Cellular robotic system (CEBOT) - CiteSeerX

Cellular Robotic System(CEB0T) as One of the Realization of Self-organizing Intelligent Universal Manipulator Toshio FUKUDA' and Yoshio KAWAUCHI" Nagoya University Department of Mechanical Engineering Furo-cho, Chikusa-ku, Nagoya 464-01, JAPAN.

**

Science University of Tokyo Department of Mechanical Engineering 1-3 Kagura-zaka, Shinjuku-ku, Tokyo 162, JAPAN.

developments: A fundamental demand t o c e l l construction is t o enable easy connection and separation, t o assure a holding force when connected and make data communication between c e l l s possible. Figure l(a) shows C E B O T ( s e r i e s 2) i n undocked state. These c e l l s are able t o dock with each other automatically by using mobile cell. The automatic approaching, docking, and separating method has already been reported in reference1 and 2. Figure l(b) shows CEBOT(series 4) in undocked state and manipulator composed of cells is shown in Fig. l(c). Each cell has one pair of hook mechanism at t h e front, passive mechanism at the rear. In addition t o t h e docking mechanism, one elementary function (such as rotating, bending, mobile) is provided in every cell. The optimal s t r u c t u r e method explained in t h i s p a p e r a r e a p p l i c a b l e t o b o t h t y p e o f CEBOT. The communication protocol and sensor which a r e described in c h a p t e r 7 a r e c o n c e r n e d with CEBOTberies 2). The CEBOT(series 4) has its own communication system, so the details of the system w i l l be reported in t h e near future.

ABS" The Cellular Robotic System(CEB0T) is a new k i n d o f r o b o t i c s y s t e m which is a b l e t o reconfigurate i t s e l f t o optimal s t r u c t u r e depending on purpose and environment. I t is a distributed robotic system consisting of separable autonomous units called "cell". In this paper, we propose an optimal s t r u c t u r e decision method which can determine c e l l type, arrangement, degree of freedom and link length. I t can be applicable f o r fixed base and mobile base type manipulators, so t h a t universal/modular manipulators can be made. S i m u l a t i o n r e s u l t s show t h e d i f f e r e n c e i n evaluation f o r different candidates and tasks and also demonstrates t h a t the s t r u c t u r e decision method works efficiently. With respect t o software s t r u c t u r e , optimal knowledge allocation is one of t h e most important issue of CEBOT. We propose a method of optimal knowledge allocation based on communication information amount. Communication among c e l l s a r e described f o r the control proposed in this paper.

D

1. INTRODUCI'ION

Nowadays the robot comes t o play an important p a r t in the industrial world. But most of them are fixed base type, so t h a t practicable tasks of them a r e limited. Then w e have studied t h e Cellular Robotic System (CEBOT) which can be applicable t o various tasks and environment[l,2]. CEBOT is one realization of autonomous decentralized cooperated c o n t r o l s y s t e m , a n d i t is a l s o d i s t r i b u t e d i n t e l l i g e n t system. CEBOT as s e l f -0r g a n i z i n g intelligent universal manipulator needs communication system among cells f o r controlling t h e s t r u c t u r e of the whole manipulator system. In order t o c a r r y out various tasks, CEBOT has t o change t o t a l form. The o p t i m a l h a r d w a r e s t r u c t u r i z a t i o n is d u e t o i t s g e o m e t r i c a l conditions mainly. But t h e optimal s o f t w a r e structurization should be done by using the other criterion. A s one of t h e c r i t e r i o n , t h e communication information amount is proposed. W e propose one of the optimal knowledge allocation method based on the estimation of communication information amount. 2. OVERVIEW OF CEBOT

In this chapter, t h e CEBOT components and systems a r e briefly overviewed t o the following

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3. BASE DETERMINATION OF MOBILE BASE TYPE FUNIPULAWR

If t h e base location has been decided by the following method, local candidates can be chosen by using t h e same algorithm as used f o r fixed base systems [2]. The straight line m is defined along t h e z-axis of t h e coordinate system in work point Pn of cell n given by d e s i r e d end e f f e c t o r position and orientation. The projection of m t o t h e x-y-plane of t h e base coordinate system is m'. Then w e define a cylinder by t h e line through Pn perpendicular t o t h e base x-y-plane with radius r (see Fig. 2). X-Xnp Y-Ynp Z-Z np m: - = - = (1) NP

