a study of turning gait control for quadruped walking vehicle

7/25/2019 A Study of Turning Gait Control for Quadruped Walking Vehicle

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IEEE/RSJ

i nternati ona Workshop on I nte ligent

Robots

and

System

lROS '91.

Nov.

3 4 . 1 99 1.

Osaka, apan .

IEEE

Cat. No.

91TH0375-6

A STUDY

O F T U R N I N G

G A I T

CONTROL

FOR QU DRUPED W L K I N G VEHICLE

Ma

L i e

M a

Pe i sun

R e s e a r c h I n n t i t u t e of Robotics

Shanghai J iao Tong Universi ty

Shanghai 200030 P.R.

hina

ABSTRACT

Thi s paper st udi es the real i zati on of

t urni ng gai t cont ro1,t aki ng a quadr uped wal k-

i ng vehi cl e as the subj ect of t he research.

Based on t he anal yses of previ ous works. a

ki nd of turni ng gai t w th the center of

gravi t y of t he vehi cl e wal ki ng al ong muti pl e

broken l i nes has been pl anned, whi ch

I s

mor e

sui t abl e for practi cal contr ol than previ ous

methods. The process of the t urni ng gai t and

i ts feasi bi l i ty are di scussed in detail . The

t urni ng gai t present ed i n the paper i s now

bei ng i mpl ement ed i n t he new y- devel op

omni di r ect i onal quadruped wal ki ng robot

J TUWH- 11.

I NTRODUCTI ON

Pl anni ng and cont rol i ng the gai t of the

wal ki ng vehi cl e and devel opi ng i ts wal ki ng

abi l i t y i s a very i mportant proJ ect in the

devel opment

of

t he wal ki ng vehi cl e.

As

to

t he quadr uped wal ki ng robot w th twel ve

degrees of f r eedom

DOFs),

the st udy of t he

gai t i s more i mportant. To expl oi t f ul l y the

potenti al capabi l i ty of moti on f l exibi l i ty

f or t he quadruped wal ki ng robot 9 we have

st udi es i n sequence t he gai t s of st r ai ght

wal ki ng on t he even ground. st ri di ng over

gul l i esC11 and obst aol esC21 cl i mbi ng over

sl opesC31 and cl i mbi ng on stai rs[ 41 etc.

and have di scussed a more general i zed gai t

cal l ed ' crab wal ki ng' i n whi ch the di r eoti on

of

moti on takes a randomangl e w th t he torso

di recti on

of

t he wal ki ng vehicl e. Heanwhi l e,

i rr egul ar gai t s whi ch coul d adapt to rough

t errai ns aut omati cal l y have al so been pai d

att enti on toC51. Apart f r omt he above st udy

of t he gait ss

i t

i s necessary to st udy a

more general i zed gai t i n order to ut i l i ze

t he hi gh adapt abl e mobi l i ty of t he vehi cl e.

Thi s study i s one of t hese ef f ort s t owards

thi s di recti on.

Tur ni ng gai t i s a more gener al i zed gai t .

Whi l e the ci rcl i ng centr e is l ocated at the

i nf i ni te di stance, i t i s equi val ent t o ' crab

wal ki ng' ; whi l e t he ci rcl i ng cent r e i s

l ocat-

ed at t he i nf i ni te di stance al ong axi s x and

axi s y then

i t

is equi val ent t o f orward.

backward and l ateral wal ki ngs; whi l e t he

ci rcl i ng centr e i s l ocated at the cent re of

t he vehi cl e, then t he vehi cl e rot ates al ong

i tself . Li ke t he contr ol of any other gai tst

t urni ng gai t cont rol not onl y needs coor di n-

at i ve movement of f our l egs, but al so needs

the consi derat i on of posture stabi l i ty and

gait f easi bi l i ty, and al so shoul d t ake speed

and evenness of the gai t i nto account .

So

the

cont rol of t urni ng gai t i s more compl i cated.

Based on t he di scussi on of turni ng gai t

pl anni ng and cont rol

1

i ng, t hi s paper st udi es

t he practi cal approach

t o

real i ze turning

wal ki ng of t he quadr uped wal ki ng vehi cl e,

t aki ng r ecentl y- devel oped

JTUWH-I1 model

as

t he subj ect of experi ments.

