Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
2,
N
o
.
1
,
F
e
br
uary
2
0
1
2
,
pp
. 90~
9
7
I
S
SN
: 208
8-8
7
0
8
¶
90
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Adaptive Neuro-
fuzzy Inf
e
rence
System Based Control of Puma
600 Rob
o
t Mani
pulator
Ouamri Bachi
r
*,
Ahm
e
d-foitih Z
o
ubir**
*Département d
e
technolog
ie
, U
n
iversité de Bechar
** Département
d’électroniqu
e,
Université des s
c
ien
ces
et
d
e
la technolog
ie d’Or
an
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 19
th
, 201
1
R
e
vi
sed Jan
2
1
th
, 20
12
Accepte
d Fe
b
10
th
, 201
2
The strong dependence of th
e co
mputed
torque control of d
y
n
a
mic model of
the robot m
a
ni
pulator m
a
kes t
h
is one
ver
y
s
e
nsitive
to uncertainti
es of
modelling and to the extern
al disturbances
. In g
e
neral, th
e vecto
r
of Coriolis
torque,
cen
trifu
g
al and g
r
avity is ver
y
complicated, consequ
e
ntly
, ver
y
difficu
lt to m
o
d
e
ll
ed. Fuz
z
y
Lo
gic Contro
ller
c
a
n ver
y
we
ll d
e
scribe
the
desired s
y
stem behavior wi
th sim
p
le “
i
f-then
”
re
la
ti
ons owing the
designer to
derive “if-then
”
rules manua
lly
b
y
trial and error
.
On the other hand, Neural
Networks perform function appr
oximati
on of a
s
y
stem but cann
o
t interpr
e
t
the solution obtained neith
er check if
i
t
s solution is plausibl
e. Th
e two
approach
es
are
com
p
lem
e
ntar
y. Com
b
ining them, Neural Networks will
allow learning
capabi
lit
y
w
h
ile
Fuzzy
-
Log
i
c will bring
knowledge
representation
(
N
euro-Fuzzy
).
This pa
per
pres
ents the contro
l
of puma 600
robot arm using Adaptive Neur
o Fuzz
y
Infer
e
n
ce S
y
stem (ANFIS) based
com
puted torqu
e
contro
ller
(t
ype PD). Num
e
rica
l sim
u
lation
using the
d
y
namic model of puma 600 robot arm
shows the effectiv
eness of th
e
approach
in im
p
r
oving the
com
puted torqu
e
m
e
th
od. Com
p
arativ
e
evalu
a
tion
with Fuzzy
com
puted torque (type PD)
control is presented to valid
ate th
e
controll
er des
i
g
n
. The res
u
lts
pres
ented em
phas
i
ze th
at a
s
a
tis
facto
r
y
traj
ector
y tr
ack
i
ng precision an
d stabilil
it
y coul
d be achiev
e
d u
s
ing ANFIS
controll
er than
F
u
zz
y control
l
er
.
Keyword:
Fuzzy com
put
ed torque cont
rol
R
o
b
o
t
c
ont
r
o
l
Ada
p
t
i
v
e
ne
ur
o-
fuzzy
i
n
fe
re
nce
syste
m
(ANF
IS).
Copyright @
20
12 Insitute of Ad
vanced
Engin
e
eering and Scien
c
e.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Ouam
ri Bachir,
Dépa
rtem
ent de technologie,
Faculté
de
s sci
e
nces et
de t
e
c
h
n
o
l
o
gi
e,
Uni
v
ersité de Bechar,
B
p
41
7,
B
echa
r
08
0
0
0
,
Al
geri
a.
Em
a
il: o
u
a
m
r
i
b
ac@g
m
ail.co
m
1.
INTRODUCTION
The c
ont
rol
o
f
r
o
b
o
t
m
a
ni
pul
at
ors
p
r
ese
n
t
s
n
o
wa
day
s
a
m
a
jor c
o
ncer
n o
f
re
searc
h
i
n
r
o
b
o
t
i
c
s.
Ind
e
ed
th
e m
a
j
o
rities o
f
t
h
e task
s en
trusted
to
th
e ro
bo
ts are d
e
licate an
d requ
ire great
p
r
ecision
in
t
h
e fast
traj
ectories. Th
e use of th
e
co
n
t
ro
l
b
y
no
nlin
ear d
e
cou
p
l
i
n
g
con
s
titu
tes
a g
ood
ap
pro
a
ch
in
t
h
is d
i
rectio
n.
Suc
h
co
nt
r
o
l
i
s
al
so kn
ow
n as
dy
nam
i
c cont
r
o
l
or com
put
e
d
t
o
rq
ue beca
us
e i
t
i
s
based o
n
t
h
e use of
dy
n
a
m
i
c
m
odel
of t
h
e
ro
bot
[
1
]
.
