TELKOM
NIKA
, Vol.12, No
.2, June 20
14
, pp. 349~3
5
6
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i2.2106
349
Re
cei
v
ed Fe
brua
ry 13, 20
14; Re
vised
April 15, 201
4; Acce
pted
May 3, 201
4
Adaptive Control of Space Robot Manipulators with
Task Sp
ace Base on Neural Network
Zhou Shuhu
a
1
, Ye Xiaoping
2
*, Ji Xiao
ming
2
, Zhang Wenhui
2
1
F
a
ir F
r
iend Institute of Electromech
naics
，
Han
g
zho
u
Voc
a
tion
al a
nd T
e
chnic
a
l Co
lle
ge
，
Z
heji
ang H
a
n
g
z
hou 3
1
0
000
2
Institute of
T
e
chno
log
y
，
L
i
sh
ui Univ
ersit
y
，
Z
heji
a
n
g
Lis
hui
323
00
0
，
T
e
lp 0578-
227
125
0, F
a
x 0
5
7
8
-22
712
50
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: hit_z
w
h
@
12
6.com
A
b
st
r
a
ct
As are co
nsid
e
r
ed, the b
ody
p
o
st
ure is c
ontr
o
lle
d a
nd
positi
on ca
nn
ot cont
rol, spac
e
man
i
pul
ator
system
model
is diffic
u
lt to
be set
up bec
ause of
distur
bance
and model uncerta
inty. An adaptive contr
o
l
strategy bas
ed
on n
eur
al n
e
tw
ork is put for
w
ard. N
eura
l
n
e
tw
ork on-li
ne
mo
de
lin
g tech
nol
ogy is
use
d
to
appr
oxi
m
ate th
e system
unc
e
r
tain
mo
del,
a
n
d
the strategy
avoi
ds solv
ing
t
he inv
e
rse Jac
obi
matrix, n
e
u
r
a
l
netw
o
rk ap
pro
x
imatio
n err
o
r
and
exter
nal
b
oun
de
d d
i
sturb
ance
are
e
l
i
m
i
nat
ed
by
vari
a
b
le
structure
c
ontro
l
co
n
t
ro
ll
e
r
. In
verse
d
y
nam
i
c
mo
d
e
l
o
f
the
contro
l
stra
te
g
y
d
o
e
s
no
t n
e
e
d
to
b
e
e
s
ti
ma
te
d
,
a
l
so
d
o
n
o
t
n
eed
to take the training pr
ocess,
glo
bally asy
m
ptotically
stabl
e
of the c
l
os
ed-loop system
is
proved based
on
the lyap
un
ov theory. T
he si
mu
lati
on
resu
lts show
that the desi
g
n
ed co
nt
roll
er can ac
hiev
e hig
h
con
t
ro
l
precisi
on h
a
s the i
m
p
o
rtant valu
e of eng
ine
e
rin
g
app
lic
atio
n.
Ke
y
w
ords
: Neura
l
netw
o
rk
；
Space rob
o
tic
；
Adaptive con
t
rol; Variab
le structure contro
l
1. Introduc
tion
Space
robot
has differe
nt
dy
namics
an
d con
s
traint
s with th
e g
r
o
und
rob
o
t: ki
netics of
mech
ani
cal a
r
m and the b
a
se of the co
upling, sin
gul
ar, limited fuel supply and l
i
mits of attitu
de
control syste
m
. These fa
ctors lead t
o
spa
c
e
rob
o
t sho
w
the strong n
onl
inear dyn
a
mi
cs
prop
ertie
s
, a
s
a
result th
e dynami
c
s
and
co
ntro
l
of sp
ace
rob
o
t than fixed
ground
robo
t is
compl
e
x, not
like
ground
fixed ba
se
of
robot
s
c
ont
ro
lled by g
ene
ral metho
d
. F
o
r exa
m
ple, t
h
e
dynamic mo
del of manip
u
lator ma
ss,
inertia matri
x
and load quality cann
ot be accura
tely
acq
u
ire
d
, an
d
external
di
sturba
nce
sign
als
have a
ce
rtain im
pa
ct o
n
the
co
ntroll
er. To
elimin
ate
thes
e non-linear fac
t
ors
,
many
advanced c
o
ntrol
s
t
rategies
s
u
c
h
as
robus
t
control ref.[1]-[3],
adaptive cont
rol
ref.[4]-[5],
fuzzy cont
rol ref.[6]-[11]
and neural
network cont
rol
ref.[12]-[15] have
been used
in
spa
c
e ro
bot
trackin
g
control.