PREVI OUS WORKS

Some previ ous works have devoted to t he

st udy of t urni ng gai t . H roseCB], who had

devel oped

TI TAN

I 1 1

quadruped wal ki ng vehi cl e

model,

present ed a ci rcul ar gai t ar ound an

arbi t rari l y l ocated turni ng center and di s-

cussed a st andard ci rcul ar gai t. The st andar d

ci rcul ar gai t i s the one whi ch maxi mzes t he

speed of wal ki ng and t he rot ati onal angl e i n

a ci rcul ar wal k. On the basi s

of

gai t pl ann-

i ng and anal yzi ng, a ci rcul ar wal ki ng experi -

ment had been car r i ed out on a

TITAN

111

model

H X Sun(1989)[ 77 al so had done

some

i nves-

t i gat i ons on turni ng wal ki ng. The approach

f or t urni ng gai t pl anni ng present ed by t he

author was di f f erent f romt hat of H rose. The

pl anni ng method adopt ed by Hi r ose is to pl an

f i rst gai ts

o

each l eg w thi n each ki nemati c

range of t he coor di nat e syst emof t he vehi cl e

,i .e.

for

each l eg to r otat e a cert ai n angl e

around the arbi tr ari l y l ocated turni ng centr e

then to i nspect the st abi l i ty of t he

vehi cl e dur i ng t he process of wal ki ng usi ng

t hi s ki nd of gai t . The method proposed by Sun

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was first to give static stable gaits when

the vehicle is walking at the low spee then

to determine whether there is any moment that

each

leg

walks out of its kinematic ranger

if

there is none. then the gait is feasible.

The above approsohas mainly daal with

continuous turning around fixed centre along

a circle. The location of each l eg is vary-

ing with time (i.e. each leg should

be

driven

with variable motion). So

it

is difficult

to achieve in the real implementation.

With

reference to

C7L

C81, and

CBI,

the.paper

presents a turning gait with the centre

of

gravity moving along broken lines, and

Implements

it

In the J?UWM-I1 model

oonstruoted by the author.

PLANNING OF TURNING GAIT WITH COG MOVING

ALONG BROKEN LINES

To

enable the vehicle walking continuously

along the turnlng

W U S P

the planned galt In

every period

of

walking should correspond to

turning walking style, i.e. walking forward

while turniag the body, and the end status

of each gait period should ensure the walking

of next gait period.

Taking planary quadruped walking vehicle

model

shown in Fig.1 as the subject of

research, we study the way to realize turning

walking. I ~ I I ~ I I I , I Vn Fig.1 denote legs in

their rectangular kinematic ranges.

The posture

variation of the vehicle in a

gait period could be expressed by moving

distanoe of COG ClC2 and turning angle as

shown. in Fig.

2. To

provide the vehicle with

the

same

initial state during connecting gait

periods so as to ensure the same turning

ability, the position of each

leg

in the co-

ordinate system connected with the vehicle

should return back to the same relative

locations as

that

of the initial gait period.

T

facilite controlling. ne suppose the OG

of the vehicle moving along broken lines C1G

and CC2. And striding sequence has also been

selected as I)- III)- II)- IV~.

In order

to

ensure static stability

of

the

planned gait, the looation

of COG of

the

vehicle when the second striding leg touches

the ground is quite important.

As

long as

the

COG

point G is properly selected, the

planned gait could

be

sure to succeed.

As shown in Fig.3. following the selected

striding sequence,

C

should

be

over line

I 1

which passes F2 1) and F4(l) so as to keep

the vehicle stable when leg

111)

is raised;

and

C

should

be

under line 12 which passes

Fl 2)

and

F3 2) so

as to keep the vehicle

stable

when

leg(I1)

is raised.

To

ensure the

sa- static stability in different periods of

the gait* let the distanoes between C and

line 11, line

12

equals t o distance between

C1 and line

11.