Im
pl
em
ent
i
ng t
h
i
s
cont
r
o
l
l
e
r
req
u
i
r
es
kn
o
w
l
e
dge acc
ur
ate
an
d
co
m
p
lete
m
o
d
e
l o
f
th
e ro
bo
t. In
su
ch
a situ
atio
n
,
t
h
is co
n
t
ro
l is p
e
rfect. Howev
e
r, in
pr
actice th
is requ
ire
m
en
t is v
e
ry d
i
fficu
lt to
satisfy
co
nsid
eri
n
g
t
h
e ex
tern
al
d
i
stu
r
b
a
n
ces acting
on
th
e rob
o
t
. Und
e
r su
ch
co
nd
itio
ns, th
i
s
co
n
t
ro
l techniq
u
e
is
v
e
ry
sen
s
itiv
e an
d
in
efficien
t [2
].
These
dra
w
ba
cks o
f
t
h
e l
i
n
e
a
ri
zat
i
on c
ont
r
o
l
ha
ve m
o
t
i
v
at
ed resea
r
che
r
s t
o
devel
op
new
ve
rsi
o
ns
an
d strateg
i
es
o
f
in
tellig
en
t an
d adap
tiv
e con
t
ro
l to
lim
it
t
h
eir effects and
to reg
a
i
n
th
e effectiv
en
ess
o
f
th
i
s
m
e
t
hod [
3
]
-
[
4
]
,
[
1
0]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
¶
Ad
apt
i
ve N
e
ur
o-f
u
zzy
Inf
e
re
n
ce Syst
e
m
B
a
se
d C
ont
r
o
l
of
P
u
m
a
6
0
0
R
o
b
o
t
Ma
ni
p
u
l
a
t
o
r (
O
u
a
m
ri
B
a
chi
r
)
91
The
FIS form
s
are a
useful c
o
m
pu
tin
g fr
amew
ork
b
a
sed
on
th
e co
n
c
ep
ts of
f
u
zzy set th
eor
y
,
f
u
zzy
i
f
–t
he
n r
u
l
e
s and
fuzzy
reas
o
n
i
n
g. T
h
e A
N
F
IS [
5
]
-
[
6]
i
s
a FIS i
m
pl
em
ent
e
d i
n
t
h
e fram
e
wo
r
k
of a
n
ad
apt
i
v
e
fuzzy ne
ural network. It combines
t
h
e ex
pl
i
c
i
t
kno
wl
ed
ge rep
r
ese
n
t
a
t
i
on
of a FIS
wi
t
h
t
h
e l
earni
ng
po
wer o
f
AN
Ns.
Us
ual
l
y
, t
h
e t
r
ansf
o
r
m
a
t
i
on of h
u
m
an kn
owl
e
d
g
e
into a fuzzy
syste
m
(in
the form
of r
u
les and
me
m
b
ersh
ip
fun
c
tio
ns) do
es
n
o
t
g
i
v
e
th
e targ
et respo
n
s
e accu
rately. So, th
e p
a
ram
e
ters
o
f
th
e FIS sh
ou
ld
be
d
e
term
in
ed
op
t
i
m
a
l
l
y.
In t
h
i
s
pa
pe
r,
an A
d
a
p
t
i
v
e
N
e
ur
o F
u
zzy
I
n
f
e
rence
Sy
st
em
(A
NF
IS
) ba
se
d C
o
m
put
ed
T
o
r
q
ue (
PD
)
cont
rol
l
e
r i
s
ap
pl
i
e
d t
o
t
h
e
dy
nam
i
c
m
odel
o
f
pum
a 60
0
ro
b
o
t
arm
prese
n
t
e
d.
To
validate the perform
a
nce, a
com
p
ari
s
o
n
wi
t
h
t
h
e f
u
zzy
cont
r
o
l
l
e
r
i
s
per
f
o
r
m
e
d un
de
r sam
e
tu
n
i
ng
. The si
m
u
la
tio
n
resu
l
t
s sho
w
ed
th
at
th
e
n
e
uro-fu
zzy tech
n
i
qu
e
p
r
esen
t
g
ood
resu
lts and
t
h
at th
is
cont
roller is
efficient and
robust.
2.
MODEL MOTION
OF
ROBOT MANIPULATOR
A robot m
a
nipulator c
o
nsists of a m
echanical struct
u
r
e, u
s
ual
l
y
a set
of
ri
gi
d
bo
di
es c
o
n
n
ect
ed i
n
series
b
y
jo
in
ts, with an end
on
th
e gro
und
,
wh
ich
is
t
h
e
ba
se o
f
t
h
e
r
o
bot
,
an
d t
h
e
en
d
b
o
d
y
o
r
e
ffect
or.