Most
of
th
e re
se
arche
s
focu
s on
joint
-
sp
ace tra
c
ki
ng.
Ho
wever, i
n
many cases,
the d
e
si
red
trajecto
ry
i
s
descri
bed
in
task-spa
ce
a
nd the
ro
bot
is
controlled by
the torque in
p
u
t in joint-sp
a
c
e, this
is
kno
w
n a
s
the task-spa
ce tracking pro
b
lem.
Ref.[16]-[17]
bring fo
rward
adapt
ive co
ntrol metho
d
s
. In the pro
c
e
ss of de
si
gning, the
para
m
eters
of dynamic
equatio
ns n
e
ed be line
a
riz
ed, so co
mplicate
d
pre- calcul
atio
n is
requi
red. Ref.[18] proposes an
fuzzy
-neural
control
me
thod whi
c
h does not
requires the exact
model
of robot. But much
parameter is adj
ust
ed, that affects the real-tim
e. Ref.[19] has
pre
s
ente
d
a neural
n
e
two
r
k co
ntrol me
thod,
un
ce
rta
i
n mod
e
l can
be id
entified
adaptively
by
neural n
e
two
r
k, b
u
t this
control
schem
e only
c
an
g
uara
n
tee th
e
system
unif
o
rmly ultimat
e
ly
boun
ded (UUB).
In
this pap
er,
an ada
ptive neural-netwo
rk cont
rolle
r i
s
pro
p
o
s
ed
to
deal
with th
e
task spa
c
e
tracking
prob
lem of sp
ace
robot m
anip
u
lators
with uncertain kin
e
matics
an
d dynamics.
T
he
tracking
controller i
s
mo
del
-inde
pen
dent;
this
cont
rol method obtai
ns cont
rol
la
ws by
the
n
e
ural
netwo
rk onli
n
e mod
e
ling
tech
nolo
g
y. The n
eural
n
e
twork a
p
p
r
ox
imation e
r
rors a
nd
extern
al
boun
ded
dist
urba
nces are
eliminate
d
b
y
sliding
mo
d
e
varia
b
le
structure
contro
ller. The
cont
rol
method n
e
ither re
quires
a
n
estimate of
inverse
dyna
mic mod
e
l, nor re
quires
a time-con
sumi
ng
training p
r
o
c
ess. Base
d o
n
the Lyapun
ov theory,
this co
ntrol met
hod proves g
l
obal a
s
ymptotic
stability of th
e whole
cl
osed-lo
op
syst
em. The
ne
u
r
al
cont
rolle
r ca
n n
o
t onl
y achi
eve hi
gher
pre
c
isi
on
with
out cal
c
ul
atin
g the inve
rse
Ja
cobi
an
m
a
trix, so it re
d
u
ce
s the
calculation q
uanti
t
y,
but al
so
me
et re
al-time
requi
rem
ents.
So it
ha
s
great
value
in en
gine
erin
g ap
plication
s
.
Simulation re
sults
sho
w
th
at the cont
roller ca
n achiev
e highe
r preci
s
ion.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 2, June 20
14: 349 – 35
6
350
This p
ape
r p
r
esents
a ne
ural n
e
two
r
k
adaptiv
e cont
rol metho
d
to copy
with trackin
g
probl
em of
space robot
m
anipul
ators with
un
ce
rt
ain kinem
atics a
nd
dyn
a
mi
cs with
ta
sk spa
c
e.
Con
s
id
erin
g t
hat exa
c
t mo
del i
s
difficult
to obtain, thi
s
co
ntrol
meth
od u
s
e th
e n
eural
net
work to
identify syste
m
paramete
r
s. Ro
bu
st co
ntrolle
r is
de
signed to
elim
i
nate the a
pproximation e
r
rors
of neu
ral
net
work
and
external
di
sturb
a
n
ce
s. Th
e
co
ntrol m
e
thod
neither requi
res
an e
s
timat
e
of
inverse dyna
mic mo
del, n
o
r
cal
c
ulate
s
the invers
e Jaco
bian matri
x
.
