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5
In
s
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A
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c
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[
1
-
6
]
.
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[
5
-
8
]
.
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[
9
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1
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.
B
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1
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Naz
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1
2
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Th
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Mo
b
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R
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b
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t H
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A
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Dyn
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151
I
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d
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E
RO
B
O
T
C
o
n
s
id
er
a
m
o
b
ile
r
o
b
o
t
k
n
o
w
n
a
s
HI
L
AR
E
.
As
it
is
s
ee
n
in
f
i
g
u
r
e
(
1
)
,
it
h
as
t
w
o
f
ix
ed
w
h
ee
ls
a
n
d
an
o
f
f
-
ce
n
ter
ed
w
h
ee
l.
Fig
u
r
e
1
.
T
h
e
m
o
b
ile
r
o
b
o
t H
I
L
AR
E
As
t
h
e
d
y
n
a
m
ic
eq
u
atio
n
s
o
f
th
e
r
o
b
o
t
ar
e
d
ev
elo
p
ed
b
y
L
a
g
r
an
g
e
m
u
ltip
lier
m
et
h
o
d
,
th
e
to
ta
l
k
in
e
tic
en
er
g
y
(
T
)
an
d
p
o
ten
tial
en
er
g
y
(
U)
o
f
t
h
e
s
y
s
te
m
m
u
s
t
b
e
co
m
p
u
ted
.
T
h
en
,
b
y
co
n
s
tr
u
cti
n
g
th
e
L
a
g
r
an
g
ian
f
u
n
ctio
n
(
L
=
T
–
U
)
an
d
f
o
llo
w
i
n
g
t
h
e
L
a
g
r
an
g
ian
ap
p
r
o
ac
h
n
o
n
li
n
ea
r
eq
u
ati
o
n
s
o
f
m
o
tio
n
ca
n
b
e
o
b
tain
ed
.
T
h
e
L
ag
r
an
g
ia
n
eq
u
atio
n
ca
n
b
e
f
o
r
m
ed
as
:
6
1
j
ji
j
i
i
i
D
Q
q
L
q
L
dt
d
(
1
)
w
h
er
e
i
Q
is
th
e
g
e
n
er
alize
d
f
o
r
ce
r
elate
d
to
th
e
g
en
er
alize
co
o
r
d
in
ate
i
q
,
an
d
j
is
u
n
k
n
o
w
n
f
o
r
ce
r
elate
d
to
ea
ch
n
o
n
h
o
lo
n
o
m
i
c
co
n
s
tr
ain
t
o
f
m
o
b
ile
b
ase.
No
w
,
u
s
i
n
g
L
a
g
r
an
g
ia
n
eq
u
atio
n
th
e
d
y
n
a
m
i
c
eq
u
atio
n
s
o
f
th
e
s
y
s
te
m
ca
n
b
e
o
b
tain
ed
in
th
e
co
m
p
ac
t
f
o
r
m
as:
T
A
B
q
,
q
V
q
M
(2
)
in
w
h
ic
h
n
R
is
to
r
q
u
e
v
ec
to
r
ex
er
ted
to
th
e
j
o
in
ts
,
n
n
R
q
M
)
(
is
t
h
e
i
n
er
tia
m
atr
i
x
,
B
is
co
n
s
tan
t
in
p
u
t
m
atr
i
x
,
n
R
q
q
V
)
,
(
is
a
v
ec
to
r
wh
ich
p
r
ese
n
ts
co
r
io
lis
a
n
d
g
r
av
itatio
n
al
f
o
r
ce
s
a
n
d
A
is
a
m
atr
ix
w
h
ic
h
r
ep
r
esen
t
s
t
h
e
k
i
n
e
m
at
ic
co
n
s
tr
ai
n
t
s
o
f
t
h
e
r
o
b
o
t
HI
L
A
R
E
r
elate
d
to
n
o
n
h
o
lo
n
o
m
ic
co
n
s
tr
ai
n
ts
o
f
w
h
ee
ls
.
Mo
r
eo
v
er
,
to
elim
in
ate
t
h
e
u
n
k
n
o
w
n
f
o
r
ce
s
f
r
o
m
t
h
e
d
y
n
a
m
ic
eq
u
atio
n
o
f
th
e
s
y
s
te
m
,
th
e
m
atr
i
x
S
is
d
ef
in
ed
i
n
s
u
c
h
a
f
o
r
m
t
h
at
A
S
=0
.
