Exo Skelton s

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Development

o

ac tive anthropom orphicexoskeletons

M V u k o b r a t o v i c D H r i s t ic Z S t o j i l j k o v i c

n s t i t u t e

o r

Auto ma t ion & Telecommunicat ions , Mi lhai /o P upin ' , PO Box 906, Beograd, YugosIav ia

A bs t r a c t - - T he basic pos t u la t es o f t h is n ew app r oach t o t he s tudy o f an t h ropom or ph i c sy stem s

dynamics are given in the paper . In compar ison wi th other attempts, th is approach enables the

ma xima l redu ct ion o f d imensional ity , bein g based on prescr ib ing synergy, to o ne pa r t of the

system, As an i l lust rat ion of the me thod, an exam ple is g iven of a com plete synergy synthesis

fo r t he ad opted conf i gura ti on o f t he an thropom orph i c sys tems.

Ke yw ord s- - An thr om orp h i c sys tems, exoske le tons , rehab i l it a t ion , parap leg ia , exoske le ton , robo ts

ntroduc t ion

TH HUMAN SKE LE TON can be t r e a t ed a s a com plex

n o n l i n e a r m u l t i v a r i a b l e s y s te m . T o p r o v i d e c o m -

p l e t e s k e le t a l a c t i v i ty th e h u m a n h a s o v e r 6 0 0

m u s c l e s a v a i la b l e , w h i c h r e p r e s e n ts m o r e t h a n 3 0 0

e q u i v a l e n t a c t u a t o r s o f b i l a t e r a l a c t i o n t . I n t e r m s o f

t h e m e c h a n i c a l s c h e m e , t h e s y s t e m o f s k e l e t a l

a c t i v i t y h a s o v e r 3 0 0 d e g r e e s o f f r e e d o m a v a i l a b l e .

W h e n i t i s i n t e n d e d t o m a k e a n a r t if i c ia l m o d e l o f a

l o c o m o t i o n - m a n i p u l a t i v e tw o - l e g g e d m a c h i n e t h e

p r o b l e m a r i s e s a s t o h o w t o r e d u c e t h e h i g h d i m e n -

s i o n a l i t y a t t h e d y n a m i c a c t u a t o r l ev e l . S e v e r a l

a t t e m p t s h a v e b e e n m a d e t o r e d u c e th e d i m e n s i o n a l -

i t y o f t h e n a t u r a l l o c o m o t i o n - m a n i p u l a t i v e sy s t em

w h e n s y n t h e t i s i n g a s y s t e m u s i n g a r t i f ic i a l s k e l e t a l

ac t i v i t y .

T OMOVId an d BEL LMAN 1970) r e duc ed t he s ke l e t a l

a c t i v it y t o a v e r y li m i t e d n u m b e r o f m o v e m e n t s

u s i n g s t i m u l a t i o n o f t h e n a t u r a l l o c o m o t o r s y s t e m .

T h i s i s c o n s i d e r e d t o b e a m o d e s t p r o j e c t , s i n c e n o t

e n o u g h i s k n o w n a b o u t t h e c o - o r d i n a t i o n o f m o v e -

m e n t s d u r i n g a r ti f ic i a l l o c o m o t o r s t i m u l a t i o n

VoDoVNIK

e t a l .

1967; 1968).

t The ms/or part of the muscular system is organised in the form of

muscle pairs

I n a n o t h e r a p p r o a c h t h e d y n a m i c s o f l e g g ed

m o t i o n i s s t u d i e d ; i t i s t r e a t e d a s a r i g i d b o d y w i t h

s i x d e g r e e s o f f r e e d o m d e f i n e d b y e q u a t i o n s w i t h a

d i s c o n t i n u o u s r i g h t - h a n d s i d e , d e s c r i b i n g t h e c o n -

t i n u o u s m o t i o n o f t h e b o d y M c G H E E , 1 9 68 ; FR A N K

a n d M C G H E E , 1 96 9). D i s c o n t i n u i t y a p p e a r s o w i n g

j j l

Fig.

z M

J J J J J J J J

I Ze r o - m om en t po i n t z . m . p . )

Firstreceived 20th November 1972 andin fina lform 26th January

1973

Fig . 2 Jo in t d i s tr i bu ti on w i th b iped conf i gura t ion

t o t h e f a c t t h a t t h e f o r c e s a r e g e n e r a t e d a l t e r n a t e l y

w h e n t h e l o w e r e x t r e m i t y c o n t a c t s th e g r o u n d . T h e

p r o b l e m i s t h u s r e d u c e d t o t h e c a l c u l a t io n o f f o r c e s

a n d t o r q u e s g e n e r a t e d b y t h e e x t r e m i ti e s , f r o m w h i c h

s i x v e l o c i t i e s c a n b e c o m p u t e d ; t h e a n g l e s a n d

p o s i t i o n s w i t h r e s p e c t t o t h e s t a t i o n a r y s y s t e m a r e

t h e n o b t a i n e d b y m e a n s o f i n te g r a t i o n . T h i s

a p p r o a c h i n v o l v e s t h e u s e o f a m a t h e m a t i c a l m o d e l

i n t h e f o r m o f c l a s si c a l e q u a t i o n s o f m o t i o n o f a

r i g i d b o d y i n s p a c e u n d e r t h e i n f lu e n c e o f d r i v i n g

f o r c e s a n d t o r q u e s . T h e r e s u l t i s t h a t t h e s y s t e m i s

r e p r e s e n t e d b y s ix d e g r ee s o f f r e e d o m w h i c h d e t e r -

m i n e i t s d i m e n s i o n a l i t y , a n d t h u s i t i s n e c e s s a r y t o

66 Me dica l and Bio logical Engineering Janu ary 1974


2/14

d e t e r m i n e f o rc e s a n d t o r q u e s b y m e a n s o f a p p r o -

p r i a t e c o n t r o l t h r o u g h f e e d b a c k f o r t h e p u r p o s e o f

g e n e r a t i n g r e p e a t e d m o t i o n i n o r d e r t o a c h i e v e a

s t a b l e g a i t . A s e r i o u s d i s a d v a n t a g e o f t h i s a p p r o a c h

i s t h a t m a s s l e s s l e gs h a v e b e e n a d o p t e d . I f th e

m a s s e s o f t h e l e g s w e r e c o n s i d e r e d , t h e y w o u l d c a u s e

c o n s i d e r a b l e e x t e n s i o n s i n t h e r e p r e s e n t a t i o n o f t h e

s y s t e m m o d e l , a n d t h e s y n t h e s i s o f t h e c o n t r o l

m e c h a n i s m w o u l d b e c o m e e x t r e m e l y c o m p l e x . T h e

a d d i t i o n o f e a c h l e g i n t r o d u c e s a t l e a s t t h r e e a d d i -

t i o n a l d e g r e e s o f f r e e d o m , u n d e r t h e c o n d i t i o n s o f

s i m p l e j o i n t s . T o r e a l i s e t h e g a i t a l g o r i t h m , a t l e a s t

t h e s a m e n u m b e r o f c o n t r o l s i g n a l s is n e ce s s a r y .