Global
a
s
y
m
ptotic stabil
i
ty
of the cl
ose
d
-loop
system i
s
p
r
oved
ba
sed on
Lyapu
n
o
v theory. Si
mu
lation
re
su
lts sh
ow that
the
controlle
r ca
n
achieve hi
gh
er preci
s
io
n.
2. D
y
namic e
quation
s of
space ro
bot
w
i
th ta
sk sp
ace
The Figu
re 1
sho
w
s the m
odel of one
-a
rm
sp
ace rob
o
t. The coo
r
d
i
nate system
can b
e
defined as
fol
l
ows:
0
B
: the spacecraft plat
form,
(1
,
,
)
i
Bi
n
: the
i
st
link-ro
d of m
anipul
ator,
i
J
: the joint
whic
h
c
o
nnec
ts
1
i
B
with
i
B
,
i
C
:
the mass’ cente
r
of
i
B
,
i
a
，
3
i
bR
re
sp
ect
i
v
e
ly
:
positio
n ve
ctor th
at is fro
m
i
J
to
i
C
and f
r
om
i
C
to
1
i
J
,
3
i
kR
: the unit
vecto
r
of rotative
dire
ction
i
J
,
3
i
rR
: the po
sition
vector of the
mass’
cente
r
i
B
,
3
g
rR
: th
e
un
kno
w
n ve
c
t
or
of the system
’s ce
ntroid,
3
e
pR
:
positio
n vecto
r
of the mani
pulator’
s
en
d,
3
i
IR
: the inertia
of the lin
k-ro
d relative to i
t
s centroid,
I
O
: the in
ertial
o
r
igin,
g
O
：
: the
ce
ntroi
d
of t
he
who
l
e
sy
st
em,
i
m
: the ma
ss of
i
B
,
M
：
1
n
i
i
M
m
I
、
E
、
B
respectively : the inhe
rit
s
coeffici
ent, manipul
ator’
s
e
nd co
ordi
nate
s
syste
m
, the basi
c
body coordi
nate
s
sy
stem.
Figure 1. Parameters of m
anipul
ator
Free-floating space
robot
dynamic equat
ion can be written as follow ref.[20]:
()
(
,
)
Mq
q
B
q
q
q
(1)
Whe
r
e
,,
n
qqq
R
are
joint po
sition,
velocity and
accele
ration
vectors;
()
nn
M
qR
is
symmetri
c
p
o
sitive definit
e inertia m
a
tri
x
;
1
(,
)
n
R
qq
q
B
is
Coriolis
/ c
entrifugal
forc
es
;
1
n
R
is
control torq
ue
.
As the robot
in task is
gen
erally given
b
y
the Ca
rtesi
an coordi
nat
e syste
m
. Th
e pap
er
can
sele
ct th
e di
spla
cem
e
nt of the
robo
t’s en
d-
actu
ator i
n
Carte
s
ia
n spa
c
e
as th
e sy
stem
out
put
y
. Thus the sy
stem’s
augm
entation outp
u
t can be
writ
ten as:
()
yh
q
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Adaptive
Control of Space
Robot Manipulato
rs with T
a
sk Space Base .... (Zhou Shuhua)
351
Whi
c
h
n
yR
indicates the
po
si
tions a
nd atti
tudes
of
the manipul
ator end-actu
ator in
Carte
s
ia
n co
ordin
a
tes; for planar two li
nk ro
bot, n
= 2. When calculating the de
rivative of it.
The
pape
r ca
n get
the following
equatio
n:
()
yJ
q
q
(3)
In the
abovi
ng e
quatio
n,
()
[
(
)
(
)
]
br
J
qJ
q
J
q
re
pr
es
e
n
t
s
th
e
J
a
c
o
bia
n
ma
tr
ix,
/
bb
J
yq
，
/
rr
J
yq
.
