Development of a Coaching System Considering User Specific

Trans.

of the Society of Instrument and Control Engineers Vol.35, No.5, 638/644 (1999)

[

Development

計 測 自動 制 御 学 会 論 文 集

[Vol.35,No.5,638/644 (1999) ]

]

of

a

Coaching

System

Considering

User

Specific

Characteristics•õ

Darrell

The

kip

is a fundamental

competition. length

We

pattern center-of-mass

kip

motion results,

the

shows

of

propose how

for

the

modeling the

gymnast

a coaching

system

evaluates

3-link

the

dynamics

model.

a variety

gives

attempt

an

3-link

the

expert

using

A

basic information

and

of

kip

patterns

based

on

of

the

3-link

the

coaching

learns

without center

performing

detailed

of

generate

comparision

and

levels

a variable

can

evaluate

of

all

that

center-of-mass

model

then

at

shown

gymnast's

We

model.

this

have

pendulum

characteristics novice

apparatuses

simulations

of success.

of the

MIYAZAKI*

of gymnastic

Our

of

significant

which

Fumio

optimized

region

verifies

and

model.

The

target

each

on

and

movements

expert

novice

3-link

a midpoint

characteristic

JOO*

performed

a pendulum

of

yield

the

Sangwan

movement

with

sufficient

which

that

we

kip

parameters

and

with

example

is

complex

variations

the

these

the

model

the

NAKAWAKI*,

gymnastic

analyze

pendulum

considering mass

E.

modeled

kip.

Based

on

information.

how

to

An

perform

the

kip

successfully. Key

Words:

kip,

coaching

1.

The

kip

nastics

is

a

Research in

a

tuated

wrist

attention

horizontal

hip

bar

to of

changes

of

studies

into

the

of

and

of

mass

novice's

using

as

little

the

body's to

be

reason

effects

as

while

of to

mass.

Joint the

nasts.

in

the

the

the

hands

timing

is

and

† ISER'97で Dept

. of

Engineering 1-3

一 部 発 表(1997 Systems

consid-

a

Science,

Osaka

Machikaneyama-cho,

Graduate

University

Toyonaka,

School

of

(Revised

December December

19, 16,

as

to

mechanical

into

link

measurement

type

of

if

analyze

the

this

3-link

the

in

gym-

3-link

model)

characteristics

analysis

to

kip

the

achieve

of

improve

performed

horizontal

on

and kip

the

link

pen-

body's

cen-

with

zero

and

We by

the

variable

can

using realize

optimizing

expert's

trajec-

results.

generates center

hips.

of

the

bar

trajectory

conditions

a

variable

being and

similar

kip's

The

from

of

were

mass

kip

position

shoulders

of

model

the

model. the

hands

based

the

and

realizing

model

center

3-link using

divided

and

on

the

trajectory

ment

be

performance.

to

movement

and

a

can

of

an

approximate

mass

pattern

kip

move-

obtained

from

Osaka the

(Received

mass

The

via motion

to

and

able

gymnast's

tory Science,

used

lead

between

only

skill.

.6)

and Human

a gymnast

(pendulum

gymnast's

is of

via

based

pendulum

torque

kip

performances;

results

dulum ter

be

guideline

length kip

energy also

can

novice

expert

the

realized

approach

expert's

These

the

potential

by

propose:

which

•Ea

to

analysis

bimodel

the

a swinging

kip

kip

We •Ea

and

performs

between

mastering

robot.

mainly

difference

performed

related

the

and

These

on

gymnast

using

types:

failure.

gravity

research

system

posture

concentrate

of

possible

efficiently

planar

performances

and

main The

po-

studied6)•`8).

success

the

based

Recent two

3-link

kip

research

the

the

the

*

kip

The

the

above

characteristic

been

for

being

a

Fig.

of

control

pattern

novice

above

using

key

1

per-

a focus

Acrobot

with

have

center the

pendulum

1).

position.

the

and

torque

bar

the

kip

performance.

horizontal

ered

the

the

as

length

underac-

been

methods

bring

science,

patterns

of

skill

center

of

realize

give

results

variable

gym-

been an

has

a sinusoidal

expert

to

The on

kip

has

robot

a handstand

sports

compared

attempted

to

proposed

the field

redundancy,

(Fig.