T
h
er
ef
o
r
e,
th
e
s
tate
-
s
p
a
ce
p
r
esen
tatio
n
o
f
t
h
e
s
y
s
te
m
r
ep
r
esen
ts
a
s
e
t
o
f
f
ir
s
t
-
o
r
d
er
d
if
f
er
en
tial e
q
u
atio
n
s
as t
h
e
f
o
llo
w
in
g
:
1
2
2
1
)
(
0
MS
S
f
S
x
x
x
T
(
3
)
3.
DYNA
M
I
C
M
O
DE
L
O
F
T
H
E
RO
B
O
T
I
n
th
i
s
s
ec
tio
n
,
t
h
e
k
in
e
m
atic
m
o
d
el
o
f
th
e
m
o
b
ile
r
o
b
o
t
HI
L
AR
E
is
p
r
esen
ted
.
T
h
e
m
o
b
ile
r
o
b
o
t
h
as
t
w
o
f
i
x
ed
w
h
ee
l
s
an
d
a
o
f
f
-
ce
n
ter
ed
o
r
ien
tab
le
w
h
ee
l
(
Fi
g
.
1
)
.
T
h
e
p
ar
am
eter
s
o
f
r
o
b
o
ts
ar
e
p
r
esen
ted
:
3
is
th
e
an
g
le
o
f
r
o
tatio
n
o
f
o
f
f
-
ce
n
ter
ed
o
r
ien
tab
le
w
h
ee
l
ab
o
u
t
th
e
v
er
tical
ax
i
s
,
d
is
th
e
o
f
f
-
ce
n
ter
len
g
th
o
f
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
4
,
No
.
2
,
J
u
n
e
2
0
1
5
:
1
50
–
15
5
152
w
h
ee
l,
C
i
s
t
h
e
m
as
s
ce
n
ter
o
f
th
e
m
o
b
ile
p
lat
f
o
r
m
,
is
t
h
e
h
ea
d
in
g
a
n
g
le
o
f
th
e
m
o
b
ile
r
o
b
o
t,
i
is
t
h
e
r
o
tatio
n
o
f
th
e
i
th
w
h
ee
l
ar
o
u
n
d
its
ax
le
,
L
is
t
h
e
d
is
ta
n
ce
f
r
o
m
C
to
th
e
ce
n
ter
p
o
in
t
o
f
t
h
e
w
h
ee
l
.
A
l
s
o
,
th
e
an
g
le
is
d
ef
i
n
ed
as
th
e
a
n
g
le
b
et
w
ee
n
th
e
a
x
le
1
x
an
d
a
lin
e
f
r
o
m
t
h
e
ce
n
te
r
o
f
ea
ch
w
h
ee
l
t
o
m
a
s
s
ce
n
ter
C
.
On
e
ca
n
co
n
s
id
er
th
a
t f
o
r
t
h
e
r
ig
h
t f
ix
ed
w
h
ee
l
0
an
d
f
o
r
th
e
f
ix
ed
w
h
ee
l.
Fu
r
t
h
er
m
o
r
e,
ea
ch
w
h
ee
l
o
f
t
h
e
HI
L
AR
E
h
as
t
h
e
f
o
llo
w
i
n
g
n
o
n
h
o
lo
n
o
m
ic
co
n
s
tr
ain
t
s
:
E
ac
h
w
h
ee
l
ca
n
o
n
l
y
m
o
v
e
in
t
h
e
d
ir
ec
tio
n
o
f
it
s
p
lan
e.
E
ac
h
w
h
ee
l
m
u
s
t
h
a
v
e
p
u
r
e
r
o
lli
n
g
w
it
h
o
u
t a
n
y
s
lip
p
ag
e.