The m
odel
of
m
o
ti
on (
o
r
dy
nam
i
cs) of su
ch a m
echani
s
m
i
s
usual
l
y
descri
be
d by
t
h
e fol
l
o
wi
n
g
matrix
equ
a
tion
:
)
(
)
(
)
,
(
)
(
q
F
q
G
q
q
q
C
q
q
M
&
&
&
&
&
+
+
+
=
Γ
(
1
)
Whe
r
e
Γ
is the
1
×
n
v
ector
o
f
actu
a
to
r
jo
in
t t
o
rq
u
e
,
)
(
q
M
is th
e
n
n
×
symmetric po
sitiv
e-defin
ite in
erti
a
matrix
,
q
q
q
C
&
&
)
,
(
is th
e
1
×
n
vect
o
r
o
f
C
o
ri
ol
i
s
a
nd c
e
nt
ri
f
ugal
t
o
r
q
ue,
)
(
q
G
) is th
e
1
×
n
v
ector
of
g
r
av
itatio
n
a
l torqu
e
s,
q
q
q
&
&
&
,
,
are the
joi
n
t displacem
ent, ve
l
o
city, and acceleration vectors,
)
(
q
F
&
is th
e
1
×
n
v
ector o
f
act
u
a
to
r jo
in
t
friction
forces,
and
n
c
o
r
r
es
po
n
d
s t
o
t
h
e
num
ber
of
d
e
grees
o
f
free
d
om
of t
h
e
r
o
b
o
t
.
We
p
o
se in th
e fo
llo
wi
n
g
:
q
q
q
e
d
−
=
=
~
: Vector
o
f
th
e po
sitio
n error,
q
q
q
e
d
&
&
&
&
−
=
=
~
: Vect
o
r
of th
e v
e
l
o
ci
ty error,
q
q
q
e
d
&
&
&
&
&
&
&
&
−
=
=
~
: Vect
or of t
h
e acceleration error.
Whe
r
e
d
d
q
q
&
,
and
d
q
&
&
are resp
ectiv
el
y th
e v
ectors o
f
d
e
sired
p
o
s
ition
,
d
e
sired
velo
city an
d
d
e
sired
acceleration.
To
en
sure the lin
earizatio
n and
th
e
d
e
co
up
lin
g
of th
e n
onl
i
n
ear
sy
st
em
descri
bes by
t
h
e equat
i
o
n (
1
)
in
clo
s
ed
loop
, we in
trodu
ce a linearization cont
rol (c
om
puted torque)
b
a
sed
on
ex
act kn
ow
ledg
e of
the r
o
bo
t
m
odel
and i
t
s
im
pl
em
ent
a
t
i
on al
l
o
ws us di
re
ct
. The l
o
o
p
of
t
h
e l
i
n
eari
zat
ion i
s
achi
e
ve
d
by
cho
o
si
n
g
a t
o
r
q
ue
Γ
app
lied
to th
e
robo
t, as
fo
llows:
)
(
)
(
)
,
(
)
(
0
q
F
q
G
q
q
q
C
q
M
&
&
&
+
+
+
Γ
=
Γ
(2)
Sub
s
titu
tin
g
Γ
i
n
exp
r
essi
o
n
(
1
)
and t
a
ki
ng i
n
t
o
acco
u
n
t
)
(
q
M
th
at is a reg
u
l
ar m
a
trix
, we
h
a
v
e
n
d
ecoup
led
linear system
s:
0
Γ
=
q
&
&
(3
)
Whe
r
e
0
Γ
is an
au
x
iliary inp
u
t
o
f
the select co
n
t
ro
ller.
A proportional derivative control (
PD
) is a
typical choice for
0
Γ
,
given by the equation:
)
(
)
(
0
q
q
K
q
q
K
q
d
p
d
v
d
−
+
−
+
=
Γ
&
&
&
&
(
4
)
B
y
t
h
e re
pl
ace
m
e
nt
of
(
4
)
i
n
(
3
)
,
w
e
get
t
h
e
f
o
l
l
o
wi
ng
er
ro
r
equat
i
o
n:
Evaluation Warning : The document was created with Spire.PDF for Python.
¶
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
2,
No
. 1,
Fe
br
uar
y
20
1
2
:
9
0
– 97
92
0
=
+
+
e
K
e
K
e
p
v
&
&
&
(
5
)
Th
e erro
r equ
a
tio
n
(5) is a linear
d
i
ffe
r
e
n
tial
equ
a
tio
n of
seco
nd
or
d
e
r
.
Whe
r
e
p
K
and
v
K
are p
o
sitiv
e defin
ite d
i
ago
n
al
m
a
trices, so
th
e clo
s
ed
l
o
op
system b
eco
m
e
s l
i
n
ear
d
ecoup
led
.
