FINAL REPORT

BY

DIPAK P . NAIK

PRINCIPAL INVESTIGATOR : PROF. PAUL H . DEHOFF

N89-25268 ( b A S A - C R - 1 8 5 3 E 7 ) C E C H A L I S B AB& I b f k L L J C E h T G S X E E E f i E C R T H E

C E S I G L (3-P BE A C I G CHANGE

LEACE S I A I X C N F i R a l Rspr t Uaiv,) 55 F CSCL 228 U n c l a s ( t c r t h Carolina

82/18 02 197 11

MECHANICAL ENGINEERING AND ENGINEERING SCIENCE' DEPARTMENT UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE N.C. 28223

(1988 - 1989)

https://ntrs.nasa.gov/search.jsp?R=19890015897 2018-06-12T02:37:48+00:00Z

.

Robot gripping of objec ts i n space is i n h e r e n t l y demanding and dangerous and nowhere is t h i s more c l e a r l y r e f l ec t ed than i n the design of the robot grippe-r. An object which escapes t h e gripper i n a micro g environment i s launched not dropped. To prevent t h i s the gr ipper must have sensors and s igna l processing t o determine t h a t ‘the object is properly grasped, eg g r i p poin ts and gripping forces and, i f not, t o provide information t o the robot t o enable closed loop cor rec t ions t o be made. This report descr ibes the sensors and sensor s t r a t e g i e s employed i n t h e hASA/GSFC Spl i t -Rai l P a r a l l e l Gripper. given followed by t h e design of t h e sensor s u i t e , sensor fusion techniques and supporting algorithms.

Objectives and requirements a re

.

CONTENTS

ABSTRACT LIST OF FIGURES NOMENCLATURE SR. NO.

1. 2.

-. 3 . 4 . 5 .

6. 7.

8. 9. 10. 11. 12.

REFERENCES

DESCRIPTION

Introduction Literature Review The Gripper Sensor System Wheatstone Bridge Bridge Power Supply Electrical and Magnetic Disturbances Filtering Signal Amplification

,.

b

Determination of Error Vector Determination of Axerr, Ayerr, and &err Determination of %err, Aeerr,

and Averr

Modes of Grasping Signal Processing Experimental Set-Up Calibration Closure

PAGE NO.

1 1 2 2 3 6 6

7 7 8 8

9

10 10 11 12 12

14-17

+++

F I G . NO

5 6

7 . 8

9 10 11 12 13 1 4 15 1 6 17 18 1 9 20 2 1 22 23 24 2 5

2 6 27

28 2 9 30 31 3 2

- TITLE

Gripper Object I n t e r a c t i o n The Gripper Object Geometry Loca t ion of S t r a i n Gauges and Q u a r t e r - B r i d g e C i r c u i t L o c a t i o n s of Grip Force Gripper Opening Measurement Using a P o t e n t i o m e t e r De te rmina t ion of R o l l and Yaw Error D i f f e r e n t Modes of Grasp ing System Hardware C i r c u i t For S t r a i n Gauge A C i r c u i t For S t r a i n Gauge B C i r c u i t Fo r S t r a i n Gauge C C i r c u i t Fo r S t r a i n Gauge D Close Loop C o n t r o l of Gripper The Exper imenta l S e t u p Face and P r e s s u r e P la te For F i n g e r P a d Details of Face Pla te Grid Senso r Response A e l V/S Ay1 (Azl = 1)

S e n s o r Response del V/S Ay1 ( A 2 1 = 9) S e n s o r Response Ae2 V/S Ayl (Azl = 1)

S e n s o r Response Ae2OV/S Ay1 ( A 2 1 = 9) Sensor Response A e 3 V/S Azl (Ay1 = 1) Sensor Response de3 VIS Azl (Ay1 = 9) S e n s o r Response Ae5 V/S Ay2 (A22 = 1) S e n s o r Response Aeg V / S Ay2 (A22 = 9 )

Senso r Response beg V / S Ay2 ( A 2 2 = 1)

Sensor Response beg V/S Ay2 (Az2 = 9 ) Senso r Response be7 V/S Az2 (Ay2 = 1) Sensor Response A e 7 V/S A 2 2 (Ay2 = 9 ) S e n s o r Response V/S Appl ied Force ( F i n g e r 1) Sensor Response V / S Applied Force ( F i n g e r 2 ) Flow C h a r t F o r C o n t r o l Algori thm

4

PAGE NO

18 1 9 20 21

22

23 24 25 26 27 27 29 30 31 32 33 3 4 35 36 37 38 3 9 40 4 1 4 2

4 3 4 4 45 4 6 4 7 48 4 9

(ii)

NOMENCLATURE

a : Larger S i d e of Cross S e c t i o n of Gripper F i n g e r b : Smaller Side of Cross S e c t i o n of Gripper F i n g e r d : C e n t e r t o C e n t e r D i s t a n c e Between Two S t r a i n

Gauges [CI : C a l i b r a t i o n m a t r i x dx : T r a n s l a t i o n a l Displacement i n X Dire-ct ion E : Young's Modulus E r : Error Vector FX : Grip Force F X Y : Grip Force w i t h b y offset

: G r i p Fo rce w i t h Az offset : S h e a r Modulus : Gauge F a c t o r : Trans fo rma t ion Matrix : I n p u t Voltage t o Bridge 1, V o l t s ( F i n g e r 1) : I n p u t Voltage t o Bridge 2, V o l t s ( F i n g e r 1) : I n p u t Voltage t o Bridge 3, V o l t s ( F i n g e r 1) : I n p u t Voltage t o Bridge 4 , V o l t s ( F i n g e r 1) : I n p u t Vo l t age t o Bridge 5, V o l t s ( F i n g e r 2 ) : I n p u t Voltage t o Br idge 6, V o l t s ( F i n g e r 2 ) : I n p u t Voltage t o Bridge 7 , V o l t s ( F i n g e r 2 ) : I n p u t Voltage t o Bridge 8, V o l t s ( F i n g e r 2 ) : I n p u t Voltage t o P o t e n t i o m e t e r , V o l t s : S e c t i o n Modulus

b

A e I : Output o f Q u a r t e r Br idge 1, V o l t s ( F i n g e r 1) A e 2 : Output of Quar t e r Bridge 2 , V o l t s ( F i n g e r 1)

A e 3 : Output of Quar te r Bridge 3 , V o l t s ( F i n g e r 1) A e 4 : Output of Q u a r t e r Br idge 4 , V o l t s ( F i n g e r 1) A e 1 : Output of Q u a r t e r Br idge 1, V o l t s ( F i n g e r 2 ) A e 6 : Output of Q u a r t e r Br idge 2 , Volts ( F i n g e r 2 )

A e 7 : Output of Q u a r t e r Br idge 3, Volts ( F i n g e r 2) A e 8 : Output of Q u a r t e r Bridge 4, Volts ( F i n g e r 2 )

A e 9 : Output of p o t e n t i o m e t e r , V o l t s

CL : P o i s s o n ' s R a t i o Y : Shea r S t r a i n

Ax : O f f s e t i n X Direct ion AY 1 : Y O f f s e t on F i n g e r 1 Aylop t : Desired Y O f f s e t o n F i n g e r 1

(iii)

A, 2 Ay2opt Az 1

A z l o p t Az2 Az2opt A x e r r A y e r r &err &err b e r r +err

: Y O f f s e t on F i n g e r 2 : Desired Y O f f s e t on F i n g e r 2 : Z O f f s e t on F i n g e r 1 : Desired 2 O f f s e t on F i n g e r 1 : Z O f f s e t on F i n g e r 2

: Desired Z O f f s e t on F i n g e r 2 : T r a n s l a t i o n a l Error i n X D i r e c t i o n : T r a n s l a t i o n a l Error i n Y D i r e c t i o n : T r a n s l a t i o n a l Error i n Z D i r e c t i o n .