The pap
er h
y
pothesi
z
e
s
that
r
J
is a no
n-si
ngul
ar m
a
trix, and the
n
J
is reversi
b
le.
Thus by the
equatio
n (3
)
and e
quation
(1
), ta
king th
e external
disturban
ce
d
into acc
o
unt. The
pape
r finally can o
b
tain th
e dynamic e
q
uati
on of the spa
c
e robot i
n
task
spa
c
e:
Dy
C
y
d
(4)
Where
,
,
.
The dynami
c
equatio
n (4
) of spa
c
e ro
bo
t in task sp
ace has the foll
owin
g pro
pert
i
es [21]:
Property
1
:
()
Dq
is reversible a
n
d
boun
ded.
Property
2
:
F
o
r any
n
Z
R
, there is
1
2
TT
D
CZ
ZZ
.
3.
Design
ed
Contr
o
ller base on Neur
al Net
w
o
r
k
For th
e dyna
mic m
odel
(4
) of
spa
c
e
ro
bot, the p
ape
r can
define
r
y
as the
referen
c
e
trajec
tory,
d
y
a
s
the ide
a
l traj
ectory,
()
et
as th
e po
sition tra
cki
ng e
r
ror,
r
as the
filterin
g erro
r
slip surfa
c
e, and
nn
R
as the positive definit
e matrix, then:
()
()
(
)
rd
yt
y
t
e
t
(5)
()
(
)
()
d
et
y
t
y
t
(6)
()
()
(
)
rt
e
t
e
t
(7)
Lemma
[22]
: Let
()
()
()
et
ht
r
t
, whic
h
re
pre
s
ent
s
con
v
olution,
1
()
(
)
ht
L
H
s
and
()
H
s
is
a
nn
cla
s
s tran
sfe
r
fun
c
tion
wit
h
st
rictly exp
onentially
sta
b
le, if
2
n
rL
, then
2
nn
eL
L
,
2
n
eL
,
e
is contin
uou
s. Whe
n
t
,
0
e
，
0
r
，
0
e
, the erro
r eq
uation of clo
s
ed-lo
op sy
ste
m
of free-floatin
g spa
c
e robot
can be
writte
d as:
rr
Dr
C
r
Dy
C
y
d
(8)
If the robot m
odelin
g is a
ccurate, an
d
0
d
. T
he pap
er
can
desig
n the fo
llowing
co
ntro
l
law eq
uation
to guara
n
tee
the global a
sym
ptotic stabi
lity of closed-l
oop sy
stem.
rr
v
D
yC
y
K
r
(9)
Whe
r
e
v
K
repre
s
ent
s po
sitive definite matri
x
.
Proof: to take
Lyapunov fu
nction a
s
:
11
1
TT
CJ
B
J
J
M
J
J
J
T
q
J
1
T
DJ
M
J
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 2, June 20
14: 349 – 35
6
352
1
2
T
Vr
D
r
(10)
To cal
c
ulate i
t
s differential,
the paper
ca
n obtain the followin
g
equ
a
t
ion:
1
2
TT
Vr
D
r
r
D
r
(11)
To combin
e
the clo
s
e
d
-l
o
op e
rro
r e
q
u
a
tion (8)
and
the control
l
a
w e
quatio
n
(9).the
pape
r ca
n get
to the following equ
ation:
0
T
v
Vr
K
r
(12)
Ho
wever, in
pra
c
tical
en
ginee
ring, th
e free
-floatin
g sp
ace ro
b
o
t model
()
Dq
and
(,
)
Cq
q
are difficult to accurately obtain, and th
e external di
sturban
ce
d
exists in sy
stem, these
nonlin
ear u
n
certaintie
s will
cau
s
e the
co
ntrol pe
rform
ance to degra
de.
Con
s
id
erin
g that the neura
l
network ha
s
good no
nline
a
r app
roximat
i
on ability. the pape
r
can
ad
opt
RB
F lo
cal
gen
eralizatio
n n
e
twork to
app
roxi
mate the
un
certain
pa
rts
()
Dq
、
(,
)
Cq
q
in
the un
kno
w
n
system. T
h
u
s
the l
earnin
g
sp
eed
can
be a
c
cele
rate
d greatly and
local
minim
u
m
probl
em
s ca
n
be avoided.