B a s e d o n t h i s a p p r o a c h a n d n e g l e c t i n g t h e i n f l u e n c e

o f l eg m a s se s , a n a t t e m p t h a s b e e n m a d e t o c o n t r o l

t h e e x i s t i n g d e g r e e s o f f r e e d o m o n t h e b a s i s o f t h e

e r r o r i n t he d r i v i n g to r q u e s a n d f o r c e s

VUKOBRA-

- rovad e t a L 1 9 7 0 ) . T o a v o i d t h e l i m i t a t i o n s o f

p a s s i v e s t a b i l i s a t i o n b y w h i c h t h e k i n e m a t i c g a i t o f

t h e d y n a m i c s y s t e m , m o v e d b y t h e m a s s l e s s l e gs ,

i s b a s i c a l l y c o n t r o l l e d , a n e w a p p r o a c h t o t h e s t u d y

o f l e g g e d -m a c h i n e d y n a m i c s , p a r t i c u l a r ly f o r a n t h r o -

p o m o r p h i c s t r u c t u r e s , i s d e s c r i b e d .

M e t h o d o f p r e s cr i b ed

s y n e r g y

T h e b a s i c c o n c e p t u s e d i n t h e s y n t h e s i s o f a r t if i c i a l

s y n e r g y i s t h a t t h e l a w o f c h a n g e f o r t h e f o r c e s o f

r e a c t i o n a n d f r i c t i o n i s g i v e n i n a d v a n c e , o r t h e i r

i n t e r r e l a t i o n s h i p h a s b e e n p r e s c r i b e d . F o r e x a m p l e ,

z . m . p . * m o t i o n i s g i v e n , a n d t h e p o i n t s a t w h i c h t h e

r e s u l t i n g f r i c t i o n a l f o r c e s a c t a r e p r e s c r i b e d . T h i s

d e t e r m i n a t i o n o f d y n a m i c v a l u e s i m p o s e s d y n a m i c

r e l a t i o n s t h a t r e s u l t i n a d d i t i o n a l d y n a m i c c o n s t r a i n t s

i n t h e s y s t e m m o d e l . M a t h e m a t i c a l l y , t h i s i s e x -

p r e s s e d b y a d d i t i o n a l d i f f e r e n t ia l r e l a t i o n s t h a t h a v e

t o b e s a t i s fi e d b y t h e a n t h r o p o m o r p h i c s y s t e m

m o t i o n .

F r o m w h a t h a s b e e n s a id , i t a p p e a r s t h a t , i f s o m e

p o i n t r e p r e s e n t s t h e z . m . p . , a n d i f t h e v e r t i c a l

g r o u n d r e a c t i o n f o r ce s a r e r e d u c e d t o i t , t h e m o m e n t

M s h o u l d b e e q u a l t o z e r o ( F i g . I ) . T h e v e c t o r M

h a s e v i d e n t l y a h o r i z o n t a l d i r e c t i o n , a n d h e n c e t w o

d y n a m i c c o n d i t i o n s h a v e t o b e s a t i s f i e d : p r o j e c t i o n s

o f t h e m o m e n t o n t o t w o m u t u a l l y o r t h o g o n a l a x e s

i n t h e h o r i z o n t a l p l a n e s h o u l d b e e q u a l t o z e r o . I f

t h e f i x ed h o r i z o n t a l a x e s a r e d e n o t e d b y X a n d Y

* I f a l l e l e m e n t a ry re a c t i o n

f o r c e s r e

r e d u ce d t o t h e ce n t re o f t h e

su p p o r t sur fa ce, t h e fo r ce N a n d m o m e n t M a re o b ta i n e d . S i n ce t h e

l o a d d i a g ra m o f t h e ve r t i ca l f o r ce s i s o f t h e sa m e s i g n , t h e g ro u n d

re a c t i o n ca n a l w a ys b e re d u ce d t o t h e re su l t a n t fo r ce . Th i s re su l t a n

f o r c e w i l l b e d e n o t e d a s R a n d it s p o i n t o f a c t io n u p o n t h e g r o u n d

su r f a ce ca l l e d t h e ze ro -m o m e n t p o i n t z . m . p . ) F i g . 1 ) . I t i s t h u s

a ssu m e d t h a t f r i c t i o n a l f o r ce s ca n b e re d u ce d t o t h e re su l t a n t f o r c e

a n d m o m e n t

m 5

rn 6

m

rn ,

3 2

F ig 3 M e c h a n i c a l b i p e d m o d e l

Medica l and B io log ica l Eng ineer ing

{m o

I - 0

J a n u a ry 9 7 4

I

7


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then

x o

1 )

r= 0

With regard to frictional forces, the following

condition can be stated: the moment of frictional

forces with respect to some vertical axis ( is equal to

zero, and, as a result,

M~ = 0 . . . . . . . . . . (2)

The axis can pass through the centre of gravity, or

the centre of the foot support surface, or through the

z.m.p. In the last case, X, Y, ( co nstit ute an ortho-

gonal co-ordinate system. According to D'Alam-

bert's principle, the system must be in equilibrium.

S MO O TH L E V E L WA L K

assume that the foot of the anthr opomorp hic system

rests completely on the ground, so that fro = 0. The

inertia forces F and mom ent Mr i n the general case

can be represented as the linear forms of the general-

ised accelerations, and as quadratic forms with

respect to the generalised velocities:

i= 1 i= l j= l

i= 1 i= l j l .

5 )

where the vectors a~, bo, c~ and d~j are functions of

the generalised co-ordinates.

~ ; = / 3 3

~PPELVIC

The external forces acting on the loco motion system

include the friction forces, gravity forces and

ground reactions. We reduce the moments of these

forces and those of the inertial forces to the z.m.p.

and denote them by F and MF, respectively. Then,

eqn. 1 can be written as

M~+Mr)ex = 0

3 )

M~ + Mr) er = 0

where

M~ = total moment of gravity force with res-

pect to the z.m.p.

e~, ey = un it vectors of X a nd Y axes of the

fixed co-ordinate system.

The third equation of the dynamic relationships

(eqn. 2) can be written as

(Mr + p x F) er = 0 . . . . . . . (4)

where

p = vector from z.m.p, to the ~ axis point of

the action on the ground surface

e; = uni t vector of ~ axis.

We denote the generalised co-ordinates of the

mecha nism* by ~b~. In the synergy synthesis we

F i g 4 G a i t w i t h n e g l i g i b l e p e l v i c d i s p l a c e m e n t s

Introducing these expressions into eqns. 3 and 4,

we get

Moex+ ~

c, ex~ ,+ ~ ~

doex 5,~j=O

l = i = j = l

MGey+ ~ c, ey~,+ ~ ~ dtjerff~,~j=O

i= t i= 1 j= t

/= 1 i= l J= l

i= l

i= 1 j= l

6 )

If the locomotion system has three degrees of f r ee

d o m only, the trajectory of ~t(t) for all co-ordinates

can be f ound by integrating eqns. 6. However, the

number of degrees of freedom n is generally greater

than three; this is obvious because the equilibrium

dynamic conditions discussed do not as yet contai n

any infor mation on the type of the gait.

The laws of the remaining (n-3)-co-ordinates

change should be set so as to ensure the desired gait;

i.e. a periodic displacement of the legs correspo nding

Genera/ised co-ordinates ~ o f the mechanism represent the

system internal co-ordinates.

