Teleoperation with a dexterous robot arm
A n d r é v a n d e r H a m , S a n d o r d e n B r a v e n , G e r H o n d e r d , iv^jm J o n g k i n d C o n t r o l L a b o r a t o r y 'a D e p a r t m e n t o f E l e c t r i c a l E n g i n e e r i n g D e l f t U n i v e r s i t y o f T e c h n o l o g y P O B o x 5031 2 6 0 0 G A D e l f t T h e N e t h e r l a n d s E - m a i l : a.c.vanderham@et.tudelft.nlAbstract
I n n u c l e a r p o w e r plants s n a k e - a l i k e m a n i p u l a t o r s are used f o r t e l e m a n i p u l a t i o n . T h u s , the t e l e m a n i p u l a t o r a r m i s h i g h l y k i n e m a t i c a l l y redundant. T h i s p a p e r discusses a n e x p e r i m e n t u s i n g t w o d i s s i m i l a r robot arms c o n f i g u r e d t o b e u s e d f o r teleoperation. T h e t e l e m a n i p u l a t o r (remote) a r m i s k i n e m a t i c a l l y redundant. C o n t r o l schemes f o r 1:1 p o s i t i o n and force bilateral c o n t r o l a n d f o r s o l v i n g the c o n t r o l o f the k i n e m a t i c a l l y redundant m a n i p u l a t o r are presented a n d h a v e b e e n v e r i f i e d i n practice.
1. Introduction
T h r o u g h the u s e o f teleoperation systems i n a n u c l e a r e n v i r o n m e n t , a h u m a n operator w i l l n o t h a v e to b e e x p o s e d to h i g h l e v e l s o f r a d i a t i o n . T h e operator w i l l c o n t r o l a slave m a n i p u l a t o r , w h i c h i s situated i n the h o s t i l e e n v i r o n m e n t , b y generating position/force c o m m a n d s w i t h a m a s t e r s y s t e m .
T h i s p a p e r presents a teleoperation system w h e r e the operator controls the slave m a n i p u -l a t o r b y c o n t r o -l -l i n g a m a s t e r m a n i p u -l a t o r w h i c h c a n b e k i n e m a t i c a -l -l y d i s s i m i -l a r to the s-lave. I n o r d e r t o c o n t r o l a l l the cartesian degrees o f f r e e d o m o f the slave, the master m u s t at least have the same n u m b e r o f cartesian degrees o f f r e e d o m .
T h e t w o m a n i p u l a t o r s w i l l b e c o n t r o l l e d w i t h a bilateral c o n t r o l s y s t e m . T h i s m e a n s that the operator c a n n o t o n l y m o v e the slave m a n i p u l a t o r t o a desired p o s i t i o n b y c o n t r o l l i n g the master m a n i p u l a t o r , b u t h e c a n also f e e l a n d c o n t r o l the forces exerted b y the slave o n the e n v i r o n m e n t . T h i s a d d i t i o n a l f o r c e r e f l e c t i o n w i l l i m p r o v e the p e r f o r m a n c e o f the teleoperation s y s t e m .
T h e basis o f the b i l a t e r a l c o n t r o l s c h e m e i s f o r m e d b y p o s i t i o n c o n t r o l o f the m a n i p u l a t o r s . T h e s n a k e - a l i k e m a n i p u l a t o r s u s e d i n n u c l e a r p o w e r plants are h i g h l y k i n e m a t i c a l l y redundant. A c o n t r o l s c h e m e i s presented w h i c h , u n l i k e m o s t c o n t r o l schemes f o r s u c h robots, m a k e s f u l l u s e o f the k i n e m a t i c a l r e d u n d a n c y .
T h e b i l a t e r a l c o n t r o l system has been i m p l e m e n t e d a n d tested w i t h a k i n e m a t i c a l l y redundant robot as slave a n d a S c a r a robot as master.
2. Position control of a kinematically redundant robot
T h e p o s i t i o n o f a robot m a n i p u l a t o r is d e f i n e d as the p o s i t i o n a n d orientation o f the end-effector relative to the base f r a m e o f the robot i n cartesian space. G i v e n a certain set o f j o i n t p o s i t i o n s o f the robot ( 0 ) , the f o r w a r d k i n e m a t i c s are used to calculate the p o s i t i o n i n cartesian space ( X ) :
A r o b o t is c o n t r o l l e d b y c o n t r o l l i n g the separate axes o f the m a n i p u l a t o r . S o i n o r d e r to c o n t r o l the r o b o t i n cartesian space, a c o n v e r s i o n t r o m a cartesian space d e s c r i p t i o n i n t o a j o i n t s p a c e d e s c r i p t i o n i s n e e d e d . A straightforward m e t h o d is to use the inverse k i n e m a t i c s to c a l c u l a t e the d e s i r e d j o i n t p o s i t i o n s , g i v e n the desired cartesian p o s i t i o n .