Thi
s
eq
uat
i
on
has sol
u
t
i
on f
o
r an err
o
r
)
(
t
e
th
at
ex
pon
en
tially t
e
n
d
s to
zero. The closed-loop syste
m
with
th
is con
t
ro
ller,
wh
ere t
h
e m
o
d
e
l o
f
th
e robo
t is
k
nown
with
accu
r
acy, is asym
p
t
o
t
i
cally stab
le. In th
e
case of an i
m
preci
se kn
o
w
l
e
d
g
e o
f
param
e
t
e
rs of t
h
e
ro
b
o
t
and/
o
r
p
r
ese
n
ce of som
e
un
m
odel
l
e
d dy
na
m
i
cs,
th
e co
m
p
u
t
ed
t
o
rqu
e
co
n
t
ro
l sh
ows its lim
i
t
s.
Th
e so
lu
tion
we p
r
op
o
s
e is to u
s
e
ANFIS con
t
ro
ller who
s
e
ro
le is
ad
j
u
st, in per
m
anent, th
e para
meter
p
K
and
v
K
t
o
c
o
m
p
ensat
e
f
o
r
negl
e
c
t
e
d pa
rt
s
of
t
h
e dy
nam
i
c
m
odel
.
The
o
v
eral
l
bl
o
c
k
di
ag
ram
of t
h
e sy
st
em
und
er c
ont
r
o
l
i
s
s
h
ow
n i
n
Fi
gu
re
1.
Fi
gu
re
1.
The
ove
ral
l
bl
ock
d
i
agram
of t
h
e s
y
st
em
3.
AD
APTI
VE
NEU
R
O
FUZ
Z
Y
INFERE
N
C
E S
Y
STEM
E CO
NTR
O
L
3.
1. A
N
FIS
ar
chi
t
ecture
A typical archi
t
ecture of an
ANFIS
i
s
s
h
o
w
n i
n
Fi
g
u
re
2
,
i
n
w
h
i
c
h a ci
rcl
e
i
ndi
cat
es
a fi
xed
n
ode
,
whe
r
eas a s
quare indicates a
n
a
d
aptive
node. For sim
p
li
city, we assume th
at th
e inferen
ce system u
n
d
e
r
co
nsid
eration
h
a
s two
inpu
ts
m
,
n
an
d o
n
e
out
put
z
. Am
ong m
a
ny
FIS m
odel
s
, t
h
e S
u
gen
o
f
u
zzy
m
odel
i
s
th
e
m
o
st wid
e
ly ap
p
lied
on
e
for its h
i
g
h
in
t
e
rpretab
ility a
n
d
co
m
p
u
t
atio
n
a
l efficien
cy, an
d
b
u
ilt-in
op
ti
m
a
l
and a
d
a
p
t
i
v
e t
echni
que
s. F
o
r
a fi
rst
or
de
r S
u
gen
o
f
u
zzy
m
ode
l, a typ
i
cal ru
le set with
two
fu
zzy if / th
en
ru
les
can
be e
x
press
e
d as:
Ru
le 1
:
if
m
is
1
A
and
n
is
1
B
, the
n
1
1
1
1
r
n
q
m
p
z
+
+
=
(6)
Ru
le 2
:
if
m
is
2
A
and
n
is
2
B
, the
n
2
2
2
2
r
n
q
m
p
z
+
+
=
(7)
whe
r
e
i
A
and
i
B
are the fuzzy set
s
in the antece
dent, a
n
d
i
i
q
p
,
and
i
r
are the desi
gn param
e
ters that are
det
e
rm
i
n
ed d
u
r
i
ng t
h
e t
r
ai
ni
n
g
p
r
oces
s.
As i
n
Fi
gu
re
1, t
h
e
A
N
FI
S c
o
n
s
i
s
t
s
of
fi
ve
l
a
y
e
rs:
Fi
gu
re 2.
A
N
F
I
S Arc
h
i
t
ect
ure
ANFIS
e
d
q
d
q
&
d
q
&
&
+
-
)
(
q
M
e
&
+
+
+
-
+
+
)
(
)
,
(
q
G
q
q
q
C
+
&
&
Γ
q
q
&
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
¶
Ad
apt
i
ve N
e
ur
o-f
u
zzy
Inf
e
re
n
ce Syst
e
m
B
a
se
d C
ont
r
o
l
of
P
u
m
a
6
0
0
R
o
b
o
t
Ma
ni
p
u
l
a
t
o
r (
O
u
a
m
ri
B
a
chi
r
)
93
L
ayer
1
:
E
v
er
y
no
de
i
i
n
t
h
e
f
i
rst
l
a
y
e
r em
ploy
s a
n
ode
f
u
n
c
t
i
on
gi
ve
n
by
:
⎪
⎩
⎪
⎨
⎧
=
=
=
=
2
,
1
),
(
2
,
1
),
(
1
1
i
x
O
i
x
O
i
i
B
i
A
i
μ
μ
(
8
)
whe
r
e
i
A
μ
and
i
B
μ
can
adopt a
n
y fuzz
y
m
e
m
b
ership function
(M
F).