6 8 M e d ic a l a n d B io lo g ic a l E n g in e e r in g J a n u a ry 9 7 4


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t o t h e a l t e r n a t e s i n g l e - a n d d o u b l e - s u p p o r t p h a s e s .

T h i s i n f o r m a t i o n m a y b e o b t a i n e d a t b e s t b y

d i r e c t l y s t u d y i n g t h e h u m a n g a i t . i n t h e p r e s e n t s t a t e

o f b i o m e c h a n i c s , w e c a n a n s w e r t h e q u e s t i o n h o w a

m a n w a l k s , b u t i t is d if f ic u l t t o s a y w h y a p a r t i c u l a r

g a i t is j u s t l i k e t h a t . T h e r e f o r e a n y a t t e m p t d i r e c t l y

t o o b t a i n t h e l a w s o f c h a n g e i n a l l t h e c o - o r d i n a t e s

r s t a r t in g f r o m t h e m i n i m i s a t i o n o f s o m e g l o b a l

c r i t e r i o n ( e . g . m i n i m u m p o w e r c o n s u m p t i o n ) , d o e s

n o t s e e m t o b e r e a s o n a b le . ] I t s ee m s m o r e r e a s o n -

a b l e t o p r o d u c e e x p e r i m e n t a l ly a n d r e c o r d t h e

(ToMovI(~, VODOVNIK e t a l . 1972; 1967) . Since the

g a i t a l g o r i t h m i s s y m m e t r i c , le t u s w r i t e th e r e p e a t a -

b i l i t y c o n d i t i o n s f o r t h e h a l f - p e r i o d o f t h e s t e p T ,

according to VUKORRATOVlda n d J u m ~ I d ( 1 9 6 9 ) , as

r = _+ r q~ ,* (0 ) = + ~ ,* (T /2 ) (8 )

w h e r e t h e + o r - s i g n d e p e n d s o n t h e p h y s i c a l

n a t u r e o f t h e a p p r o p r i a t e c o - o r d i n a t e s a n d t h e i r

de r iva t i ve s .

T h e s y s t e m o f eq n . 7 , t o g e t h e r w i t h t h e c o n d i t i o n s

o f e q n . 8 , m a k e i t p o s s i b l e t o o b t a i n t h e n e c e s s a r y

t =O + t a b t = t a b P t b c

t

Fig . 5 Zero mom ent po in t d is

T p lacement dur i ng ha l f

t= tbc -4 - T

step.

t .b = t ime f rom hee l

st r ike to fu l l foot

contac t

tb~ = t ime from ful l foot

i contact to beg in

n i ng o f dep l oy

phase

T = fu l l s tep pe r iod

characteristics o f t h e b a s i c c o - o r d i n a t e s d e f i n i n g t h e

h u m a n g a i t . E v i d e n t l y , t h e s e s h o u l d b e t h e l e g c o -

o r d i n a t e s . T h u s w e h a v e t h e p o s s i b i l i ty o f o b t a i n i n g

t h e d y n a m i c l aw s o f c h a n g e i n t h e ( n - 3 ) - c o -

o r d i n a t e s o f t h e a n t h r o p o m o r p h i c r o b o t s . I n th i s

w a y , t h e s y n t h e s i s o f a r t i f i c ia l s y n e r g y i s a c c o m -

p l i s h e d a s f o l l o w s : f o r s o m e c o - o r d i n a t e s a f i x e d

p r o g r a m o f m o t i o n ( k i n e m a t i c a l g o r i th m ) i s se t, a n d

t h e m o t i o n o f t h e r e m a i n i n g c o - o r d i n a t e s i s f o u n d

f r o m t h e d y n a m i c e q u a t i o n s ( e q n s . 6) .

S e p a r a t e t h e s e ts o f v a r i a b l e s ~ i n t o t h o s e f o r

w h i c h t h e l a w o f m o t i o n h a s b e e n p r e s c r i b e d a n d

t h o s e w h o s e m o t i o n h a s b e e n d e t e r m i n e d f r o m

e q n . 6 . L e t t h e f ir s t b e d e n o t e d b y ~ , a n d t h e s e c o n d

b y r A f t e r t h e a p p r o p r i a t e t r a n s f o r m a t i o n s , t h e

d y n a m i c e q n s . 6 c a n b e r e p r e s e n t e d i n t h e m a t r i x

f o r m

4 : o 7 )

t l i l d l

w h e r e

e . d u = s o m e v e c t o r c o e f fi c ie n t s d e p e n d i n g o n

g = r ep r e s e n t in g f u n c ti o n o f ~ , r ~ , ~ *

c o - o r d i n a t e s .

I n a c c o r d a n c e w i t h th e t y p e o f m o t i o n o f le g g e d

l i v i n g o r g a n i s m s i n s t a t i o n a r y - g a i t r e g i m e s , c e r t a i n

r e p e a t a b l e c o n d i t i o n s , w h i c h r e fl e ct m a t h e m a t i c a l l y

t h e p a r t i c u l a r f e a t u r e , h a v e t o b e a d d e d t o e q n s . 7

I n t h e a u t ho r ,~ o p i n i o n , so m e d e f i n i t e o p t i m i sa t i o n c r i t e r ia a re o n l y

re l a t e d to p a r t l cu / a r lo co m o t i o n a c t i v i t i e s o f t h e h u m a n

l a w s o f m o t i o n o f t h e v e c t o r r i .e . t o c a r r y o u t t h e

c o m p e n s a t i o n s y n e r g y s y n t h e s is . A c c o r d i n g l y , t h e

s y n e r g y s y n t h e s i s f o r c o - o r d i n a t e s o f ~b* i s r e d u c e d

t o t h e s i m u l t a n e o u s s o l u t i o n o f t h e s y s t e m s o f e q n s .

7 a n d 8 . F o r t h i s p u r p o s e , v a r i o u s i t e r a ti v e m e t h o d s ,

n o t c o n s i d e r e d h e re , f o r s o l v i n g t h e b o u n d a r y - v a l u e

p r o b l e m c a n b e a p p l i e d

VUKOBRATOVIC

a n d

JuRI~Id, 1969; VUKOBRATOVIC t a l . 1972).

A s a l r e a d y m e n t i o n e d , i t i s r e a s o n a b l e t o s e l e c t

t h e c o - o r d i n a t e s 4; a s t h e a n g u l a r d i s p l a c e m e n t s o f

t h e r o b o t ' s ' le g s ' . T h i s d o e s n o t m e a n t h a t t h e y

c a n n o t b e c h o s e n f o r o t h e r c o - o r d i n a t e s o f t h e

m o d e l . H o w e v e r , l e g m o t i o n , i n f a c t , d e f in e s th e

g a i t , a n d t h i s m o t i o n i s m o r e c o m p l e x t h a n t h e

m o t i o n o f r em a i n i n g p a r ts o f t he a n t h r o p o m o r p h i c

s y s t e m s . I n t h a t ca s e , t h e c o - o r d i n a t e s r r e f e r t o

t h e u p p e r p a r t , i .e . t h e t r u n k o f th e r o b o t . I n b r i e f,

t h e s c h e m a t i c m o t i o n o f t h e r o b o t i s as f o l lo w s :

T h e l eg s ' a r e d i s p l a c e d a c c o r d i n g t o s o m e a l g o r i t h m

r e c o r d e d f r o m a h u m a n b e i n g , a n d t h e ' t r u n k ' m a k e s

p e r i o d i c c o m p e n s a t i n g m o v e m e n t s t h a t p r o v i d e f o r

a p p r o p r i a t e d i s p l ac e m e n t o f th e z . m .p , a n d d y n a m i c

e q u i l i b r i u m o f t h e s y s t e m i n t h e f r o n t a l , s a g i t t a l

a n d h o r i z o n t a l p l a ne s .