F o r a k i n e m a t i c a l l y redundant robot the i n v e r s e k i n e m a t i c s p r o b l e m has n o c l o s e d f o r m s o l u t i o n . B e c a u s e a k i n e m a t i c a l l y redundant robot has m o r e j o i n t v a r i a b l e s than its n u m b e r o f cartesian degrees o f f r e e d o m , there are a n i n f i n i t e n u m b e r o f w a y s to reach a c e r t a i n cartesian p o s i t i o n .
T h e r e are h o w e v e r n u m e r i c a l s o l u t i o n s to s o l v e the inverse k i n e m a t i c s p r o b l e m o f a k i n e m a t i c a l l y redundant r o b o t T h e s o l u t i o n that is presented here uses the transpose J a c o b i a n f o r the c o n v e r s i o n f r o m c a r t e s i a n space i n t o j o i n t space. W h e n a m a n i p u l a t o r is i n contact w i t h the e n v i r o n m e n t , the m a p p i n g b e t w e e n the j o i n t torques ( t ) and the exerted f o r c e s ( F ) o n the e n v i r o n m e n t i s g i v e n b y :
T = J
T(6)F,
(2)
w h e r e J ( 0 ) represents the J a c o b i a n o f the m a n i p u l a t o r . F i g u r e 1 s h o w s h o w this r e l a t i o n s h i p i s u s e d to a c c o m p l i s h a cartesian c o n t r o l s c h e m e .
Xd
— • JT( ê ) A 5 8f
A e^
5 8Robot +
Amplifier
eFigure 1: Transpose Jacobian inverse kinematics cartesian control scheme
T h e cartesian set p o i n t is c o n s t a n t l y c o m p a r e d w i t h the estimated cartesian p o s i t i o n . T h e r e s u l t i n g errors are m u l t i p l i e d w i t h gains and c a n be regarded as the cartesian forces that w h e n a p p l i e d to the end-effector o f the m a n i p u l a t o r , w i l l reduce the cartesian error. W i t h the transpose J a c o b i a n the cartesian error is t r a n s f o r m e d i n t o j o i n t displacements. T h e s e j o i n t d i s p l a c e m e n t s are added to the p r e v i o u s e s t i m a t i o n o f the d e s i r e d j o i n t p o s i t i o n s as i n d i c a t e d b y the intégration t e r m . T h e actual c o n t r o l is p e r f o r m e d o n j o i n t l e v e l . T h e estimated j o i n t p o s i t i o n s are u s e d as référence f o r the j o i n t p o s i t i o n c o n t r o l l e r s w h i c h use a s i m p l e P I D a l g o r i t h m . T h e c o n t r o l s c h e m e is based o n a f o r m o f stiffhess c o n t r o l o f a r o b o t w h i c h c a n be c o n t r o l l e d i n torque m o d e (figure 2). 6X Gains F ^ rm T T Robot
e
Gains F ^ rm T T Robot-Kin(6)
B y substituting the standard m o d e l f o r each j o i n t , o n e requires a m o d e l based i n v e r s e k i n e m a t i c s estimator. F o r c o n v e r g e n c e o f the estimator the d y n a m i c s o f the m o t o r are d i s a d v a n -tageous a n d therefore m a y b e o m i t t e d to a l l o w faster c o n v e r g e n c e . I n essence the m o t o r m o d e l i s s i m p l i f i e d b y a p u r e integrator w i t h a certain g a i n . B y s w e e p i n g the m o t o r m o d e l g a i n together w i t h the stiffhess t e r m , the estimator b e c o m e s as d e s c r i b e d i n figure 1.
