l e t OLDBUGSQUARE be t h e value o f BUGSQUARE a t Utak's previous position* l e t BUG MARK be the colour assigned t o Utak's digital r e p r e s e n t a t i o n on TABLE, and l e t OVERLAY be t h e o v e r l y i n g colour o f t h e BUGSQUARE. The v a l u e o f OVERLAY i s t h e c o l o u r empty e x c e p t when t h e BUGSQUARE i s w i t h i n t h e h e l d object's d i g i t a l representation.,
2.
After a pushto o r turn a c t i o n , f i r s t draw t h e g r a s p e d object, then s e t OVERLAY = COLOUR-OF (BUGSQUARE) COLOUR-OF (BUGSQUARE) = BUGMARK
3.
I f Utak is about to execute, a slide OVERLAY y* empty, t h e n d o : COLOUR-OF(BUGSQUARE) = empty OLDBUGSQUARE = BUGSQUARE Compute t h e r e s u l t o f t h e s l i d e * III«The s i m u l a t e d
and
organism-environment
i f
system
119
I f achieved p o s i t i o n s t i l l l i e s w i t h i n OLDBUGSQUARE then COLOUR-OF(OLDBUGSQU ARE) = BUGMARK else COLOUR-OF(OLDBUGSQUARE) = OVERLAY This procedure has proved s u f f i c i e n t not
solve
the
problem
r e p r e s e n t a t i o n of digital
Utak
in can
representation
of
general.
i n practice In
fact
l i e arbitrarily
but
the
digital
f a r within
the h e l d o b j e c t .
does
the
T h i s can a r i s e i f
there i s a l o n g s t r a i g h t " c a n a l " of width s t r i c t l y
between 1 and
2 u n i t s i n the o b j e c t ' s C a r t e s i a n r e p r e s e n t a t i o n . . L e t the c a n a l have l e n g t h n+1. lie
astride
In one p o s i t i o n of the o b j e c t
a column of squares.
head of t h e c a n a l
and
position
object
of
the
grasp
the
the
the
canal
Then Utak c o u l d s l i d e to the object
there* .
In
the f i r s t of
type of p o s i t i o n and has l e t i t go i n t h e second
position;
representation
When
One
he with
wants n
to
squares
execute of
a
the
solution
slide,
Utak i s
object's
digital
i n figure III.12. that
immediately s p r i n g s t o mind and can be
e a s i l y implemented w i t h i n the c u r r e n t TABLETOP philosophy following.
Before
next
closest
d i g i t a l representation; ensures
i s the
a grasp a c t i o n can be executed the 20 c l o s e s t
sguares t o Utak's square must be empty and some 24
type
between him and the empty TABLE squares o u t s i d e .
This i s i l l u s t r a t e d
of
digital
Now suppose t h a t Utak has grasped the o b j e c t i n
h o p e l e s s l y trapped
rinq
another
c a n a l may not s t r a d d l e any whole
TABLE squares, so t h a t the c a n a l does not appear i n the representation;
may
square
i n the
squares must belong t o the o b j e c t ' s
This i s shown i n f i g u r e
III.13.
This
t h a t no p o i n t of the subseguent held o b j e c t l i e s
within
III«The simulated
organism-environment system
120
FIGURE III.12
FIGURE III.12 - (a) The C a r t e s i a n r e p r e s e n t a t i o n o f an o b j e c t , w i t h a c a n a l of w i d t h 1.5. (b) The o b j e c t p o s i t i o n e d so t h a t the c a n a l i s open i n the d i g i t a l r e p r e s e n t a t i o n . Utak i s able to s l i d e t o the head of the c a n a l and grasp the o b j e c t t h e r e . (c) The o b j e c t p o s i t i o n e d so t h a t the c a n a l i s closed. I f Utak now l e t s go the o b j e c t , no s l i d e a c t i o n can get Utak beyond the b o r d e r s of h i s c u r r e n t d i g i t a l r e p r e s e n t a t i o n . He i s trapped.
121
•K
4
•
___________
FIGURE III.13
- One s o l u t i o n to the o v e r l a y problem i s shown.here. Before Utak can s u c c e s s f u l l y ' grasp an o b j e c t , two c o n d i t i o n s must h o l d . (1) The 20 squares of TABLE c l o s e s t to Utak must be empty. (2) At l e a s t one of the 24 squares forming a r i n g around the 20 c l o s e s t squares must belong t o the o b j e c t ' s d i g i t a l representation.
122 root2
units
"overlay"
of
Utak's
position,
thus
that
the
above
problem cannot a r i s e *
Another s o l u t i o n representation
of
would
require
coordinates,
require
that,
in
the
Cartesian
Utak and the o b j e c t t o be h e l d , Utak was
w i t h i n root2 u n i t s of any would
and
edge
closest
of
edge
the
object.
calculations
This in
not
however Cartesian
a type of c a l c u l a t i o n t h a t I wish to t r y and
avoid
as much as p o s s i b l e . Now
I shall
show some examples of the TABLETOP
program
in
action.
I I I . 1.3
An example of TABLETOP p_erf or ma nee ;
The:following session
with
slightly
edited.
human
user
pages, f i g u r e 1 1 1 * 1 4 , show
TABLETOP
recorded
during
the
L-shaped
from
UBC s Open House
I t shows the s t a t e of the
solved
excerpts
object
TABLE problem*
array The
snapshot i n c l u d e s a statement of the t a s k , which i s read by user, not
Utak!
The
an a c t i o n command i s s u e d by the
•
the '*•
a
B
the
state
a
first the
of the nine Utak.
(Thus
the BUGMARK
representation TABLE squares i n the
centred
on
contents
of the OVERLAY variable.),
the typed
as
user
of the TABLE a r r a y , with
showing Utak's d i g i t a l contents
1979,
subseguent snapshots show:
•
resulting
a
the
centre
square
3x3 shows
array the
response from TABLETOP.
{I have added comments w i t h i n braces l i k e IIIaThe simulated
this.j
organism-environment system
1
•
TRANSLATE B B B B B B B B B B B B B B B B B B B B B B B B B B * B B B B B B B B B B B B B B B
>
A
BY
(-10
0)
I.
E.
HOVE
IT
DP
BY
10
UNITS
B B B B B B B B B B B B B B B B B B B B B B B B B
B
B
A A A A A A
A
B
B B B B B B B B B B B B
B B
B B B B
B B B B B B B B B B B B B B B B B B B B B B B B B
OK
Fi£UKE
III.IA-
B B B B B B B B B B B B B B B B B B B B B B B B B B B B
12V
(GBASP) B B B B B B B B B B B B B B B B B B B B B B B B B B * B A B A B A B A B A B A A B B B B B B B B B B B B B B B B BBB m * c»
>
GOT
IT!
B B B B B B B B B B B B B B ,
B B B B B B B B B B
B
B B B B B B B B B B B B B B B B B B B
A
B B B B B B B B B B B B B B B B B B B B B
B B B B B B .
B B B B B B B B B
B B B B B B B B B B B B
(PUSHTO
6.0
125
N)
B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B , B ' B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B
B B B B B B B B
B B B B * A A
A A
A A A A A A A A A
& A
A A
:
BAA
.4A >
HIT!
B B B B B B B B
B B B B B B B B B B B B B B B B B B B B B B B B B B B B
(PUSHTO 1.0
B)
B B B B B B B B B B 5 B B B B B B B B B B B B B B B B B B B B B B B B B B ^ B B B B \ B B B B B B B B B B A . ^ B B * A A B B A A A B B B B B B B B B B B B B B B B B B B B B B B B B B A A A B B A A A A B B A A A A B B A A A B IB A A B B B B B B B B * B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B ..A .AA ..A
>
HIT! i
126
(PDSHTO 5-0 N ) B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B ,. _ : B B B B B B A A ft A B B * A A A B B A A B B A A B B A A B B A A B B A A B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B. B B B B B B B B B B: B B B B B B B B B B B B B B B B B B B B B B B S B B B B B B B B B o AA . AA
>
OK
127
128 I I I . 2 The simulated organism Otak and h i s tasks
III.2.1 Design
considerations
Now t h a t I have described the simulated
environment,
what
k i n d of organism should be b u i l t t o l i v e there, and what k i n d o f t a s k s should the organism be r e q u i r e d questions
are
expect a
colour
closely blind
linked
since,
human
to
execute?
These
two
f o r example, you cannot
respond
to
traffic
correctly
unless
cues
such
as
light
available.
More p r e c i s e l y , what
kind
of
actions
organism
other
to
lights
position
are
should
the
be capable o f executing and what kind of sensory
should the organism r e c e i v e from i t s environment?
input
The kinds
of
i n p u t / o u t p u t allowed t o the organism, and the kind of task he i s r e q u i r e d t o s o l v e , both mould t o a c e r t a i n extent t h e design the
mediating
mechanism,
or
organism-controller,
that
of lies
between i n p u t and output; Asking
these
questions
f a c t u a l and methodological the
organism be?
o f design immediately
questions.
I f so, what animal?
are the design d e c i s i o n s to be made? is
to
How
r a i s e s many
animal-like
should
I f not, by what c r i t e r i a I f the simulated
organism
be l i k e some s p e c i f i c animal, e x a c t l y what sensory
and motor output messages does t h a t animal's
brain
input
receive
and
behaviour
of
definitely
be
send? Since I am i n t e r e s t e d i n the animals
and
humans,
the
principles
organism
of
should
III-The simulated organism-environment system
129 animal-like. are,
The subsequent q u e s t i o n s
unfortunately,
virtually
about
sensory-motor
unanswerable; i n no case a r e a l l
the r e l e v a n t f a c t s f o r one i n t e r e s t i n g animal known. instead, again,
fall
back
I/O
One might,
upon the gross behaviour of an animal, but
i n almost no case are a l l the r e l e v a n t f a c t s known!
This collected behaviour published simpler
situation a wealth of
the
has
of
recently
information
octopus
improved.
M.J.Wells
has
about
the
physiology
and
[ W e l l s , 1978 ],
and
E.R.Kandel
has
a comparable c o l l e c t i o n o f i n f o r m a t i o n about
an
even
c r e a t u r e , the marine s n a i l A p l a s i a [Kandel,1978].
With
a view t o r e c e p t o r d e s i g n , I have perused
various
known
facts
about r e c e p t o r s i n mammals, i n c l u d i n g v i s u a l r e c e p t o r d e n s i t i e s , receptive f i e l d
s i z e s , and m a g n i f i c a t i o n f a c t o r s i n the b r a i n .