A f t e r t h e s y n e r g y s y n t h e s i s i s c o m p l e t e d , i t i s

n e c e s s ar y t o c o m p u t e t h e d r i v in g t o r q u e s n e e d e d f o r

i t s r e a l i s a t i o n . F o r t h i s r e a s o n , l e t u s w r i t e t h e

c o n d i t i o n s o f k i n e t o s t a t i c e q u i l i b r i u m a r o u n d t h e

a x e s o f a l l t h e j o i n t s ( F i g . 2 ) . A s a r e s u l t , w e o b t a i n

d i f f e r e n ti a l e q u a t i o n s o f t h e f o l l o w i n g f o r m :

i = i = l j = l

9 )

M e d i c a l a n d B i o l o g ic a l E n g i n e e r in g J a n u a r y 9 7 4 6 9


5/14

where the upper index k indica tes the jo in t number

in which the cha in has been ' broken ' ;

c~k, du k, g~ = som e vec tor coefficients

Since the fun ctions ~b(t) from eqn. 9 are know n,

al l the drivin g torqu es Ms (i = 1, 2 . . . . . n) can be

computed . I t must be ment ioned tha t , in th i s shor t

desc r ip t ion of the new method, we a re concerned

wi t h t he a n t h ropomorph i c mode l wi t hou t uppe r

ext remi t ie s . When the ' f ree ' upper ext remi t ie s a re

involved, the mode l of the dynamic re la t ionships

(eqn. 7) i s inc reased by as many second-order

di f fe rentia l equa t ions as the ' a r ms ' have degrees of

freedom (not d i scussed he re ) . S ince the upper

ext remi t ie s a re pass ive , the dr iv ing torques in the i r

corresponding ' f ree ' jo in t s a re equa l to ze ro .

xampl e o f the anthropomorphic system synergy

synthesis

The bas ic s ta tements of th is appro ach to the s tudy

of a n t h ropomorph i c sys t e ms dyna mi c s we re u se d

for the synthes i s of the compen sa t ing synergy of the

anthropomorphic sys tem i l lus t ra ted in F ig . 3 . The

upper pa r t o f the s t ruc ture i s represented by a homo -

geneous r ig id body. The lower ext remi t ie s each

possess three degrees of freedom.' l The segments of

the ext remi t ie s a re in te rconnec ted by s imple jo in t s .

Fo r leg movem ent (presc r ibed synergy of the anthro-

pomorphic mechanism), a ' rea l ' ga i t a lgor i thm was

adopted . In F ig . 4 , the laws of change in the charac -

te r i s t ic angles of the leg a re g iven in the form of

diagrams for the case of gai t on level ground.: l : The

chosen ga i t type i s cha rac te r i sed by ve ry smal l pe lv ic

movements , because the prac t ica l rea l i sa t ion of the

walking machine was kept in mind.

Accor ding to the a lgor i thm chosen, the foot of the

leg in the supp ort phase changes i t s pos i t ion f rom the

heel to the toes, as shown in Fig. 5. In this case , we

can dist inguish three phases. Let us denote by t ,o

the t ime ins tant when the suppor t i s t ransfe rred f rom

the heel to ful l foot , a nd by tbc when i t is t rans ferred

from the ful l foo t to the toes (0


6/14

T a b l e 1 . T a b l e s 2 a n d 3 g i v e t h e g e o m e t r i c a l p a r a -

m e t e r s n e e d e d f o r c o n s t r u c t i n g t h e m a t h e m a t i c a l

m o d e l g i v e n i n g e n e r a l f o r m b y t h e s y s t e m o f eq n s . 6 .

T h e m e a n i n g o f t h e s e d a t a c a n b e u n d e r s t o o d f r o m

Fig. 7 .

O w i n g t o t h e c h o s e n t y p e o f g a it , in w h i c h a v e r y

s m a l l p r o p e r p e l v i c m o v e m e n t i s p r e s e n t , a n d

a s s u m i n g s u f f ic i e nt f r i c t i o n m o m e n t w i t h t h e f o o t i n

c o n t a c t , t h e s y n t h es i s o f t h e c o m p e n s a t i n g s y n e r g y

w a s c a r r i e d o u t in tw o p l a n e s s a g i t t a l a n d f r o n t a l ) ,

w h i c h l e d t o t h e n e g l e c t o f t h e t h i r d d i f f e r en t i a l

e q u a t i o n o f t h e s y s t e m o f e q n s . 6 .

A s a p r a c t i c a l r e s u l t o f t h e s y n t h e s i s o f t h e u p p e r -

p a r t s y n e r g y o f t h e a n t h r o p o m o r p h i c s y s t e m u n d e r

c o n s i d e r a t i o n , t h e c o m p e n s a t i o n n e e d e d f o r a

r e p e a t a b l e g a i t o f t h e c h o s e n t y p e * i s g i v e n i n t h e

* u ~ represent th e so-called external' co-o rdinates of the system

differing by a constant from the internal' co-ordinates ~i. The

r e s o n for adopting external co-ordinates lies in the fact that they

r e responsible for the system stability, w hich represents a furth er

step in the realisation of a carefully considered anthropomorphic

system capable of operating under perturbed conditions, It should

be noted that, in the case of the realisation, the angle ~ also

includes the co-ordinates W (Fig. 15)

.Y

~ , , v p l a n e , f o r t h e w o r k i n g r e g i m e , a s f o l l o w s :

T = 2 s , S = 1 F i g . 8 ).

e v e l o p m e n t o f a c t i v e e x o s k e l e t o n s

U s i n g t h i s a p p r o a c h , r e h a b i l i t a t i o n d e v i c e s o f t h e

e • t y p e h a v e b e e n d e v e l o p e d o v e r s e v e r a l

y e a r s . T h e f i r s t v e r s i o n o f t h i s t y p e w a s r e a l i s e d a s

t h e

kinematic walker

I t h a d o n e d e g r e e o f f r e e d o m

f o r e a c h l e g , a n d , i n a g r e e m e n t w i t h t h i s , o n e

p n e u m a t i c a c t u a t o r c y l in d e r ) e a c h a n d a p u r e

k i n e m a t i c li n k o f p a r t i c u l a r j o i n t s . O w i n g t o t h e

n e e d f o r a n u p r i g h t s t a n d i n g ) p o s i t i o n , t h e g a i t

p e r f o r m e d w a s v e r y s i m i l a r t o t h e i n i t i a l g a i t

a l g o r i t h m o n l e ve l g r o u n d , b e i n g d e f i n e d w i t h t w o

c o n t r o l p a r a m e t e r s o n l y 1 V u K oB R A T OV I ~ a n d

JURI ~I ~, 1969). U sin g this v ersio n, sh ow n in Fig . 10,

t With the firs t version o f the exoskeleton, the *sliding gai t type

defined by one angle (Fig. 9) has been selected

F i g . 7 A n t h r o p o m o r p h i c m e c h a n i c a l s y s te m w i t h f i x e d