T
h
u
s
t
h
e
m
o
b
ile
r
o
b
o
t h
as s
ix
n
o
n
h
o
lo
n
o
m
ic
co
n
s
tr
ai
n
t
s
r
eg
ar
d
in
g
to
th
eir
w
h
ee
l
s
w
h
ich
i
s
ex
p
r
es
s
e
d
as:
0
0
3
T
T
K
(
4
)
w
h
er
e
T
c
c
y
x
is
th
e
m
o
b
ile
b
ase
p
o
s
tu
r
e
v
ec
to
r
,
T
3
2
1
is
th
e
r
o
tatio
n
v
ec
to
r
o
f
t
h
e
w
h
ee
l
s
ar
o
u
n
d
it
s
ax
le,
T
d
0
0
,
T
is
t
h
e
r
o
tatio
n
m
atr
i
x
a
n
d
is
a
d
iag
o
n
al
m
atr
i
x
o
f
r
ad
ii o
f
w
h
ee
ls
:
1
0
0
0
c
o
s
s
i
n
0
s
i
n
c
o
s
T
(
5
)
r
r
r
0
0
0
0
0
0
(
6
)
w
h
er
e
r
is
r
ad
i
u
s
o
f
ea
c
h
w
h
e
el
o
f
t
h
e
m
o
b
ile
p
lat
f
o
r
m
.
F
u
r
th
er
m
o
r
e,
ea
c
h
r
o
w
o
f
m
atr
ic
es
K
an
d
r
ep
r
esen
t th
e
p
u
r
e
r
o
llin
g
an
d
n
o
n
later
al
s
l
ip
p
ag
e,
r
esp
ec
tiv
el
y
.
T
h
u
s
t
h
e
m
a
tr
ices a
r
e
ex
p
r
ess
ed
as:
3
3
3
c
o
s
s
i
n
c
o
s
1
0
1
0
L
L
L
K
(
7
)
3
3
3
s
i
n
c
o
s
s
i
n
0
0
1
0
0
1
L
d
(
8
)
No
w
,
to
p
r
ese
n
t
t
h
e
to
tal
k
i
n
e
m
atic
co
n
s
tr
ai
n
ts
o
f
t
h
e
HI
L
AR
E
,
t
h
e
g
e
n
er
alize
d
co
o
r
d
in
ates
o
f
th
e
t
w
o
-
w
h
ee
led
m
o
b
ile
r
o
b
o
t
is
d
ef
i
n
ed
as
T
c
c
y
x
q
3
2
1
3
an
d
th
e
n
o
n
h
o
lo
n
o
m
ic
co
n
s
tr
ain
ts
o
f
t
h
e
s
y
s
te
m
ca
n
b
e
r
ew
r
it
ten
a
s
:
0
)
(
q
q
A
(
9
)
W
h
er
e
th
e
j
ac
o
b
ian
m
atr
i
x
A
r
ep
r
esen
ts
th
e
n
o
n
h
o
lo
n
o
m
ic
co
n
s
tr
ain
ts
o
f
t
h
e
s
y
s
te
m
a
n
d
it
is
eq
u
al
to
:
0
0
T
T
K
A
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Th
e
Mo
b
ile
R
o
b
o
t H
I
LL
A
R
E
Dyn
a
mic
Mo
d
elin
g
a
n
d
Mo
tio
n
S
imu
la
tio
n
(
M.Ta
leza
d
eh
)
153
T
h
er
ef
o
r
e,
m
atr
ices
A
an
d
S
w
h
ic
h
m
u
s
t
b
e
d
eter
m
i
n
ed
to
d
er
iv
e
th
e
d
y
n
a
m
ic
eq
u
atio
n
s
o
f
t
h
e
r
o
b
o
t
ca
n
b
e
r
e
w
r
itte
n
as:
0
0
0
s
i
n
c
o
s
s
i
n
0
0
0
0
0
s
i
n
c
o
s
0
0
0
0
0
s
i
n
c
o
s
0
0
0
c
o
s
s
i
n
c
o
s
0
0
0
c
o
s
s
i
n
0
0
0
c
o
s
s
i
n
3
3
3
3
3
3
d
L
d
r
L
r
L
r
L
A
(
11
)
3
3
3
3
c
os
s
i
n
1
1
1
s
i
n
1
c
os
1
1
0
0
c
os
0
s
i
n
r
L
r
r
L
r
r
L
r
L
d
d
d
S
(
12
)
4.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
I
n
th
is
s
ec
tio
n
,
d
y
n
a
m
ic
m
o
ti
o
n
o
f
th
e
m
o
b
ile
r
o
b
o
t
HI
L
AR
E
is
s
i
m
u
la
ted
.