One has t o r e s o r t to c r i t e r i a
o f elegance,
f i n a l l y , i n the AI approach, on the c r i t e r i o n feasibility. sciences, My
This
i s in
n a t u r a l n e s s , and of
computational
c o n t r a s t t o most o t h e r
experimental
where the f i n a l a r b i t e r i s experimental
feasibility..
a t t i t u d e was w e l l put by the philosopher
D a n i e l Dennett
when he wrote [Dennett,1978,p.104] 11
one does not want t o get bogged down with t e c h n i c a l problems i n modeling t h e : c o g n i t i v e e c c e n t r i c i t i e s of turtles i f the p o i n t o f the e x e r c i s e i s t o uncover very g e n e r a l , very abstract principles that will apply as w e l l t o the c o g n i t i v e o r g a n i z a t i o n of the most s o p h i s t i c a t e d human beings. So why not then make up a whole c o g n i t i v e c r e a t u r e , a Martian three-wheeled iguana, say, and an environmental niche f o r i t to cope with? I t h i n k such a p r o j e c t could teach us a great d e a l about the deep principles o f human c o g n i t i v e psychology, but i f i t could n o t , I am g u i t e sure t h a t most of c u r r e n t A.I. modeling o f f a m i l i a r human mini-tasks could not III«The simulated
organism-environment system
130 either.
11
Utak i s my
three-wheeled
Martian iguana and TABLETOP i s h i s
niche.
I l l * 2 . 2 The
sensory-motor
c a p a b i l i t i e s - of-Utak
Utak can move i n a s t r a i g h t l i n e , he can object,
and he can push*
grasp
design
of
h i s motor output immediately
the obvious f e a t u r e s of the This
is
the
fact
design
of
when
a
once.
biological
system
c o u l d be d e s c r i b e d
that
a
motor
never-ending
of
acts. as
a
series
an
pattern of
course, i s very d i f f e r e n t from a
never-ending
typical
are alert
transducer
i n p u t p a t t e r n s on
l a r g e number of output l i n e s .
on a s i m i l a r l y
another
Indeed,
patterns
series
present-day
I t seems u n l i k e l y t h a t
to understanding the computations
of
T h i s , of computer
a l l i n f o r m a t i o n through a b o t t l e n e c k formed
the s i n g l e high-speed CPU. close
output.
lines
into
channels
Thus
output
m i l l i o n s of i n p u t l i n e s
which
has
t h a t e x a c t l y one output has to be a c t i v e t o
b i o l o g i c a l system transforms
He
c o n t r a d i c t s one of
natural
execute an a c t i o n , whereas l a r g e numbers active
movable
t u r n , and l e t g o a h e l d o b j e c t .
f i v e motor outputs, only one o f which i s a c t i v e a t the
a
we
can
by get
occurring i n b i o l o g i c a l
systems i f we allow the " b o t t l e n e c k " design of c u r r e n t computers to i n f l u e n c e our t h i n k i n g . The consisting
visual
sensory
input
is
of 160 input l i n e s from
somewhat
more
realistic,
160 r e t i n a l r e c e p t o r s . , Utak
IIIaThe s i m u l a t e d organism-environment
system
131 gets
a
bird's
environment
eye
as
though
f i e l d s are arranged each
view
directly
his
eye
down
immediate The
48 f i e l d s each 16 times the s i z e of a
i n an outer, p e r i p h e r a l , zone.
the
ratio
t a b l e t o p covered of
an
object
Each r e t i n a l
by the c e l l ' s i s ignored.
impression,
adjacent squares The
Utak
impression
Utak's
which
( f i g u r e 1.3).
a set of 160
consists
computes
the
array
comes
can of
The.
colour
graylevels constitutes be
the
representation* the
from
TABLE
reflected
by a change i n the representation
a
to
new
sensed
via
a
c o l o u r s of the 8
a
r e t i n a l and
halt.
of r e t i n a l f i e l d s on
directly
digital
that
to Utaki simulation
digital
field
Object c o l o u r s
each time. Utak
superimposes
0-7,
cell
of o b j e c t to t o t a l area i n the p a r t of the
one r e t i n a l i m p r e s s i o n . tactile
fields
i n an i n t e r m e d i a t e zone
r e g i s t e r s a 3 - b i t g r a y l e v e l , or i n t e g e r i n the range reflects
retinal
as f o l l o w s : 64 i n a c e n t r a l f o v e a , 48
surrounding the f o v e a , and field
his
were on a s t a l k .
4 times the s i z e of a f o v e a l f i e l d
foveal
on
of
and
array.
Utak
or
TaBLE,
computes an
retinal
To
action impression of
the
do
tactile so
it
c e n t r e d on graylevels
by Utak w i l l only
if
be the
an o b j e c t held by
him
changes;
More s o p h i s t i c a t e d v i s u a l sensory systems are easy
to
propose,
but t h i s one i s c o m p u t a t i o n a l l y cheap and has
sufficed
so far,; The
concepts
of
speed,
mass, a c c e l e r a t i o n , and momentum
have not been implemented., a s the reader w i l l see, the to design an o r g a n i s m - c o n t r o l l e r f o r t h i s simple world
attempt r a i s e s an
IIIaThe simulated organism-environment system
132 ample
range
perception
of and
features.
interesting action
and
without
fundamental the
addition
problems of
these e x t r a
Nonetheless, the d i s t a n c e between s u c c e s s i v e
impressions
may
in
retinal
be viewed as a measure of speed i f one assumes
t h a t r e t i n a l i m p r e s s i o n s are r e c e i v e d at a c o n s t a n t r a t e .
I l l . 2.3 Examples Figure
of Utak^s sensory-motor experience
III.15
shows
the
r e t i n a l and t a c t i l e i m p r e s s i o n s
r e c e i v e d by Utak immediately p r i o r t o the f i r s t few
actions
in
the performance of s e c t i o n I I I . 1.3.
I l l - 2 . U Examples
of t a s k s f o r Utak
Here:I present a l i s t expect handle..
a
competent Their
of t a s k s , i n E n g l i s h , which
I
would
o r g a n i s m - c o n t r o l l e r f o r Utak to be a b l e to method
of
presentation
to
Utak's
o r g a n i s m - c o n t r o l l e r w i l l be d e s c r i b e d i n s e c t i o n IV.2.
"Go t o the.northeast
corner"
"Go t o the next room" "Go t o the square" "Go
round the square and
return"
"Push the square i n t o the northeast c o r n e r " "Push the square i n t o the next room" "Push the b r i c k through the door" "Push the b r i c k around the c o r n e r " "Push the L-shaped o b j e c t i n t o the next room" IIInThe simulated organism-environment system
FIGURE III.15
16151413121 1 109
8 7 6 5 1 . 3
2 1 0 1 2 3 4 5 6 7
c
c
( c c c
c c
7|7
c
7|0 7 1 7
7I 7
7 I 7 71 0 01 0 OJ 0 7 j 7 71 0 0 ( 0
(
c c
7(7
7| 0 01 0 0 ( 7
7|7
7| 0 710
71 7 7J 0 7 | 7 7|
c
0(7
01
0I 7
0 OJ 7
0 0]0 0)7
7J7 71 0 0)0 017 0
c c (
.('
c (
* > *
(ROLL 5.0 HE) ( 4 . 2 4 1 6 4 0.735398) (THLOOK)
9
10 111213141516 . 16
134. 161511*13121
1109
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
1 0 1 1 1 2 1 3 1 '11516 16
15
14
if
13
12
f
11
f
10 9
(
-
c c
— 1
1
•
1 1
0
•
1
0
0
1
0
0
8 7
I I 6 1
0
4 1
j 7 i o '
iv
(
c
0 | 0 | 0 1 0
(*
0 j 0
3
01
jo" 0 | 0 | 0 1 0
| 7 I 0 '
5
1
0: 2
OJ0|0| 0
0 1 0| 1
i 7 | o ' 7 | . 7 | 7 j 7* 7 1 7 * 1
c
I
7 1 0 J0 | 0 | 7 |
0
0
0 I 01
|7|0
0 J 0 | 0 | 7 0 | 01
17J0J
0 | 0 | 0
|7|0
01 0 | 0 | 7
1
(
c
j
70
j
2 0(
3 0 1 0 |
4
c
1 "»
1
0
|
(J
1
0
.1
5
i
c
6 0
I 2
7 8
c
9
c
10 11
c c
12 13 14 15
c .
c
c (
B B B . * _ . - & >
* >
*
N i l .
(ROLL ( 1 .
1 . 0 E) 1 . 5 7 0 7 9 6 )
(THLOOK)
16
135 When a compass d i r e c t i o n appears i n the task refers
to
Utak's
own l o c a l o r i e n t a t i o n system, which need not
c o i n c i d e with the TABLETOP o r i e n t a t i o n . the
first
r e t i n a l impression
not
It i s initialized
i s received.
f a c i n g at that time becomes north do
when
Whatever d i r e c t i o n he
i n h i s o r i e n t a t i o n system.
I
claim to have a system or even the o u t l i n e s of a system
t h a t can handle a l l these t a s k s ; I am p r e s e n t i n g to
statement t h i s
show
the
ultimate
design
this l i s t
here
goals f o r a r o b o t ^ c o n t r o l l e r f o r
Utak.
I I I . 3 An extension The from
and two g e n e r a l i z a t i o n s of TABLETOP
purpose of t h i s s e c t i o n i s t o d i s c u s s i s s u e s that a r i s e
the design
of TABLETOP.
These a r e not germane t o the main
argument o f my t h e s i s but are of right.
They
are
also
some . i n t e r e s t
relevant
to
questions
in
their
in
own
automatic
assembly. The
first
issue
TABLETOP s i m u l a t i o n , achieve
exactness?
concerns exactness.