L
ayer
2
:
E
v
ery node i
n
this layer calculates the
fi
r
i
ng
streng
th
of
a
r
u
le vi
a
m
u
lt
iplication
2
,
1
),
(
)
(
2
=
×
=
=
i
y
x
w
O
i
i
B
A
i
i
μ
μ
(
9
)
L
ayer 3:
Th
e
i
-th node in this layer cal
culate
s the ratio of the
i
-th rule’
s
firi
ng stre
n
g
th to t
h
e sum
of all rules
firin
g
stre
n
g
ths
:
.
2
,
1
,
2
1
3
=
+
=
=
i
w
w
w
w
O
i
i
i
(
1
0)
whe
r
e
i
w
is re
fer
r
e
d to
as t
h
e
no
r
m
alized firin
g
stren
g
ths
.
L
ayer
4
:
I
n
th
is layer
,
ev
er
y
no
d
e
i
has t
h
e f
o
l
l
owin
g
f
unctio
n:
2
,
1
,
)
(
4
=
+
+
=
=
i
r
y
q
x
p
w
z
w
O
i
i
i
i
i
i
i
(1
1)
whe
r
e
i
w
is th
e
o
u
t
p
u
t
of
layer
3,
an
d
(
)
i
i
i
r
q
p
,
,
is the param
e
ter set. The
pa
ram
e
ters in t
h
is layer are
refe
rre
d to
as t
h
e c
o
n
s
eq
ue
nt
param
e
ters.
L
ayer
5
:
T
h
e
single
n
ode
in
this lay
e
r c
o
m
putes
the
o
v
era
ll out
put a
s
the
sum
m
ation
of
all incom
i
ng si
gnals
,
whic
h is e
x
pre
ssed as:
∑
∑
∑
=
=
=
=
=
i
i
i
i
i
i
i
i
i
w
z
w
z
w
O
2
,
1
,
2
1
2
1
5
(
1
2
)
The output
z
in
Figure
1 ca
n
be re
written as [7]-[9]:
2
2
2
2
2
2
1
1
1
1
1
1
)
(
)
(
)
(
)
(
)
(
)
(
r
w
q
y
w
p
x
w
r
w
q
y
w
p
x
w
z
+
+
+
+
+
=
(
1
3
)
The ANFIS di
stinguishes itself from
norm
a
l fuzzy l
ogic syste
m
s by
the adaptive pa
ra
m
e
ters, i.e.,
bot
h the
p
r
em
ise an
d c
onse
q
u
e
nt pa
ram
e
ters are a
d
justab
le
. The m
o
st rem
a
rka
b
le feat
ure
of t
h
e
ANFIS
is it
s
hybrid learni
ng algorithm
.
The ada
p
tation
pr
ocess o
f
the
param
e
ters of the A
N
FI
S is divided int
o
tw
o steps.
For
the
first st
ep
of t
h
e co
ns
eque
nt
param
e
ters traini
ng
, the Least S
q
uar
e
s m
e
thod
(L
S
)
is u
s
ed
, beca
use th
e
out
put
o
f
the
AN
FIS
is a lin
ear c
o
m
b
ination
of t
h
e c
o
ns
e
que
nt
param
e
ters.
The
p
r
em
ise pa
ram
e
ters are fi
xed
at this step. After the c
o
nsequent pa
ram
e
ters ha
ve
b
een adjusted, the a
p
proxim
a
ti
on err
o
r is b
ack
-p
r
opa
gated
(BP) through
every layer to update the pre
m
ise para
m
e
te
rs as the second ste
p
. This
part of the ada
p
tation
pr
oce
d
u
r
e is
b
a
sed
on
the
gr
adient
desce
n
t pri
n
ciple,
whic
h is the
sam
e
as in the t
r
aini
ng
o
f
the B
P
neu
r
al
netw
or
k. T
h
e con
s
eq
ue
nce p
a
ram
e
ters identified by
the
LS
m
e
thod are
optim
al in the
sense o
f
least
squ
a
res
un
de
r the
co
n
d
ition that t
h
e
pr
em
ise param
e
ters a
r
e fi
xed
.
3
.
2
.
Adapt
i
ve neuro-
fuzzy
co
ntro
ller
In
o
r
de
r to
kee
p
the
r
o
b
o
t, i
n
joi
n
t spa
ce, a
desire
d tra
j
ect
ory
a
n
d
its suc
cessive
deri
vatives a
n
d
,
whic
h
descri
be
respectively the
desire
d
velocity and de
sired acceleration, the st
rate
gy of
the ANFIS
c
ont
rol
consists to adjust in perm
anent th
e values
of the co
rrect
or gai
n
s. The
neur
o
-
f
u
zzy
cont
roller de
vel
o
p
e
d
co
nsists on
two
inpu
ts,
er
ro
r
(
e
) an
d c
h
an
ge
of
er
ro
r
(
e
de
&
=
) de
fined
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEC
E
94
Trian
g
learn
i
p
ara
m
4.
S
l
ogi
c
deg
r
e
¶
E
Vo
l.
