A Design of an Extended State Observer for the Motion/Force Control of Constrained Robotics Systems

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13 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

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A Design of an Extended State Observer for the Motion/Force
Control of Constrained Robotics Systems

Y. Huang
1)
M. Svinin
2)
Z. Luo
2)

S. Hosoe
2)

1)
Institute of Systems Science, AMSS, Chinese Academy of Science, P.R.China

2)
Bio
-
mimetic Control Research Center, RIKEN, Japan

The

work

deals

with

mosition/force

control

of

constrained

robotic

systems
.

The

control

system

is

based

on

the

use

of

an

extended

state

observer

(ESO)

that

can

estimate

the

dynamic

processes

in

nonlinear

systems
.

In

essence,

ESO

implements

a

non
-
model

based

compensation

for

the

nonlinear

dynamics

and

environment

uncertainty

in

controlling

both

the

end
-
effector

motion

and

the

interaction

force
.

The

proposed

strategy

is

tested

under

simulation

where

a

robot

finger

is

constrained

by

a

wall
.

The

simulation

results

show

feasibility

and

a

very

good

performance

of

the

ESO
-
based

control

scheme
.

Assume

that

the

end
-
point

of

the

robot

is

constrained

by

the

external

environment

and

the

geometric

constraints

can

be

described

as
:


where

is

the

vector

of

task

coordinates

associated

with

the

robot

end
-
effector,



is

the

vector

of

joint

angles,

is

the

number

of

scalar

constraints
.

One

obtains

the

dynamic

equations
:



where

is

the

inertia

matrix
;

is

the

combined

vector

of

Coriolis,

centrifugal,

frictional

and

gravitation

forces
;

is

the

vector

of

joint

torques
;

the

vector

is

the

generalized

reaction

force

of

the

constraint
.

Then

the

analytical

expression

for

the

reaction

force

and

the

independent

coordinates

can

be

obtained
:



where

( ( )) 0,:
n m
X R R
 
  
n
X R

n
R

m
( ) (,),
T
T
M H J f
X



 
     
 

 
( )
n n
M R

 
(,)
n
H R
  
n
R


m
f R

f
q

























1
1
1
1
1
1
1
1
1
)
(
]
[
)
(
,
)
(
)
(
)
(
DM
D
DM
H
DM
D
D
DM
f
C
MC
C
H
M
q
C
M
C
MC
C
q
T
T
T
T
T
T






( ),( ) ( ) 0.( ).
D J D C C q
X
j

Q = Q Q = Q= Q

&
&
Problem

Description

,
0
0
0



dt
U
D
U
C
M
f
T
q

0 0
e s t i m a t i o n o f e s t i m a t i o n o f
,
M M D D
( ),
( ),
q q
f f
q F U
f F U
  



  



















)
(
)
(
)
(
1
3
3
3
1
2
2
3
2
1
1
1
2
1
q
Z
G
Z
U
q
Z
G
Z
Z
q
Z
G
Z
Z
q
q
q
q
q
q
q
q
q
q
q
q






1
2
3
,
:,
q
q
q q
Z q
output Z q
Z F








q
U
q
input
,
:
Extended state












)
(
)
(
1
2
2
3
2
1
1
1
2
1
f
Z
G
Z
Z
U
f
Z
G
Z
Z
f
f
f
f
f
f
f
f
f




1
2
:
f
f f
Z f
output
Z F







:,
f
input f U
Extended state
3 0
2 0
q q q
f f f
U Z U
U Z U
  



  


0
0
q
f
q U
f U







Dynamic
linearization
,
1 1 1
0 0 0
1 1 1
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
m
m
m
dyn
M D
D
f
dyn
T T T T T T T
q q f
d
d
d
T
f
d
F C M C C MCq H C M C C M C I U C M C C D U dt
F DM D D DM H
- - -
- - -
é ù
· = - + + - -
ê ú
ë û
· = - Q+
ò
&
&
14444444444442 4444444444443
144444444444442 44444444444443
1444444444442 444444444443
&
&
1 2
,
1 1 1 1 1 1
0 0 0
( ) ( )
f
f
M D
D
T T T
q f
d
d
DM D DM M C U DM D DM D I U dt
- - - - - -
é ù
- + -
ê ú
ë û
ò
44444444444444 444444444444443
14444444444442 4444444444443
144444444444444442 44444444444444443
Extended state observer(I):
Extended state observer(II):
The

simulation

model

comes

from

the

experimental

device

of

a

multi
-
fingered

robot

hand

shown

in

Fig
.
1
.

Suppose

that

the

finger

is

commanded

to

polish

a

wall

that

can

be

described

as
:

and

exert

the

contact

force

.

However,

instead

of

the

exact

geometric

constraint,

we

only

have

a

vague

approximation

about

the

constraint

as

follows
:



Simulation

Research

.
y const k z
  
.
y const

5
f

Basic

Control

Strategy

Motion in the task space(Y
-
Z space)

Experimental setup of the multi
-
fingered robot
hand and kinematic scheme of the finger

Manipulator dynamic estimation( , )

( )
q
F t
3
( )
q
Z t
force response

Force dynamic estimation( , )

( )
f
F t
&
2
( )
f
Z t