arms

M a s s M a n d m o m e n t o f i n e rt ia ~

m Jx Jv Jz

O . 1 8 O . 0 0 0 0 7 O . 0 0 0 6 5 O . 0 0 0 5 2

O 3 8 O . 0 0 4 4 O 0 0 4 4 O . 0 0 0 4 5

0 9 8 0 . 0 1 3 8 0 . 01 4 1 0 . 0 0 3 5

O . 8 3 O . 0 0 7 9 O 0 0 6 2 O . 0 0 7 1

4 . 7 0 . 2 11 0 . 1 9 0 0 . 0 3 1

0 . 9 8 0 . 0 1 3 8 0 . 0 1 41 0 . 0 0 3 5

O . 3 8 O . 0 0 4 4 O . 0 0 4 4 O . 0 0 0 4 5

O . 1 8 O . 0 0 0 0 7 O 0 0 0 6 5 O . 0 0 0 5 2

E x o s k e l e to n i n c l u d e d w e i g h t o f p a t i e n t a l o n e

7 1 k p

D i s t a n c e I ( m )

i Ix ly I,

1 0 . 1

2 0 0 O . 40 0

3 0 0 0 . 4 5

4 - - 0 . 0 4 7 O . 1 0 . 0 9

5 -- - - - -

6 0 0 - - 0 . 4 4 5

7 0 0 - - 0 . 4 0 0

8 -- - - - -

D i s t a n c e r ( m )

i rx ry rz

1 O 0 3 0 0 O 0 3 8

2 0 0 0 . 2 2

3 - - O 0 3 3 0 O 3 3

4 - - 0 . 0 3 4 0 . 0 9 3 0 . 0 6 9

5 O. 03 8 0 O . 42

6 - - 0 . 0 3 2 0 - - 0 . 1 3 9

7 0 0 - - 0 . 1 9 2

8 O. 03 0 0 - - O . 05 9

M e d i c a l a n d B i o l o g ic a l E n g i n e e r in g J a n u a r y 9 7 4 7


7/14

t h e f i r s t e x p e r i m e n t s w e r e p e r f o r m e d w i t h t w o

p a t i e n t s a t t h e O r t h o p a e d i c C l i n i c i n 1 9 69 a n d 1 97 0.

T h e r e s u l ts w e re v e r y m o d e s t : t h e p a t i e n t w a l k e d

a s s i s t e d b y t w o m a l e n u r s e s . S o m e e x p e r i e n c e w a s

a l s o a c q u i r e d a b o u t a t t a c h i n g t h e c o r s e l e t a n d t h e

m a c h i n e i t s el f t o t h e p a t i e n t s b o d y .

I n t h e c o u r s e o f f u r t h e r w o r k , t h e m o d e l o f a

partial active exoskeleton ( F i g . 1 l ) w a s d e v e l o p e d ,

w h i c h m a d e i t p o s s i b l e t o r e a l i s e s y n e rg y o f t h e l eg s

w i t h t h r e e d e g r e e s o f f r e e d o m ; w h i l e th e h i p j o i n t s

h a d t w o d e g r e es o f f r e e d o m a n d a j o i n t d r i v e i n t h e

f r o n t a l p l a n e , w h e r e b y i t w a s p o s s i b l e a l s o t o a c h i e v e

c o m p e n s a t i o n i n t h a t p l a n e ( a n g l e v ), w h i c h c o n t r i -

b u t e d c o n s i d e r a b l y t o t h e r e a l i s a ti o n o f a g a i t m o r e

l i k e t h a t o f a h u m a n . C l i n i c a l t e s t s o n t h i s m o d e l

w e r e p e r f o r m e d i n 1 9 7 1 w i t h t h r e e p a t i e n t s . T h e g a i t

o f t h e p a t i e n t s w a s a c h i e v e d i n a p a r t i c u l a r g o - c a r t ,

a n d m o r e k n o w l e d g e w a s a c q u i r e d o f t h e p h e n o -

m e n o n o f f o rc e s tr a n s f e r r e d f r o m t h e m a c h i n e t o t h e

m a n ( a n d v i c e v e rs a ) , lo c a l p r e s s u r e s a n d t h e l i k e .

C o n s t r u c t i o n a l l y , w i t h t h e e x c e p t i o n o f t h e c o r s e le t

a n d t h e c o n t r o l s y s t e m , t h i s m o d e l i s v e r y s i m i l a r t o

t h e l a t e s t o n e :

Complete active exoskeleton The

c o m p l e t e a c t i v e

e x o s k e l e t o n i s i n t e n d e d f o r t h e r e h a b i l i t a t i o n o f

p a r a p l e g i c s w i t h r e l a t i v e l y h i g h l e s i o n s , e x c l u d i n g

m u s c u l a r a c t i v i t i e s o f t h e l e g s a n d t h e w a i s t - p e l v i c

r e g i o n . I n a d d i t i o n t o c o n t r o l o f t h e l e gs , c o n t r o l o f

t h e u p p e r p a r t o f t h e b o d y i s a ls o p o s s i b l e w i th t h i s

t y p e o f e x o s k e l e to n . T h u s t h e p r e s c r i b e d g a i t a l g o -

r i t h m i s o b t a in e d .

T h e c o m p l e t e e x o s k e l e t o n ( F i g . 1 2) is m a d e u p o f

t h r e e m a i n s u b a s s e m b l i e s :

c o r s e l e t w i t h t h e a d j o i n i n g s u b a s s e m b l i e s

l e f t an d r i gh t l eg (F ig . 6) .

T h e c o r s e l e t 1 w a s c o n s t r u c t e d , u s i n g s t a n d a r d

t e c h n iq u e s , o f p o l y e s t e r r e s in r e i n f o r c e d w i t h p o l y -

a m i d e f ib r e s. T h e c o r s e l e t e n v e lo p e s t h e b o d y o f t h e

p a t i e n t f r o m h i s p u b l i c - i s c h i a t i c r e g i o n u p t o t h e

u n d e r a r m s , o v e r t h e c h e s t a n d b a c k . I t i s f a s t e n e d

o v e r t h e s h o u l d e r s b y m e a n s o f l e a th e r s t r a p s ( l a ) .

T h e f r o n t a l p a r t ( l c ) o f t h e c o r s e l e t i s a s e p a r a t e

u n i t , w h i c h i s f a s t e n e d b y V e l c r o s t r i p s ( l b ) t o t h e

d o r s a l p a r t . T h e v e n t r a l p o r t i o n o f t h e f r o n t a l p a r t

( c o v e r ) ( l d ) i s r e i n f o r c e d b y a s h a p e d p i e c e o f

d u r a l u m i n s h e e t i n o r d e r t o i n c r e a s e t h e s t i f f n e s s o f

t h e p e l v i c p a r t o f t h e c o r s e l e t . A l e a t h e r b e l t ( 2 )

c o n t a i n i n g 1 4 e l e c t r o p n e u m a t i c 3 - w a y v a l v e s i s

f a s t e n e d t o t h e c o r s e l e t , a n d s e r v e s t o c o n t r o l s i x

p n e u m a t i c c y l i n d e r s ( t h r e e p e r l e g ) a s w e l l a s t w o

m e m b r a n e a c t u a t o r s ( 3 ) , w h i c h a r e p n e u m a t i c a l l y

c o n t r o l l e d i n p a r a l l e l a n d s e r ve a s a c t u a t o r s f o r

m o v e m e n t s i n t h e f r o n t a l p l a n e . P n e u m a t i c p u l s e s

a r e c o n v e y e d f r o m t h e e l e c t r o p n e u m a t i c v a l v e s t o

t h e c o r r e s p o n d i n g a c t u a t o r s v i a a p n e u m a t i c c a b l e

f o r m e d b y p o l y a m i d e tu b e s .