Acrobot,

Various

joint

up

control

In

The 2-link

in

competition

movements

planar

Takashima4)5) sition

of

of fields.

robotics1)•`3).

the

movement

levels

gymnastic

joint

in

all

number

in

torque

fundamental

at

covering

formed

kinematic

Introduction

important

performed

information,

variable

length

pendulum

model.

This

model

is

used

1997) 1998)

to

verify

the

TR 0005/99/3505-0638 (c)1997 SICE

characteristics

of

the

kip.

We

present

a

計 測 自動 制 御 学 会論 文 集

method of performance improvement which matches the novice's body characteristics based on the analysis of the center-of-mass and the detailed 3-link movement. Section 2 presents the analytical result of the variable length pendulum realizing the center of mass trajectory as the gymnast performs the kip. Section 3 describes the details of the 3-link model where the results of the pendulum model are input to observe the characteristic movement of the kip. Section 4 explains the coaching system which creates coaching information based on the two models. Analysis of the results from the two models determines this information. The novice uses this information to im-

第35巻

第5号

/=-l12fl+gsin0+ We

2.

define

Model for The Kip

state

Toda11) had studied the variable length pendulum as an example of the nonlinear application of vibration theory. The example shows that swinging the pendulum while varying its length can raise its center of mass without using external torque at the fulcrum. The results of force and torque analysis on the horizontal bar suggest that little torque is applied to the horizontal bar as the gymnast

ml

the

state

and ƒÁ=1/l.

A Pendulum

We

rewrite

U where

u=ƒÁ=-ƒÁ2i.

end

point

point

forward t2

is the

If

we

angle, of

think

of

l is the

gravity, the

kip

length,

and in

c

terms

m

is

the

is

the

viscosity

of

the

variable

mass,

equations

time)

to

using

function,

is

(midpoint

this

3.

and the

from

to

use

from

backward

the

t1

swing

following

crite-

CT:

CT1=2u2dt

(5)

Optimizing

the

criterion the

pendulum

function

change

in

tryagin's

dynamics

results the

in

a

trajectory

pendulum's

maximum

considering which

length.

principle,

the

the

By

above

minimizes

applying

Hamiltonian

Ponbecomes:

H=-1u2+fT/ as

a

(6) is

two-point

g is the

an

adjoint

boundary

vector.

value

We

rewrite

Eq.

mass

we

can

upward

horizontal mizes

imagine from

bar. the

the We

required

the

gymnast

(1=aH=f(Q,u)a~

(7)

coefficient. length

starting

point

consider muscle

pulling

a

kip

burden

to

his

a point

pattern acting

aHafT

'ip-

pen-

center above

which on

(1)

problem:

a~ dulum,

to

determine

optimized the

We

mid define

optimized

then

determine

Fig.

to

time)

and

to in

starting,

trajectory

trajectory t1

time)

shown

the

kip

trajectory

point as

choose

The

2 where ƒÕ •¸ R3•~1

acceleration

above

gymnast's

swing

(end

rion

the

conditions.

(starting

to

We

along

boundary

gymnast's center of mass as the kip is performed. We use this model to represent the gymnast's center of mass as he performs the kip. 2.1 A Kip Trajectory Based Variable Length Pendulum Model We modeled the overall motion of the kip's center of mass as a pendulum with a varying length to simulate the characteristics of the kip trajectory (Fig. 2). The following equation is used to represent the dynamics of a variable length pendulum.

where Į

the

where ƒ¿=ƒÆ,

I'3

trajectory

lmll

vector ƒ¶=(ƒ¿, ƒÀ, ƒÁ)T,

0=2/3gysincx-/3c72/mJ=f(Q,u) (4)

performs the kip7). According to this result, we find that a variable length pendulum is sufficient to represent the

(1)

(3)

vector.

the

9+2l+c2B+gsin8=o

639

Fig. 2 A simplevariable lengthpendulum following a kiptrajectory

prove performance. An example shows how the novice learns how to perform the kip successfully with the proposed system.