Then the coordinate of

C

Y

Fig.1 Kinematic Range

of

the Quadruped

Rak ing Vehicle

Fig.2 Position and Posture for a Period

of the Turnlng Galt

1

Y

I

\ w

I

Fig.3 Locus of COG of the Vehicle along

Broken Lines



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( GxpGy) coul d be obt ai ned f rom gemotri cal

rel ati onshi p. Connect

G

w th C1 and C2, then

we coul d obtai n GI and G2 on l i ne CC whi ch

have di st ances

S

perpendi cul ar to l i ne

11 s

i s t he l east stabl e margi n) and G3. CA on

l i ne C20 whi ch have di st ances

s

perpendi cul ar

to l i ne 12. The broken l i ne f r omC to C1.

G2,

GI

G3, G4 and C2 gi ven above i s t he l ocus

of COG for t he turni ng gai t .

PROCESS OF

TURNI NG GAI T

AND I TS FEASIBI LI TY

ANALYSIS

To faci

1

i ate

contr ol

1

i ng of t he gai t , we

di vi de t he turni ng peri od i nto seven sub-

peri ods, del i m t ed by t i me tO to t7. Now

let's di scuss in detail .

tO

--

t l

:

I n t hi s sub- peri od, l eg

I )

stri des fr om

Fl 1)

to Fl(2) and COG

of

the

vehi cl e ffictves f roff i I t o G1.

To

ensure st ati c

stabi l i ty, G1 shoul d l ocate wt hi n tr i angl e

F2(1)F3(1)F4(1) and be at a di st ance or

more than

s

froml i ne

11.

As

t he vehi cl e

moves i n t r ansl ati on duri ng thi s sub- per i od,

s

as l ong

as

the posi ti ons of al l l egs at

i ni ti al t i me to and endi ng ti me tl are w thi n

thei r ki nemati c ranges, the posi t i ons of al l

l egs dur i ng t he whol e peri od w l l not

go

out

of thei r ki nemati c range. The coor di ant es of

four l egs rel ati ve to coor4i nat e systeff i

xl cl yl at t i me t l are:

where . T 1

=

cos

r

si n subscri pts xi

, yi i ndi cat e that parameters are rel ati ve

to coordi nate systemof t he vehi cl e xi ci yi ,

{x(ti )t Y ti)) is t he coor di nat e of

COG

rel ati ve to coordi nat e systemof the vehi cl e

at t i me t i - 1 .

I - s i nr cos 7 1

t l i t2:

The COG of t he vehi cl e moves t o

G2 passi ng

I 1

under the suppoet i ng

of

f our

l egs. G2 i s at a di st ance of s or mor e than

s

from

11.

Corr espondi ngl y, the coordi nat es

of f our l egs rel ati ve to the coordi nat e

systemat t hi s ti me are:

xi( t2) xr(t1) -(x(t2)

3 )

i

y (t2))

=

i y i

t l ?

l y(t2))

i = 1 ,

11

111, IY)

t2

>

t3: Leg 111) mves f romF3(1) to

F3(2) and the COG moves f r om

C2

to

C .

The

coor di nat es of four l egs at t i ne t3 are:

4 )

t3

?

t 4; I n thi s sub-peri od, l eg

I 1

i s

f i rst rai sed and then t he vehi cl e is turned

w th angl e around it s

COG

I f board ef f ect of

ci rcl i ng is negl ect ed, the coordi nat es of

f our l egs at t i me t4 are:

t4

>

t5: Leg(I 1) r eaches F2(2) and COG

moves fr om t o G3.

C

shoul d be l ocat ed

wt hi n t r i angl e F1(2)F3(2)F4(2) and be at a

dl st ance

of s

f rom

12.

The coordi nat es at

t i f f i e

5

are as f ol l ows:

t5 >

t 6 ;

COG moves f romC3 t o C4 pass-

i ng 12.

C

shoul d be l ocat ed w t hi n

t r i -

angul ar F1(2)F2(2)F3(2) and be at

a

di st ance

of

s

from

12

The corr espondi ng coor di nat es

of f our l egs are:

From the poi nt of vi ew of contr ol i ng,

di f f erent turni ng angl e and COG movi ng

di stance CI C2 ar e chosen to pl an t heir gai t s

and to deterffi i ne thei r f easi bi l i ty.

Al l

t he

f easi bl e parameter s are gat her ed to f orm

a

set. Thus, i n real cont r ol , we ooul d det er-

mne i f the gi ven i ni ti al turni ng par ameter s

are feasi bl e accordi ng to t hi s set.