How accurate
and how, i f at a l l , could For
the
moment
I
i t be extended to
will
assume t h a t the
r e f e r e n t f o r the terms "accuracy" and "exactness" i s Cartesian
representation
represented
t o a l i m i t e d p r e c i s i o n i n some computer.
of
an
object
of
shapes,
i s the
using
the
real
usual
numbers
The motion
may, i n the worst case behaviour of TABLETOP, be
h a l t e d i f a p o i n t o f the moving o b j e c t comes w i t h i n root2 p o t e n t i a l o b s t r u c t i o n , whether or not a c o l l i s i o n Ilt«The simulated
of
a
would occur i n
organism-environment system
1 36 the
Cartesian
obstacle corner
representation.
intersects
and
i f the
intersects
the
a
path
TABLE of
same
This
Otak, or
opposite
c o r n e r * . The
arbitrarily
far
the
the
Cartesian
approach of potential How the
Otak, or
can
this
(Otak) The
onto the
by
edge
that is
stored
as
an
coordinates standard
line
The
an
i s
each
TABLETOP c o l l i s i o n
point
may
collision
may
the
intersection cure
i s
be
not
point,
or
correspond
arise
remedied?
attention to
In
the be even
to
a
i f the
line
of
angle
with
a
In
the
describing
case
of
the
course
of
whenever a TABLE s q u a r e the
a
moving
by
Then
square e d g e (s) (are)
projecting i s
entered
t r a v e r s i n g edge i s s t o r e d
i s entered
collision
s e v e r a l edqes a
each
on
the
which
time the TABLE,
caused
retrieved.
point*
this
are
the
idea
of
Otak
Cartesian
sguare
Then the
i f any,
pointer
path
the
at
to
be
Cartesian
computed
by
any
algorithm. based
on
Cartesian
representations
and
scales
magnification,
of
object, to
projecting higher
one
to
close
this.,
obstruction i s
second
close
object.,
edge..
of
the
the
held
makes a n e a r - z e r o
back to
obstructing
of
a
edge o f
arbitrarily
affairs
TABLE a r r a y ,
representation(s) marked
of
I f a square
an
of
These cases can
restrict
cure
for
encounters
I
a pointer
square.
i f an
edge.
approaching
first
but
point
object,
state
cures
objects an
an
obstructing
possible
point
point*
point
Cartesian
TABLETOP c o l l i s i o n collision
a
TABLE s q u a r e
from
occur
square : a r b i t r a r i l y
diagonally
worse,
can
III»The s i m u l a t e d
onto
the
each time
of
TABLE
repeatedly at
higher
re-determining
organism-environment
the
system
137
obstructing
squares.
point,
i f
a n y , h a s been f o u n d
I call
this
the
The
focus
process
halts
when
the
collision
t o w i t h i n the r e q u i r e d
method.
To
explain
i t
I
R
of
accuracy. need
some
terminology. . A C-representation representations coordinate
operations
or
more
A coordinate
t o some
fixed
distinct
with
Say t h a t
respect
a
line
replaced
segment by a l i n e
translation,
of
by
some the
and s c a l i n g
c o o r d i n a t e : system.
Let
a
(R,C) be a r e c t a n g l e o f any s i z e (R,C)
has
been
window W i f
A l l p a r t s o f R that l i e wholly any
objects, using
C-representation
to a given
Cartesian
system C i s o b t a i n e d
initial
W on a C - r e p r e s e n t a t i o n
tabled
collection
of a sequence of r o t a t i o n ,
or o r i e n t a t i o n .
a)
one
s y s t e m C.
application
window
of
(R,C) i s a
R
outside W are
that intersects
segment t h a t t e r m i n a t e s
removed
and
an edge o f W i s at
that
edge*
In computer g r a p h i c s terms, R i s c l i p p e d * . b)
The c o o r d i n a t e
system C i s t r a n s f o r m e d
into
a
new
system
by •
rotating
i t into
a
moving t h e o r i g i n
•
applying
scale
direction,
so
alignment
with
to the centre factors,
that
one
t h e e d g e s o f W, o f W, in
each
coordinate
t h e s i d e s of W c o i n c i d e with t h e
s i d e s o f TABLE. c)
The C - r e p r e s e n t a t i o n
Suppose
the
(R,C) i s p r o j e c t e d o n t o
coordinate IIIaThe
system
simulated
TABLE.
C* i s t h e r e s u l t
of a p p l y i n g
organism-environment
system
138 to
a
coordinate
translation,
system
and
C
scaling
a
operations
s e r i e s can always be reduced and
two
series
to one
as
i n b)
rotation,
the
by a p p l y i n g
above.
one
to
rotation,
is
Such a
translation, Let Q' be
Q,
in
i n v e r s e s of the o p e r a t i o n s i n t h e . s e r i e s .
r e s o l u t i o n of the c o o r d i n a t e system C maximum
several
s c a l i n g s . , L e t Q be a u n i t square i n C'.
r e c t a n g l e i n C t h a t i s obtained order,
of
defined
the
reverse Then the
to
be
of the lengths of the s i d e s of Q i n the o r i g i n a l
the
system
C, I
c an
now
describe
p r e c i s e l y the focus meth od f o r
more
f i n d i n g a s a c c u r a t e l y as d e s i r e d the c o l l i s i o n between
Otak's
c o l l e c t i o n EO the.
obje c t s
intended
path
and
s i d e s of TABLE.
CP2,.
T able
the
verge
the
Let E be the
an o b s t a c l e .
of
all
in
the environment, l e t C be the
and
l e t W c o i n c i d e with
C-representation Let
Find
potential
all
(R ,C) ,
Otak's intended messaqe
path..
"no
r e s o l u t i o n of C of
any,
the
WO r
Let 6 be the r e s o l u t i o n r e q u i r e d .
window W.
the
if
of the o r i g i n a l C a r t e s i a n r e p r e s e n t a t i o n s
o r i g i n a l c o o r d i n a t e system CO,
CP1.
and
point.
collision
be the new obstructing
collision
the
with
r e s p e c t to the
C-representation* TABLE
squares
I f there are none then e x i t
i s l e s s than of
(R,C)
found".
o b s t r u c t i n g square encountered.
path
with
Otherwise, i f the
6, then compute the
intended
alonq
with
the
point first
Find t h e . c o o r d i n a t e s
t h i s p o i n t i n the o r i g i n a l c o o r d i n a t e system CO
and
of
exit
III«The simulated organism-environment system
139
with these
coordinates
Otherwise, CP3,.
for
the
point
of
collision.
continue..
Take the s m a l l e s t r e c t a n g l e W
1
direction
of
motion
t h a t i s a l i g n e d with
the
of Otak and that c o n t a i n s a l l the
p o t e n t i a l o b s t r u c t i n g squares found i n
step
CP2.
Let
(R,C)= (R« ,C) , the window W=W«, and go to step C P l .
A m a g n i f i c a t i o n always occurs at step CP1 w"' i s s m a l l e r than the p r e v i o u s window W.
i f the new
window
The r e c t a n g l e W
will
1
always be a l i g n e d with the c o o r d i n a t e axes except, p o s s i b l y , first
time t h a t CP3
step CP1
i s executed*
Thus a r o t a t i o n
i s executed i n
at most once.
This r o t a t i o n , permitted by a l l o w i n g the window W» not
to
be
aligned
with
s p e c i a l type of case* obstructing
squares
corner-to-corner
be
in
Namely,
the
case
where
the
form a d i a g o n a l across the TABLE a r r a y , as
and
than
one
potential
both
approximately
l i e approximately p a r a l l e l to each
A window a l i g n e d with the axes would not, i n t h i s
smaller
CP3
the axes, i s necessary to handle
can happen i f an edge and Otak's path both extend
other.
the
the
current
m a g n i f i c a t i o n could occur.
window,
and
case,
consequently
As a r e s u l t of t h i s s i n g l e
no
rotation,
the intended path of Otak i s always p a r a l l e l to one of the
axes,
say the v e r t i c a l . Suppose
the TABLE g r i d has n u n i t squares along each
Then the r e c t a n g l e W
of CP3
every
CP3
execution
of
w i l l have h o r i z o n t a l width
a f t e r the f i r s t ,
side..
one
in
s i n c e a l l the
squares
IIIoThe simulated organism-environment
system
140 i n t e r s e c t e d by a v e r t i c a l l i n e l i e
in
horizontal
w i l l t h e r e f o r e be n i n every
scale
execution of CP1 greater
than
use*
One
after
1,
execution of CP1 This
factor
may
a
CP1
t h e . second. . horizontal
Since
n
column.,
is
magnification
seem
an
integer
occurs i n every
it
out
is
because,
if
the
c o n s i s t s only of convex shapes, the p r o j e c t i o n
onto TABLE can be done such
very
fast
hardware was
method might become f e a s i b l e . .
with
some
simple
available, this
i n any dimension.
parallel
magnification
Another reason i s t h a t t h i s
method* i n s i m p l e r form, can be used to solve l i n e a r problems
The
l i k e a c o m p u t a t i o n a l l y expensive method to
reason I have sketched
If
single
a f t e r the second.
C-representation
hardware.
in
a
A f i n a l reason i s t h a t an
same
programming extension
of the f o c u s method i s used i n SHAPE, the s p a t i a l planner i n the o r g a n i s m - c o n t r o l l e r of Utak. The
parallel
hardware
f o r each TABLE sguare. broadcast
to
r e g u i r e d c o n s i s t s of one component
Given a
every component.
line
L,
its
coordinates
are
Each component computes whether
i t s corresponding TABLE sguare l i e s to the r i g h t o f , to the
left
of, or i s i n t e r s e c t e d
take
one time u n i t . by for
L e t t h i s computation
Then the p r o j e c t i o n o f a convex shape S
m l i n e s takes m time u n i t s , one f o r each l i n e , one
operation is
by, the l i n e L.
extra is
intersected
corresponding
AND this. by,
operation
by
each
bounded
plus the time
component.
The
AND
I f a TABLE square l i e s to the r i g h t of* or every
component
line signals
of
t h e . shape. S,
"inside
S";
then
the
otherwise
the
III«The simulated organism-environment
system
141
component s i g n a l s " o u t s i d e S". . One
other
question
naturally
TABLETOP be g e n e r a l i z e d t o
three
answer
the
is
yes,
provided
arises.
or
Can the design of
higher
projection
dimensions?
The
of an n-diraensional
convex polytope onto a g e n e r a l i z e d TABLE array can be
computed.
The g e n e r a l i z e d TABLE c o n s i s t s of an n-dimensional array o f u n i t hyper-cubes. projecting
The s c a n - t a b l e a
convex
technigue
polygon
onto
used
the
must
be
easy
passes through.
to
compute
TABLETOP
TABLE does not
g e n e r a l i z e to n dimensions.. To apply the it
in
scan-table
which hyper-cubes
In t h r e e dimensions
this
is
face i n t e r s e c t s . axes
there
is
no
simple
does
not
seem
algorithm
to
sketched above f o r computing convex
polygon
onto
hyper-plane one simply hyper-cube
of
the
l i e s t o the l e f t hyper-plane. completes This swept
translation,
of
u n i t cubes the
corresponding
generalize.
in parallel
TABLE computes
in
final
AND
scan-table
projection easily..
parallel,
operation
the
However, the method
the
generalizes
the
to
for
for
each
of
a
For
each
each
unit
hyper-cube
of, to the r i g h t o f , or i s i n t e r s e c t e d
by,
the
hyper-cube
computation,.
method
out
problem
n-dimensional a r r a y , whether the
One
the
technique
When the face i s o b l i g u e to a l l the c o o r d i n a t e
l i n e - t r a c i n g a l g o r i t h m i n two dimensions., Thus technique
easily
a hyper-plane
the
d e t e r m i n i n g , f o r each face of a polyhedron, which
for
by
a or
can
also
leading to
be
used t o compute.the
hyper-plane
compute
the
in
segment
the of
hypercubes
course a
of
a
hyper-sphere
IIIaThe s i m u l a t e d organism-environment
system
142
( g e n e r a l i z a t i o n of a doughnut s l i c e ) swept out by hyper-plane one
in
the
course
of a r o t a t i o n ;
(a p a r t of)
In t h i s l a t t e r
has t o compute whether a hyper-cube i s i n s i d e ,
intersected
by
the
TABLETOP method can
surface of a hyper-sphere; be g e n e r a l i z e d to higher
+
+
In t h i s chapter
+
case
outside, Thus the
a
or
basic
dimensions.