1999年5月

the

of the mini-

center

We

can

Newton-like tween

(8)

easily

simulate

this

method10). the

two

points

set

The until

of

equations

trajectory

the

end

is

point

using

optimized

a be-

boundary

condi-

of tions

(at

t1

for

the

forward

swing

or

t2

for

the

backward

mass. swing)

We

rewrite

the

pendulum

dynamic

equation

(Eq.

are

Fig.

as

a set

of

state

3

shows

within a

plot

of

a given

convergence

expert

gymnast's

the

limit. kip

trajec-

equations: tory

ƒÆ =ƒÀ

satisfied

(1))

(2)

see

and that

the

optimized

the

gymnast's

center center

of

mass of

mass

trajectory. trajectory

We

can

shows

640

T. SICE

Vol.35 No.5

May

1999

Fig.

Fig. 3

Optimized trajectory and swing timing

indicating

boundary

5

Forward

and

backward

swing

timing

range

conditions

(a) Midpointtarget region for the expert

Fig. 4

similarity

with

we can

realize

ing

on

the

and

backward

optimal

kip

the

Midpoint target region

minimized

a variety

position swing pattern

kip

pattern.

of optimal

of the times. depends

kip

midpoint, However, on

the

Furthermore,

patterns

depend-

and

forward

swing

the

existence

of an

choice

of these

pa-

(b) Suggested midpoint target region for the novice Fig.

6

Midpoint

target

regions

for

the

expert

and

novice

rameters.

2.2

Characteristics of Kip Movement (1): Change in swing direction We change the midpoint position, and swing timing to determine a variety of optimal kip patterns. Fig. 4 represents the midpoint target region where expert-like trajectories exist between a given starting and end point. We think of this as a target region where the backward swing should begin. Fig. 4 shows the region which takes on an oblong shape in the y-direction. This region represents an area 40cm in height where the probability of performing the kip is high. Fig. 5 shows the permissible timing region of the forward and backward swing. The permissible timing range represents the point P of the target region and this timing range tends to shrink as you move the midpoint away from the point P. These results show that timing is more important than strength for the kip and timing is clearly the key to mas-

tering the skill. Fig. 6 (a) and (b) show the expert and novice's center of mass trajectory for their kip performance. For each figure, we use the variable length pendulum, consider the initial conditions for each example and determine a corresponding midpoint target region. The expert changes the direction of swing inside the midpoint target region as shown in Fig. 6(a), while the novice passes through the midpoint target region continuing the forward swing to a high midpoint (Fig. 6(b)). The body falls downward during backward swing resulting in failure (b). In other words, the shift in swing direction in the midpoint target region is strongly related to the successful completion of the kip. 3.

A 3-link System

for A Kip Movement

We consider the problem of determining the joint movement to realize the kip based on the optimized center of

計測 自動 制御 学 会 論 文集

第35巻

第5号

1999年5月

641

Table 1

Joint angle limits

T(X,Y,t)=U(X,t)+V(X)Y where ten

T(X with

, Y,

(11)

t) •¸

respect

R3•~1

to

is the

state

joint

vector

X

torque

vector

writ-

and

U(X,t)=AJ#cm(ƒÁcm(t)-JcmƒÆ)+B+C

(12)

V(X)=A(E-J#/cmJcm) 3.2

Input

We

define

of joint

Fig.

mass

trajectories

tion

is

2).

the

We

gymnast

which

We

for

the

show

use

human-like

model

tem

in

we

unlimited

of

determining

can

freely

the

sim-

7)

of kip

the

kip

wrist),

of the

Y,

Ya,

3-link

which

and

model

to

reduces

provides only

the

torque

a means

human-like

to

limit

movements,

to

torque.