2
,
N
o
.
⎩
⎨
⎧
=
=
de
e
This pap
e
g
u
l
ar
me
mb
e
i
ng
algo
r
i
th
m
m
eter of me
m
b
Struct
ure
o
S
IM
ULATI
O
To show
m
e
t
hod, a
si
m
es of
free
do
m
T
Para
m
Mass
Mass
Mass
Coef
f
Coef
f
Coef
f
Coef
f
Coef
f
Coef
f
Len
g
t
Len
g
t
Len
g
t
1,
Fe
br
uar
y
2
−
=
−
q
q
q
q
d
d
&
&
e
r
con
s
id
er
s
t
rshi
p f
unc
t
i
o
n
that co
m
b
in
e
b
er
sh
i
p
f
uncti
o
o
f ANFIS us
e
O
N RESULT
t
h
e c
ont
ri
b
u
t
i
m
ul
at
i
on w
a
s
m
, whose
pa
ra
m
T
able 1. Para
m
m
eters
of the fir
s
t body
of the second b
o
of the thir
d bod
y
f
icient o
f
visc
ous
f
icient o
f
visc
ous
f
icient o
f
visc
ous
f
icient of dry
fric
t
f
icient of dry
fric
t
f
icient of dry
fric
t
t
h of the fir
s
t bo
d
t
h of the second
b
t
h of the third bo
d
2
012
:
90
–
9
t
he
ANFIS s
n
s with
p
r
od
u
e
s least squa
r
o
n.
e
d i
s
s
h
o
w
n i
n
Fig
u
S
i
on of t
h
e
co
n
app
r
ove
d o
n
m
eters are
p
r
e
m
eters of t
h
e P
1
m
o
dy
2
m
y
3
m
friction
1
f
of t
h
friction
2
f
of t
h
friction
3
f
of t
h
t
ion
4
f
of the 1
s
t
ion
5
f
of the 2
n
t
ion
6
f
of the 3
r
d
y
2
1
r
l
=
b
ody
3
2
d
l
=
d
y
a
l
=
3
9
7
tru
c
ture wit
h
u
ct in
fere
nce
r
e m
e
t
hod
w
i
n
Figur
e 3
.
u
re
3.
Str
u
ct
u
n
t
r
ol
by
AN
F
a m
odel
of
a
e
sented on
ta
b
u
m
a 60
0
ro
b
o
h
e 1st body
h
e 2nd bo
dy
h
e 3r
d body
s
t body
n
d
body
r
d body
h
first
o
r
de
r
S
rule are us
e
th
g
r
ad
ien
t
d
u
re of
A
N
F
I
S
F
IS a
nd i
t
s i
m
a
ro
bot
m
a
ni
p
b
l
e
1
[
11
]
:
o
t
m
a
ni
pul
at
o
r
S
ug
en
o m
o
d
e
e
d at the fuz
z
d
es
cent m
e
tho
m
provem
ents
p
ul
at
or pum
a
6
r
us
ed i
n
si
m
u
Va
l
10,
5
2
10,
2
3
8,
76
7
2,
52
N
7
N.
m
1,
75
N
3,
6
N.
10
N.
m
2,
5
N.
0,
1
4
0,
4
3
0,
4
3
ISS
N
:
2
(
1
4)
e
l
cont
ai
n
i
ng
z
ificatio
n
lev
e
d i
s
used t
o
com
p
ared to
6
0
0
,
fo
r the
u
latio
n
l
ues
2
1
Kg
3
6
Kg
7
Kg
N
.m.s
/
rd
m
.s
/
rd
N
.m.s
/
rd
m.s
/
rd
m
.s
/
rd
m.s
/
rd
4
9
m
3
2
m
3
1
m
2
088
-87
08
64
ru
les.
e
l. Hyb
r
i
d
ad
ju
st th
e
the fuzzy
first three
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
¶
Ad
aptive N
e
ur
o-f
u
zzy
Infere
n
ce Syste
m
B
a
se
d C
ontr
o
l of
P
u
m
a
6
0
0
R
o
b
o
t
M
a
nip
u
lat
o
r (
O
u
a
m
ri B
a
chir
)
95
We consi
d
ere
d
a re
fere
nce
traj
ectory, e
n
suri
ng c
o
n
tinuit
y
in position,
velo
city and a
cceleration,
give
n by
:
⎪
⎪
⎩
⎪
⎪
⎨
⎧
+
+
=
+
+
=
+
+
=
)
2
cos
(sin
5
4
)
2
sin
(cos
4
2
)
2
sin
(sin
6
3
3
2
1
t
t
q
t
t
q
t
t
q
d
d
d
For the
fuzzy
cont
roller, whi
c
h
was calcula
ted from
the c
o
nve
n
tional c
o
m
puted torque
controller (
()
(
)
35
,
35
,
35
;
300
,
300
,
300
diag
K
diag
K
v
p
=
=
),
uses tria
ng
ular m
e
m
b
ership
fu
nctio
ns
(f
or i
n
p
u
ts a
n
d
out
puts
)
give
n by
Fig
u
r
e 4:
Figu
re
4.