: R o t a t i o n a l Error I n P i t c h

: R o t a t i o n a l Error I n R o l l

: R o t a t i o n a l Error I n Y a w b

+++

GN OF -TO W G E ME-

Robot gripping of objects in a micro g environment is inherently dangerous and demanding and this is clearly reflected in the design of the robot gripper. First, an object which the gripper is grasping is necessarily attached to something (Fig. 1) to prevent it from drifting away. Thus it cannot shift its position while it is beiqgrasped and this in turn means that the robot and gripper must do the compliance. Second, an object which escapes the gripper is launched not dropped. Third, because the environment is space, the gripper and sensor system must be very reliable (simple) as repairs are most inconvenient,

The gripper mechanism used is the NASA/GSFC Split-Rail Parallel Gripper. instrumenting this mechanism and giving it the intelligence necessary to accomplish the requirements (sometimes conflicting) described above. The sensor system is described as are the governing equations, electronics and algorithms. Likely error modes are discussed as is the signal processing necessary to make the proper oorrections. Sensor fusion techniques are presented to make use of all available existing sensory data and still keep the system simple.

This report describes our approach to

Over t h e l a s t nine years t he s t a t e of a r t i n robot ic force/torque technology has been developed t o a high degree i n research labora tor ies such a s Draper Labs, J P L , S R I , MIT and elsewhere [l- 301. The i n t e r e s t of providing i n some cases a robot arm w i t h an ac t ive adaptable compliant w r i s t has been l a rge ly emphasized[2, 4 , 1 9 , 2 4 1 . The main component of such a w r i s t i s a several degree of freedom force sensor . The l i t e r a t u r e [l, 2 , 3, 4 , 5, 6, 18, 2 0 , 231 commonly descr ibes sensors based upon s t r a i n gauges.

A t l a s t count there were over a dozen d i f f e ren t transducer designs which resolve, e i t h e r d i r e c t l y or i nd i r ec t ly , t h e forces and torques ac t ing on the robot hand. A s research too l s , these sensors have r e l i e d on the host computer t o ca l cu la t e forces and torques from transducer readings. I n addi t ion, the host computer has been responsible f o r a number of associated functions such a s c a l i b r a t i o n s , sensor biasing e t c . Unfortunately, such

1

sys t ems have n o t found much u s e o u t s i d e of t h e l a b o r a t o r y s i n c e t h e i r a p p l i c a t i o n requires c o n s i d e r a b l e effort on t h e p a r t of t h e u s e r . Although many of t h e n e c e s s a r y t o o l s have been developed , t h e y have y e t t o be embodied i n one cohe ren t u s e r - f r i e n d l y package. T h i s report is t h e r e s u l t o f a s t u d y t o d e l i n e a t e t h o s e f e a t u r e s which can be implemented on a processor dedicated t o force, p o s i t i o n and o r i e n t a t i o n s e n s i n g .

F i g . 2 shows t h e s c h e m a t i c diagram of t h e parallel j a w gripper d e s i g n e d for o u r a p p l i c a t i o n a n d re l ies 'on d i s t r i b u t e d c o n t a c t f o r a s e c u r e grasp. operates on w e l l known rack a n d p i n i o n p r i n c i p l e , t h e r a c k b e i n g coup led t o t h e f ingers a n d hav ing a common p i n i o n which i s b e i n g a c t u a t e d by a d.c. motor. o u t a t e i t h e r e n d s of t h e gripper d u r i n g a d e f i n i t e p o r t i o n of a n o p e r a t i n g c y c l e are enveloped by a protective c a s i n g . The s u r f a c e of t h e j a w are c u r v e d w i t h cross shaped grooves which match similar p r o j e c t i o n s on object s u r f a c e ( F i g . 3 ) . The g r i p p e r f i n g e r s are d e s i g n e d i n such a way t h a t small deflections are permissible i n jaw. s e n s i n g j a w s r e q u i r e s a compromise between e l a s t i c i t y and s t r u c t u r a l s t i f f n e s s t o a v o i d e x t e n s i v e deflections r e d u c i n g t h e p o s i t i o n a l accu racy . measured i n d i r e c t l y by f o u r s t r a i n gauges on e a c h j a w . s e n s o r environment of t h e gripper is minimal . maximum th row is 7 i n c h e s and i t s effective gr ip force is 100 pounds. The g r i p p e r mot ions are c o n t r o l l e d by microprocessor exchanging data w i t h t h e central robo t c o n t r o l l e r such as p o s i t i o n , g r a s p force, s e n s o r data e tc .

T h i s gripper

The racks which p r o t r u d e

The d e s i g n of force

The forces and t h e i r offsets are

The g r i p p e r The

A s te leoperat ion fundamen ta l ly r e q u i r e s s t a t i c grasp, t h e s e n s o r sys t em s h o u l d be able t o s e n s e magni tudes and l o c a t i o n s of g r i p f o r c e a c c u r a t e l y so t h a t t h e object shown i n F i g . 2 f i t s snugly i n t o t h e c o r r e s p o n d i n g recesses i n j a w s . f o l l o w i n g c o n d i t i o n s ,

Senso r system f o r t h i s a p p l i c a t i o n must s a t i s f y

1. High a c c u r a c y a n d r e s o l u t i o n 2 . Compact s i z e and l i g h t weight 3 . Robus t and R e l i a b l e 4 . High s e n s i t i v i t y and s h o r t r e s p o n s e t i m e

T r a n s d u c e r s used f o r measuring t h e s i x component v e c t o r d e s c r i b i n g t h e e r r o r s i n g r i p p e r p o s i t i o n a n d o r i e n t a t i o n w i t h r e s p e c t t o t h a t of t h e o b j e c t t o be g r a s p e d has t o f u l f i l f o l l o w i n g r e q u i r e m e n t s :

1. S t r a i n range:m 0 - 1550 p i n c h / i n c h

2

. . .

2. 3 .

4 . 5 . 6. 7 .