OP

Fig. 2: Cylinder used f o r base coordinate calculation. 4. 0-

AP

We propose a 2-step algorithm which in t h e f i r s t step calculates structures satisfying t h e actual task and in the second s t e p selects t h e optimal s t r u c t u r e out of t h e common candidates which minimizes t h e evaluation function. The f i r s t s t e p consists of one s t e p s e l e c t i n g l o c a l candidates f o r each work point and then selecting common candidates. In case of mobile base type robots t h e coordinates and orientation of t h e base is calculated f i r s t (see chapter 3) and then t h e same s t r u c t u r e decision method as f o r fixed base type robots is used. To describe t h e task f o r the robot we divide t h e path into N work points. A t each work point t h e following properties are given: (1) Desired end-effector position and orientation. pn(Px,Py,Pz~Pa,Pb~Pc) (2) Required force and moment a t t h e end-effector. Fn~fx,fy,fz,mx,my,mz~ (3) Required positioning accuracy. En(dx,dy,dz.ex,ey,ez) (4) Manipulator base setting position and orientation: Qo(qx.qy'qz,qa,9b.qc) (5) End-ef f ect o r type. (6) Physical c o n s t r a i n t s i n t h e work s p a c e : S,(X,Y z) The candidate selection method f o r t h e fixed base type has been reported before [21. To simplify t h e problem t h e cells a r e considered t o be equal in size and only rotation, bending and sliding joints a r e available as joint cells. The method generates a list of candidates satisfying basic geometric c o n s t r a i n t s like link i n t e r f e r e n c e , m o v a b l e r a n g e of j o i n t s a n d combination impossibility [21. For each work point such a list of local candidates is created and then common candidates a r e selected. To find the optimal configuration f o r t h e given task, these common candidates a r e evaluated by t h e evaluation function described in the following chapter.

where Np, Op, Ap a r e vector projections in mdirection:

Evaluating equations (11, (2) and (3) g i v e s t h e base coordinates Qn as Qn

= (

Xnq

Ynq

9

Znq Pvnq

enq

nq

The point where m breaks through t h e surface of t h e in Eq. (3) defined cylinder is defined as R. The length of PnR is chosen as an integer multiply of t h e elementary cell size 1 and thereby t h e cylinder radius r can be calculated as:

-

r

=

I

r2

kl i z

PnR2

(5)

=

k

=

...

1,2,3,

(6)

With r and equation (4) t h e coordinates and orientation of t h e base Qn can be computed. If m is perpendicular t o t h e x-y-plane with N = O =O,Ap=l (7) P P equation (4) becomes

Qn

5. STRU-

OP

= ( Xnp

- kl, ynP, h, 0, 0, tan-' - 1

STRUCI'URE DECISION MEl'EOD

(4)'

EVALUATION FUNCTION

5.1 Structure Evaluation Function Definition

NP

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We define t h e s t r u c t u r e evaluation function as t h e sum of 4 parameters: N N S = (alpn + a2Hn) + a3 Ln + a4C (8) n=l n=l Pn: positioning inaccuracy a t work point n Hn: required end effector torque a t work point n Ln: movement of cell joints t o bring t h e end effector from work point n t o n+l C: cell cost parameter N: t o t a l number of work points al, a a3, a4: weight parameters, a d j u s t a b l e depengent on task.

or Cell

Fig. 3: CEBOT model f o r deflection calculation. Coordinate Transformation Considering Gravitation 5.2

Cell

Cell i

Cell i-1

Position accuracy Pn and required torque H parameters are calculated in section 5.3 and 5 . 8 In the following a preparatory calculation is described considering gravitational force in the cell coordinate transformations. To describe CEBOT which is composed by many connected c e l l s we define a separate coordinate system f o r a l l cell centers and connection surfaces. The coordinate system of c e l l 1 is equal t o t h e base coordinate system. With gravity and the method of homogenous coordin t e transformations [41 t h e transformation matrix Yk from c e l l k t o c e l l i is given as

I.

Fig. 4: Definition of A' matrix. Ai

B

iYk

=

Trans(Gil).Rot(oTk).iTil

Kil Fi

=

(12)

W e define t h e matrix A; which combines t h e three matrices Bi. Ci and Di (see Fig. 4) as:

(9)

A; = B i

where Gk: transformation matrix from geometric center of cell k . t o center of gravity of t h e same c e l l k, ITk: transformation matrix from center point of c e l l k t o c e l l i (T-matrix).