T h e inverse k i n e m a t i c s has been s o l v e d w i t h a n iterative a l g o r i t h m . T h i s i s u s u a l l y n o t bénéficiai t o the c o n t r o l speed o f the System. T h e e s t i m a t i o n o f the j o i n t p o s i t i o n s s h o u l d n o t take too l o n g . F o r s m a l l c h a n g e s i n the cartesian set p o i n t the e s t i m a t i o n i s rather fast. T h e r e f o r e a s l o p e filter i s a p p l i e d to l i m i t the set p o i n t changes t o a m a x i m u m cartesian v e l o c i t y i n o r d e r t o a c h i e v e a g o o d p e r f o r m a n c e o f the System.
T h e c o n v e r g e n c e speed o f the n u m e r i c a l a l g o r i t h m dépends o n the gains w i t h w h i c h the cartesian errors are m u l t i p l i e d . T h e s e gains s h o u l d be set f o r a sufficient h i g h c o n v e r g e n c e speed. It is d i f f i c u l t t o set t h e g a i n s f o r t h e m a x i m u m p o s s i b l e c o n v e r g e n c e speed because this m a x i m u m w i l l d i f f e r w i t h différent c o n f i g u r a t i o n s o f the robot m a n i p u l a t o r .
3. Bilateral control of two robot manipulators
I n o r d e r to c o n t r o l the s l a v e m a n i p u l a t o r , the operator needs a master System to generate p o s i t i o n and force c o m m a n d s . I n o u r case this interface i s p r o v i d e d b y a master m a n i p u l a t o r w i t h a force/torque sensor p l a c e d o n the end-effector o f the robot. T h e forces generated b y the operator w i l l b e c o n v e r t e d i n t o p o s i t i o n c o m m a n d s f o r a cartesian p o s i t i o n c o n t r o l l e r o f the r o b o t as s h o w n i n figure 3 .
Figure
3: Cartesian stiffness control
T h e desired p o s i t i o n d i s p l a c e m e n t (SX) i s calculated as:
àXd = GxFop,
(3)
w h e r e F o p i s the v e c t o r w i t h forces a n d torques generated b y the operator a n d G x i s a d i a g o n a l m a t r i x . T h e d e s i r e d d i s p l a c e m e n t i s added to a référence p o s i t i o n ( X r ) . I n this w a y the end-effector o f the r o b o t w i l l appear to act l i k e a s p r i n g w i t h a certain stiffness a l o n g the cartesian degrees o f f r e e d o m o f the m a n i p u l a t o r . A s the a c t i o n o f a gênerai s p r i n g w i t h the same cartesian degrees o f f r e e d o m as the m a n i p u l a t o r i s d e s c r i b e d b y :
F - KxôXf (A\
w h e r e K x is a d i a g o n a l m a t r i x w i t h the stiffness coefficients o n its d i a g o n a l , the end-effector o f them a n i p u l a t o r w i l l h a v e the same stiffness characteristics as this s p r i n g i f G x equals K x '1.
T h e bilatéral c o n t r o l System i s a c c o m p l i s h e d b y u s i n g the slave p o s i t i o n as référence f o r the p o s i t i o n c o n t r o l l e r o f the master m a n i p u l a t o r and the master p o s i t i o n ( X m ) as référence f o r the p o s i t i o n c o n t r o l l e r o f the s l a v e m a n i p u l a t o r . T h i s i s s h o w n i n figure 4 w h e r e the subscripts ' m ' a n d
Master-side
Ô X d m +/C~~~\ +
cartesian
controlled
master
t
Fop
Slave-side
Fe
cartesian
controlled
G x
sslave
Figure 4: Bilateral control System for wo robot manipulators
D u e t o the l i m i t e d b a n d w i d t h o f the p o s i t i o n c o n t r o l l e r o f the slave, the s l a v e p o s i t i o n w i l l deviate a l i t t l e f r o m the m a s t e r p o s i t i o n d u r i n g free m o t i o n (Fe=0). T h i s p o s i t i o n e r r o r is feit b y the
operator a n d h e w i l l a l w a y s h a v e t o exert a certain force o n the m a s t e r m a n i p u l a t o r t o m o v e the s l a v e m a n i p u l a t o r . W i t h this f o r c e h e i s able to c o n t r o l the speed o f the m o v e m e n t . T h e operator w i l l also f e e l a p o s i t i o n e r r o r that is caused w h e n the slave operator m a k e s contact w i t h the e n v i r o n m e n t .