Transve r se s e n s i t i v i t y : n e g l i g i b l e Accuracy of t h e measuring system: Force: +-0.25 lbs

R e s o l u t i o n of t h e system: 0 . 5 l b s L i f e : Load c y c l e s l o 7 fo r l o n g d u r a t i o n o f t i m e Temperature r ange : -looo t o 4000 F Measuring t e c h n i q u e : F a s t data l o g g i n g and p r o c e s s i n g

Torque: +-0.25 i n - l b s

The s e n s o r sys tem of t h e gripper t o s a t i s f y t h e above r e q u i r e m e n t s i s composed of f o u r s t r a i n gauges on each f i n g e r as shown i n F i g . 4 (a) . a c c u r a t e l y control magnitude of gr ip force Fx ( F i g . 5 ) and i t s c o r r e s p o n d i n g offsets Ay and A= which locate t h e p o i n t of act ion of g r ip f o r c e . f o u r pa i r s of s t r a i n gauges t ha t can s e n s e t h e magnitudes and l o c a t i o n s of g r i p force u s i n g a n a l g o r i t h m to’be d i s c u s s e d l a t e r . of t h e two would t o u c h the object f irst , both t h e f i nge r s are i n s t r u m e n t e d w i t h f o u r s t r a i n gauges e a c h . The gripper throw is measured t h r o u g h a potentiometer.

Our p r imary object b e i n g t o

The s e n s o r sys t em p r e s e n t e d c o n t a i n s

S i n c e it i s d i f f i c u l t t o predict which f i n g e r e i t h e r

I n order t o v a r y t h e p o s i t i o n of gripper t o a c c u r a t e l y a l i g n i t s e l f t o g r a s p t h e object t h e v a r i o u s dr ives of robot j o i n t s s h o u l d be c o n t r o l l e d s y s t e m a t i c a l l y i n r e s p o n s e t o t h e s i g n a l s coming from v a r i o u s t r a n s d u c e r s . The p rocedure t o do t h i s i s e l a b o r a t e d as follows.

S t r a i n gauges A, B, C and D form s e p a r a t e l y q u a r t e r of a bridge as shown i n F i g . 4 ( b ) . The o u t p u t o f t h e Wheatstone bridges 1 and 2 for s t r a i n gauge A and B is p r o p o r t i o n a l t o t h e bend ing moments Ma and M b a t gauge l o c a t i o n s A and B. The r e l a t i o n between Fxy, Ma, M b and d, t h e c e n t e r t o c e n t e r distance between the gauges A and B i s as follows,

Fxy * d Ma - M b

Br idge 1 o u t p u t Ael f o r gauge A now c a n be e x p r e s s e d as

= Fxy * C 1 * d l / ( E * Z )

and GF : Gauge F a c t o r of S t r a i n Gauge Vi : I n p u t Voltage t o Half Bridge

. . . . . (1)

A C i r c u i t 1

3

\

d : C e n t e r t o C e n t e r D i s t a n c e Between Two S t r a i n

d l : D i s t a n c e Between Force Fxy and S t r a i n Gauge A E : Young's Modulus 2 : S e c t i o n Modulus Fxy: Gr ip Force w i t h Ay offse t A e 1 : Output of H a l f Bridge C i r c u i t

Gauges

S i m i l a r l y o u t p u t of bridge 2 fo r s t r a i n gauge B 4s as follows,

432 = Fxy * c 2 * d2 /(E * 2) . . . . . (2 )

Where, b

432: Output of Q u a r t e r Bridge C i r c u i t V2: I n p u t Voltage t o Q u a r t e r Bridge C i r c u i t 2

d2 : D i s t a n c e Between Force Fxy and S t r a i n Gauge B

E q u a t i o n s (1) and (2 ) can be r e a r r a n g e d as follows i f V i = V2, i . e . if C1 = C2, t h e n

i . e . ,

S u b s t i t u t i n g t h e v a l u e of Fxy t h u s o b t a i n e d i n e q u a t i o n (1) d e t e r m i n e s t h e v a l u e of d l which i n t u r n d e t e r m i n e s t h e o f f set Ay ,

The f o r c e Fxz g e n e r a t e s a t o r q u e a b o u t y a x i s . The cross s e c t i o n of f i n g e r b e i n g r e c t a n g u l a r i n s h a p e , t h i s t o r q u e t r i e s t o t w i s t t h e f i n g e r .

I t i s w e l l known (321 for r e c t a n g u l a r cross s e c t i o n t h a t

4

. . C ' .*

Ty = G * y * (a * b * b) /(3 t 1.8 * b / a ) Where,

Ty : Torque due t o Fxz y : S h e a r S t r e s s Produced b y Ty G : S h e a r Modulus

S i n c e ,

T h e o u t p u t of q u a r t e r bridge 3 for s t r a i n gauge C is g i v e n by f o l l o w i n g e x p r e s s i o n .

2.0 * Fxz * Az * (1 + p) * C 3 * (3 + 1.8 * b / a )

a * b * b * E . . . . . ( 4 ) Where,

A e 3 : Output of Q u a r t e r Bridge C i r c u i t p : P o i s s o n ' s Ratio a : Larger Side of Cross S e c t i o n of Gripper F i n g e r b : Smaller S i d e of Cross S e c t i o n of Gripper

V3 : I n p u t Voltage t o Q u a r t e r Bridge C i r c u i t 3 FxZ: Grip Force w i t h dz o f f s e t

F i n g e r

and , R1 * R3

* GF c3 = v3 ..................... (Ri + R2) * (R3 + R4)

= c33 * Ae3 ( A s Fxz = F~~ ) Where,

C 3 3 = c o n s t a n t

. . . . . ( 5 )

Ci, C2 a n d C 3 i n e x p r e s s i o n s 1, 2 and 4 are c o n s t a n t s . Equa t ion (3) g ives t h e magnitude of g r i p force Fx ( = Fxy =

F x z ) . E q u a t i o n s (1) (o r e q u a t i o n ( 2 ) ) and ( 5 ) gives t h e y and z o f f s e t s , Ay and Az of g r i p force r e s p e c t i v e l y .

The o u t p u t of t h e q u a r t e r b r i d g e 4 i s d i r e c t l y p r o p o r t i o n a l t o t h e bending s t r a i n of gauge D d u e t o moment

5

generated a t contact points between f inger pad and object i n inaccurate grasping.

As i n t h e case of bridge 1 w e have f o r s t r a i n gauge D bridge 4 output is as follows,

&4 - Md * C4 /(E * 2) . . . . . ( 6 )

V4 : Input Voltage t o Quarter Bridge C i r c u i t 4

i . e . Md - &4 * E * Z / C4

Where, - c44 * A e 4

C44 - constant

b

. . . . . ( 7 )

The signed q u a n t i t y m, t h e moment a t s t r a i n gauge D i s t h e r e f l ec t ion of e r r o r i n p i t ch of t h e gr ipper .

T h e voltage appl ied t o a s t r a i n gauge bridge creates a power l o s s i n each a r m , a l l of which must be d i s s ipa t ed i n t he form of heat . This c a u s e 3 t h e sensing g r i d of every s t r a i n gauge t o operate a t a higher temperature than t h e subs t r a t e t o which it is bonded. T h i s a f f e c t s t he gauge performance. Following f ac to r s determine t h e optimum exc i t a t ion l e v e l of any s t r a i n gauge appl ica t ion . 1. S t r a in gauge g r i d a rea (Active gauge length x ac t ive

g r i d w i d t h ) . 2 . Gauge r e s i s t ance . 3 . Heat s i n k proper t ies of t h e mounting sur face . 4 . Environmental operating temperature range of t h e gauge

5 . I n s t a l l a t i o n and w i r i n g technique. i n s t a l l a t i o n .