+
+
I have d e s c r i b e d the design of the TABLETOP
s i m u l a t i o n system, and
gone
into
sufficient
detail
that
the
e s s e n t i a l problems t o be handled i n an implementation are
clear.
I have a l s o shown how
obtain
more
accurate
t h i s design could be
collision
points,
and
extended
how
the two
t a b l e t o p could be g e n e r a l i z e d t o three or more particular
I
introduced
the
accurate c o l l i s i o n p o i n t s .
focus
This
design of SHAPE, the s p a t i a l
to
dimensional
dimensions..
method f o r o b t a i n i n g more
will
reappear
later
simulate
an
environment
advantages of such a
system
as are
simple that
as some
a of
a s s o c i a t e d with r e a l world
s l o p p i n e s s are avoided,
hardware i s r e q u i r e d , and
the
prototype
organism-controller
next chapter
sensory-motor is
the
required
tabletop.. the
The
problems
no a d d i t i o n a l
experience
easily reproducible.
I d e s c r i b e a c l a s s of algorithms
f u n c t i o n i n g of the
in
planner.
In c o n c l u s i o n , c o n s i d e r a b l e programming e f f o r t i s to
In
of In
a the
fundamental to the
organism-controller. III»The simulated
organism-environment system
143 CHAPTER IV TOWARDS THE DESIGN OF A ROBOT-CONTROLLER
The the
purpose of t h i s chapter i s to present
design
and
implementation
an
reguire
two
parts,
a
design
seems
data p a r t c a l l e d the world model or
c o g n i t i v e map and a process p a r t c a l l e d the a c t i o n c y c l e . latter
consists
to
of a r o b o t - c o n t r o l l e r f o r Utak.
As d e s c r i b e d i n the i n t r o d u c t o r y chapter, any such to
approach
This
of a loop c o n t a i n i n g the three subprocesses o f
p e r c e p t i o n , p l a n n i n g , and a c t i o n . The chapter i s s t r u c t u r e d as f o l l o w s . I present In
the
an analogy second
In the f i r s t
t h a t i s u s e f u l i n approaching
section
I
present
the
which
any
made
scenario
o f the
complete r o b o t - c o n t r o l l e r f o r Utak should
d i s p l a y t o be a c c e p t a b l e . progress
problem.
p a r t s r e q u i r e d of any
r o b o t - c o n t r o l l e r and i n the t h i r d I present a behaviour
the
section
In the f o u r t h s e c t i o n I d e s c r i b e
i n one approach to the design and
of a r o b o t - c o n t r o l l e r , and i n the l a s t
section
I
the
implementation describe
an
a l t e r n a t i v e approach t o t h i s problem.
IV.1
An analogy
I s t a r t with a thumbnail between
the
scientific
sketch of t h e
method
and
well-known
analogy
the process of p e r c e p t i o n
IVnTowards the design of a r o b o t - c o n t r o l l e r
144
since
this
was
the
organism-controller* some phenomenon. and
an
hypothesis i s used are
experiment almost
point
Consider
an
f o r my
hypothesis. to p r e d i c t
done
-
exactly
as
To
test
what w i l l
an experiment.
and makes
design
experimenter
He o r she wants t o understand
proposes
actions
starting
of
the
;
investigating the
phenomenon
i t s validity
be observed
if
this
certain
He or she c a r r i e s out the
observations.
If
the
observations
p r e d i c t e d then the experimenter's
are
degree of
confidence or b e l i e f i n the hypothesis i n c r e a s e s . . One then that
the
hypothesis
explains
the
observations.
If
o b s e r v a t i o n s are not as p r e d i c t e d but the hypothesis can be
an
improved
predicted
and
adjustment
hypothesis. cannot
then
be
there
is
still
an
currently
explain
otherwise:
ignored.
higher
experiment
hypothesis
observation by
an
easily
principle,
before
but
o b s e r v a t i o n s are not as by
simple
parameter
makes a s t r u c t u r a l change, i f to
accommodate
them..
which the experimenter
hypothesis
then
i t is
If
cannot
noted
but
With t h i s new h y p o t h e s i s , or o l d hypothesis
confidence, and
the
accommodated
makes
the more
h y p o t h e s i s t o these, and so on* in
If
the experimenter
p o s s i b l e , t o enable the
with
the
modified t o accommodate the o b s e r v a t i o n s , e.g. by changing a
parameter* then the degree of confidence remains as in
says
experimenter
designs
another
observations,
accommodates
E v e n t u a l l y the hypothesis
the will,
be so w e l l adjusted t o the o b s e r v a t i o n s t h a t the
hypothesis w i l l be g e n e r a l l y accepted as a u s e f u l d e s c r i p t i o n o f one
aspect
of
Nature.
The hypothesis w i l l be c o n s i s t e n t with
IVaTowards the design of a r o b o t - c o n t r o l l e r
145
a l l the o b s e r v a t i o n s so f a r , or i n other words may
be
regarded
as the t r u t h a t t h a t p a r t i c u l a r time and p l a c e ; . Note the :pragmatic most
satisfactory
action.
at
nature of s c i e n c e :
whatever
a p a r t i c u l a r time i s used
For i n s t a n c e , Newtonian mechanics was
immensely
successful
theory
even
theory
is
as a b a s i s f o r
an a c c e p t a b l e and
though i t was
known t h a t i t
could not e x p l a i n the p r e c e s s i o n of the p e r i h e l i o n of Mercury., Now
return
to
Otak i n h i s simulated world. . At a l l times
Utak maintains an h y p o t h e s i s about
the world, c a l l e d
the
world
model.. Each p a r t of the world model has an a s s o c i a t e d degree c o n f i d e n c e , and these degrees of confidence may to
time*
In general the degree
vary
from
time
of confidence a s s o c i a t e d with a
p a r t i c u l a r p a r t w i l l i n c r e a s e with time; only the occurrence some
guite
experimenter external
unusual
event
will
cause
i s Utak; the phenomenon
world;
the
of
observations,
to
it
to
decrease.
be
explained
of The
is
the
or p i e c e s of evidence, are
provided by the s e r i e s of sensory impressions impinging on Utak; and
any hypothesis or world model must be c o n s i s t e n t , as f a r as
possible, least,
with the s e r i e s of sensory impressions.. At
the
very
the c u r r e n t world model must be c o n s i s t e n t with the most
recent sensory impression. In
t h i s analogy, £§_rception i s the a c t of accommodating the
world model to e x p l a i n the
current
sensory
impression*
while
m a i n t a i n i n g c o n s i s t e n c y as f a r as p o s s i b l e with p r e v i o u s sensory impressions.
When there i s no e x t e r n a l l y imposed task, p l a n n i n g
is
on
deciding
an
experiment
to
gather
more
evidence
to
IV«Towards the design of a r o b o t - c o n t r o l l e r
146 c o r r o b o r a t e the
c u r r e n t world
out
actions.
the
planned
dependent
on
the
the c u r r e n t
If
a l l p a r t s of the
world
world,
considerable
hypothesis
even
s t a t e o f TABLETOP.
i t may
though
in
perform
then
minimal
degree
accomplish sensory
accommodated perception* cycle* world
of
model* t h e n
impression.
He
passes
control
accomplish first
the
few
retinal
the
Utak
the
the
basis
and is
given
interprets
still
task
speed
the
parts
particular to a
and be
act. high
knows
the
may the
be
current
mistaken
which
to the
planner
task.
An the
and
even
this
cycle
the
sensory
accommodate
it* world
on
i s r e c e i v e d , i n t e r p r e t e d and
by
retinal
Then
and he
model, and
initial
executed.
design
of
* (TA.BLETOP) * B B B B B B B B B B B B B B B B 3 B 3 B B B B B B B B B B B B B B B B B B B B 3 3 8 * B 3 * B 3 * B B * B 3 *B C C C C B * B C C C C 3 * B C C C C B * B C C C C B * 3 B * B B * B B * B B * B B * B * B * B B. * B B * B B * B B B B B B B B B B B B B B B B B B * B B * B B * B * B B * B B * B ' 3 * B * B B * B * B B * B B * B * B * B * ' . '3 * B B * B 3 * B B * B B * B B * B 3 * B * B B B B B B 3 B B B B B B B B B B B B B B B B B B B B . B B B B B B B B B B B B B B 3 0
B
8
B
B
3
B
3
FIGURE I V . 2
(c)
The d e f a u l t w o r l d m o d e l WM-O.
a
A FIGURE I V . 2
(e)
The w o r l d m o d e l WM-1 a f t e r t h e f i r s t r e t i n a l impression RTI-1 received.
FIGURE IV.2 (d)
Retinal
i
7
O o o O O SB O o o O o O
7 o
7 i
/
7
i
i m p r e s s i o n RTI-1.
o
o
o
o
©
o
o
©
©
o
o
©
o
o
O o cnnnnnan o o •••••••• o o o •••••••• 0 o •••••••E o o •••nnnnc o o o• • • • • • c n o
o o
o o o
1
i V u
7
7
7
7
7
7
7
7
7
7
7
y
7
7
7
7
i
#»»
o o
.9
©
©
o
o
to o
p.
o
o
© _ •
T h i s shows the gray l e v e l s r e c e i v e d by Utak's r e t i n a from the TABLETOP w o r l d . The c e n t r a l '7' i s the image o f Utak. The o v e r l a i d dashed l i n e s show the line-segment i n t e r p r e t a t i o n .
FIGURE IV.2
T h i s may
(f)
Task statement "Go round the square o b j e c t to the south-east c o r n e r " .
be t r a n s l a t e d as: " F i n d a square o b j e c t . " "Keeping the square o b j e c t on your r i g h t , to t o a p o i n t near the square o b j e c t on the s i d e away from your c u r r e n t p o s i t i o n " S t i l l keeping the square o b j e c t on your r i g h t , go from t h i s p o i n t to the s o u t h east c o r n e r . "
•
•
A
FIGURE IV.2
(g)
PLAN-1, ACT-1, superimposed on
WM-1.
The t h i c k e n e d l i n e s correspond t o the l i n e segment i n t e r p r e t a t i o n of RTI-1. The o t h e r segments forming the boundary of the t a b l e t o p a r e h y p o t h e s i z e d .