Then the ne
u
r
al network m
odel eq
uation
can be
writte
n as:
()
()
()
T
il
j
l
d
l
Dq
qq
()
()
T
il
j
l
d
qq
(13)
(,
)
()
()
T
il
jl
c
l
Cq
q
zz
()
()
T
il
j
l
c
zz
(14)
Whe
r
e,
,
zq
q
，
il
，
il
repre
s
e
n
ts we
ights of
the n
eural
net
wo
rk,
()
jl
q
，
()
jl
z
rep
r
e
s
ent
s radial ba
sis f
uncti
o
n
of the input vector. And
()
d
q
and
()
c
z
respe
c
tiv
e
ly
rep
r
e
s
ent
s its modeling e
r
rors, an
d is a
s
sume
d to be boun
ded.
Whe
r
e. The
pape
r re
sp
ectively define
ˆ
and
ˆ
as the
estimate valu
e of
and
,
and
and
as
their es
timation errors
.
ˆ
(15)
ˆ
(16)
Then the
cont
rolle
r equ
ation (9)
sho
u
ld b
e
revise
d as:
ˆ
()
(
)
s
g
n
(
)
ˆ
TT
rr
v
s
yy
K
r
k
r
(17)
Whe
r
e
||
||
s
kE
,
Dr
C
r
EE
y
E
y
d
。
The ada
ptive law is d
e
si
gn
ed as:
ˆ
{(
)
}
ii
i
r
i
qy
r
(18)
ˆ
{(
)
}
ii
i
r
i
Qz
y
r
(19)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
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930
Adaptive
Control of Space
Robot Manipulato
rs with T
a
sk Space Base .... (Zhou Shuhua)
353
Whe
r
e
0
T
ii
，
0
T
ii
QQ
.
To put the
eq
uation (13
)
a
nd (1
4) i
n
to t
he eq
uation
(9), and
co
mb
ine into the
e
quation
(17
)
.the pap
er ca
n get to the followi
ng e
quation:
ˆ
ˆ
((
(
)
ˆ
))
TT
T
dc
r
yy
d
y
()
s
g
n
(
)
ˆ
T
rv
s
yK
r
k
r
(20)
Putting
r
y
yr
，
r
y
yr
into the equatio
n(20), and
red
u
c
ing it. the pa
per can get to
:
ˆ
((
s
g
n
(
)
ˆ
))
TT
dc
v
s
rr
K
r
k
r
()
(
)
TT
rr
yy
E
(21)
Putting the equation (8) in
to the abovin
g equatio
n to
calculate, a
nd the
pap
er can obtai
n the
followin
g
equ
ation:
sgn(
)
vs
D
rC
r
K
r
k
r
((
))
TT
rr
yy
E
(22)
4. Stabilit
y
Anal
y
s
is
The p
ape
r
ca
n define
the f
o
llowin
g
Lya
p
unov fu
n
c
tion
s to p
r
ove th
e stability of
clo
s
ed
-
loop sy
stem.
Proof:
11
11
11
1
22
2
nn
TT
T
kk
k
k
k
k
kk
Vr
D
r
Q
(23)
Then
11
11
1
2
nn
TT
T
T
kk
k
k
k
k
kk
Vr
D
r
r
D
r
Q
(24)
In the light of
the prop
erty (1) and p
r
o
perty
(2), the aboving equ
atio
n can b
e
revi
sed a
s
:
11
11
()
nn
TT
T
kk
k
k
k
k
kk
Vr
D
r
C
r
Q
(25)
Putting the e
quation
(22
)
into the ab
o
v
ing equ
atio
n (2
5).the p
a
per
ca
n get
to the followi
ng
equatio
n:
1
sgn(
)
{
}{
(
)
}
n
TT
T
T
vs
k
k
r
k
k
Vr
K
r
k
r
r
r
E
z
x
r
11
11
1
{}
{
(
)
}
nn
n
TT
T
kk
r
k
k
k
k
k
k
k
kk
k
qx
r
Q
(26)
To put the ad
aptive law eq
uation (18) a
nd t
he equ
ation (1
9) into t
he abovin
g e
quation,
||
||
s
kE
, so the pape
r can get to the followin
g
eq
uation:
0
T
v
Vr
K
r
(27)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 2, June 20
14: 349 – 35
6
354
From (27), a
nd takin
g
0|
s
k
into account. The pap
er
can get to
2
n
rL
. From the
lemma, the paper
can de
ri
ve
22
n
eL
L
，
2
n
eL
, in which
e
is
c
o
n
t
in
uou
s
.