Considering

the

difficult to

Sys-

results

that

the

the

with

novice to

of an

torque

compared

ever,

patterns

(14)

analytical show

when

pat-

movement

joint

The

model

choose

joint

Redundancy

to

3-link

the

reduces

vector,

Y=Ya+Yb

sec-

7)

The

number

limits

and

previous

(Fig.

kip.

an

which

the

model the

allows

Kinematic

as

the

We

age

value

T1=Tave

and

write

the

the

kip

the

torque

of

Reid

3.

any

1 is set

as

it

torque

to an

Kopp's

Ya,

How-

would find

and

vector,

lower

and

applying

of joint

on

2

gymnast

without

input

performance

considerably

joints

expert

based

torque

1 is

those as

set

gymnast's

joint

well

perform

wrist.

expert

of

aver-

results7)

follows:

Dynamics

dynamics

represented Ą

3-link

(the

input

Yb.

shown

when

movements

3.1

a

a method

3-link

The

as

redundant

torques

terns.

manipulator

performing

kinematically

joint

3-link

obtained

(Section

ulate

7

Vector an

1

motion

(13)

of by

3-link

the

robot

manipulators

following

is

generally

T Ya=Yl00(15)

equation:

=A(Į)Į+B(Į,Į)+C(Į)

(9) Y1=V 11(X)(rave-U1(X,t))

where

A(ƒÆ) •¸

R3•~3

is

an

inertia

matrix,

B •¸

R3•~1

where ƒÈ a torque

vector

C •¸

R3•~1

joint

torque

caused

is

by

centrifugal

a gravitational vector,

and

torque

and ƒÆ •¸

Coriolis

is the

R3•~1

joint

the

3-link

dynamics

is

described

by

equation,

the

kinematic

angle

is

taken

represented

as

the

3-link

torque

of mass,

Jcm •¸

respect

to

doinverse,

system's

E •¸

R3•~3

redundancy

can

U1,

Eq.

V11, (11)

and

Y1

which

is

equation

with

respect

to

joint

1.

gymnast's

joint

movement

is

limited

to

the

body's

muscle

structure

and

tendon

arrangement.

We

set

be

the

(10) position

is the

an

of the

Jacobian

center is

of

on

the

joint

movement

as

shown

in

Table

1 and

follows:

is the

R2•~3,

the

T1, line

a second-order

set

R2•~1

the first

vector.

8=Jrn(r'cm(t)-Jcme)+(E-JtmJcm)Y where ƒÁcm(t) •¸

coefficient.

from

a

limits13) explicitly

adjustment

terms

joint, differential

an

are

The When

is

forces,

vector, ƒÑ •¸

R3•~1

(16)

is

of

matrix mass,

identity

system's

matrix,

is

and

vector,

its Y •¸

Yb,

as

follows:

Yb=r~ap

(17)

ae

center

written

J#/cm

input

with

1382a22

pseu-

3a2~timax pa=1a timax+",min

R3•~1 ai=2

is

an

tor,

input we

can

vector.

are

able

By to

realize

determine ƒÁcm(t)

jectory.

By

we

rewrite Ą

the

following

a

respect

equation12):

a

an

appropriate

human-like

from

introducing with

selecting

the vector to

the

kip

optimized

input movement.

We

pendulum

X=(ĮT, ĮT state

vector

vec-

to

is

3.3

tra-

)T •¸ X

where ā

an

adjustment

Piking

R6•~1, obtain

The Fig.

coefficient.

Characteristics

center 3)

is

input

of

Kip

Movement

(2):

movement of

mass to

the

trajectory 3-link

(like model

the which

one realizes

shown

in a

kip

642 Table

T. SICE 2

Starting 3-link

and

end

point

values

for

the

pendulum

Vol.35 No.5

May

1999

and

system

(a) An exampleofa successful kip(expert)

Table

3

Coefficients

used

in the

input

vector

(b) An example of an unsuccessful kip (novice)

Table

4

Parameters

of the

simulated

3-link

Fig.

system

9

Examples

of kip

success

and

failure

patterns

Fig. 10 A gymnasticcoachingsystem pattern (Fig. 8). Table 2 shows the initial and final conditions, the parameters of Table 3 shows the parameters of the input vector, and Table 4 shows the 3-link model parameters. Fig. 8 (a) and (b) represent a low and high midpoint trajectory within the midpoint target region of Fig. 4. The piking movement is considered an important move-

(a) A low midpointkiptrajectory

ment in performing the kip successfully8). The gymnast performs the pike by swinging his ankles near the horizontal bar when changing from the forward swing to the backward swing. Although there are different opinions about the timing of the piking movement, from Fig. 8, about 60-70% of this movement is completed by the end of the forward swing which shows similarity with Hay's result8). The 3-link movement respect to Fig. 6 (a) and (b) is shown in Fig. 9. If we focus on the hip movement during the forward swing, we can see from (1) to (3) of Fig. 9(a) that the expert extends his legs and then raises them quickly from (4) to (6). From (7), we can observe the legs being extended once again. The need to keep the center of mass low until the midpoint reaches the target region is shown in the hip motion from (1) through (6). We can verify this notion with the artificially created kip motion as shown in Fig. 8. 4.