*

Ci

*

(13)

Di

where Bi: transformation matrix from center point of c e l l (i-1) t o connecting s u r f a c e , both have t h e same orientation, Ci: differential transformation matrix from connecting surface of cell (i-1) t o next c e l l i. Di: transformation matrix from connecting surface of c e l l i t o center point of t h e same cell.

5.3 Position Accuracy of Manipulator End Effector

5.3.1 Position Inaccuracies Caused by Gravity, Deflection and Torsion

The matrix Ci can be calculated using equation

CEBOT consists of many connected cells. We consider t h e e n t i r e manipulator a s a r i g i d structure, take in account t h e manipulator weight and payload and the compliance of the coupling mechanism. With d i f f e r e n t i a l d e f l e c t i o n and torsion a t the connecting mechanism we calculate t h e p o s i t i o n i n g e r r o r v e c t o r Ed f o r t h e m a n i p u l a t o r model shown i n Fig. 3. The differential transformation vector for cell i and the force/moment vector Fi a r e defined as:

(10) and with

sin

e

-->

ei , cos Qi 1

giz ci

-->

- 6iz 1

-

1 follows:

6iy

diz

6ix

diy

=

- 6iy

0

6ix 0

diz 0

1

I

W e now calculate equation (15) and (16). where

where d i j : d i f f e r e n t i a l t r a n s l a t i o n i n j direction. : differential rotation about j-axis. f i j : force in j-direction. : moment about j-axis. rewrite equation (10) and (11) into We

aij

m is the t o t a l number of cells. m = Kil 2 (IYkDil@ Fk) k=l

Ai

mkh

The operator

@ is

defined as follows:

v e c t o r n o t a t i o n using t h e r i g i d i t y matrix Ki (6 x 6):

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(15)

Since t h e position e r r o r can be positive and negative. The position inaccuracy parameter Pn is computed as t h e maximum of E, among a l l work points F = [ mx

my

mZ

fx

n ' 1 (f X P ) 0 ' 1 (f x P)

fy

f z lT

+ I } +

adjustable

where W(n):

weight matrix (6 x 6) f o r

work point n.

I}

5.4 Required Torque at Joint

€In is t h e required s t a t i c torque which is necessary t o handle a payload by the end effector of CEBOT. Tn is transformed t o scalar by summing t h e forces which are caused by t h e m a s s of t h e c e l l s and payload. Tn follows as:

hl...

can be calculated using equation (15). Deflection Ed of t h e manipulator end effector is calculated adding t h e d e f l e c t i o n s a t t h e connecting faces of each cell:

Hn becomes: Hn = T:

where Wn: point n.

Wn * Tn (23) weight matrix (6 x 6) t o Hn f o r work

summarized in vector notation:

5 . 5 C e l l Movement Parameter

The elements of E a r e calculated evaluating t h e l e f t side of equadon (16).

The movement parameter Ln is the sum of t h e rotating angle displacements of t h e joint cells and moving distance of t h e a mobile cells when movine: t h e end effector from work point n t o work point -(n+l). m'

5.3.2 Position Inaccuracies Caused by Joint and Mobile C e l l s

Ln =

k=l Where is t h e r o t a t i o n j o i n t a n g l e o n t c e l l k between work point n difference and (n+l)and b f i s t h e distance between work point n and (n+l).

Position inaccuracies caused by j o i n t and mobile cells a d d i t i o n a l l y d e f l e c t t h e e n d effector. The joint axis and z-axis of t h e cell center coordinate system are t h e same f o r c e l l i. Then t h e position accuracy vector of one c e l l is: el

=

[ pix, piy, piz, elx. ely, elz

1

OF

5.6 Cell Cost

(18)

There a r e many kinds of cells with different functions, hardware and software e f f o r t s and depends on cell type. We thereby cell cost defined t h e c e l l cost parameter as t h e sum of the individual cell costs. m ci (25) i=1

The p o s i t i o n i n g e r r o r o f e a c h c e l l is transformed t o t h e end effector coordinate system and t h e sum of all e r r o r s gives Ep as: m' Ep ("Ti 6 Xi1 @ ek 1 (19) k=l where m': t o t a l number of joint and mobile cells, j : c e l l number counting only joint and mobile c e l l s ( c e l 1 a t t h e b a s e coordinate system is no. 1). xk: transformation matrix from cell center point t o joint coordinate system of c e l l k.