So
w
h
en
t
,
0
e
,
0
r
and
0
e
.
5. Simulation Example
About the fre
e
-floating
sp
a
c
e robot, the
t
able 1 sho
w
s two
-
DOF
space ro
bot si
mulation
para
m
eters.
0
50
0
mk
g
，
1
12
mk
g
,
2
10
mk
g
，
0
1.
0
bm
，
1
1.0
bm
，
2
0.
75
bm
，
1
1.
0
am
，
2
0.75
am
，
2
0
66
.
Ik
g
m
，
2
1
1.5
.
Ik
g
m
，
2
2
0.5
.
Ik
g
m
.
The de
sired traje
c
tory of t
he end of sp
ace manipul
ator is:
1
10
.
5
c
o
s
(
)
d
x
t
2
10
.
5
s
i
n
(
)
d
t
x
Base initial value:
0.1
b
q
, des
ired trajec
tory:0.
The extern
al interferen
ce
s are:
f
=
1
[0
.
1
s
i
n
qt
，
2
0.
1
s
in
]
T
t
q
The filtered tracking e
r
ror p
a
ram
e
ters are:
(6
,
6
)
diag
；
Controlle
r gai
n:
(
1
0,
10
)
v
Kd
i
a
g
；
0.6
s
k
Neu
r
al netwo
rk
i
n
itial weig
hts
a
r
e 0.
the width
of all b
a
s
is fun
c
tion
s
are
10. T
he
center
of
basi
s
fun
c
tio
n
is ran
domly
sele
cted in the
input and
output domai
n. Hidde
n no
des a
r
e 40 bi
ts.
The
simul
a
tio
n
result
s
are
sho
w
n
in th
e
Figu
re
2
~ F
i
gure
4. T
he
Figure 2
sho
w
s the t
r
a
cki
ng
scena
rio ma
p of the po
sition of ma
nipulato
r
’s
e
nd. The Fig
u
re 3
sho
w
s desi
r
e an
d
real
trajecto
rie
s
of
base. Th
e Figur
e 4
sho
w
s torque of two
joints.
Figure 2. De
sire traje
c
tory
and re
al traje
c
tory of end
As can
be
se
en fro
m
the
Figure 2, the
prop
os
ed
co
n
t
rol metho
d
can en
su
re th
e a
c
tual
track of the e
nd actu
ator,
and well tra
c
k the de
sir
ed
trajecto
ry. From the Figu
re 3, the pape
r can
find that the desig
ned ne
ural netwo
rk co
ntrolle
r
may effectively approa
ch un
kn
o
w
n mod
e
l within
t = 2 s, and at the same tim
e
doe
sn’t nee
d great
control torque.
The furthe
r si
mulation
s sh
ow that the st
rong
er
the
system’s u
n
kno
w
n no
nlinea
ri
ty is, the
greate
r
the
re
quire
d
control
torqu
e
is
re
q
u
ired
to
a
c
hie
v
e better
cont
rol p
r
e
c
isi
on,
it is ne
ce
ssary
to increa
se th
e co
ntrol to
rq
ue outp
u
t. Co
nsid
erin
g that
the spa
c
e
ro
bots u
s
u
a
lly
work
und
er l
o
w
spe
ed conditi
on in order t
o
maintain th
eir po
st
ures,
the pro
p
o
s
ed
control meth
od ca
n provide
ample time fo
r learning of n
eural n
e
two
r
k,
and meet fully the require
ment of real-ti
m
e.