The bridge exc i t a t ion voltage f o r our appl ica t ion i s se lec ted from Grid Power D e n s i t y Curves [33]. Select ing the most appropriate power-density l i n e s of t he char t depends, pr imari ly upon two considerat ions: degree of measurement accuracy required, and subs t r a t e heat-sink capaci ty .

C T R I U L AND M-IC DISTURR-

In t e r f e r ing voltages may be induced i n t he leads a n d measuring g r ids by e l e c t r i c a l and magnetic disti irbances. T h i s influence can be subs t an t i a l ly reduced when the

6

i n d i v i d u a l cables are twisted a n d shielded. o n l y p r a c t i c a b l e p r o t e c t i o n a g a i n s t magne t i c d i s t u r b a n c e s [34], w h i l s t s h i e l d i n g s u p p r e s s e s t h e i n f l u e n c e of e lectr ical d i s t u r b a n c e .

T w i s t i n g is t h e

I n p r a c t i c a l a p p l i c a t i o n s of t h e Wheatstone bridge i n s t r a i n gauge measurements it i s o f t e n h e l p f u l and advantageous t o u s e f i l t e r i n g t e c h n i q u e s i n t h e s i g n a l c o n d i t i o n i n g stage t o improve t h e r e s u l t s . p o r t i o n of s i g n a l is of main i n t e r e s t , b u t t h i s part i s submerged by a big n o i s e level, a l o w pass filter c a n be used t o improve the s i g n a l t o n o i s e r a t io . t h e dynamic p o r t i o n of t h e s i g n a l is of i n t e r e s t b u t i s p r a c t i c a l l y h idden w i t h i n a big d.c. par t , d e c o u p l i n g can be a c h i e v e d by i n t r o d u c i n g a h igh-pass f i l t e r . band p a s s f i l t e r i s applied which allows c o n c e n t r a t i o n on t h e i n t e r e s t i n g f r e q u e n c y range. A l o w pass RC f i l t e r is i n c o r p o r a t e d i n bridge c i r c u i t r y for o u r a p p l i c a t i o n .

When t h e s ta t ic

If on t h e c o n t r a r y ,

dost o f t e n a

The o u t p u t from a s t r a i n gauge bridge is a matter of I n order t o u s e a commerc ia l ly a v a i l a b l e A/D m i l l i v o l t s .

c o n v e r t e r it i s n e c e s s a r y t o a m p l i f y t h i s voltage t o t h e order of 5000 fo r s t r a i n gauges A and B and t o t h e order of 8000 for s t r a i n gauges C and D. AD 524, AD625 a n d INA 256 WG which give a d j u s t a b l e g a i n t o 10000 are used t o a c h i e v e t h i 6 . However, t h e s e i n s t r u m e n t a m p l i f i e r s are p rone t o d r i f t .

In s t rumen t amplifiers AD624,

If a m p l i f i c a t i o n = G A I N ( G a i n of a m p l i f i e r ) , t h e n t h e amplif ier o u t p u t

For c a l c u l a t i o n pu rposes t h e ana logue voltages need t o be c o n v e r t e d t o d i g i t a l e q u i v a l e n c e . 1 2 b i t A/D c o n v e r t e r of Macin tosh which g i v e s a n equ iva lence of +- 2047 ( D e c i m a l form) c o r r e s p o n d i n g t o 10 V i n p u t t o t h e A / D c o n v e r t e r .

T h i s s h a l l be done u s i n g

A dec ima l form cumber i n t h e computer Aedi i s t h u s

I t f o l l o w s t h e n t h a t ,

7

Where K is fixed constant.

In Fig. 5 we introduce a graphical representation of local frames for gripper as well as for object. For proper grasp, the homogeneous transformations matrix Tq, describing object frame relative to gripper frame shall be a 4x4 unit matrix. In that case, local frame of object as well as that of gripper shall be superimposed on each other.

In case of improper grasp, in order to define Tr, we will need six quantities: three involving translation and three more involving rotation. The three tranplational quantities are Axerr, Ayerr and Azerr corresponding to three offsets and the three rotational quantities are deer=, &rr and Averrcorresponding to error in roll, pitch and yaw orientation of gripper with respect to object.

We now define error vector Er describing these six components as follows,

These six quantities now.can be determined as follows:

To keep track of gripper opening between two fingers we have incorporated a potentiometer (Fig. 6). As the fingers move closer or away from each other , the potentiometer output voltage varies proportionately. The output voltage bepot of potentiometer can be calibrated in terms of gripper opening. Let gripper opening be Axopt when object is properly grasped between the fingers. If the potentiometer reading Ae7 corresponds to Ax offset, then Axerror given by following expression,

. . . . . ( 9 )

Ayerr and Azerr are given by following expressions,

8

Ayl - Ay2 . . . . . (10)

mere, Ayl , A Z 1 and Ay2 , Az2 a r e t h e y and z o f f s e t s indicated by s t r a i n gauges on f i rs t and second f inge r respect ively.

The e r r o r i n o r i en ta t ion ( r o l l and yaw) w i g . 7 ) is given by following expressions,

. . . . . ( 1 2 )

. . . . . (13)

&err - Mdopt ’ Md . . . . . (14) The value of 4 corresponding t o Md has t o be ca r r i ed

out by c a l i b r a t i n g t h e s t r a i n gauge D .

assumption t h a t wh i l e grasping an object contact i s made on both t h e f i nge r s simultaneously. However, i n general , t h i s need not be so. To ge t r i d of t h i s discrepancy, we propose following.

D e r i v a t i o n of equations (9-14) i s based on one

I f t he s t r a i n gauge readings show t h a t contact i s made only on one f inger , t he robot i s d i rec ted t o t r ave r se t h e gripper assembly i n appropriate x di rec t ion till a contact i s made on another f inge r . received from t h e appropriate s t r a i n gauges. dis tance t raversed by gr ipper assembly i n order t o have contact on another f inge r . Then we have,

T h i s can k c v e r i f i e d by s igna l s Let dx be the

9

The value of Ax can now be subs t i t u t ed i n equations (9- 13) t o f i n d out various components of e r r o r vector E r .

Before deciding on t h e control algorithm based on our mathematical der iva t ions it would be advantageous t o f igu re out a l l poss ib le modes of grasping t h e object between t h e gripper jaws. There a re three possible modes of-grasp a s shown i n Fig. 8 .

Mode 1: This mode i s shown i n Fig. 8 ( a ) . I n t h i s case d i r ec t ion of l o c a l axes of object and those of gr ipper j a w s a r e exac t ly t h e same. I t is t h e most i dea l and hence most r a r e case. This case being t r i v i a l w i l l not be considered here. b

Mode 2 : I n t h i s case Fig. 8 (b) I t h e object is Improperly grasped w i t h certain output s igna ls i n appropriate br idges. T h i s would be t h e most l i k e l y mode present i n majority of the grasping problems.