T
h
e
p
ar
am
e
ter
o
f
th
e
r
o
b
o
t
is
g
iv
e
n
as:
c
m
is
t
h
e
m
as
s
o
f
th
e
m
o
b
ile
p
lat
f
o
r
m
,
c
I
is
th
e
m
o
m
e
n
t
o
f
in
er
t
ia
o
f
t
h
e
m
o
b
i
le
p
latf
o
r
m
,
w
m
is
th
e
m
as
s
o
f
ea
ch
w
h
ee
l
a
n
d
w
I
is
th
e
m
o
m
e
n
t o
f
i
n
er
tia
o
f
ea
ch
w
h
ee
l a
b
o
u
t i
ts
a
x
is
.
Fu
r
t
h
er
m
o
r
e,
th
e
v
al
u
es
o
f
t
h
e
p
ar
am
e
ter
s
ar
e
g
iv
e
n
as:
kg
m
c
94
,
kg
m
w
2
.
5
,
kg
m
w
2
.
5
,
kg
m
w
2
.
5
,
m
r
08
.
0
,
m
L
13
.
0
an
d
m
d
1
.
0
.
T
o
s
i
m
u
la
te
th
e
p
a
th
g
e
n
er
atio
n
o
f
t
h
e
m
o
b
il
e
p
latf
o
r
m
,
i
t
is
as
s
u
m
ed
t
h
at
th
e
r
o
b
o
t
m
o
v
es
f
r
o
m
i
n
itia
l
p
o
s
itio
n
(
x
c
=0
m
,
y
c
=0
m
,
=0
r
ad
)
to
f
i
n
al
p
o
s
it
io
n
(
x
c
=1
.
5
m
,
y
c
=
-
0
.4
m
,
=0
r
ad
)
d
u
r
in
g
ti
m
e
o
f
s
t
f
4
.
T
h
e
p
ath
o
f
th
e
r
o
b
o
t is sh
o
w
n
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I
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ased
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t H
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RE
F
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NC
E
S
[1
]
O
m
ra
n
p
o
u
r,
H.,
&
S
h
iry
,
S
.
(
2
0
1
2
).
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d
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M
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le Ro
b
o
ts.
I
AE
S
In
ter
n
a
ti
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l
J
o
u
rn
a
l
o
f
Ro
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o
ti
c
s a
n
d
A
u
t
o
ma
ti
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n
(
IJ
RA
)
,
1
(1
),
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9
-
63
.
[2
]
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h
ra
v
e
sh
,
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.
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rsh
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h
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.
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.
R.
(2
0
1
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).
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No
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R
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ize
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Re
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In
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Au
t
o
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(
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RA
)
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1
(4
),
2
1
4
-
2
2
2
.
[3
]
Ko
ra
y
e
m
,
M
.
H.,
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a
z
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m
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z
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h
,
M
.
,
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z
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ir
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d
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.
(2
0
1
1
)
.
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l
traje
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f
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s.
S
c
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ti
a
Ira
n
ica
,
18
(5
)
,
1
1
3
8
-
1
1
4
7
.
[4
]
Na
g
a
r
a
ja,
H.,
A
s
w
a
n
i,
R.
,
&
M
a
li
k
,
M
.
(2
0
1
2
).
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lan
t
W
a
terin
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A
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to
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In
ter
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Au
t
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ma
ti
o
n
(
IJ
RA
)
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1
(
3
),
1
5
2
-
1
6
2
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Th
e
Mo
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ile
R
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elin
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(
M.Ta
leza
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)
155
[5
]
Ra
h
im
i,
H.
N.,
&
Na
z
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m
iz
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d
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h
,
M
.
(2
0
1
4
).
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n
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rs:
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v
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.
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v
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e
d
Ro
b
o
ti
c
s
,
28
(
2
),
6
3
-
76
[6
]
Ba
u
z
il
,
G
.
,
Brio
t,
M
.
,
&
Ri
b
e
s,
P
.
(1
9
8
1
,
A
p
ril
).