* (BOLL 9.0 E) ( T A B L E T O P ) (THLOOK) * B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B * B '* B * B * B * 3 C * B C * B * B C * B * B * B * B * B * B * B * B * B * B « 3 B B B B B B B B B * B * fl * B * B * B * * B * B * B * B * B * B * B " " * B * B * B * B * B * B * B * B * B • B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B
F I G U R E
|
V .
a (4.)
ScWfcc-n
B B B B 3 B B 3 B B B B B B C C C B C C C B C C C C B C C C B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B 3 B B 3 B B B
S-A
FIGURE IV.2 ( i ) R e t i n a l i m p r e s s i o n RTI-2
«
6
4-
i I J
4-
0 4
r i i
4 1
b
o 6
o
0
o.
o 0
*
0 '& ' -1
0
0 d « » 0 0' 0 0 0 0
o' 0 0 0° 0 !thi * 0 0 • • n n n n n n d d 0* d 0° • • • • • • a n 0° o° 0 e d d 0 0° b d 0° •••••••• d 0 6 0 6 0° 0° o 0 a 0-® 0 o 0 0° 0' 0° d d 0 d 0
0 0
©
n
*
0
0
0 0
4
0 The p r e d i c t e d
o
O
0 0' d
0
i
o
o
0
0
A
a
0
0
6
0 0° 0 o
6
0 ©
0
i
0 0 0° 0* 0 0 0 0 6
0
o
0
g r a y l e v e l s are i n s c r i b e d i n the top r i g h t
hand c o r n e r of a l l but the f o v e a l r e t i n a l f i e l d s . The predicted
l i n e segment i n t e r p r e t a t i o n i s shown by the
o v e r l a i d dashed l i n e s a t the l e f t hand s i d e and a t r e t i n a l f i e l d ( ( o f ) . The o n l y d i f f e r e n c e between p r e d i c t e d g r a y l e v e l s occurs at
(yfl);
t h i s r e s u l t s i n a new
segment i n t e r p r e t a t i o n o v e r l a y i n g
both f i e l d s
and a c t u a l
line
(*) and (G) .
FIGURE IV.2 ( j )
World model WM-2,
w i t h PLAN-2 and ACT-2.
The p o s i t i o n and shape of o b j e c t 1 have been updated - i t i s no l o n g e r a square o b j e c t . The p r e v i o u s p l a n , PLAN-1, had t o be m o d i f i e d s l i g h t l y .
• * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
B B B B B B B B B B B B B B B B 3 B 3 B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B C C C C B B C C C C B B C C C C B B C C C C B B B B B B B B B B B B B B B B B B * B B B B B B B B B B B B B B B B 3 B B B B B B B B B B B B B B B B B B B 8 B B B B B B B B B B B " B B B B B B B B B B B
*
3
* * * * B
* B B B B 3
B B
3 B D - B B 3 B B B B B B 3 B B B B B B B B B 3 B B 3 B B 3 3 3 8 B B 3 B B
FIGURE. IV.2
o
7
(1)
o o
o e
Retinal impression RTI-3.
7
o
O
6
o 0
o o
o
o *
o a
o
o
©
o B
o
o to
e
o
o• o
©
©
o
a
O
o C? a
o
o
2l
• •
O
o« o
• o
•••aaooQ •••••••• ••••••33 • • • • • • • a
e
o
o'
o
o o
o
o
o
O
o
o
«
t>
o
O
0
1
¥• • o*>
a
t
of
• • • • • • E W o CCCC3EEn e « o o o *> c « a o o •
o
7 to
o
o
-*
o
o
6
6
o
o e
©
o
o
O
7
o
o o
r
o o o o oo •••••••• O o«
• o
7
o
o o
o
•
©
o
o
«
«
o
O
o
o
7
r
o
o
O
o
•
The actual gray levels d i f f e r i n several places from the predicted gray levels (in the RH corner of each f i e l d ) . The row of O's across the top forces the north verge out by four units. The 2 and 6 i n the top RH corner forces the introduction of a new object. F i n a l l y , the several differences at middle right force another change in the shape of object 1.
FIGURE IV.2 (m)
World model WM-3,
with PLAN-3 and ACT-3.
OBJECT
PLAN - *5
The north verge moved out by four units; object 2 i s new and i s square while the old object 1 can no longer be considered square; therefore, object 2 i s assumed to be the square object of the task.
Z
* >
(BOLL 3.0 2) (T&BLETOP) (THLOOK) ( 3 . 1. 570796)
• B B ' B B B B B B B B . B B B B B B B B B B B * B
- B B B B B B B B B B B B B B B B B B B B B B
* B *
B
B
B B B B B B B B B B
* B * B * B * B * B * B * B *'B * B
C C C C
'
* B *
C C C C
C C C C C C C C
•
*
B
B
B B
* B * * * *
B B B B
B
B B
* 3 * B
B B B B B B B B B B
B B B
B
* B * B * B
* * * *
3 B B B
* * *
B B B
B -B B B B B B B B B B
* 3 * B * B * B *B * B * B * B *
B B
B .
B
B B B B
B
* B B B B . B B B B B B B B B B B B B B B B B B B
F I G U R E
B B B B B
j\f.
a
gnD
B B B B B B B B B B B
^*u.a+t*n
S-(5&
B. 3 3 B B B B B
FIGURE IV.2 (p)
7
7
1
7
e>
0
r
T
7
7
7
7
0
o
o
o
o
0
0
0
CF
a
0
•
o 0"
o
O •*
o
o
o
*
D
o
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o o e>O • • • • • • • • o o d o« o O o 0 « o« o cf o
a
t>
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o
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R e t i n a l impression RTI-4.
••: 7*
e
o
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o
ao*> »> o o o
7 L 9
o o
0"
o 9
a
O
The gray l e v e l d i f f e r e n c e s on the r i g h t - h a n d s i d e f o r c e the east verge to be moved out by two u n i t s , and a new o b j e c t , o b j e c t 3, to be i n t r o d u c e d .
FIGURE IV.2 (q) World model WM-4,
w i t h PLAN-4 and ACT-4.
The e a s t verge moved out by two u n i t s ; new obj e c t 3
*
( 1 -
* *
0
S )
3 . 1 4 1 5 9 3 )
( T A B L E T O P ) B
*
B
*
B
*
B
B
*
B .
*
B
*
1.
( R O L L
>
B
B
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B
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B
B
B
B B B
*
B B C
B
C C
C
C
C
C
B B
B
*
B
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C
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B C
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B
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B
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B
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B B
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*
B
* 3 • B B B B B B B B B B B B 3 B 3 B 3 3 3 B 3 B B B B B B B B B B B B B B B B B B B B B
B B
B B •
FIGURE IV.2 (s)
7
7 7
7
7
R e t i n a l i m p r e s s i o n RTI-5.
7
7
7
7
t
7
7 7* 7
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7
r
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V
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e
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o
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e
c (9
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r
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7
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oft i
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Once a g a i n , the gray l e v e l d i f f e r e n c e s on the r i g h t hand s i d e f o r c e the east verge out by two u n i t s and a change i n the p o s i t i o n and shape of o b j e c t 3. The gray l e v e l s f o r o b j e c t 2 ( j u s t below c e n t r e ) were e x a c t l y as p r e d i c t e d .
FIGURE IV.2
(t)
World model WM-5,
w i t h PLAN-5
A
0
OQ36CT
i
PLAM-5
The east verge moved out by two u n i t s ; shape of o b j e c t s changed.
n o B B B B B B B B B B B B B B B B 3 B B B B B B B B B B B B B B B B B 3 B B B
* C C C C C C C C C C C C
* *
c c c. c
*
B B B B B B B B B B B B
*
*
* *
•
B
B
B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B
B
B B B 33 B B BB 077 DR = 0 3. 20, T = 0. *
PICTURE
3 B B B B BB 3 28T
B
B B B B B 3 B B B B B B B B B B B B B 3 B B B
iv\a(V) S t ^ a f t o n £-6
FIGURE I V . 2 (v) R e t i n a l i m p r e s s i o n
o o 0
o
0
o
0
o
o
2
0
o
o o 0
o
0 o
RTI-6.
O
4|
7
7
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4j
7
7
7
7
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7
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7
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7
7
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0 0 0 o o 0
0 0 0 7 o o o 0 7 o o o 7 •••EIHEOE 0 7 o o • • • • • • • • •44- 4- • • • • • • • • 7 • • • • • • • • 0 o •••••••• 0 7 o o o o 0 0 0 7 o o o o o 0 0 7 o
0
O
O
o
O
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A
4 ii
The p r e d i c t e d gray l e v e l s a r e n o t shown h e r e because o n l y one d i f f e r e n c e between p r e d i c t e d and a c t u a l occurs: i n t h e Fovea a t t h e l e f t hand end o f o b j e c t 3. T h i s f o r c e s a v e r y s m a l l change i n o b j e c t 3.
FIGURE IV.2
(w)
World model
WM-6.
i V c = i t I
»
\ v \
V
The shape of o b j e c t 3 changed v e r y
slightly.
x
173 d i s t a n c e can a l s o be regarded Utak
travels,
impressions
if
one
as a measure of speed
makes
the
are r e c e i v e d at a constant
The TABLETOP s i t u a t i o n S-2
assumption
with that
which retinal
rate.
a f t e r the e x e c u t i o n of the
a c t i o n i s shown i n (h) and the new
retinal
received
g r a y l e v e l values of 2 i n the
( i ) . The two
neighbouring
impression*
first
upper r i g h t hand s i d e are.not as p r e d i c t e d by WM-1; the
position
and
shape
of
objectl
must
be
RTI-2,
consequently changed
to
be
c o n s i s t e n t with RTI-2, while m a i n t a i n i n g c o n s i s t e n c y with RTI-1. As a r e s u l t of t h i s change o b j e c t l
i s no longer square
i s some doubt as to whether i t should s t i l l the
square o b j e c t of the task statement..
other v i s i b l e , p o t e n t i a l l y square, square
there
identified
with
There i s , however, no
o b j e c t with which the
task's
o b j e c t could be i d e n t i f e d , short of h y p o t h e s i z i n g one i n
an a r b i t r a r y p o s i t i o n beyond covered
by the r e t i n a .
the
(j).