M
e
m
b
ership
fu
nct
i
on
o
f
the
in
put
s an
d t
h
e
out
pu
ts of
the
f
u
zzy
cont
roller
Figu
re
5, s
h
o
w
s the
be
havi
ou
r
of the
r
o
b
o
t in p
u
r
su
it
of the
desire
d traj
ectory in bot
h
cases
of t
h
e
com
puted t
o
r
q
ue c
ont
rol,
f
u
z
z
y
logic a
n
d
by
A
N
FI
S.
e
e
&
,
μ
-1
-0
.
5
0
0.
5
1
0
0.
2
0.
4
0.
6
0.
8
1
Degr
e
e
o
f
m
e
m
ber
s
h
i
p
NP
N
Z
P
P
P
0
0.
5
1
1.
5
2
2.
5
3
0
5
10
15
Ti
m
e
(
s
)
P
o
s
i
t
i
on 1 (
r
ad)
P
o
s
i
t
i
on
t
r
ac
k
i
ng
of
t
he 1s
t
s
egm
ent
des
i
r
ed
f
u
zzy co
n
t
r
o
l
A
N
F
I
S
c
ont
r
o
l
0.44
0.
441
10
.1
7
10
.1
8
10
.1
9
10
.2
0
0.
1
0.
2
0.3
0.
4
0.
5
0.
6
0.7
0
1
2
3
E
rro
r 1
(ra
d
)
P
o
s
i
ti
on
t
r
ac
k
i
ng
er
r
o
r
1
Ti
m
e
(
s
)
f
u
zzy co
n
t
r
o
l
AN
F
I
S
c
o
n
t
r
o
l
0.
3
0.4
0.5
0.
6
-0
.
0
4
-0
.
0
2
0
Evaluation Warning : The document was created with Spire.PDF for Python.
¶
I
S
SN:
2
088
-87
08
IJEC
E
V
o
l. 2,
No
. 1,
Fe
br
uar
y
20
1
2
:
9
0
– 97
96
(a
)
First se
gm
ent
(
b
) Sec
o
nd
se
g
m
ent
(
c
)
Thir
d segm
ent
0
0.5
1
1.5
2
2.
5
3
-1
0
-5
0
5
10
Ti
m
e
(
s
)
P
o
s
i
t
i
on 2 (
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ad)
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I
J
ECE
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208
8-8
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¶
Ad
aptive N
e
ur
o-f
u
zzy
Infere
n
ce Syste
m
B
a
se
d C
ontr
o
l of
P
u
m
a
6
0
0
R
o
b
o
t
M
a
nip
u
lat
o
r (
O
u
a
m
ri B
a
chir
)
97
Figu
re 5 (
a
,
b
,
c
). T
r
a
j
ectory
pursuits of
positi
on and
position errors
with t
h
e
fuzzy l
ogic
that by the
ANFIS
We see clearly that the control perform
a
nces by AN
FIS are
better tha
n
those in the fuzzy
logic; this
is interprete
d by the faster conve
rgen
ce
of
position trac
king error to zero
(precision and
stability), in the case
of
A
N
F
I
S c
o
ntroller.
T
h
e r
o
b
o
t reac
hes t
h
e
desire
d tra
j
ectory in a
ti
m
e
less tha
n
that
of fuzzy control.
We
found sim
i
lar results for
the case
of the
pursuit in
velocity and accele
r
ation.
5.
CO
NCL
USI
O
N
In this a
r
ticle, we
ha
ve
pre
s
ented a sim
p
le tec
hni
que
o
f
c
ont
rol by
AN
FIS
that c
ont
rib
u
tes
to
im
pro
v
ed
pe
rf
orm
a
nce o
f
th
e
linearizin
g c
o
ntr
o
l ap
plied t
o
r
o
b
o
t m
a
nipul
ators.
The sim
u
lation
results show that the
ANFIS c
o
ntro
ller is better t
o
fuz
z
y cont
roller in
robustne
ss
(adjustm
ent of
the rate
of
vari
ations
of the
PD
gains.) and i
n
trac
king prec
ision a
n
d sta
b
ility. The sim
u
lation
study clearly
indicates the
finer pe
rf
o
r
m
a
nce
of
ada
p
tive
neu
r
o-
fuzz
y
cont
rol,
bec
a
use it is in
h
e
rently
adaptive
in
nat
u
re
. It a
ppea
r
s
fr
om
the resp
ons
e p
r
ope
rtie
s that it has a
hig
h
per
f
o
r
m
a
nce in
presenc
e
of the
plant param
e
ters unce
r
tain
a
n
d un
k
n
o
w
n dis
t
ur
bances
. It
is
use
d
to control syste
m
with unknown m
odel
.