Mode 3: I n t h i s case Fig. 8 ( c ) , there i s a phase d i f fe rence of 90 degrees between t h e loca l axes of ob jec t and gr ipper jaws. T h i s s i t u a t i o n i s t h e most undesirable one.

Having discussed t h e modes of grasping w e now examine how these various modes can influence t h e design of con t ro l algorithm.

The s t r a i n gauge readings output b y t h e sensor u n d e r load are. r e l a t e d by following expression.

. . . . . (15)

Where [ C ] i s a ca l ib ra t ion matrix. The v a l i d i t y of equation (15 ) i s based on two assumptions:

1. Linear i ty : The response of the s t r a i n gauges var ies l i n e a r l y w i t h the applied load.

2 . Superposit ion: The e f f e c t on each s t r a i n gauge reading due t o F x z , , A , , , A z and A0 a re a d d i t i v e .

10

~

L

The bas ic sensor ca l ib ra t ion

~

procedure consists of applying four known l i n e a r l y independent [Hlk , k==1,4 and recording t h e r e su l t i ng s t r a i n gauge readings [ A e l i j , i = = 1 , 4 ; j = 1 , 4 . The components of [H]ki and [ A e J i j a r e denoted by [ h l k i , j - 1 , 4 and [ A e I i j ,i = 1 , 4 respect ively.

Then ca l ib ra t ion matrix [C] can be obtained from following equation,

[ C l [&I-' * [ H I

Once ca l ib ra t ion matrix is computed e r r o r vector Er can be found o u t t o solve inverse k i n e m a t i c problem t o determine robot j o in t displacements t o move t h e gr ipper at proper locat ion and orientation. b

A microprocessor control led gr ipper sys t em i s proposed a s shown i n Fig. 9 t o carry o u t preliminary experiments. The c i rcu i t s being used f o r amplifying various s t r a i n s igna l s a r e as shown i n Figs. 10-13. The problem of data processing required i n conjunction w i t h t h e sensors i s overcome through t h e u s e of * C * processor of Macintosh which i s capable of handling complex data , computing error vector and s to r ing the information fed i n from t h e sensors. Modifications o r addi t ion to the cont ro l s t ra tegy can simply be ca r r i ed out by a l t e r i n g t h e software.

Fig.15 shows t h e f i r s t experimental setup f o r c a l i b r a t i n g s t r a i n gauges A, B and C. screwed t o t h e f inger pad of t h e gripper and has a carefu l ly marked g r i d on it a s shown i n Fig.16 and Fig.17. Grid p l a t e once mounted on t h e f inger pad def ines the Y and 2 co- ordina tes of t he g r i d nodes, Gripper f ingers a r e loaded through a pressure p l a t e , cable, d i a l gauge ( t o measure accurately t h e applied force) and a v ice . The pressure p l a t e has pointed cone a t i t s center. The point of appl icat ion of force on f inger pad can be e a s i l y varied by locat ing t h i s pointed cone a t desired node poin ts .

The face p l a t e is

Using t h e experimental se tup shown i n F i g . 1 5 the sensor response fo r various loads a t Y and Z o f f s e t s i s n o t e d a s shown i n Figs. 18-31. Sensor response i s measured a t a l l nodes however, only representat ive examples a re shown i n Figs . 18-31. Fig.18-31 shows t h e the var ia t ion of s t r a i n gauge response as magnitude of force and o f f s e t s y and z changes. One more experimental setup f o r measuring the response of a l l s t r a i n gauges t o bending moment i n YZ plane i s being made a t t h e time of w r i t i n g t h i s f i n a l r epor t . The

1 1

s t r a i n gauges A, €3 and C c a n be calibrated u s i n g f o l l o w i n g p rocedure .

CALIBRATION

L e t de [del Ae2 Ae3 A e s ] T r e p r e s e n t t h e s t r a i n gauge r e a d i n g s o u t p u t by t h e s e n s o r unde r load. L e t F [F AY A= elT be t h e force vector. Then F and Ae are related b y

Where [ C l = ( c i j ) is a 4 x 4 c a l i b r a t i o n m a t r i x .

The basic s e n s o r c a l i b r a t i o n p r o c e d u r e c o n s i s t s of a p p l y i n g f o u r known l i n e a r l y independen t s e n s o t l o a d i n g s Fk, k = 1 , 4 and r e c o r d i n g t h e r e s u l t i n g s t r a i n gauge r e a d i n g s Aek. The components of Fk a n d Aek are d e n o t e d by f k j , j - 1 , 4 and Vki, i - 1 , 4 r e s p e c t i v e l y . The sys t em of e q u a t i o n s r e p r e s e n t e d by e q u a t i o n (1) r e s u l t s i n f o u r e q u a t i o n s for each row of ( 1 6 ) . S i n c e w e have carried o u t o n l y one set of exper iment ( fo r s t r a i n gauges A, B and C ) , w e s h a l l be u s i n g three e q u a t i o n s for t h e data shown i n F i g s . 18-29. T h i s s y s t e m of e q u a t i o n s can be solved u s i n g s t a n d a r d methods for s o l v i n g s i m u l t a n e o u s e q u a t i o n s . Repea t ing t h i s p r o c e d u r e for three rows y i e l d s a s o l u t i o n for 3 x 3 c a l i b r a t i o n m a t r i x C . Once w e c a r r y o u t t h e second set of e x p e r i m e n t s , 4 x 4 c a l i b r a t i o n m a t r i x c a n be carried o u t t o compute error vector E r as discussed ea r l i e r .

Up t o t h i s p o i n t w e have i g n o r e d any possible bias i n ---the s e n s o r . I n p r a c t i c e , each of t h e s t r a i n gauge w i l l _. -.

o u t p u t a s m a l l non z e r o v a l u e unde r z e r o load. T h i s v a l u e i s a c o n s t a n t o f fse t o r DC shift which m u s t be compensated fo r t o a c c u r a t e l y o b t a i n e x p e r i m e n t a l da t a . T o a c c o u n t f o r t h i s b i a s , t h e e q u a t i o n (1) i s m o d i f i e d as follows.

[FI = [ C l [ A e - B l . . . (17) The sensor b i a s B i s o b t a i n e d b y reading t h e s t r a i n

gauge o u t p u t u n d e r z e r o load. I n d i v i d u a l sensor b i a s i s accoun ted i n t h e data shown i n F i g s . 1 8 - 2 9 .

W e have, i n t h i s r e p o r t b r i e f l y discussed how a 3 x 3 c a l i b r a t i o n m a t r i x c a n be computed from t h e r e s p o n s e of t h e s e n s o r s t a k e n f o r f i r s t e x p e r i m e n t a l s e t u p . One more e x p e r i m e n t a l s e t u p i s b e i n g c a r r i e d o u t t o compute a l l e l e m e n t s of 4 x 4 c a l i b r a t i o n m a t r i x C . T h i s r e p o r t h a s demons t r a t ed t h a t b u i l d i n g a s e n s o r s y s t e m based upon s t r a i n

1 2

, ,

gauges is possible for reorienting and locating parallel jaw gripper with respect to the object to be grasped and offers a reliable and mechanically rugged solution. involved in reorienting gripper with respect to object are as shown in Fig. 32. Experiments to test a control algorithm as shown in Fig. 32 are yet to be carried out.