0.4
0.6
0.8
1
1.2
1.4
1.6
0.4
0.6
0.8
1
1.2
1.4
1.6
x/m
y/
m
real
desired
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Adaptive
Control of Space
Robot Manipulato
rs with T
a
sk Space Base .... (Zhou Shuhua)
355
Figure 3. De
sire and
real trajecto
rie
s
of Base
Figure 4. Con
t
rol torqu
e
of two joints
6. Conclusio
n
In this pape
r,
an adaptive
neural
-n
etwork
co
ntrolle
r is pro
p
o
s
ed
to deal with
the task
s
p
ac
e tr
ack
i
n
g
pr
ob
le
m o
f
s
p
ac
e r
o
b
o
t
ma
ni
pulators wit
h
un
ce
rtain
kin
e
mati
cs and
dynamics.Th
e tracking
co
ntrolle
r is mo
del-in
dep
end
ent, this control method obt
ains
control laws
by the neural
netwo
rk o
n
lin
e modelin
g techn
o
logy
, Th
e neural network a
p
p
r
oxim
ation errors a
nd
external bo
un
ded di
sturb
a
n
c
e
s
are elimi
nated by
slidi
ng mode vari
able structu
r
e
controll
er. T
h
e
control meth
od neithe
r
re
quire
s an e
s
t
i
mate of inverse
dynami
c
model, no
r requires a tim
e
-
con
s
umi
ng training p
r
o
c
ess. Based on t
he Lyapun
ov
theory, this control meth
od prove
s
gl
obal
asymptotic
st
ability of the
whol
e clo
s
e
d
-
loop
sy
stem.
the neural
controlle
r can
not only achi
eve
highe
r p
r
e
c
isi
on with
out
calcul
ating the
inverse
Ja
cobian
matrix, so it
red
u
ce
s the
cal
c
ul
ation
quantity, but also m
eet rea
l
-time
re
qui
re
ments. So it
has
gre
a
t value in e
ngine
e
r
ing a
ppli
c
ati
ons.
Simulation re
sults
sho
w
th
at the cont
roller ca
n achiev
e highe
r preci
s
ion.
Ackn
o
w
l
e
dg
ments
The pa
per i
s
su
ppo
rted
by National
sci
en
ce an
d
technol
ogy
sup
port Plan
Project
(No.2
013BA
C
16B0
2
), Z
h
ejiang P
r
ovin
cial
Na
tu
ral Scien
c
e
F
o
u
ndation (No.
LZ12F
020
01)
and
(No.
LY14
F0
3000
5), Z
hej
iang P
r
ovin
ci
al Edu
c
at
io
n
De
pa
rtment
Scie
nce
Re
sea
r
ch P
r
oje
c
t
(No.Y2
013
30
000), Zh
ejian
g
Provinci
al Scien
c
e a
nd T
e
ch
nolo
g
y Project (No. 20
13C311
0).
Referen
ces
[1]
Dub
o
w
s
k
y
S,
Papa
do
pou
los
EG.
T
he kinem
atics, D
y
nam-
i
cs and
contro
l
of free-fl
yin
g
s
pace r
o
b
o
tic
s
y
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IEEE Trans on Ro
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tics and Auto
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19
93; 9(
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43.
[2]
REN Y, MA Baoli. Ad
aptiv
e
Contro
l of Sp
a
c
e Rob
o
t S
y
st
em Base
d on
Back stepp
ing
Desig
n
.
Acta
0
5
10
15
20
-5
0
0
50
Joint 1/N.
m
0
5
10
15
20
-1
0
0
10
20
t/s
Joint 2/N.
m
100
0
5
10
15
20
-0
.1
5
-0
.1
-0
.0
5
0
0.05
0.1
t/s
real
desired
Base /r
ad
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 2, June 20
14: 349 – 35
6
356
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autic
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a
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n W
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en
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hang
XD, JIA QX, SUN
H
X
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U M. T
he R
e
sear
c
h
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Ro
b
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t F
l
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i
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t T
r
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y
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i
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a
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e
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y
a
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r
tificial ne
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r
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e
ls
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g sh
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n
t coffee drink.
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l J
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r
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o
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hang W
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hu H. Adapt
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h
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e C
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e Mani
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i C, Z
h
a
o
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i
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E
NG B, MA
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e
ng, XIE W
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Hon
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deli
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an
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Co
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F
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Space
Rob
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w
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t
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F
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e
x
i
b
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