1HPLEMENTATI

ON

OF TURN NG CAI T CONTROL

1

A

Bri ef I ntr oducti on to J TUWN- I 1

Quadr uped Wa

I

k ng Vehi cl e

The devel oped J TUWM I 1 omni di recti onal

quadruped wal ki ng vehi cl e

(as

shown in Fi g.4)

adopts the pantograph l eg mechani sm Each l eg

has t hree DOFs and i s dri ven i ndependent l y by

DC servo motor. The cont rol systemadopt s t wo

l evel s of cont rol , i . e. comput er contr ol and

anal ogue ci rcui t control . The parameter s of

al l DOFs are detect ed by potent i ometer9

t he



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Fig.( JTUM-11 Quaduped Walking Vehicle

foot bottom of eaoh l e g are mounted with

microswltches to deteot the ground status of

the swinging

leg so

as to detect the sur-

roundings. Posture sensor is mounted on the

body of the vehicle

so

as to detect the

inclining angle of the vehicle. The limiting

speed of the developed walking vehicle under

the static gait is

1.7

km/h (the walking

speed of single leg is 0 25 km/h) and could

realize omnidirectional walking.

2.

Cont ro

Implementation Approach to Turning Gait

In the real control of the gait1 the

turning angle and COG moving distance (or

turning centert locus

of

turing curve) are

first be given to the system. The walking

vehicle wi

1 1

connect using circular curve and

divide it into several broken lines. In each

broken line, the vehicle will walk according

to the above discussed turning gait with O

moving along broken lines, then the whole

turning process will move continuously along

multiple lines.

The controlling software, which is

programmed in the mixed

C

language and

8086

assembly language, consists of human-machine

interfaoe with menuss gait determination and

sequence cont ol. nformation processing three

parts. In the turning gait control, the

feasibility the gait should first be deter-

mined according to the

predefined

set: in the

walking process, the vehicle could judge the

road using the microswitch at the foot bottom

of the swinging leg. Fig.5 shows the ground

statuses which

JTUWN-I1

walking robot could

pass. Presently the turning process could

be realized on the even ground and the ground

with concave and convex.

CONCLUSION

It

has been shown from the

experiment of

JTUWN-I1 walking robot that the presented

turning gait and controling strategy is

feas bl e.

Turning gait control is currently under

study. We hope to improve the turing speed

and the turning angle of each period while

the walking stabi ity is ensured at the same

time. Besides,

CM

variation caused by the

moving of the

leg

and the swinging phenomenon

in the process'of walking should be overcome

in the real implementation,

REFERENCES

1. P.S.Na. H.Yu, Gait Analysis during Gully

Striding for a Quadruped Walking Robot.

2. J.S.Chen. P.S.Ma, JTUWH-If Quadruped

Walking Robot and its Controlling Software,

Software Development and Application,

Vo1 3

1891.

3. J .N . Pan,

J.S.

Chen, Research on

Slope

Climbing for a Quadruped Walking Robot, Proc.

of 3rd. National Youth Conf. on Robots.

p.262

4.

Q.

Wang, Stabi ity Analysis and Control

of Stair Climbing Gait for a Quadruped Walk-

ing Robot, Proc. of 3rd National Youth Conf.

on Robots, p.537, 1988.

5.

Q.W. He, P.S. Ha,

A

Study of Realtime

Adaptive Gait to Rough Terrains, Proc. of

3rd. National Youth Conf. on Robots, p.224,

1889.

6. S.Hirosel H.Kikuchi and Y. Umetani, The

Standard Circular Gait

of

a Quadruped Walking

Vehicle, Advanced Robots, Vol.

1,

No.2,

7. H X Shunt Research on the Quadruped

Walking Robot. Ph.D dissertation,

1888.

8. J .C . Du, Simulation Research on

Transition Gaits of the Quadruped Walklng

Robot, Shanghai Jiao Tong University, Naster

dissertation, 1881.2.

Robot,

b . 5 ,

1880, pp.30-34.

,

889.

pp. 143-164s1886.


a study of turning gait control for quadruped walking vehicle

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