T h e b a s e s (5 ) o f th e e x o s k e l e t o n h i p j o i n t s a r e

a l s o f a s t e n e d t o t h e c o r s e l e t , g i v i n g t h e s e c o n d

d e g r e e o f f r e e d o m t o t h e h i p j o i n t s ( r o u n d t h e

l o n g i t u d i n a l a x i s ). B y m e a n s o f t h e le v e r ( 5 a ) b e l o n g -

i n g t o t h e l e g s u b a s s e m b l y , th e d r i v e o f th e m e m -

b r a n e a c t u a t o r s ( 3 ) i s t r a n s m i t t e d t o b o t h l e g s a n d

s y n c h r o n i s e d b y m e a n s o f a l e v e l ( 4 ) s u r r o u n d i n g

t h e c o r s e l e t f r o m t h e r e a r s i d e i n t h e f o r m o f a n

e l o n g a t e d U . S i m u l t a n e o u s l y , i t d r i v e s t h e l i n e a r -

f e e d b a c k p o t e n t i o r n e t e r d e t e c t i n g t h e p o s i t i o n i n

t h e f r o n t a l p l a n e .

T h e l e g c o n t a i n s t h r e e m a i n s u b a s s e m b l i e s : t h e

t h i g h w i t h t h e m a i n h i p j o i n t ( 6 ) , d r i v i n g a n

a c t u a t o r i n t h e f o r m o f a p n e u m a t i c d o u b l e - a c t i n g

c y l i n d e r ( 7) , a n d t h e a d j u s t a b l e f e m o r a l b o n e ( 8) .

T h e m a i n h i p j o i n t i s c o n s t r u c t e d i n t h e f o r m o f a

s i m p l e d r y b e a r i n g ( T e f l o n s l i d i n g s u r f a c e s ) w i t h

a d j u s t a b l e f r i c ti o n . T h e p r e c i s i o n fe e d b a c k p o t e n t i o -

m e t e r i s l o c a t e d i n t h e c e n t r a l h o l e , i ts z e r o b e i n g

a d j u s t a b l e f r o m o u t s i d e . T h e e l e m e n t s c o n n e c t i n g

t h e b a s e p o r t i o n s o f t h e c o r s e le t w i t h t h e s t a t i o n a r y

p a r t ( c u p ) o f t h e j o i n t ( 6 ) a r e f a s t e n e d t o t h e l a t t e r ,

a s w e l l a s t h e l e v e r c o n n e c t i n g i t t o t h e a c t u a t o r ( 7 ).

T h e a c t u a t o r i s m a n u f a c t u r e d f r o m l i g h t a l lo y s , w i t h

t h e e x c e p t i o n o f t h e r o d , w h i c h i s m a d e o f p o l i s h e d

I n o x s t e e l . A t a n a i r p r e s s u r e o f 1 0 b a r , a n e t a c t i v e

f o r c e o f 1 14 k p i s o b t a i n e d . T h e f e m o r a l b o n e ( 8)

i s m a n u f a c t u r e d i n t h e f o r m o f a 2 - m e m b e r t e le s c o p i c

t u b e m a d e o f I n o x s t e e l ( w a l l th i c k n e s s , 0 . 8 m m ) ,

l ~ T = 2 s e c S =

~

Fig 8 Nominal gait trajectory for

biped model with fixed upper

extremities

T = step peri od

S coefficient of step size

7 2 M e d i c a l a n d B i o l o g i c a l E n g i n e e r i n g J a n u a r y 9 7 4


8/14

the length of which can be adjus ted to the pa t ient

by means of a knur led nut (Sa ) . The leg support

(8b) is made of Inox steel sheet and covered with

sponge rubber . This pa r t i s fa s tened both to the

othe r pa r t of the femora l ' bone ' (8) and to the

auxil iary strut (8c).

The ' sh ank ' wi th the main ' knee ' jo in t (6a) , which

is identical to the 'hip ' joint (6), a lso contains the

auxil iary joint (6b). The actu ator (7a) is identical

to the h ip ac tua to r (7) . The ,bon e ' of the ' shank ' (9)

with the kn urled n ut (9a) is of very similar design to

tha t of the femora l ' bone ' (8) , whi le the auxi l ia ry

strut (10), with i ts nut (10a), is made of duralumin

tubes . The leg support i s cons t ruc ted in the same

way as the femoral part of the leg support (8b).

The ' foot of the leg i s connec ted by means of the

' ankle jo in t ' (11) and the auxi l ia ry jo in t (1 la ) to the

' shank ' pa r t of the ' l eg ' . As we l l a s the o the r two,

the main jo in t conta ins a feedback potent iomete r .

The actuator of the ' foot ' (12), is of a design very

force compon ent of the sys tem supported on the

foot; this has been used in the real isat ion of the

system stabil isat ion.

Electronic system for com plete exoskeleton control

A block schemat ic of the comple te exoske le ton

contro l is given in Fig. 14. The left-leg ime-base genera-

tor (XBCL) s the synchro nisat io n frequency source. The

period T can be regulated within the l imits of 1-5 s .

The electronic c ircuit of the right-leg t ime-base

genera tor (TBCR) is a delay circuit . Ou tput signals

from the XRGL and T~CR circuits are re la ted by the

express ion VR(t ) =

VL t+ T/2).

Fig. 14 shows al l

seven se rvosys tems for the cont ro l of the t ime

changes of the charac te r i s t ic jo in t angles ~IL, ~2L,

43L, ~blR, ~b2R, ~3R and u. S yn ch ro nis m o f the tim e

changes of the angles is preserved by the very fact

tha t a l l func t ion genera tors a re s t r ict ly t ime con-

necte d b y the electro nic circui ts XBGL and TBGR.

Mo re precisely, the references of the servosystem are

Fig. 9 Simplest bipe d gait

C~m l--cos ot)

2 T

T = half period of the step

similar to that of the actuators (7 and 7a). but is of

smal le r d iamete r and shor te r . The ' foot ' (13) i t se l f

i s made of Inox shee t , s t i f fened by drawn r ibs and

swaged edges , and covered on the upper s ide wi th

expanded p las t ic s sheet . The lower pa r t o f the ' foot '

(14) is a lso made of Inox steel sheet and covered on

the lower s ide wi th semi-hard sponge rubber and

fas tened to the upper p a r t by means o f a longi tudina l

axle (swivel joint ) giving a certa in ad apta bil i ty in the

fronta l p lane . Also , on the lower s ide of the ' foot '

(14), three force transducers with stra in gauges are

s i tua ted , and a rranged in such a way as to measure

the ve r t ical compo nents of the resul tant force a t the

points of contac t o f the exte rna l and in te rna l ba l l s

of the foot and the hee l wi th the ground (F ig . 13) .