The
original
a c t i o n i s decided The
new
s i t u a t i o n S-3
predicted
to
has been found objectl
turns
object.
plan
is
or
has
been
The
remains
new
world model i s
unchanged and
another
i s shown i n (k) and the next
retinal
(1).
retinal
o b t a i n WM-3 and the
shape
T h i s d i f f e r s c o n s i d e r a b l y from
impression.
i n t e r p r e t a t i o n s are d e r i v e d and accordingly
that
on.
i m p r e s s i o n , RTI-3, obtained the
area
Thus the known o b j e c t l i s r e t a i n e d , f o r
the moment, as the t a s k ' s square WM-2
be
and
the world
(m). of
A new the
New model
square supposed
out to be f a r from square.
line-segment WM-2
modified
object, object2, square
object
Thus the new
object2
IVnTowards the design of a r o b o t - c o n t r o l l e r
174
is
assumed to be the square
the: p o s i t i o n
of
o b j e c t of the task statement.,
the edge of the "room" i s not as expected
has t o be moved out by f o u r u n i t s . new and
plan from
Also,
The
planner i s c a l l e d
the c u r r e n t p o s i t i o n of Utak going
and
and
a
around o b j e c t 2
back to the southeast corner i s c o n s t r u c t e d . . Since t h e r e i s
a gap
between o b j e c t l
and the s i d e of the room, and
s i n c e a path
going v i a the gap should be s h o r t e r than going on the other s i d e of o b j e c t l , the new
plan goes through
Another a c t i o n i s decided situation
S-4
(n)
and
on
and
retinal
by two
results
u n i t s . . The
object
object3
presented
g r a y l e v e l of one the
it),
model
is
Wti-4
decided on and The ETI-5 of
new
(s) *
the
embedded
fours
be
in
From
consistent
as
a
were
the to
evidence assume
t o the edge of the with
the
the line-^segment
small
(q) ;
a
retina;
evidence
from
interpretation
so i n s t e a d object3 i s assumed., The new the plan remains unchanqed, and
an
world action
executed. s i t u a t i o n i s S-5
has
to
( r ) , with new
be moved out by two
shape of o b j e c t 3 changed* (t) ,
The
retinal
impression
Again t h i s i s not q u i t e as p r e d i c t e d ; the east
room
in
(p) . .
where
side.
t h i s i n t e r p r e t a t i o n i s not c o n s i s t e n t
obtained from
RTI-4
i s interpreted
east
i n BTI-4 alone i t would
is
resulting
i n the east s i d e of the room being moved out
against
(which
executed,
hand s i d e
s m a l l t h i n o b j e c t not q u i t e extendinq
RTI-3
gap.
impression
g r a y l e v e l s of zero along the r i g h t predicted
this
and the p o s i t i o n
In the accommodated
the . plan remains the same.
The
side
world model
next s i t u a t i o n S-6
and WM-5
(u)
and
IVaTowards the design of a r o b o t - c o n t r o l l e r
175
r e t i n a l impression RTI-6 are obtained actions*
RTI-6
(v)
o b j e c t 3 which was and
the
occur*
IV.4
S-6,.
shows c l e a r l y the gap between o b j e c t l
only deduced from p r e v i o u s r e t i n a l
current
situation
after several intermediate
world
model
WM-6
(w)
impressions
correctly
Thus i n t h i s example no more
The
approach to
idea
statements
The
about
world model c o n s i s t s
the
shape
of
the
of
evidence
correctly.
between s c i e n c e
a
verge,
o b j e c t s on the t a b l e t o p , and the shapes of statement
collection
the
objects..
help determine when
to
new
what
of
a
extent
evidence
p o s i t i o n s of end-points terms
Each
i s t o have an a s s o c i a t e d degree of confidence based on c o l l e c t e d from a s e r i e s of r e t i n a l
modified
of
the p o s i t i o n s of
impressions.
degree of confidence i s to be used i n the . accommodation to
can
implementation
i s to take s e r i o u s l y the analogy
and p e r c e p t i o n *
reflects
accommodation
so the remainder of the plan w i l l be executed
A first
and
Cartesian
old
statements
i s r e c e i v e d . . The
of l i n e s
and
coordinate
other system
This process,
should
statements
spatial
be give
facts
in
c e n t r e d on Utak.
A
s p a t i a l problem i s to be solved by p r o j e c t i n g a l l or part of the world
model
onto
a
screen
—
Utak's map-in-the-head --
s o l v i n g the problem there and t r a n s l a t i n g the. s o l u t i o n plan —
back i n t o the C a r t e s i a n c o o r d i n a t e system.
there i s a world model and may
a p l a n , even though
--
then the
At a l l times
initially
these
be simple d e f a u l t s * IV«Towards the design of a r o b o t - c o n t r o l l e r
176 The'implementation of these i d e a s order
given
by
the
list
of
r e c o n c i l i n g a world model with ignored
on
the
basis
models.
a task statement,
that
Steps 1-5
I
could
for
my
purposes and a
in
the
get
was by
6,
initially
with
simple
r e g u i r e r e c o n c i l i a t i o n of
two
were accomplished and then step 7,
the
implementation of a s p a t i a l planner* c u r r e n t techniques
approached
program p a r t s i n IV.2. . Step
p a t h - f i n d i n g problems t h a t did not world
was
was
tackled.
I found
that
f o r p a t h - f i n d i n g were not r e a l l y s a t i s f a c t o r y t h a t an approach based on
skeleton
of
shape
promised
described
i n the next chapter. .
to
be
the
use
u s e f u l . ..
of
the
T h i s work i s
F i r s t I w i l l d e s c r i b e the world model.
IV. 4._1
D e f i n i t i o n of the
The nodes
data s t r u c t u r e f o r a world model c o n s i s t s of a t r e e
linked
corresponding
the
by
relations.
The
root
of the
t o the f l o o r s p a c e . . The
isolated
corresponding
objects
on
to an o b j e c t may
the o b j e c t i s complex and
the
of
t r e e i s a node
to Otak, c a l l e d $org, which has one
corresponding to
world model
son,
$floor,
sons of $ f l o o r correspond
tabletop.,
The
node
N
i n t u r n have sons i f the shape of
i s best d e s c r i b e d
in
a
hierarchical
manner. . A node corresponds to a shape on the t a b l e t o p and consisting
of
the c o n t a i n i n g r e c t a n g l e
a l i g n e d with the axes
that
contains
boundary shape as a c i r c u l a r l i s t
(the s m a l l e s t
the
shape),
is a
rectangle
the
actual
of s t r a i g h t - l i n e segments,
IV«Towards the design
list
the
of a r o b o t - c o n t r o l l e r
177
shapes of any relations any.
holes i f present, and
between t h i s node and
Each node has
between
two
i t s own
objects
a s u b l i s t c o n s i s t i n g of
i t s descendants i n the t r e e , i f
c o o r d i n a t e system,
specifies
the
and
translation
r e q u i r e d to get from the c o o r d i n a t e system of one a
other. .
r e l a t i o n i s simply
a list
the
rotation
node2's.
to
get
from
In the implementation
a
relation
and
rotation
node
to
(nodel node2 o f f s e t )
the o f f s e t i s a t r i p l e c o n s i s t i n g of the and
the
x-
nodeVs
and
the where
y-translation
c o o r d i n a t e system to
so f a r , the r o t a t i o n has
always
been zero, By s p e c i f y i n g the world model i n t h i s manner i t i s easy modify
the
world
model
motion of an o b j e c t caused to
to
r e f l e c t the motion of Utak or the
by the motion of Utak.. M l
be done i s t o modify one r e l a t i o n * .
of d e t a i l .
tabletop
shape
in
F i g u r e IV. 3 shows the world model t r e e f o r a
situation*
When
a
retinal
impression
has
r e p r e s e n t o b j e c t s or verge.
be d i s t i n g u i s h e d from so
accommodate
that
the verge
finally
(explain)
world
them.
The:
d e s c r i b e these o p e r a t i o n s
and
those
Then the o b j e c t r e g i o n s must
regions
the
impression
been r e c e i v e d i t must be
analyzed to f i n d those r e g i o n s which r e p r e s e n t space
stage
has
increasing
IV.4.2 P e r c e p t i o n : accommodation to the f i r s t r e t i n a l
which
that
This tree representation
can a l s o be used to s p e c i f y a complicated levels
to
in
model next
(steps 3,4,5
an
interpretation
can
be modified to
three:
sub-sections
of IV.2) .
IVeTowards the design of a r o b o t - c o n t r o l l e r
FIGURE IV.3
VERGE
"A
(a) A w o r l d model, drawn on the E u c l i d e a n plane.
o f f s e t - Ri\
Shape of v e r g e , w i t h c o o r d i n a t e o r i g i n A
Shape of OBI, with coordinate o r i g i n B.
Shape of 0B2, with coordinate o r i g i n C.
(b) Tree c o r r e s p o n d i n g to the world model of ( a ) .
179
2. J. Edge and r e g i o n A
region
finding
i n the r e t i n a l impression i s a connected
set of
r e t i n a l c e l l s where a l l the c e l l s have a zero g r a y l e v e l , o r e l s e a connected
a l l have a non-zero g r a y l e v e l . d e f i n e d u s i n g edge-adjacency.
s e t on the r e t i n a i s
Two c e l l s are edge
adjacent
i f
they have:an edge o r part of an edge i n common., Thus d i a g o n a l l y adjacent c e l l s are not edge adjacent. for
any
two
edge-adjacent cells
retinal
c e l l s i n t h e r e g i o n , there i s a c h a i n o f
r e t i n a l c e l l s which s t a r t s a t
and f i n i s h e s at the other.
the
border
in this
one
with
a
non-zero
direction,
would
of
given
graylevel
would
crawling
always f i n d the boundary
of a
be t r a v e r s e d by the
t u r t l e i n a clockwise d i r e c t i o n and any other boundary hole)
the
such t h a t a t u r t l e ,
non-zero r e g i o n on i t s r i g h t . , Thus the (outer) region
of
The border between two r e g i o n s
has a d i r e c t i o n a s s o c i a t e d with i t , along
a r e g i o n i s connected i f ,
(i.e. a
the r e g i o n would be t r a v e r s e d i n a c o u n t e r - c l o c k w i s e
direction* The
b a s i c b u i l d i n g block f o r f i n d i n g the edges of a r e g i o n
i s the " i n t e r - c e l l - e d g e " of
retinal
cells
(ICE) which i s created between any p a i r
where
the
g r a y l e v e l of one i s zero and the
g r a y l e v e l of the other i s non-zero* , a f i r s t impression
produces
a l l the
connected
scan
of the r e t i n a l
r e g i o n s and marks the
p o s i t i o n of each ICE with a data s t r u c t u r e l i n k e d t o each member c e l l of t h e ICE. The next o p e r a t i o n l i n k s the ICEs of one r e g i o n i n t o one or more
disjoint
circuits..
Since more i n f o r m a t i o n i s needed f o r
IV«Towards the design of a r o b o t - c o n t r o l l e r
180 l a t e r grouping
operations,
when
an
ICE
i s being,
traversed
several
e x t r a p i e c e s of i n f o r m a t i o n are added: the d i r e c t i o n of
traverse
(N E S W), the g r a y l e v e l s of the c e l l s of the ICE, and
the
s i z e s of these c e l l s , the r e s u l t being c a l l e d a chunk.
l a s t two items the world
are needed l a t e r as evidence
model.