(b) A high midpoint kiptrajectory

Fig. 8

A high midpoint center of mass trajectorybased kip

Improving the User's Performance with the Coaching System

We developed a coaching system (Fig. 10) based on the results of the observations in the previous sections. This coaching system generates information to improve and

計 測 自動 制 御 学 会 論 文集

第35巻

diagnosis the user's performance while considering the user's body characteristics14). After the user initializes this system, the user inputs body measurements. The corresponding body segmentation determines the pendulum and 3-link model parameters. Then, video image data of the user's kip attempt is input to the system, and the system transforms the video image data into the bimodel simulation determined from the pendulum and 3-link model. The pendulum (as represented by the first block) provides basic coaching information while the 3link model (as represented by the second block) provides detailed coaching information. Basic coaching information consists of:

第5号

1999年5月

643

(a) Initial attempt of the kip without coaching assistance.

(1) the midpoint target region; (2) optimal center of mass trajectory; and (3) swing timing information. The novice can then determine whether the swing switching point and timing are correct by viewing the information on a graphical display. Detailed coaching information consists of: (1) artificially generated movement correction based on the center of mass trajectory; and (2) the corresponding energies and joint torque. The novice makes motion corrections using the above coaching information with each attempt of the kip. An example of this coaching process demonstrates the effectiveness of this system as it shows the novice how to perform the kip successfully (Fig. 11). In Fig. 11(a), we can see the novice's initial attempt. The novice's center of mass passes through the midpoint target region and changes swing direction at a high point which results in failure. The coaching system gives the user a better understanding of the cause of failure and the necessary adjustments of the piking movement. Timing of the piking movement is important in varying the height of the midpoint, yet in this case, the user's attempt still results in failure (Fig. 11(b)). Based on the analysis of the forward swing, a thrust of the chest as the body passes below the bar showsimprovement in forward swing motion (Fig. 11(c)). The user nears the finish at a point near the top of the horizontal bar and performs a kiplike movement. Although the user can bring the body's center of mass closer to the horizontal bar, the user is unable to finish the kip completely. Readjustment of the grip as the body swings upward allows the gymnast to overcome friction between the palms and the bar. This motion correction brings the body into the front support position over the horizontal bar (Fig. 11(d)). The above improvement process of the coaching system required 8

(b) The novice forms the piking movement by raising the legs and improving shoulder timing.

(c) The novice starts the forward swing with the hips raised and arches the chest as the body passes below the bar. Timing of the piking movement is further improved.

(d) The novice readjusts the grip over the bar near the end of the backward swing completing the kip successfully. Fig. 11

An example of a coaching process for coaching the novice in performing the kip successfully. Notice the midpoint as it drops into the target region as the novice improves performance.

644

T. SICE

Vol.35 No.5

days (approximately 1 hour per day). 5.

Conclusion

We proposed a coaching system which makes use of a variable length pendulum and 3-link model. This system inputs video images of the novice's kip attempt and transforms them into parameters for the pendulum and 3-link model. The corresponding simulation results yield basic and detailed coachinginformation. The novice used the system to improve performance and successfully completed the kip within four steps. We are currently developing a 3-link robot to study the subtle body motions of the kip when subject to external friction. The results will verify the characteristics of performing the kip as well as suggest additional coaching information for the novice. Although our approach enabled us to explain the skill required to realize the kip, it may be necessary to consider a muscle model which includes the characteristics of the body in order to refine our coaching information. Ex-