In th i s way i t i s poss ib le to moni tor cont inuous ly

the in tens i ty and pos i t ion of the resul tant ve r t ica l

Medi cal and Biological Engineering January

Fig. 10 Kinematic wa lker 1969 )

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structure (Fig. 6). In the same sketch, the necessary

des igna t ions of angles a re g iven for eas ie r explana-

t ion of the real ised synergy.

ealisation of global feedback

In the case of pe r turba t ions , even when in te rna l

synergy ~b~(t) s strictly fulfilled, the external synergy

can be pe r turbed. For example , the whole sys tem

can ro ta te a round the leg in the s tance phase in

which the exte rna l angles fl~ , be ing respons ib le for

gait s tabi l i ty, change. T he rela t io n between the

exte rna l and in te rna l co-ordina tes i s shown in a

simplified sketch of the b iped (F ig. 16a), for the

nonpe r t u rbe d a nd pe r t u rbe d s t a t e . Th i s e xa mpl e

i l lus t ra tes how the exte rna l synergy can be spoi led

even when correc t ly sa t i s fy ing the in te rna l synergy.

This means , in the genera l case , tha t the re la t ionship

be tween the exte rna l and in te rna l synergy of the

a n t h ropomo rph i c sys te m c a n be r e p re se n t e d by

Fig. 11 Partial exoskeleton 197 0)

synchronous ly connec ted , whi le the synchronism of

the rea l changes of the angles a l so depends , apa r t

f rom the re fe rences , on the charac te r i s t ic s of the

servosystems.

A desc r ip t ion of one se rvosys tem only wi l l be

given, s ince they a re a l l cons t ruc ted in the sam e way.

A per iodic t ime change of angle ~blL wi th the pe r iod

T is gene rated by the c ircuit G~bIL. The out put

vol tage of the genera tor i s com pared w i th the vol tage

on pote nt iom ete r PL1. The p otent iom ete r i s mou nted

in the ankl e joint ~blL. Afte rde tec t ion and ampl i f ica -

t ion of the e rror , depending on the e rror s ign , one of

circuits PGL or PGU starts to generate pulses. The

pulse f requency can be adjus ted in advance wi th in

the range 10-25 Hz . T he pulse width i s dependen t

on the e rror ampl i tude . Elec t romagne t ic va lves a re

pulse-powered by circuits PCL and PGU (pulse-

genera tor cyl inder lower-end pos i t ion and pulse -

genera tor cyl inder upper-end pos i t ion , re spec tive ly) ,

and they open the a i r s t ream towards the upper and

lower pos i t ion , re spec t ive ly , of the p i s ton of the

assoc ia ted pneumat ic cyl inder .

F ig . 15 i llus t ra tes the e lec t ronic rea l i sa t ion of the

presc r ibed (F ig . 4) and the compensa t ing (F ig . 8)

synergy in pa ra l le l , for compari son. I t a l so shows

the rea l i sa t ion of the comple te synergy, measured b y

me a ns o f t he s e rvo -po t e n t i ome t e r sy s te m du r i ng t he

ga i t o f t he a n t h ropomorph i c sys t e m. The me a su re d

(rea l ised) synergy i s, na tura l ly , expressed in in te rna l

angles . Fo r th i s reason, the e lec t ronic rea l i sa t ion of

the presc r ibed program is g iven in in te rna l co-

ordina tes , too . Fo r reasons o f c la r i ty , F ig . 15 shows

a ske tch of the sys tem corresponding to the rea l i sed Fig. 12 Complete exoskeleton 197 1-7 2)

74 Medical and Biological Engineer ing January 974


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Fig 13 Artif icial foo t with forc e transducers

the matrix equation

fl = B~6+c c = constant . . . . (10)

The regulation procedures for stabilisation of the

perturbed stationary r6gimes of the gait will not be

dealt with here. They are the subject of another

paper by VUKOBRATOVIC and STEPANENKO (1972).

We shall briefly describe the regulating scheme

based on measuring dynamic reactions during the

walk, which avoids the use of gyroscopic instru-

ments.

It is evident that some relatio nship exists between

the force of dynami c reaction F = (Fx, Fr , Fz) and

the appropriate dynamic moments about three axes

connected to the z.m.p.s, M = Mx, Mr, Mz).

Components Fx and Fy define the moments

abou t th e 2: axis only. With the previous assump tion

of a sufficient moment of the frictional forces, we

only take into account the component Fz, which

contributes to the appropriate moments round the

X and Y axes. We also assume that the int ern al

synergy is realised sufficiently accurately, and that

the perturbation only appears in the system external

co-ordinates.

Fig. 16b illustrates schematically the measureme nt

of the vertical component of the dynamic reaction,

from which one can write the following relationships:

s FBz-- Fez) = Mx )

d~ Faz-d2 FBz+ F~z) = Mr

l l )

where FAZ ez

and Fez are the vertical components

of the reaction, measured at the points A, B and C.

It should be emphasised that, in the nominal

regime, the moments Mx and Mr are by definition

equal to zero (z.m.p.). Owing to the perturbed

vertical component Fz, they do, in fact, have values

AMx and AMr. We assume these perturbations to

he small.

For the model illustrated in Fig. 3, the components

of the moment for z.m.p, can be written as

.,v,'x = ,~ x(~ ;, ~, ~, ~,,.,,, ,~, ,~,, ,~,, ,~,) )

M , = M, .(~; , ~, , / :, , , : ,, , l , , o, ,~, , L, .8 ,)

12)

Since the accelerations are the most sensitive factor

and a direct consequence of the load change, the

increments in moment for the perturbed regime are

I I r I I

' ~ ] , - I E ~ Z 3 1 q r - 3

Fig 14 Block diagram o f complete exoskeleton synergy realisation

Med ical and Biological Engineering January 974 75


11/14

t /

' ~ I i84

~ I I

I

%

\ \ ~ \ i

i I

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given as

A M x

? Mx A~+ ? Mx AS + ~ ? Mx ..

~7~- 3 :1 ~7 Aft, (13)

cqMr A ~ + ~Mr Ai)+ ~ eM r Aft,

Thus i t is assumed that the internal algorithm

develops precisely by means of special tracking

systems, and that the change in acceleration occurs

simply because of the appropriate change in forces.

If we extend this assumption further , i t is natural to

assume th at all increments o f acceleration of all

e lements o f the an thropomorph ic m echanism in the

sagittal plane are identical; i.e.

t f

In that case, solving eqn. 13 for the accelerations in

the sagit tal and frontal plane, we get

A ~ - A , A 5 -

Az . . . . . (14)

A A

f l represents the complete set of the external co-

ordinates of the system. In the case considered, the

increments of the acceleration of the external co-

ordinates are A~ and AS.

\

lal

(bl

Fig 16 Sche matic illustration of vertical reactions

where

A M r OMx _ AM x aMy )

A l

= ~b ~5

]

I

A M [c3Mx 6 ~Mx'~ ]

AM [~ Mr 6 c3Mr~ [

[8 M x 6 9 Ma \ ~Mr I

[ ~M r & 8Mr~ gMx I

- - - 2 a - - - -

Taking into account eqn. 10, i t is possible to obtain

the relationship between the accelerations:

q~ = B -x f . . . . . . . . . (16)

With regard to the system of eqn. 9, it is possible to

define the compensating driving torques in the

function of the increments of acceleration of the

' internal ' synergy:

A M = A A ~ . . . . . . . . (17)

where A = ]laull an d a u = 3MdO~,.