The
f o r t h e segments
of
Some ICEs l i e along the edge of the r e t i n a and
s p e c i a l chunks have to be used. The
linking
i s done by t a k i n g one ICE a s s o c i a t e d with the
r e g i o n i n question and i t e r a t i v e l y
f i n d i n g i t s successors
using
the geometry of the r e t i n a l impression u n t i l a c l o s e d c i r c u i t i s formed.
I f an ICE a s s o c i a t e d
with
the
region
still
remains
c i r c u i t i s started.
This i s
unlinked
i n a c i r c u i t then another
continued
u n t i l a l l the ICEs are exhausted.
Next,
a grouping
o p e r a t o r t r a v e r s e s each c h u n k - c i r c u i t and
groups c o n s e c u t i v e chunks having a segment,
pt2 d i r n l e n type
evidence)
p t 1 , p t 2 , d i r n , l e n , s p e c i f y the endpts,
t o t a l l e n g t h r e s p e c t i v e l y of a s t r a i g h t EXTERIOR
d i r e c t i o n , and
l i n e segment.
"Evidence"
is
the a
retina
list
or
of pairs
i s interior
the
retina.
(graylevels cell-sizes)
derived
from the component chunks, shortened The
to
by grouping
identical
is
intended
pairs
meaning of "evidence" here i s how well the l i n e
segment was defined by the g r a y l e v e l s i n the r e t i n a l It
"Type" i s
or INTERIOR depending on whether the segment c o i n c i d e s
with an edge o f
together;
into
A segment i s a l i s t (pt1
where
the same compass-direction
to
provide
restrictions
on
how
impression. much
the
IVaTowards the design of a r o b o t - c o n t r o l l e r
181 parameters of t h i s l i n e segment could be changed t o subsequent the
retinal
current
operation
impressions
retinal
is a
without
impression..
accommodate
losing consistency
The
end
result
every
lines
that
right-handed
This
is
also
turtle
known
turns
r e t i n a i s found.
list
regions,
for
a
f o r every
left-handed
counter-clockwise
At
traverse. In
one
i s t r a v e r s e d once and the
the
same time, the maximum
segments t h a t c o i n c i d e with
an edge of the
T h i s i s c a l l e d "max-resegs" below. of the edge and
where . each
borders.
a
border
is
segment-circuit, turtle-turns,
corresponds t o f l o o r s p a c e * and
has
on
i t s p-list
a b o r d e r - l i s t of one p-list
with
max-resegs, and
IV.4.2.2 I n t e r p r e t i n g the f i r s t the fovea of the eye
r e g i o n f i n d i n g stage i s
region
and
In
of
counts 1 f o r
as the T o t a l T u r t l e T r i p theorem;.
g r l - c l a s s , number of sguares, Each
circuit
i t s e l f and
counts -1
computed.
f i n a l output
of
crosses
each s e g m e n t - c i r c u i t
number of consecutive
The
this
of the t r i p the t o t a l w i l l be e i t h e r 4 f o r
t r a v e r s e or -4
f i n a l operation* total
nowhere
90° t u r n and
90° t u r n . . At the end a clockwise
of
segment-circuit.
Suppose a t u r t l e t r a v e r s e s an a r b i t r a r y c l o s e d straight
with
or
properties their
a the
more name,
values..
r e t i n a l impression -
a r e t i n a l c e l l with a cell
with
zero g r a y l e v e l
non-zero
graylevel,
n e c e s s a r i l y 7, corresponds to e i t h e r an o b j e c t , the verge, or to Utak h i m s e l f . with
zero
r
In the p e r i p h e r a l p a r t s of the eye
graylevel
may
correspond
a retinal
to an area of the
cell
tabletop
IV«Towards the design of a r o b o t - c o n t r o l l e r
182 which i s not e n t i r e l y graylevel
of
7 may
floorspace, correspond
and
similarly
one
with
a
to an area of t h e ; t a b l e t o p which
i s not e n t i r e l y o b j e c t or boundary. „ In any are
one r e t i n a l impression
interpreted
connected,
as
i f two
the r e g i o n s of zero g r a y l e v e l
floorspace;.
Since
or more disconnected
all
floorspace
is
regions of zero g r a y l e v e l
appear i n the r e t i n a l impression the i n t e r p r e t a t i o n must p r o v i d e that
these are connected*
I f a l l the f l o o r s p a c e r e g i o n s have a
segment c o i n c i d e n t with an edge of the needs
to be done; i t i s assumed t h a t they are
the area of the t a b l e t o p covered one
retina
of
the
surrounded passage
two
or
more
no
action
connected.outside
by the r e t i n a l i m p r e s s i o n .
floorspace
regions
is
If
completely
i n the r e t i n a l impression by a non-zero r e g i o n then a
must
be hypothesized
r e g i o n and the
nearest
natural
to
place
i t s l e n g t h to a between
then
two
between the surrounded
neighbouring
hypothesize
minimum,
is
region.
The
such a passage, i n order to keep the
floorspace regions.
can e a s i l y be found
floorspace
floorspace
line
of
shortest
distance
T h i s l i n e of s h o r t e s t d i s t a n c e
from the s k e l e t o n of the complement
of
the
f l o o r s p a c e r e g i o n s ; t h i s w i l l be d e s c r i b e d i n s e c t i o n V.4.2.. The
non-zero r e g i o n s are
objects
or
verge.
the
surrounded
verge
surrounds
as
either
T h i s i s s t r a i g h t f o r w a r d i n two
non-zero r e g i o n completely itself
interpreted
surrounds
isolated
cases.. I f a
a zero r e g i o n , and
is
not
by a zero r e g i o n , then t h i s i s i n t e r p r e t e d as
of
the
tabletop,;
a
non-zero
region
If
a
zero
region
completely
then
this
latter
region
is
IVaTowards the design of a r o b o t - c o n t r o l l e r
183 interpreted
as
an
isolated
object
with
a
high
degree
of
I f n e i t h e r of these two cases holds then the max-resegs
of
certainty.
the
outer
boundary
of
the non-zero r e g i o n
with t u r t l e - t u r n s = 4 ) i s examined.
(the unigue
Remember
that
border
"max-resegs"
records the maximum number of c o n s e c u t i v e segments of the border of
the r e g i o n t h a t c o i n c i d e with edges of the
value
is
If i t s
z e r o , one or two then the r e g i o n i s i n t e r p r e t e d as an
i s o l a t e d o b j e c t , otherwise
as p a r t of the
i l l u s t r a t e s t h i s i n t e r p r e t a t i o n scheme. in
retina..
t h i s way i s s u b j e c t
to
revision
subseguent r e t i n a l impressions
or
verge..
Figure
IV.4
Any i n t e r p r e t a t i o n made a
are r e c e i v e d .
"double-take" A region
when
initially
i n t e r p r e t e d as an i s o l a t e d o b j e c t may l a t e r t u r n out t o be correctly
i n t e r p r e t e d as boundary, and v i c e versa.
i l l u s t r a t e s a p o s s i b l e double
more
F i g u r e IV.5
take.
IV.4.2.3 Accommodating the d e f a u l t world model to the f i r s t retinal
impression
The d e f a u l t world model with which Otak "wakes up" simplest
p o s s i b l e : a square
has
must be m o d i f i e d retinal
After
the
first
retinal
been r e c e i v e d and i n t e r p r e t e d , t h i s world (accommodated)
to
be
consistent
with
model this
impression.
F i r s t the i n t e r p r e t e d r e t i n a l impression what
the
f l o o r s p a c e centred on h i s p o s i t i o n ,
and c o n t a i n i n g no i s o l a t e d o b j e c t s . , impression
is
restrictions,
is
i f any, the r e t i n a l impression
examined
for
places on the
IVaTowards the design of a r o b o t - c o n t r o l l e r
FIGURE IV.4
Examples o f . r e g i o n
interpretation.
Max-resegs = 2 ISOLATED OBJECT
Max-resegs = 3 Verge
Max - r e s e g s = 4 Verge
FIGURE IV.5
A doubletake.
In t h i s i n i t i a l p o s i t i o n the robot t h i n k s i t i s c l o s e to the n o r t h edge of i t s environment.
What the robot p r e v i o u s l y thought was verge i s r e - i n t e r p r e t e d as p a r t of an i s o l a t e d object.
186
a c t u a l d i m e n s i o n s of the
world
model.
impression and
c o n s i s t s of
the
retinal
$floor's
a type.
restriction
impression;
conseguently the
rectangle
a
I f the
segment
coincides
consequently
W
type
an
edge
of
of
this
$org-$floor
offset,
containing
rectangle
these r e t i n a l
value
of
initially of
restrictions
given
beyond
and
modified
a
by
the
to
the
side
of
value
of
restriction
of
and
The
sides
$ f l o o r , are as
region
containing
further
the
is
impression;
the
(i*e;,
or
segment
this
restriction.
(0,0,0), default
by
retinal
side
the
INTERIOR
of a f l o o r s p a c e
the
this
rectangle,
be
p o s i t i o n of
of
retinal
which i s i n t e r i o r
boundary
$ f l o o r must l i e a t o r the
may
i s defined
region
$floor
from the
i s EXTERIOR, t h e
the
position
than)
type
$ f l o o r must be
of
with
the
rectangle:of
of
the
containing
The
a floorspace
by
or
and
of
i s computed
boundary of
defined
S,
a value
restriction.
which
rectangle
restriction
I f INTERIOR, t h e
the:containing this
One
containing
f o r each s i d e o f t h e
EXTERIOR. of
the
N,
E,
default of
the
compared
with
necessary to
satisfy
them* Now the
that
$floor
computed. $floor. regions whole o f
the is
The If
fixed, next
none
coincide
of
with
is the
parts to
a retinal within
only
and
containing of
the
derive
the
rectangle
world
model can
actual
shape
s e g m e n t s of b o u n d a r i e s o f
floorspace
Otherwise,
origin
other
item
$ f l o o r appeared
boundaries of the $floor.
coordinate
edge, the
regions
or
retinal are
parts of the
IVnTowards t h e
in
shape
as of
the
be of
floorspace words
impression,
taken
design
other
of
the
then
the
shape
of
$ f l o o r appeared
of a r o b o t - c o n t r o l l e r
187
w i t h i n the r e t i n a l segments lie
of
boundaries
strictly
segment
impression.
within
sequences
segment c i r c u i t
of
rectangle,
have
current to
be
retinal linked
impression..
sequence
are
extended
to
edges
of
the
containing
the c o n t a i n i n g
r e c t a n g l e are i n t r o d u c e d
p a i r o f segment sequences*
The shape of $ f l o o r i s then
o f the r e t i n a l impression,
of
also
marked
complete. isolated-object
and added t o the world
model.
rectangle,
the
i t s c o o r d i n a t e system from $ f l o o r , and i t s shape are
a l l computed. to
existing
to these segments.. Second, h y p o t h e t i c a l segments
an i s o l a t e d - o b j e c t r e g i o n , i t s c o n t a i n i n g
offset
These
up i n t o one continuous
L a s t l y , a node has t o be c r e a t e d f o r each
Given
which
new h y p o t h e t i c a l segments. . F i r s t t h e end
between each c o n s e c u t i v e
region
of
with the e x t e n s i o n s marked as "HYPO" i n the evidence
the
"HYPO",
the: sequences
by c r e a t i n g h y p o t h e t i c a l e x t e n s i o n s t o
each
l i s t s attached along
are
o f r e g i o n s i n t e r p r e t e d as verge,
the
segments and by adding segments
These
the f i r s t
The d e f a u l t world retinal
model has now been accommodated
impression.