=

c

c=c

6. SIMULATION RESU'L'I'S

We simulated t h e case of a task with two given work points (see Fig. 5). The method was verified supposing no obstacles in the work space and a smooth and plane floor on which t h e mobile cell can move everywhere in t h e x-y-plane. We choose two candidates of the fixed base type and two of t h e mobile base type which have t h e least and second least number of cells among all manipulator candidates satisfying t h e task (see Fig. 6). Table

The t o t a l position inaccuracy is given as t h e sum of Ep and Ed (20)

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Table 1: Structure evaluation function parameters f o r 4 selected common candidate structures.

1 shows values of t h e s t r u c t u r e evaluation function S and its parameters. In Table 1 it can be realized t h a t parameter values change independently. For example when comparing candidate 1 and candidate 3 in position accuracy a t work point 2. Position inaccuracy of t h e fixed base type is caused by its rather long arm and i t is therefore inaccurate in gravity direction, but candidate 3 has horizontal inaccuracy because of its moving mechanism. Figure 7 and 8 show the s t r u c t u r e evaluation function S when changing the weight matrix f o r position inaccuracy f o r one specific a x i s with w e i g h t s s e t t o 1 i n a l l o t h e r d i r e c t i o n s . I t can be c l e a r l y v e r i f i e d t h a t changing t h e weight matrices has influence on t h e d e c i d e d o p t i m a l s t r u c t u r e . The optimum is therefore task dependent and influenced by t h e weight matrices.

P: Positioning Accuracy, H: Holding Torque, L: Joint Displacement, C: Cost 7. COMMUNICATION SYSTEM AMONG CELLS.

7.1 Necessity of communication. In order t o be an autonomous, decentralized and coordinated system, it is n e c e s s a r y t o communicate between c e l l s when cells build up manipulator and c a r r y on given tasks. The reasons a r e shown as follows.

1j

~:eoro.o.o.o.o.o,

O:p, uss.o.m.o.f.0, (p:P2co.-lso.lso.x.o.ol

and

Before constructing manipulator(undocked state): (1) A moving master c e l l has t o know if cells with

t h e desired function a r e there. (2) The master cell has t o choose one t a r g e t c e l l

J -

from t h e suitable function cells. (3) The master has t o measure relative angle and

distance. (4) Coordinated control is realized by communica-

tion.

Fig. 5: Definition of work points 1 and 2.

I"

1-1 '.P

".P.

After constructing manipulator(docked state): (1) Control cell structure. (2) Transmit data t o other cells. (3) Self checking.

I .

I

r.p.

1

".P.

C4ndid.r.

1

2

2

".P.

".P.

1

2

Fig. 6: Common candidates f o r work point 1 and 2 (4 selected).

In order t o realize this system each cell has rotating communication sensor f o r undocked s t a t e and communication bus f o r docked s t a t e . The communication sensor f o r undocked s t a t e has one LED(infrared type) f o r t r a n s m i t t e r and o n e p h o t o d i o d e f o r r e c e i v e r . In d o c k e d s t a t e , communication i s d o n e by communication bus(C0MBUS). The COMBUS is c o n n e c t e d by 14 pin-connector which is located on f r o n t o r back face.

2

".P. Ca"d,.I.tc

7.2 Communication method.

I

w.p.

i

work point

7.3 Communication protocol.

Communication in docked s t a t e is done by s e r i a l 12 bits. These 12 bits a r e divided three p a r t of 4 b i t s ( H , M, L - D i g i t ) . Mean of information is transmitted on H-Digit. M-Digit means sender cell-address and L-Digit means receiver cell-address. Communication in undocked s t a t e is done by 8 parallel bits . Owing t o these control words, it is possible t o change actuator position and transmit data. 8 EXPERTMENTAL

RESULTS IN DOCKED STATE.

WU

Fig. 7: Changing t h e welght matrix along t h e x-axis.

Fig. 8: Changing t h e weight matrix along t h e y-axis.

The communication experiments a r e carried out b a s e d on t h e communication D r o t o c o l . The experiment of the communication -with COMBUS is

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m

n

done and the output of COMBUS is shown in Fig. 9. In e a c h s t e p number i n t h e F i g . 9, t h e communication can be executed as follows: 1 ; The cell-0 c a l l s t h e cell-3. 2 ; The cell-3 answers it. 3 ; The cell-0 requests t h e data value of PD1 t o t h e cell-3. 4 ; The cell-3 transmits t h e data value of PD1. 5 ; The cell-0 announces t h e end of communication with t h e cell-3. 6 ; The cell-3 responds t o it.