Com bining eqns. 16 and 17, the impo rtant rela-

t ionship is obtained that serves as the basis for

deriving the stabil isation algorithm:

A M = AB -a A f . . . . . . . (18)

15)

Fig 17 Hea lthy person in exoske/eton

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Fig 20 Fi lm insert from cl inical tr ials

Medical and Biological Engineering

In the majority of cases the patients favourably

accepted the machine in i ts present form, and did

not reject i t af ter prolonged an d repeated tr ials.

A com paratively high level o f reliabil i ty of the whole

technical system has been attained, enabling uninter-

rupted tr ials of two hours duration and more.

Conclusion

The results presented in this paper illustrate the

efforts made over many years to realise an active

orthotic system, which could be applied to the

rehabili tation of handic apped persons. The basic

aim is to release the paralysed paraplegic person

from the wheelchair , the only existing means of

locomotion which is available in closed environ-

ments. Since only the opinions of medical experts

and paralysed patients are conclusive as to the f inal

success of the project , i t must be confessed that the

problem has not by any means been solved. In other

words, the exoskeleton, as a m eans o f rehabili tation,

is by now at the star t of a systematic clinical evalua-

tion. I t should be emphasised that the exoskeleton is,

in i ts present state, capa ble of enabling the gait upo n

level ground aided by supporting canes of a para-

plegic patient with a high lesion. These canes do not

introduce any driving energy, but play the role of

the simplest stabil ising system .* At the sam e time,

control schemes for perturbed working regimes

were being developed, thus init iating work on the

rea lisa tion o f the au tomat ic m ain tenance of dynamic

equilibrium. In this phase of the investigation,

force feedback, obtained by measuring the dynamic

reactions at the contact point, together with the

support measurement, has proved to be a fair ly

reasonable parameter . Thanks to this control

scheme, up to the present, gyros copic instruments

for the assessment of stabil isation c orrection signals

have not been necessary.

Furthe r e valuation of the exoskeleton will be

continued with the aim of prolonging the gait phase

upon level ground and performing the action of

ascending and descending stairs. Also the compen-

sating system will be further developed, since its

realisation has been based on measuring dynamic

reactions during the gait .

In the forthcom ing 3-year project , which will

continue to be supported f inancially by the Social

and Rehabili tation Service, Washington, DC, the

final goal is to provide fo r the paraplegic a safe gait

upon level ground and stairs using canes, the only

purpose o f which are to secure microcompensat ion

of the regulating system. By keeping to such a simple

correction system, the project becomes realist ic,

because i t makes i t possible to do without the very

complicated and economically unjustif ied computer

system which cou ld p roduce exact au tomat ic

balancing.

9R has to be emphasised that, for feedback in volv ed b y dynamic

reaction , it is necessary to "correct" the autom atic stabi/isatio n due

to imperfections of the serve system

January 974

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On the other hand, the question still remains as to

how much has got to be done in this field of robot

application in order to allow the paraplegic to be

able to leave his wheelchair. This question cannot

be fully answered without several years of systematic

investigation of the system in other orthopaedic

centres. At present it is evident that, in the realising

of an artificial gait for paraplegics, the patients them-

selves can be given as a free parameter only the

decision on the type of action. It seems that this

means for restoring locomoti on properties to severely

handicapped persons must be developed until the

fundam ental problem of sensory feedback is solved.

Only then it will be possible to establish a natural

relationship between the pat ient s intenti on and the

machine that makes his desired movements possible.

Acknowledgment--The

work was done, and the paper

was written, under support by a Grant of the Social

Rehabil itation Service, Washington, DC.

References

FRANK, A. and McG~EE, R. (1969) Some considerations

relating to the design of autopilots of legged vehicles.

J. Terramech. 6.

MCGHEE, R. (1968) Some finite state aspects of legged

locomotion. Math. Biosci. 2, 67-84.

TOMOVI~, R. and BELLMAN,R. (1970) Systems approach

to muscle control.

Math. Biosci.

8, 265-277.

VUKOBRATOVIC,M. (1972) Artificial locomotion systems:

Dynamics, control algorithms, stability. Ph.D. Thesis,

Moscow.

VUKOBRATOVI ~,M., t~lRI~, V. and HRISTI ~,D. (1971)

Control of two-legged locomotion systems. Proc. 4th

IFAC Syrup. Autom. Contr. in Space,

Dubrovnik.

VODOVNIK, L ., CROCHET1ERE,W . and RESWlCK,J. (1967)

Control of a skeletal joint by electrical simulation of

antagonists.

Med. Biol. Eng. 5.

VUKOBRATOVIt~, M., FRANK, A. and JORI616, D. (1970)

On the stability of biped locomotion. IEEE Trans.

BME--17, 25-36.

VUKOBRATOVI ~,M. and Juslt~l~, D. (1969) Contribution

to the synthesis of biped gait. IEEE Trans. BME-16,

1-6.

VODOVNIK, L., KRALJ, A., KELglN,D. and BOROVgAK,L.

(1968) Theoretical and experimental investigations of

dynamic processes during movements of electrically

stimulated extremities. Final report to the Institute

Milhailo Pupin.

VUKOBRATOVIC,M . and STEPANENKO,J. (1972) On the

stability of anthropomorphic systems. Math. Biosci.

15, 1-37.

VUKOBRATOVIC, M.,

STEPANENKO, J. ~IR IC, V. an d

HRISTI6, D. (1970) Cont ribution to the study of

anthropomorphic systems. Proc. 5th IFAC Congr.,

Paris.

L e d 6 v e l o p p e m e n t d e x o s q u e l e t te s a n t h r o p o m o r p h e s a c t iv e s

Sommaire---Les postulats servant de base/t cette nouvelle approche ~t l ~tude de la dynamique des syst~mes

anthropomorphes sont explicit6s dans cette communication. Par rapport aux autres tentatives,

cette approche rend possible une r6duction maximale de dimensionnement en prenant comme

point de d6part l attribution du ph6nom6ne de synergie ~t une quelconque pattie du syst6me. A

titre d illustration de la m6thode consid6r6e, il est fourni une synth~se synergique complete de la

configuration retenue pour les syst~mes anthropomorphes.

D i e E n t w i c k l u n g v o n a k t i v e n a n t h r o p o m o r p h e n G l i e d e r f O s s e r n

Zusammenfassung Die Grundpostulate dieses neuen Versuchs einer Studie der Dynamik von anthropo-

morphen Systemen werden in dieser Arbeit dargelagt. Im Vergteich zu anderen Versuchen macht

dieses Vorgehen eine weitestgehende Reduzierung der Dimensionalit/it dadurch m/Sglich dass,

es sich darauf stiitzt, einem Teil des Systems Synergie zuzuschrieben. Als Illustration der Methode

wird ein Beispiel einer vollst~indigen Synergie-Synthese ftir die angenommene Konfiguration des

anthropomorphen Systems angeftihrt.

8 M e d i c a l a n d B i o l o g i c a l E n g i n e e r i n g J a n u a r y 1 9 7 4

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