The major steps

+++

1 3

I ,

REFERENCES

1. Ruocco S . R . : "Robot Senso r s and Transduce r s "

2 . Lestelle, D . : "Gripper w i t h F i n g e r B u i l t - I n Force /

John Wiley C sons , N e w York (1989) .

Torque S e n s o r s ", Proceed ings of t h e 5 t h I n t e r n a t i o n a l Conference on Robot Vision a n d Senso ry C o n t r o l s , pp. 69-77, (1985) .

*

-

3 . P i l l e r G. : "A Compact Six-Degree of Freedom Force/Torque Senso r For Assemdly Robots", P roceed ings of 1 2 t h I n t e r n a t i o n a l Symposium on I n d u s t r i a l Robots, 6 t h I n t e r n a t i o n a l Conference on I n d u s t r i a l Robot Technology, pp.121-129, (1982) .

Tsuneo Yoshikawa; S i x Axis Force Senso r s" , I c h i r o Futamata

4 . Yoshih iko Nakamura : "Design and S i g n a l P r o c e s s i n g of

Robotic Research, The F o u r t h I n t e r n a t i o n a l Symposium, ( E d . B o l l e s , R.C. and Roth, B . ) pp. 75-81, (1987) .

5. B i c c h i , A. ; Dario, P. ; * " I n t r i n s i c T a c t i l e Sens ing For A r t i f i c i a l Hands", Robotic Research, The F o u r t h I n t e r n a t i o n a l Symposium, ( E d . B o l l e s , R . C . a n d Roth, B . ) pp. 83-90, ( 1 9 8 7 ) .

6 . O o m i c h i , T . : "Mechanics a n d M u l t i p l e Senso ry Bilateral Miyatake, T . C o n t r o l of a F i n g e r e d Manipula tor" , Aekawa, A . Hayashi ,

Robotic Research, The F o u r t h I n t e r n a t i o n a l Symposium, ( E d . Bol les , R . C . a n d R o t h , B . ) p p . 145-153, ( 1 9 8 7 ) .

7 . Nevins , J . L . ; Whi tney , D . E . : "Assembly Research", T u t o r i a l on Robotics Second E d i t i o n Lee, C . S . ; Gonzalez, R . C . ; Fu, K . S . pp . 39 -57 .

a . "Force Sens ing and C o n t r o l " , T u t o r i a l on Robotics Second E d i t i o n L e e , C . S . ; Gonzalez, R . C . ; Fu, K . S . Chapter s i x P P . 323-326.

1 4

I 5 . c

0

9. "Use of Sensors in Programmable Automation", Tutorial on Robotics Second Edition Lee, C.S.; Gonzalez, R.C.; Fu, K . S . pp. 327-338.

10. Shimano, B.; Roth, B. : "On Force Sensing Information and it's Use In Controlling Manipulators", Proceedings of the Eight International Symposium on Industrial Robots, pp. 119-126.

11. Paul, R. ; Shimano, B. : "Compliance and Control" ' - - - Proceedings of the Joint Automatic Control

Conference, pp. 694-699, (1976).

12. Whitney, D.E.: "Force Feedback Control of Manipulator Fine Motions", b

Journal of Dynamic Systems, Measurement and Control, pp. 353-359, (1977).

Controlled Manipulators ", IEEE Transactions on System, Man and Cybernetics, Vol. SMC-1, No. 6 pp. 418-432, (1981).

13. Mason, M.T.: "Compliance and Force Control for Computer

14. Raibert, M.H.: "Hybrid Position / Force Control of Craig, J. J. Manipulators",

ASME Journal of Dynamic Systems, Measurement and Control, Vol. 102, pp. 126-133, (1981).

15. Salisbury, J.K. : "Active Stiffness Control of A Manipulator in Cartesian Coordinates", Proceedings of th 19th IEEE Conference on Decision and Control. pp. 95-100, (1980).

16. Chi-Haur Wu; Paul, R. :"Resolved Motion Force Control of Robot Man ipula tor", IEEE Transactions on System, Man and Cybernetics, Vol. SMC-12 No. 2,pp. 266-275, (1982).

17. Cutkosky, M. : "Grasping As A Contact Sport", Prasad Akella Howe, R. ; Imin Kao

Robotic Research, The Fourth International Symposium, (Ed. Bolles, R . C .

. and Roth, B.) pp. 199-206, (1987).

18. Martin, K.F:"Force Sensing in Magnitude, Direction Lockman, H. and Position",

Trans. ASME VO1. 109, pp. 286-290. (1987).

1 5

1 9 . Cutkosky, M.R.; Wright, P.K. : P o s i t i o n S e n s i n g w r i s t s For I n d u s t r i a l Manipula tors" , P roceed ings of 1 2 t h I n t e r n a t i o n a l Symposium on I n d u s t r i a l Robots, 6 t h I n t e r n a t i o n a l Conference on I n d u s t r i a l Robot Technology, pp.427-438, (1982) .

a n d Non-Tact i le S e n s o r Environment", P roceed ings of t h e 2nd I n t e r n a t i o n a l Conference on Robot V i s i o n a n d Sensory C o n t r o l s , pp. 159-170, (1982) .

20. Dillman, R . :"A Senso r C o n t r o l l e d Gripper With Tactile

21. W i l l i a m s , D.F.; A l l e n , D.M. ;"A R e m o t e On-Line Technique For Accura t e Robot Programming Employing Combined T a c t i l e a n d V i s u a l Sensing", P roceed ings of t h e 2nd I n t e r n a t i o n a l Conference on Robot V i s i o n a n d Sensory C o n t r o l s , pp. 391-398, (1982) .

22. Nguyen V. : "Cons t ruc t ing Force-Closure Grasps", P roceed ings of 1986 IEEE I n t e r n a t i o n a l Conference on Robotics a n d Automation,Vol . 111, pp. 1368-1373, (1986) .

23. Cunningham, R . ; Brooks , T. ; Dotson, R . :" Smart Force/Torque S e n s i n g Systems For Robots", P r e p r i n t from t h e P r o c e e d i n g s of t h e ASME Second I n t e r n a t i o n a l Computer E n g i n e e r i n g Conference, 41982).

Drake,S.H. Automatic Assembly", 2 4 . Watson, P .C : "Pedes t a l and Wrist Force S e n s o r s for ;

Proceed ings of t h e 5 t h I n t e r n a t i o n a l Symposium on I n d u s t r i a l Robots, (1975) .

2 5 . Kozo Ono, :"A N e w Design For 6-Component Force/Torque Yotaro H . Sensors" ;

Mechanical Problems i n Measuring Force a n d Mass. Mar t inus N i j h o f f P u b l i s h e r s , D o r d r e c h t . pp. 39-48. ( 1 9 8 6 ) .