May

1999

9) S. Matsui: Kinesiology of a Gymnastic Movement, Department of Physical Education, 16-11, 631/636 (1966) (in Japanese) 10) Y. Uno, M. Kawato and R. Suzuki: Formation and Control of Optimal Trajectory in Human Multijoint Arm Movement, Biological Cybernetics, 61, 89/101 (1989) 11) M. Toda: Vibration Theory. New Physics Series, Baifukan, Tokyo, Japan (1968) (in Japanese) 12) Y. Nakamura: Advanced Robotics-Redundancy and Optimization. Addison-Wesley Publishing Company, Inc. (1995) 13) A. Liegeois: Automatic Supervisory Control of the Configuration and Behavior of Multibody Mechanisms, IEEE Transactions on Systems, Man and Cybernetics, SMC-712 (1977) 14) C.E. Clauser, J.T. McConvilleand J.W. Young: Weight, Volume and Center of Mass of Segments of the Human Body, AMRL-Technical Report 69-70, Wright-Patterson Air Force Base, OH. (1969)

Darrell

NAKAWAKI He received

M.S. in Electrical

and the Ph.D. from Osaka University From 1988 to 1993, he had worked

periments with EMG (electromyography) will determine the strength limits for wrist, shoulder and hip joints and a corresponding set of kip patterns reflecting these limits. References 1) M.W. Spong: The Swing Up Control Problem for the Acrobot, IEEE ControlSystems,49/55 (1995) 2) G. Boone:Minimum-timeControlof the Acrobot, in Proceedingsof the 1997International Conferenceon Robotics and Automation,4, 3281/3287,Albuquerque,New Mexico, April (1997) 3) M. Smith, M.A. Lee, M. Ulieru and W. Gruver: Design Limitationsof PD versus Fuzzy Controllersfor the Acrobot, in Proceedingsof the 1997 IEEE International Conferenceon Robotics and Automation, 2, 1130/1135, Albuquerque,NewMexico,April (1997) 4) S. Takashima:Controlof Gymnaston a HighBar, in Proceedingsof the 1991 International Conferenceon Intelligent Roboticsand Systems,3, 1424/1429,Ibaraki, Japan (1991) 5) S. Takashima:DynamicModelingof a Gymnaston a High Bar, in Proceedingsof the 1990 International Conference on Intelligent Roboticsand Systems,2, 955/962, Osaka, Japan (1990) 6) T. Komatsu,Y.Sakuma,T. Tsuji and K. Abe: A Relationship between Posture Changesand the Twisting Moment Exertedon the horizontalBar duringthe Kip, OsakaPhysical Education Research,30, 20/27, (1991)(in Japanese) 7) J.G. Reid and P.M. Kopp: A Force-TorqueAnalysisof the Kip on the HorizontalBar, Canadian Journal of Applied Sports Sciences,8-4, 271/274(1983) 8) J.G. Hay: The Biomechanicsof Sports Techniques.EnglewoodCliffs,NJ: Prentice-HallInc., 311/312 (1978)

the B.S.,

En-

gineering from California Polytechnic University, Pomona in 1988 and 1991, respectively,

well International,

Pacific

in 1999. at Rock-

Scientific,

and Accu-

logic assisting in the development of fiberoptic communications, fire detection and computer

Sangwan

equipment.

His current

trol systems, fer methods.

learning

interests

systems,

are in con-

and skill trans-

JOO He is presently

a Research

Associate

at Os-

aka University, he received his Bachelor's at Chungnam National University in Korea, and his M.E.

Fumio

and Ph.D.

at Osaka University

in 1993

and 1998 respectively. His current research terests include Human-Machine-Interface,

inau-

tomatic assembly system and its design, 3-dimensional measurement.

and

MIYAZAKI

(Member)

He received in Mechanical 1982,

the B.E., M.E. and Ph.D. degrees Engineering in 1975, 1977 and

respectively,

all from

Osaka

University.

He is a professor in the Faculty of Engineering Science, Osaka University and is a visiting professor in the Institute of Space and Astronautical Science. He worked with the Center for Robotic Systems in Microelectronics at the University of California, Santa Barbara from 1987 to 1988 as a visiting associate professor. His current

research

and adaptive control, space robotics.

interests

include

vision-based

learning

control,

and