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Vo
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3
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Sep
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201
5
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18
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19
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I
SS
N:
2089
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4856
186
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Da
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b
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a
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th
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ap
p
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p
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ip
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[
1
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n
ip
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ca
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d
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[
2
]
.
T
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m
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ta
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p
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m
a
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ip
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m
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lat
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o
f
j
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s
[
3
,
4
]
.
Desp
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it
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k
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[
5
]
.
Sin
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k
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m
atic
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o
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p
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alle
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b
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f
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s
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[
6
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.
T
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elec
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o
f
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f
f
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m
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m
at
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r
o
b
lem
s
in
p
ar
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r
o
b
o
ts
[
3
]
.
Kin
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m
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f
p
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r
o
b
o
ts
ca
n
b
e
b
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ilt
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Den
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Har
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Ho
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D
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5
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[
7
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B
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k
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d
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t
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k
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m
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b
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s
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p
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b
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d
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b
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ap
p
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o
p
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[
8
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T
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b
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r
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IJ
RA
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2089
-
4856
A
Tech
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187
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y
to
u
s
e
t
h
e
tech
n
iq
u
e
f
r
o
m
[
1
0
]
.
B
ec
au
s
e
o
f
d
esiri
n
g
co
n
ti
n
u
e
to
u
s
e
o
p
ti
m
ized
al
g
o
r
ith
m
to
s
o
lv
e
k
i
n
e
m
ati
c
p
r
o
b
lem
s
o
f
p
ar
allel
r
o
b
o
ts
.
T
h
is
p
ap
er
p
r
esen
ts
a
n
alter
n
ati
v
e
co
n
f
i
g
u
r
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io
n
to
d
o
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n
g
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ad
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e
o
r
d
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co
m
p
lica
ted
o
b
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tiv
e
f
u
n
ctio
n
s
to
t
h
e
s
i
m
p
ler
f
o
r
m
.
T
h
e
n
e
w
tec
h
n
iq
u
e
o
f
ch
a
n
g
in
g
v
ar
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les
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tr
o
d
u
ce
d
i
n
th
is
p
ap
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is
s
u
i
tab
le
f
o
r
p
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o
b
o
ts
w
it
h
d
i
f
f
er
e
n
t
s
tr
u
ctu
r
e.
T
h
er
ef
o
r
e,
th
e
o
b
j
ec
tiv
e
d
esire
o
f
u
s
in
g
a
s
in
g
le
m
et
h
o
d
to
s
tu
d
y
t
h
e
k
i
n
e
m
atic
s
f
o
r
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k
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n
d
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l r
o
b
o
ts
w
ill g
r
ad
u
a
ll
y
b
ec
o
m
e
r
ea
l.
2.
T
H
E
F
O
RM
O
F
T
H
E
E
Q
UAT
I
O
N
WH
E
N
T
R
ANSF
O
RM
I
NG
P
AR
AL
L
E
L
RO
B
O
T
K
I
NE
M
AT
I
CS P
RO
B
L
E
M
I
NT
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T
H
E
O
P
T
I
M
I
Z
A
T
I
O
N
P
RO
B
L
E
M
Su
p
p
o
s
e
th
a
t
(
,
,
,
,
,
)
P
p
p
p
x
y
z
is
t
h
e
v
ec
to
r
r
ep
r
esen
tin
g
p
o
s
itio
n
a
n
d
o
r
ien
tatio
n
o
f
e
n
d
ef
f
ec
to
r
o
f
t
h
e
r
o
b
o
t.
T
h
e
ai
m
o
f
k
i
n
e
m
a
tic
co
n
tr
o
l
is
to
ac
h
iev
e
h
i
g
h
ac
cu
r
ac
y
o
f
p
o
s
itio
n
an
d
o
r
ien
ta
tio
n
o
f
th
e
e
n
d
ef
f
ec
to
r
.