A
n
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v
ig
a
ti
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su
b
-
s
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m
u
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g
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ra
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so
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o
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e
m
o
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il
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o
t
HIL
A
RE.
In
1
st I
n
.
.
C
o
n
f
.
o
n
Ro
b
o
t
Vi
si
o
n
a
n
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ry
Co
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ro
ls,
S
tr
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tf
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rd
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u
p
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-
Avo
n
,
UK
(
p
p
.
4
7
-
58)
[7
]
Ko
ra
y
e
m
,
M
.
H.,
Na
z
e
m
i
z
a
d
e
h
,
M
.
,
&
Ra
h
im
i,
H.
N.
(2
0
1
3
).
T
ra
jec
to
r
y
o
p
ti
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iza
ti
o
n
o
f
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o
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m
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a
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rs d
e
p
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to
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m
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id
st m
o
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in
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o
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sta
c
le
s.
Acta
M
e
c
h
a
n
ica
,
2
2
4
(5
)
,
9
9
5
-
1
0
0
8
[8
]
G
a
li
n
d
o
,
C.
,
F
e
rn
n
d
e
z
-
M
a
d
rig
a
l,
J.
A
.
,
&
G
o
n
z
á
lez
,
J.
(2
0
0
7
).
M
u
lt
ip
le
a
b
stra
c
ti
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n
h
ier
a
rc
h
ies
fo
r
mo
b
il
e
ro
b
o
t
o
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ra
ti
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n
in
la
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e
e
n
v
iro
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me
n
ts
.
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p
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r
P
u
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l
ish
i
n
g
Co
m
p
a
n
y
,
In
c
o
rp
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ted
[9
]
Ko
ra
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e
m
,
M
.
H.,
Na
z
e
m
iza
d
e
h
,
M
.
,
&
No
h
o
o
ji
,
H.
R
.
(
2
0
1
4
).
Op
ti
m
a
l
p
o
in
t
-
to
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p
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i
n
t
m
o
ti
o
n
p
lan
n
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n
g
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f
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-
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o
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ic
m
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il
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th
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se
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e
o
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m
u
lt
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le
o
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sta
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les
.
J
o
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a
l
o
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e
Bra
zili
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n
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o
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iety
o
f
M
e
c
h
a
n
ica
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S
c
ien
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e
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n
d
En
g
i
n
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e
rin
g
,
36
(1
),
2
2
1
-
2
3
2
[1
0
]
Ko
ra
y
e
m
,
M
.
H.,
Na
z
e
m
iza
d
e
h
,
M
.
,
&
Ra
h
im
i,
H.
N.
(
2
0
1
4
)
.
Dy
n
a
m
ic
o
p
ti
m
a
l
p
a
y
lo
a
d
p
a
th
p
lan
n
in
g
o
f
m
o
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il
e
m
a
n
ip
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rs am
o
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m
o
v
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o
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st
a
c
les
.
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v
a
n
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d
R
o
b
o
ti
c
s
,
28
(
2
0
),
1
3
8
9
-
1
4
0
2
[1
1
]
W
,
Ch
e
n
H,
W
o
o
P
Y (
2
0
0
0
)
T
ime
o
p
ti
m
a
l
p
a
th
p
lan
n
in
g
f
o
r
a
w
h
e
e
led
m
o
b
il
e
ro
b
o
t.
J R
o
b
o
t
S
y
st.
1
7
:
5
8
5
–
5
9
1
[1
2
]
Na
z
e
m
i
z
a
d
e
h
,
M
.
,
Ra
h
im
i,
H.
N.,
&
Kh
o
iy
,
K.
A
.
(2
0
1
2
)
.
T
ra
je
c
to
ry
p
lan
n
in
g
o
f
m
o
b
il
e
ro
b
o
ts
u
sin
g
in
d
irec
t
so
lu
ti
o
n
o
f
o
p
ti
m
a
l
c
o
n
tro
l
m
e
th
o
d
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e
n
e
ra
li
z
e
d
p
o
in
t
-
to
-
p
o
i
n
t
t
a
sk
.
Fro
n
ti
e
rs
o
f
M
e
c
h
a
n
ica
l
En
g
in
e
e
rin
g
,
7
(1
)
,
23
-
28
Evaluation Warning : The document was created with Spire.PDF for Python.