2 6 . Gerelle, E . : "Force Feedback C o n t r o l " , Proceedings of t h e 8 t h I n t e r n a t i o n a l Symposium on I n d u s t r i a l Robots , pp. 194-205, ( 1 9 7 8 ) .

2 7 . Masuo Kasai a t a 1 : " T r a i n a b l e A s s e m b l y System With An A c t i v e Sensory Table P o s s e s s i n g 6 Axes", P roceed ings of t h e 1 1 t h I n t e r n a t i o n a l Symposium on I n d u s t r i a l Robots , pp. 3 9 3 - 4 0 4 , ( 1 9 8 1 ) .

1 6

28. Van Brussel H. at a1:"Further Developments of the Active Adaptive Compliant Wrist (AACW) for Robot Assembly" , Proceedings of the 11th International Symposium on Industrial Robots, pp. 377-384, (1981).

29. Teoh, W.; Workman, G.L.: "Intelligent Gripper With Force Stiles, D. Feedback", Chu, Y.N. ..

Proceedings of the 3rd International Conference on Robot Vision and Sensory Controls, pp. 385-388, (1983). .

30. Parker, J.K. : "Position and Force Control When Positioning Objects With Robot Hands", IEEE International Conference .on Robotics and Automation, Vol. I, pp. 35-40, (1986).

31. Murray, W.M.:"Strain Gage Techniques: Fundamentals and Stein, P.K. Applications", Vol. 11, MIT, Cambridge,

Mass., p. 304, (1956).

32. Singer, F.L.:"Strength of Materials", Harper and Brothers Publishers, New York, p.69, (1951).

33. "Optimizing Strain Gage Excitation Levels", Measurement Group Tech Note TN-502, Measurements Group, Inc., Raleigh, North Carolina.

34. Mardiguian, M. :"How to Control Electrical Noise"

+++

1 7

P

2

Plane Surface

(a) I n d u s t r i a l Appl i ca t ion

Z

- Fixed (0 DOF)

(b) Application In Space

FIG. 1 GRIPPER OBJECT INTERACTION

18

. . . . . . , . -. - . .. . .

ORIGINAL PAGE BLACK AND WHITE PHOTOGRAPH

- (a) Front View

-r ... - .. . .

(b) End View

FIG. 2

THE GRIPPE?.

1 9

L . . . . .. . _. -.> .

FIG. 3

OBJECT GEOMETRY

20

V

A

. .

LOCATION OF STRAIN GAUGES AND QUARTER BRIDGE CIRCUIT

2 1

I

.* i

#I

Object 7

FIG. 5

LOCATION OF GRIP FORCE

2 2

1 2 3

Physical Constructionn

2

Schematic Representation

FIG. 6 GRIPPER OPENING MEASUREMENT USING A POTENTIOMETER

2 3

U.

P i t c h

FIG. 7 DETERMINATION OF ROLL AND YAW ERROR

2 4

yg t t

U-

DIFFERENT FIG.

MODES 8 OF

U GRASPING

8

YO

t

25

I

STRAIN GAUGES + AMPLIFIER + FILTER + A/D CONVERTER _I) . I

F I G . 9

SYSTEM HARDWARE

c

2 6

A

c 7 MICROPROCESSOR .

v - DRIVES CONTROLLER 4 D/A CONVERTER

2

U 0

> (Y d +

U 0

> N d I

1

a u m 3 a (3

C

W L

cn

.C

Y m u a

0

- .-I

0 r( :I-- I 1

f-

F

2 7

0 0

> Y aD

u 0

> cy .-I + .-I

I

u L4 0

cy

m u 0) 3

(3

C

a

- a L 3 v)

f l I I I

1

I '

U

0 m m

I 0 In m

YI

0 1

a Q E l L v )

8 LL

2 8

! . b

Y (D

C .C

a I r, v)

Q

f

f

Y 0

X u)

0 m (7

0 In rl

0

-f

t- 29

Y aD W

a L 0 d

:I-- )

I

f

0 m m

4 t - 30

, .

ISolue Inuerse Klnematics Probleq

v Main Robot Controlle

I

FIG. 14

CLOSE LOOP CONTROL OF GRIPPER

31

pc 3

k a, a a

32

i

Cone

Grid 7

Face “1 plate

FIG. 1 6 Face & P r e s s u r e P l a t e Fo r F i n g e r P a d

3 3

Grid 7

FIG. 1 7 De ta i l s of F a c e P l a t e Grid

34

c.

(1)

( 2 )

( 3 )

(5 )

5

y = 18.9089 + 2.1 0 0 7 ~ R = 0.99 y = 41 + 3.8667~ R = 0.99 y = 65.2444 + 5 . 6 8 ~ R - 0.99 y - 89.9722 + 7.5367~ R - 0.99 ( 4 ) .' y = 112.9139 + 9.635~ R - 0.99

zloffret - 1 b

I I I 1 I

0 2 4 Y-Of f set 8 1 0

LEGEND 4

1 : 4 . 4 Lbs

2 : 8 . 8 Lb.

3 : 13.2 Lbs

4 : 1 7 . 6 Lbr 5 : 2 2 Lbs

3

2

1

FIG. 18 Sensor Response Ael V / S Ay1 (Azl = 1)

3 5

200

y = 20.3667 + 1.7867~ R - 0.97 (1)

y = 43.7861 + 3.671 7~ R 0.98 ( 2 )

y = 67.35 + 5.6967~ R - 0.99 ( 3 ) y - 90.5894 + 7.6483~ R - 0.99 ( 4 )

y=115.1972+9.7517X R-0.99 ( 5 )

.

100-

0 0 0 2 4

I I

6 8 1 0 Y-Of f set

5

LEGEND

1 : 4 . 4 Lbr

2 : 8 . 8 Lbs

3 : 13.2 Lbs

4 : 17.6 Lbs

4

3 5 : 2 2 Lbs

2

F I G . 19 S e n s o r Response Ael V/S A y l ( A z l = 9 )

36

i. L

y = 27.2833 + 1.6513~ R = 0.97 (1)

y = 56.971 1 + 3.592~ R = 0.99 ( 2 )

y = 87.2056 + 5.61 x R = 0.99 ( 3 )

~=119.1444+7.5533~ R-1.00 ( 4 )

y = 150.1889 + 0.6867~ R ( 5 ) 1.00 300

zloffset - 1

0 <

5

LEGEND

1 : 4 . 4 Lbs

4 2 : 8 . 8 Lbr

3 : 13.2 Lbo

4 : 17.6 Lbs

5 : 2 2 Lbs 3

2

1

2 4 6 8 1 0 0 Y-Of f set

F I G . 20 Sensor Response Ae2 V / S Ay1 (Azl = 1)

37

(1) y = 26.2167 + 2.2133~ R = 0.96 y = 58.1917 + 3.7883~ R = 1.00 ( 2 )

y = 90.6356 + 5.79~ R = 0.99 ( 3 )

y = 122.4 + 7 . 8 N 7 ~ R - 0.99 ( 4 )

y = 156.4 + 9.6933~ R = 0.99 (5 )

r l o f f r e t - 9 -

0 2 8 1 0 4 6 Y--Of f set

LEGEND 1 : 4 . 4 Lbs

2 : 8 . 8 Lbs

3 : 13.2 Lbs 4 : 1 7 . 6 Lbs 5 : 2 2 Lbs

FIG. 21 S e n s o r R e s p o n s e Ae2 V / S Ay1 ( A z l = 9 )

