Kinematics of Haptics and Telerobotic Systems

How Haptic Interface Works ?

Human Operator

Discrete InterfaceVirtual Environ.Haptic Display

Typical Transmission Mechanism

• Capstan drive

A. Okamura, Stanford, ME327

Typical Transmission Mechanism

• Friction drive

A. Okamura, Stanford, ME327

Transmission Kinematics

A. Okamura, Stanford, ME327

Position Measure, Velocity Estimation

A. Okamura, Stanford, ME327

Noisy signal of velocity and acceleration

Force/Torque relationships

From joint to end-effector

• Forward kinematics

Joint torque from Cartesian Desired Force

1q! 2q! 3q!

knobs

Control Panel

AdvantageCheap (usually no computer or sensors are required)

DisadvantageHuman must do inverse kinematics in their hand !

Joint Rate Control

( )q1-MF J Robot JointControl

Joystick

( )tx! ( )tq!Computer

q

Resolved Rate Control

Cartesian ratecommand

Control Reference Frame

• Advantage– Modest computational requirements– Can be adapted to task (ex. Change ref. frame or

ref. PT) – Small workspace and DOF of Master

Resolved Rate Control (cont.)

Control ref. frame

Visual information

• Disadvantage– Cognitive load

• operator must differentiate desired trajectory• rate control of orientation is difficult

– Watch out for singularities !• Need to consider singularity avoidance algorithm

Resolved Rate Control (cont.)

Master SlaveHand Grip Gripper

Same DH Table

Definitions• Indexing: provision of an arbitrary offset between master and

slave configurations• Scaling: ability to multiply position commands by an arbitrary

constant

Master/Slave Control (Homeo morphie)

Consider a M/S system which is moved by at the master resulting in slave motion

Master/Slave Control (cont.)

( )MMJ q1-

ixD

oxD

( )oMSJ qq +

ixD oxDMqD dqD

Pl

If and then1=Pl 0=oq

( ) ( )SSMMSM JJ qqqq == ,

and( ) ( ) iiMMSSo xxJJx D=D=D - qq 1

oq

Master/Slave Control (cont.)

oMSoif qqqq +=¹ ,0 Index

( ) ( ) IJJ MMoMS ¹+ - qqq 1

Scale

MPSPif qlql =¹ ,1

( ) ( ) PMMMPS JJ lqql ¹-1

MS qq =

Controller must make sure that

Master/Slave Control (cont.)

Ms TT 06

06 =

since DH tables are same, this implies

also, if torque of each joints are same

sm tt =

then, force feedback become automatically same

sm FF =

MS qq =If controller must make sure that

Master/Slave Control (cont.)

Master Slave

Joint i Joint i

G G

+ -Mq Sq

One such controller is : (one for each joint)

Master/Slave Control (cont.)

.

• Advantage– Simple architecture (eg. 6 analog controller)– Good operator interface (1:1 motion and force

control)

• Disadvantage– Master and slave must be same design– Master and slave must be in same configuration– Can’t index or scale except by DH scaling

Generalized Master/Slave

• Master and slave completely different• Communication option

– 4x4 frames– Cartesian increments

Mq Sq( )MMT q06

1-Kin

s ( )MMJ qs1( )ssJ q1-

( )tT06

( )tx!

Indexing using 4x4 frames

SM OO =Actually, in world frame pOO SM +=

MT06

ST06

}{ SM FF 66 /1) No Index

Indexing using 4x4 frames

SM OO =

MT06

ST06

MF62) With an index effect

SF6

jMST : the current j-th index effect

¢MT

06

1+jMST

SMjMS TTT 0

6

1061

-

+ ÷øöç

èæ ¢=New index effect è

Human comfort zone

Index Change Procedure, 4x4 frames

1. Normal teleoperation

2. Operator press (and holds) index button

3. Operator moves to new position , release button

4. Resume manipulation

( ) jMSMS TtTT 0

606 =

ST06 = constant, slave position locked

¢MT

06

SMjMS TTT 0

6

1061

-

+ ÷øöç

èæ ¢=

( ) 106

06 += j

MSMS TtTT

Scaling using 4x4 frames

( ) jMSMS TtTT 0

6

4

3

2

1

06

úúúú

û

ù

êêêê

ë

é

=

ll

ll

is NOT ok ?

[ ]

úúúú

û

ù

êêêê

ë

é

úúú

û

ù

êêê

ë

é

=

1000

06

z

y

x

pS

ppp

RT l

Although

is ok ?

Master-Slave 기준 좌표계 설정

O

O

O

Instrument arm 1

Camera arm

O

O

RootRoot

Control arm L

Master Slave

Master-Slave 기준 좌표계 설정

O

O

O

Instrument arm 1

Camera arm

O

O

RootRoot

Control arm L

Master Slave

!"#.%&'(𝑇 = +#,-..

&'(𝑇

Master-Slave 기준 좌표계 설정

O

O

O

OInstrument arm 2

Instrument arm 1

Camera arm

O

O

O

Control arm R

RootRoot

Control arm L

Master Slave

Master-Slave 기준 좌표계 설정

O

OO

O

Instrument arm 2

Instrument arm 1

Camera arm

O

O

O Control arm R

RootRoot

Control arm L

Master Slave

Indexing using Cartesian Increments

( ) ( )ttXtXXX MMMS D--=D=D

[ ]¢= yqfmmmM zyxX

MS

S

XX

X

D=D

=D

Resume 3.Master Move 2.

0Set 1.

Easier !

where

To re-index

Indexing using Cartesian Increments

M

p

p

S XX Dúúú

û

ù

êêê

ë

é

=D

6

1

l

l!

ji pp ll ¹

Better !

Flexible !

Rate Control Option

• Resolved rate control is an option with generalized master/slave

• Slave moves with a rate proportional to master deflection

• Needs some kind of “spring return”

( )0XXX MS -=D a

Summary

Features Indexing Scaling Kinesthetic Correspondence

Ease operation

JR (O) O X Low

RRC (O) O X

MS X X O

GMS O O O High