T h e force r e f l e c t i o n c a n b e m a d e c l e a r w i t h a f e w équations that c a n b e d e r i v e d f r o m f i g u r e 4 . T h r o u g h the p o s i t i o n c o n t r o l l e r s o f both the m a s t e r a n d the slave, the f o l l o w i n g équations w i l l h o l d :
X = X
m- Gx Fe,
(5)*m
*
Xs
+ GxmFOP-
(6)
S u b s t i t u t i o n o f e q u a t i o n 5 in e q u a t i o n 6 y i e l d s the next r e l a t i o n s h i p :Gx
sFe = Gx
mFop
( 7 )H e n c e , i f G xs i s c h o s e n e q u a l t o G x , ^ the forces exerted by the s l a v e m a n i p u l a t o r on the e n v i r o n -m e n t are e q u a l t o the forces exerted b y the operator on the -m a s t e r -m a n i p u l a t o r .
4. Implementation and results of the bilateral control System
T h e b i l a t e r a l c o n t r o l System has b e e n i m p l e m e n t e d f o r the O c t o v e r a r o b o t as the k i n e m a t i c a l l y redundant s l a v e m a n i p u l a t o r . T h i s is a m a n i p u l a t o r w h i c h has s i x j o i n t s to c o n t r o l f o u r cartesian degrees o f f r e e d o m , the p o s i t i o n (represented by three v a r i a b l e s ) a n d the o r i e n t a t i o n o f the e n d -effector i n the h o r i z o n t a l p l a n e (one v a r i a b l e ) . T h e master m a n i p u l a t o r is a B o s c h S c a r a r o b o t w h i c h h a s f o u r j o i n t s to c o n t r o l the same f o u r cartesian degrees o f f r e e d o m as the O c t o v e r a robot. B o t h robots are e q u i p p e d w i t h a s i x degrees of f r e e d o m force/torque sensor at the w r i s t of t h e m a n i p u l a t o r .
A transputer b a s e d system h a s b e e n u s e d to i m p l e m e n t the b i l a t e r a l c o n t r o l a l g o r i t h m s . T h e main feature o f this transputer s y s t e m is that it p r o v i d e s a m u l t i t a s k i n g e n v i r o n m e n t i n w h i c h several processes c a n r u n in p a r a l l e l . T h i s p r o p e r t y i s e s p e c i a l l y u s e d t o i m p l e m e n t separate c o n t r o l processes f o r the t w o different robots. T h e t w o m a n i p u l a t o r s are thus r e a l l y c o n t r o l l e d in p a r a l l e l .
T h e b i l a t e r a l c o n t r o l System that has b e e n presented c a n be d i v i d e d into f o u r different c o n t r o l l e v é i s as s h o w n i n figure 5. U p to a n d i n c l u d i n g the stiffness c o n t r o l l e v e l the c o n t r o l l e v é i s h a v e b e e n i m p l e m e n t e d separately f o r the t w o robots. T h e c o n n e c t i o n b e t w e e n the t w o robots is established i n the last l e v e l , the bilateral c o n t r o l l e v e l .
bilateral control
stifmess control stifmess control cartesian control cartesian control
joint control joint control Master Slave
Figure 5: Bilateral control structure
T h e c o n t r o l m e t h o d that has b e e n presented to c o n t r o l a k i n e m a t i c a l l y redundant r o b o t has b e e n i m p l e m e n t e d a n d tested f o r the O c t o v e r a robot. F i g u r e 6 s h o w s the r e s u l t i n g cartesian p o s i t i o n responses w h e r e the m a n i p u l a t o r i s m o v e d t r o m the ( X , Y ) p o s i t i o n (1.5,0.0) to (1.4,0.1). T h e s o l i d l i n e s i n d i c a t e d b y X s a n d Y s represent the cartesian set p o i n t after the slope filter w h i c h has b e e n set to a m a x i m u m cartesian v e l o c i t y o f 0.03 m/s. T h e dashed l i n e s i n d i c a t e the estimated cartesian p o s i t i o n . T h e a c t u a l cartesian p o s i t i o n i s represented b y the s o l i d l i n e s i n d i c a t e d b y X and Y .
1.42 r r i i i ë. o.oe| g i j i 1 1 i 1 Vj^y- • • • ! : > ^ Y y i 1 i i i tim» [s]
Figure 6: Cartesian responses for the kinematically redundant robot
T h e estimated cartesian p o s i t i o n f o l l o w s the cartesian set p o i n t v e r y fast. T h e actual p o s i t i o n i n the Y d i r e c t i o n f o l l o w s the estimated p o s i t i o n faster than i n the X d i r e c t i o n . T h i s différence results i n a déviation f r o m the desired p a t h a n d is d u e to different responses o f the j o i n t c o n t r o l l e r s o f the robot.