38

0 2 4 6 8 10

100

yloftiet - 1

o ! I 1 I 1 I

LEGEND

1 : 4 . 4 LBS 2 : 8.8 Lbr 3 : 13.2 Lbs 4 : 1 7 . 6 Lbi

5 : 22 Lbr

5 4

L 1

FIG. 22 Sensor Response Ae3 V/S Azl (Ayl = 1)

39

y = 26.0444 - 2.3533~ R = 0.99 (1)

y = 47.4361 - 4.2517~ R 1.00 ( 2 )

y = 73.741 7 - 6.435~ R 1 .00 ( 3 )

y=100.8528-8.9017~ R-1.00 ( 4 )

y-126.8308-11.2017~ R-1.00 ( 5 )

120

100

- 80 kJ -4 0 > 4 -I 4

2 - 60 0 0)

a 40

20

yloffret - 9 b

A zlopt

/

0 2 8 10

LEGEND 1 : 4.4 Lbs

2 : 8.8 Lbr

3 : 13.2 Lbr

4 : 17.6 Lbs

5 : 22 Lbs

5 4 3 2

FIG. 23 Sensor Response Ae3 V / S A z l (Ay1 = 9)

4 0

Q

0 0

y = 15.3958 + 1.7595~ R = 0.95 (1)

y 32.9856 + 3.51 0 3 ~ R - 0.97 ( 2 )

y = 50.4256 + 5.4467~ R - 0.98 ( 3 )

y = 69.4564 + 7.3265~ R = 0.98 ( 4 )

y 862979 + 9.3743~ R - 0.98 ( 5 )

200

n e, 4 0 > -4 4 4 100

2 8 10

5

1

2

3

4

5

4

3

2

1

LEGEhi : 4 . 4 Lbs

: 8.8 Lbs

: 13.2 Lbs

: 1 7 . 6 Lbs

: 2 2 L b P

FIG. 2 4 Sensor Response Ae5 V/S Ay2 (A22 = 1)

41

y = 14.7856 + 1.9447~ R = 0.99 (1)

y = 32.221 1 + 3.88~ R = 0.97 (2) y = 50.8589 + 5.684~ R = 0.98 (3)

y = 69.1369 + 7.7162~ R - 0.98 ( 4 )

y = 87.4172 + 9.5763~ R = 0.99 (5 )

1 z2offa.t - 9

100

0

5

4 LEGEND 1 : 4.4 Lbr 2 : 8.8 Lbs 3 : 13.2 Lbs 4 : 17.6 Lbs

3 5 : 2 2 Lbs

..

FIG. 25 Sensor Response Ae5 V / S Ay2 (A22 = 9 )

4 2

y = 19.1667 + 1.3973~ R = 0.98 (1)

y = 40.9103 + 2.9882~ R - 0.97 ( 2 )

y 62.7175 + 4.5645~ R = 0.98 ( 3 )

y = 84.491 4 + 6.61 2 8 ~ R - 0.99

y = 108.8461 + 7.811~ R - 0.99 ( 5 )

- ( 4 )

I z2of f se t - 1

0 2 4 6 8 1 0 Y-Offset

LEGEND

1 : 4 . 4 Lbs 2 : 8 . e US

3 : 13.2 Lbr 4 : 1 7 . 6 U s

5 : 2 2 Lbs

FIG. 2 6 S e n s o r Response Aeg V / S Ay2 (A22 = 1)

43

200

1 0 0 ,

0 - 0 2 4 6 8 10

5

4 LEGEND

1 : 4.4 Lbs

2 : 8.8 Lbt

3 3 : 13.2 Lbs

4 : 17.6 Lbs

5 : 22 Lbs

2

1

FIG. 2 7 S e n s o r Response A e g V / S A y 2 ( A z 2 = 9 )

4 4

2-Offset V/s A

FIG. 2 8 Sensor Response A e 7 V/S Az2 (Ay2 = 1)

LEGEND 1 : 4 . 4 Lbs

2 : 8 . 8 Lbs 3 : 13.2 U s 4 : 17.6 Lbs 5 : 22 Lbs

45

y = - 9.7028 + 2.4383~ R = 0.99 111

y = - 17.2972 + 4.5883~ R = 0.99 ( 2 ) y - - 27.9444 + 7.2467~ R = 1.00 (3)

y = -37.8417+9.855~ R-0.99 ( 4 )

y = - 47.9194 + 12.255~ R = 0.99 ( 5 )

0 2 4

y2offret - 9 .

I 1

6 8 10 2-Of f set

5

4

3

LEGEND 1 : 4 . 4 Lbs

2 2 : 8 . 8 Lbs

3 : 13.2 Lbs

4 : 17.6 Lbs

5 : 22 Lbs 1

FIG. 2 9 S e n s o r R e s p o n s e de7 V / S A z 2 (Ay2 = 9 )

4 6

300

200

100

0 I

y = - 1.4381 + 8.961~ R I 1.00 (1)

y = - 2.719 + 10.T114~ R = 1.00 ( 2 )

y = - 1.0485 + 6.1625~ R = 1.00 ( 3 ) 2

yloffret - 1 zloffret - 1

0

1

LEGEND

1 : el

2 : e2

3 : e3 3

10 2 0

Force (Lbs)

30

F I G . 30 S e n s o r R e s p o n s e V / S Applied Force ( F i n g e r 1)

4 7

200

100

- 01 e) 4 0 > -4 4 4 -4 E

Q,

- a

0

-100 0

Y I -2.2119+7.474~ R-1.00 (1)

y - -2.9876+8.044~ R-1.00 (2)

y = - 0.4714 - 0.439~ R - 0.98 ( 3 ) 2 1

y2offset - 1 r2offret - 1

I

1 0 20 Force ( a s )

30

LEGEND

1 : e5 2 : e6 3 : e7

3

F I G . 31 S e n s o r Response V / S A p p l i e d F o r c e ( F i n g e r 2 )

48

S t a r t U Read e j , j = 1 , 9 i-i

I N o contac t on on jec t

I Contact only on f i n g e r 1 Yes

Compute y l , z l and Fx

(c NO Compute E r = [dx dy dz 0 8 01

Contact only on f i n g e r 2 Y e s

Compute y2, 22 a n d Fx

N o

Icontact on both t h e f i n g e r s ] Compute E r = [dx dy dz 0 0 01

Compute E r = [dx dy d z 1 0 Q ]

N e w pos i t i on and o r i e n t a t i o n of gr ipper =

E a r l i e r pos i t i on and o r i en ta ion + E r

No

* Solve Inverse Kinematics Problem t o Send commands t o d r i v e f i n d j o i n t r o t a t i o n angles of robot con t ro l l e r -b

r

Move robot end e f f ec to r t o grasp t h e object

F I G . 32 F low C h a r t For C o n t r o l Algorithm 4 9