IV.4.3 P e r c e p t i o n ; accommodation to - subsequent
retinal
im p r e s s i o n s Once interprets the
a
world
model
has
been c o n s t r u c t e d t h a t c o r r e c t l y
("explains" i n the analogy
retinal
impressions
received
with so
scientific
f a r , i t i s used
f a c i l i t a t e the accommodation of subsequent r e t i n a l An
overall
view
of
this
accommodation
method)
process
to
impressions. w i l l now be
IV»Towards the design of a r o b o t ^ c o n t r o l l e r
188
described. is
Given the decided-on a c t i o n , a p r e d i c t e d
constructed,
and from t h i s
world model
a p r e d i c t e d r e t i n a l impression
produced by p r o j e c t i n g the p r e d i c t e d
world model onto
structure
with
topologically
T h i s r e t i n a l impression in
identical
a retinal
array
impression.
d i f f e r s from a normal r e t i n a l
impression
t h a t every r e t i n a l c e l l has a p o i n t e r back t o the segment(s)
of the
world
graylevel* impression the
model After
which the
caused
action
i t to
is
have
its
i s compared with the p r e d i c t e d r e t i n a l
differences
between
the
accommodate
the new
retinal
two
used
relation
(r,9)
POSHTO(v) relation (s,$)
If
and
the
is
impression
and
to i n d i c a t e what
line
world model
by
relation
by
(r-v,e).
by (r-v,9)
the
(s+v,
FIGURE V.6
upper*
,jp
ow e
tow
L
P
1j
corridor
at of
places
in
classifies
by SKEL-1. . Rt the same
the
skeleton
such
as
a
even width, where SKEL-1 would compute a
double row of s k e l e t o n p o i n t s , SKEL-2 computes none. What
i s needed
i s t h e : i n t r o d u c t i o n of p o i n t s i n between
c e l l s of the array as of
introduce
a s k e l e t o n p o i n t between
disjoint
sets
V. 7,.
points,
examples
with
figure
skeleton
of
The
contact
as
obvious any
suggested
way two
points*
t o do t h i s i s to HV-adjacent
This
however, because many p a i r s of HV-adjacent c e l l s , ridge-line,
have
HV-adjacent
contact
conservative
neighbourly one
member
algorithm
and
two
i f they
non-empty
sets
are
any
consequently
Consequently a
identical
S I , S2
i f there i s at l e a s t one neighbourly of
f a r from
c o n d i t i o n must be used. , Define two c e l l s o f
the network to be neighbourly HV-adjacent,
cells
doesn't work,
p o i n t s , and
many s p u r i o u s ridge p o i n t s would get introduced. more
by the
or a r e
of c e l l s t o be p a i r of
the pair from S1 and one from S2.
cells,
The modified
i s as f o l l o w s ; V»Path-finding and the s k e l e t o n of a planar
shape
217 Alqorithm
SKEL-3.
Steps 1,2,3 4,
as f o r SKEL-2.
[Create ridge p o i n t s ] . For a l l i,j=1,2, ... n, ( i < j)
do
i f not neighbourly (contacts (Pi) , c o n t a c t s (Pj) ) then c r e a t e - r i d g e - p t R i j between P i and P j . 5,.
[ Define . s k e l e t o n p o i n t s ] , SKEL=
{ a l l created ridge-points ] u ( P i | number-of-contacts-of (Pi) > 1 j
F i g u r e V.8 shows the r e s u l t of using SKEL-3 on two examples..
1*2.5
Ridge-foliowing The
cells.
points
the
A r i d g e c e l l may
network
or
network. ridge
of
a
point
skeleton be
either
created
a
cell
of
the
an
unordered
collection
which, t o be u s e f u l , must be organized
of l i n k e d r i d g e c e l l s ; to the o p e r a t i o n ,
neighbouring
chains
I use the term r i d g e - f o l l o w i n g to
refer
on a network to which SKEL-3 has been a p p l i e d ,
ridge
resulting
collection
connected
graph
of
structure
graph o f the corresponding Return
again
of
into
o f i n s e r t i n g l i n k s between r i d g e c e l l s and assembling more
original
between two c e l l s of the o r i g i n a l
The output of SKEL-3 i s
cells
w i l l be r e f e r r e d t o as r i d g e
to
the
cells cells,
into
"junctions"
links,
closely Euclidean
and
three
or
so that the
junctions
is
a
approximating the s k e l e t a l shape.
mountain metaphor;. Imagine
s t r a d d l i n g a r i d g e with one's l e f t and r i g h t f e e t
just
oneself to
V«Path-finding and the s k e l e t o n of a planar
the shape
c
m
9
J5
^
'S
"a
3
3
3
©
d
#
i ®
%
#
3j?
'3
4>
%
0),
line
then
and
they
are
can
i f two
separated
be
rotated
by
n
in a
staggered
f a s h i o n so t h a t they have a h o r i z o n t a l centre l i n e but
are s t i l l
separated
conversely.
To
by
be
exactly
n
i n t e r m e d i a t e , sguares;
more p r e c i s e , suppose t h a t i n a two-square
s i t u a t i o n the c o o r d i n a t e s o f one square are
(ix,iy).
Then
m = Max {| i x j , | i y | j . any
two-sguare
and
the
axis
relative
to
the
other
d i s t a n c e between the squares i s
The staggered r o t a t i o n lemma then says t h a t
situation
can be transformed
i n t o any other i n
which the a x i s d i s t a n c e between the sguares i s the same..
Shrinking
lemma.
Given
a
two-square
situation
with
axis
d i s t a n c e n between the squares, and suppose (m - 1)*root2 < n < m*root2 holds
f o r some i n t e g e r m > n.
r o t a t i o n s such that i n the f i n a l
Then there e x i s t s a sequence of situation
the
axis
distance
between the squares i s m. (Proof: one 45° r o t a t i o n The
proof
of
the
plus one staggered r o t a t i o n . ) merge
lemma
now f o l l o w s by a l t e r n a t e
a p p l i c a t i o n s of the s h r i n k i n g lemma and the
staggered
rotation
256 lemma.
Expanding
lemma.
Given
a
two-square
situation
with
axis
d i s t a n c e m between the squares, and suppose n - 1/2 < m*root2 < n + 1/2 holds f o r some i n t e g e r n > m. rotations
such
that
between t h e squares
in
Then there e x i s t s a
sequence . of
the f i n a l s i t u a t i o n the a x i s d i s t a n c e
i s n.
(Proof: one staggered r o t a t i o n plus one 45° r o t a t i o n . ) The
proof of the
applications lemma.
of
split
lemma
the expanding
now
follows
by
alternate
lemma and the staggered
S u c c e s s i v e a p p l i c a t i o n s of the
merge
lemma
rotation
prove
the
following
Collapsing,
theorem.
Given
any
sequence of r o t a t i o n s such t h a t
initial
the
final
s i t u a t i o n there i s a situation
contains
only one square.
Conversely,
the question i s whether t h e . s p l i t lemma can be
g e n e r a l i z e d to multisquare s i t u a t i o n s .
Spreading an
theorem.
arbitrarily
The answer i s yes.
Given any s i t u a t i o n with S squares and given
l a r g e number X, there i s a sequence of r o t a t i o n s
such that i n the f i n a l s i t u a t i o n t h e r e are s t i l l
S
squares
and
the d i s t a n c e between any two squares i s a t l e a s t X. Proof
(outline).
Pick a
pair
of
squares
with
minimum
axis
257 distance
and
take
the c e n t r e of one
of these as the c e n t r e of
rotation for a l l following rotations. in
t u r n u n t i l a l l the sguares
l i n e s through to
occur
rotation
moving any
closer
rotate
other squares,
squares,
as
would
so
that
the
other.
occur
diagonal
allowed
centre
the
any
lines
diagonal
of
In p a r t i c u l a r ,
in
up without
sguare
can always be
by p i c k i n g a
than any
of an o b j e c t , can be s p l i t
4 5°
No merges must be
An i n d i v i d u a l sguare
t o t h a t square
•compact' s e t s of depiction
l i e on e i t h e r of the two
the centre of r o t a t i o n .
in this jiggling.
moved without
F i r s t j i g g l e each
original
merges..
are
in
Now the
h o r i z o n t a l / v e r t i c a l p o s i t i o n , then c a r e f u l l y stagger back to the diagonal position.
45° r o t a t i o n
does
the
standard
position.
s u f f i c i e n t spreading has
occurred.
staggering
regains
The
The c o l l a p s i n g and
the
splitting, Repeat t h i s
spreading theorems are
t h a t Funt's o b j e c t r o t a t i o n scheme cannot work.„
enough
to
the until
show
258 REFERENCES
[ Amarel, 1 968 ] Amarel,S. On r e p r e s e n t a t i o n s of problems of r e a s o n i n g about a c t i o n s . , I n : D.Michie (ed.), Machine Intelligence 3, Edinburgh U n i v e r s i t y Press, 1968. t Anderson, 1978 i] Anderson,J.R. Arguments concerning representations f o r mental imagery. P s y c h o l o g i c a l review, 8 5(4), (July 1978), pp. 249-277. j. Arbib & L i e b l i c h , 1 9 7 7 3 Arbib,M.A. , and L i e b l i c h , I . Motivational learning of spatial behaviour. In: J.Metzler (ed.). Systems Neuroscience, Academic Press, New York, 1977, pp. 221-239. [Baker,1973] Baker, R i c h a r d . A spatially oriented information processor which simulates the motions of r i g i d o b j e c t s . A r t i f i c i a l I n t e l l i g e n c e , 4 (Spring 1973), pp.29-40. [Barrow & Tenenbaum, 1 978 ] Barrow,H.G., and Tenenbaum,J.M. Recovering i n t r i n s i c scene c h a r a c t e r i s t i c s from images.. I n : Hanson,A.R, and Riseman, E. M. , (eds.). Computer V i s i o n Systems. Academic Press, New York, 1 978, pp. 3-26. , I B a r t l e t t , 19 32.] Bartlett,F.C. 1932.
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