T h e b i l a t e r a l c o n t r o l system has b e e n i m p l e m e n t e d w i t h a l i n e a r stiffness o f 5 K N / m f o r b o t h robots. T h e stiffness o f the t w o robots has to be the same f o r a 1:1 force r e f l e c t i o n . F i g u r e 7 s h o w s the force a n d p o s i t i o n responses o f an e x p e r i m e n t w h e r e the slave m a n i p u l a t o r approaches a n object i n the X d i r e c t i o n . T h e object has a n estimated stiffness o f 5 0 K N / m .
'O 1 2 3 4 S 6 7 •m» [s]
0 1 2 3 4 5 6 7 tint* [s]
Figure 7: Force (left) and position (right) responses of the bilateral control system
D u r i n g free m o t i o n the slave m a n i p u l a t o r f o l l o w s the master m a n i p u l a t o r . T h e operator has to exert a f o r c e o n t h e m a s t e r i n o r d e r t o achieve this m o v e m e n t . W h e n the s l a v e m a k e s contact w i t h the e n v i r o n m e n t this is feit b y the operator. D u r i n g contact the forces exerted b y the slave are e q u a l to the forces exerted b y the operator o n the master. S o b o t h 1:1 p o s i t i o n a n d 1:1 f o r c e b i l a t e r a l c o n t r o l h a v e b e e n r e a l i z e d .A t present t h e stiffhess o f the master i s set t o a constant v a l u e . P r e v i o u s research ( H a m , 1994) h a s p o i n t e d o u t that adaptation o f the stiffness greatly i m p r o v e s the p e r f o r m a n c e . T h e n e x t step i s to i m p l e m e n t t h e adaptive l a w s f o r this s y s t e m .
5. Conclusions
I n this p a p e r a t e l e o p e r a t i o n s y s t e m f o r t w o d i s s i m i l a r robot m a n i p u l a t o r s h a s b e e n presented. T h i s s y s t e m i s based o n cartesian p o s i t i o n c o n t r o l o f the m a n i p u l a t o r s a n d establishes b o t h 1:1 p o s i t i o n a n d 1:1 force b i l a t e r a l c o n t r o l .
A c o n t r o l m e t h o d h a s b e e n presented w h i c h uses a l l the j o i n t s o f a k i n e m a t i c a l l y redundant robot t o c o n t r o l t h e cartesian p o s i t i o n o f this robot.
T h e b i l a t e r a l c o n t r o l s y s t e m has b e e n i m p l e m e n t e d f o r a k i n e m a t i c a l l y redundant slave m a n i p u l a t o r a n d a S c a r a robot as master m a n i p u l a t o r . T h e system w o r k s as i n t e n d e d , the operator c a n m o v e the slave m a n i p u l a t o r to a d e s i r e d p o s i t i o n a n d w h e n the slave m a k e s contact w i t h the e n v i r o n m e n t h e c a n c o n t r o l the forces exerted b y the slave o n the
e n v i r o n m e n t .
References
B e r g e r , J . S . ,
Design and realisation of an extension of the operating system of transputers
and an application of this with the implementation of a complex robot control system.
M a s t e r s thesis ( i n D u t c h ) , D e l f t U n i v e r s i t y o f T e c h n o l o g y , C o n t r o l L a b o r a t o r y , 1 9 9 4 .C r a i g , J . J . ,
Introduction to Robotics; mechanics and control.
A d d i s o n - W e s l y p u b l i s h i n g c o m p a n y , 1 9 8 6 .H a m , A . C . van der, A bilateral position-force controller with gain scheduling for
telemanipulation.
I M A C S i n t e r n a t i o n a l s y m p o s i u m o n s i g n a l p r o c e s s i n g , r o b o t i c s a n d n e u r a l n e t w o r k s , V i l l e n e u v e d ' A s c q , F r a n c e , A p r i l 1994.K l o m p , C ,
Sensor based fine motion control.
P h . D . thesis, D e l f t U n i v e r s i t y o f T e c h n o l o g y , C o n t r o l L a b o r a t o r y , 1 9 9 4 .Pieterse, H . L . ,