E b b

(aiEx) i=1

(xEbj)

+

(sec)

(29)

j=l

where n: T o t a l number of cells which t r a n s m i t information t o t h e cell-x. m: T o t a l number o f c e l l which r e c e i v e information from t h e cell-x. 9.3 Knowledge Allocation Method.

9. EVALUATION OF COMMUNICATION.

When a task is given t o t h e cellular robotic system, many cells c o n s t r u c t t h e u n i v e r s a l m a n i p u l a t o r a u t o m a t i c a l l y . The g e o m e t r i c conditions have been described in the chapter 3, 4, and 5. Based on this result, a control system of t h e manipulator must be considered. CEBOT is one of t h e distributed intelligence system. Each c e l l can carry out any tasks by using its own knowledge and a c c e s s i n g t h e o t h e r c e l l s ' knowledge. The accessing knowledge is realized by communication among c e l l s . The communication i n f o r m a t i o n amount of t h e s y s t e m c h a n g e s , according t o t h e knowledge a l l o c a t i o n i n t h e system,. In general, it can be considered t h a t t h e less communication information amount implies t h e b e t t e r knowledge allocation f o r t h e distributed intelligence system. Then t h e knowledge allocation in t h e CEBOT is done by considering t h e minimum communication information amount among cells which can be considered a knowledge unit.

9.1 Definition of communication amount between

10. CONCLUSION

Each c e l l can communicate with other cells. So it is necessary t o define an estimation method of t h e communication amount. Based on t h e information theory, if a phenomenon(E1 occurs with t h e whose p r o b a b i l i t y of P(E), t h e amount of information I(E) is defined as I(E)=log2(1/P(E)) (bit). (26) Then we apply this definition t o CEBOT. CEBOT has two channel capacities which a r e in case of t h e undocked s t a t e and the docked state. Taking into account these two states, we can define the amount of information of CEBOT as T(E)= log2(1/P(E))+dt (sec), (27) where d t denotes a time required t o send a bit.

This paper deals with the optimal s t r u c t u r e d e c i s i o n method f o r C E B O T as u n i v e r s a l manipulator. The method is able t o decide both type of manipulator structures, f o r fixed base as well as mobile base types. The efficiency of t h e method w a s shown by simulations. And communication system and experimental results of it are also described. We proposed one method of t h e optimal knowledge a l l o c a t i o n based on t h e d e f i n e d estimation of communication. On account of t h e optimal s t r u c t u r e decision method and this communication system, CEBOT can become one of t h e s e l f - o r g a n i z i n g u n i v e r s a l manipulator.

9.2 Evaluation of communication amount of c e l l

We g r e a t l y acknowledge Dr. Hajime Asama in Riken f o r his support and comments on this study.

Fig. 9: COMBUS timing diagram.

Evaluation function aEb which shows the amount of information from the cell-a t o the cell b is defined here as aEb=dtl* E1Og2(1/P(Ei))+ dt2* log2(l/P(Ej))(sec) where d t l : A unit time f o r transmitting one b i t in undocked state. dt2 : A unit time f o r transmitting one bit in docked state. P(Ei): Probability of E in undocked state. in docked state. P(Ej): Probability of A c e l l communicates with hany cells, so t h a t the c e l l whose address is x receives t h e o t a l amount and t h e of information which is denoted as c e l l transmits the information which is shown as XEbj. Then t h e amount of communication is defined as

REFERENCES 1. Fukuda, T.

a n d Nakagawa, S.: "Dynamic Reconfigurable Robotic System", Proc. IEEE Conf. on Robotics and Automation, Vol. 3, pp.1581-1586, 1988 2. Fukuda, T., Nakagawa, S., Kawauchi, Y.. and BUSS, M.:"Self Organizing Robots Based on C e l l Structures - CEBOT", Proc. IEEE Int'l Workshop on Intelligenct Robots and Systems(IROS'88), pp. 145-150, 1988. 3. Takano, "Development of Simulation System of Robot Motion and I t s Role in Task Planning and Design Systems", Proc. 3rd ISRR (1985), pp.223230. 4. Paul, R.P.: "Robot Manipulator: Mathematics, Programming and Control", 1981.

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