REFERE
NC
ES
[1]
S
P
O
NG
M
.
W
.,
and M
.
V
i
d
y
as
a
g
ar, "Robo
t D
y
n
a
m
i
cs
and
Contr
o
l,"
John Wiley
and Sons
,
In
c,
1
989.
[2]
EGELAND O.,
"On the robustn
ess of the comp
uted torqu
e
tech
nique in man
i
pu
lator Con
t
rol,"
P
r
oc.IEE
E. In
tern
.
Conf.
Robotics a
nd Automation,
1986, p
.
1203-1
208.
[3]
S
U
F
I
AN As
hraf M
azhar
i,
S
u
ren
d
ra Kum
a
r M
e
m
b
er IEEE
, "He
u
ris
tic
S
earch
A
l
gorithm
s
for Tu
ning P
U
M
A
560
Fuz
z
y
PID Controlle
r,
"
International Journal
of Computer
Scien
c
e
, Jun. 200
8, pp
.
277-286.
[4]
HALA Bezine,
Nabil Derbel an
d Adel M. Alimi
,
"Fuzzy
co
n
t
rol
of robot manipulators:
some issu
es on design and
rule base size reduction
,
"
Engin
eering App
lica
t
i
ons of Artif
icia
l
Intell
igen
ce
, Sep
t
2002, vol. 15
,
Issue 5, pp. 401-
416.
[5]
J.
S.
R.
Ja
ng,
" A
N
FIS: Ada
p
tive
-
ne
tw
ork-based f
u
zzy
inf
e
ren
ce s
y
stem, "
I
EEE T
r
ans Syst. Man.
Cybernet
, 1993,
23(3), pp
. 665-8
5
.
[6]
J.S.R. Jang, C.T. Sun,
E. M
i
zuta
ni, "Neuro-fuzz
y and s
o
ft com
puti
ng: A computation
a
l approach
to learning an
d
machine intell
ig
ence," 1997
,
Up
per Saddle River
, Pren
tice-Hall
.
[7]
V.A. Constan
tin, "Fuzzy
logic an
d ne
uro-fu
zzy
ap
plications explained,"
Englewoo
d Cliffs, 1995
,
Prentice-Hall.
[8]
C.T.
Lin
,
C.S.G
.
Lee
,
"Neura
l fu
zz
y s
y
s
t
em
s: A neuro-fuzz
y s
y
n
e
r
g
ism
to intel
lige
n
t s
y
stem
s,"
Up
per Saddle River,
1996, Pren
tice-
Hall
.
[9]
J. Kim, N. Kasabov: "H
y
F
IS, A
d
aptiv
e
neuro-fu
zzy
in
feren
c
e s
y
stems and thei
r
application to
no
nlinear d
y
namical
s
y
ste
m
s,
"
Neura
l
Networks,
1999
, 12
(9), pp. 130
1–19.
[10]
G. MKHOURY,
M.Saad, H.Y.Kannan,
C.Asmar, "Fuzzy
PID control of a Fiv
e
DOF Robot
Arm,"
Journal of
intel
ligen
t and
robotic
systems
, J
u
ly
2004, vol. 40
, pp
. 299-320
, IS
SN: 0921-0296.
KADD
OUR E.
L.
, "Simulation
de la
comma
nde dy
namique
d’un bras
manipulteur à 6 ddl appli
qué au robot puma 600,
"
1995,
USTO
.
BIBLIOGRAPHY OF
AUT
HORS
Ou
amri Bach
ir
was born in 19
72 in Bejaïa, Algeria.
He receiv
ed his BS degree from the
Electrical
Engin
eering Institute of the Universi
ty
of Bejaïa in 1
998, and the M
S
degree from
the Univ
ersity
o
f
Oran in
2004.
He is curr
ently
Assistant Professor of Electrical
and Computer
Engine
ering a
t
the Univers
i
t
y
of Bechar (Alg
eria)
.
His
curre
nt res
ear
ch int
e
res
t
inc
l
udes
intel
ligen
t pro
c
e
ss control,
t
e
leop
erat
ion,
te
lerobo
tic
and
autom
a
t
i
on
Ahmed-Foitih Z
o
ubir
He received th
e Eng.
Degree in El
ec
t
r
onics in 1980, the Magister
Degree
in Auto
matic in
1988 and the Doctorat
d’ét
at in 2004
fr
om the University
of Sciences
and Technolog
y of Oran USTO
(ORAN, Algeria)
. Since 1982 h
e
is a
lecturer
an
d resear
cher
m
e
m
b
er of the Elec
troni
cs
Departm
e
nt
, U.S
.
T.O. His
curre
nt res
ear
ch int
e
res
t
includ
es
Robotic, Computer au
tomation
,
control of
industr
ial pro
cesses an
d supervision, I
d
entification
of process, Soft
computing
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