T
h
er
ef
o
r
e,
it
is
n
ec
e
s
s
ar
y
to
d
eter
m
i
n
e
t
h
e
j
o
in
t v
ar
iab
le
i
s
o
th
at
t
h
e
er
r
o
r
o
f
p
o
s
itio
n
a
n
d
o
r
ien
tatio
n
is
s
m
allest
w
h
ile
s
atis
f
y
i
n
g
th
e
co
n
d
it
io
n
s
o
f
s
tr
u
ctu
r
al
co
n
s
tr
ai
n
t
s
.
,
.
.
.
1
,
2
n
: is th
e
v
ec
to
r
o
f
j
o
in
t v
ar
iab
les.
J
o
in
t sp
ac
e
D
d
eter
m
i
n
es t
h
e
d
o
m
a
in
o
f
th
e
f
o
llo
w
in
g
j
o
in
t v
ar
iab
les:
1
1
1
2
2
2
ab
ab
ab
n
n
n
(
1)
w
h
er
e:
a
i
an
d
b
i
ar
e
co
n
s
tr
ain
t
s
o
f
j
o
in
t v
ar
iab
les
i
.
()
Tf
: f
u
n
ctio
n
d
escr
ib
in
g
th
e
d
ev
i
atio
n
o
f
p
o
s
itio
n
a
n
d
o
r
ien
tati
o
n
o
f
th
e
e
n
d
ef
f
ec
to
r
.
T
h
e
p
r
o
b
lem
d
eter
m
in
i
n
g
th
e
v
alu
e
o
f
th
e
j
o
in
t
v
ar
iab
les is
w
r
itte
n
as
f
o
llo
w
s
:
(
,
,
.
.
.
)
12
;1
T
f
m
in
im
iz
e
n
ab
i
i
i
D
i
n
i
(2
)
T
h
is
is
th
e
eq
u
a
tio
n
o
f
p
ar
allel
r
o
b
o
t
k
in
e
m
atic
s
p
r
o
b
lem
w
h
en
tr
an
s
f
o
r
m
ed
i
n
to
p
r
o
b
lem
o
p
ti
m
izi
n
g
n
u
n
k
n
o
w
n
n
o
n
li
n
ea
r
f
u
n
ctio
n
,
w
it
h
li
n
ea
r
co
n
s
tr
ai
n
ts
.
3.
ASSOC
I
AT
E
D
E
Q
UAT
I
O
N
O
F
P
ARAL
L
E
L
RO
B
O
T
WH
E
N
DR
I
VE
N
B
Y
RE
VO
L
UT
E
J
O
I
NT
S O
R
P
RI
SM
AT
I
C
J
O
I
NT
3
.
1
.
Ass
o
cia
t
ed
equa
t
io
n w
hen d
riv
en
by
re
v
o
lute
j
o
ints
I
n
p
ar
allel
r
o
b
o
t
3
R
R
R
d
r
iv
e
n
b
y
r
e
v
o
lu
te
j
o
in
ts
a
s
Fi
g
u
r
e
1
.
Fig
u
r
e
1
.
P
a
r
allel
r
o
b
o
t w
it
h
3
R
R
R
s
tr
u
ctu
r
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
.
3
,
Sep
tem
b
er
201
5
:
18
6
–
19
5
188
B
ec
au
s
e
th
e
r
o
b
o
t
h
as
s
y
m
m
etr
ical
s
tr
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ta
k
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g
i
n
to
co
n
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id
er
th
e
clo
s
ed
lo
o
p
v
ec
to
r
eq
u
atio
n
p
ass
i
n
g
th
r
o
u
g
h
t
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e
p
o
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ts
,
,
,
01
O
P
D
A
O
o
f
th
e
1
st
li
m
b
:
0
1
0
1
O
O
O
D
D
A
A
O
(
3
)
T
h
e
d
etailed
eq
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atio
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h
as f
o
r
m
:
01
01
01
01
3
.
c
os(
30
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.
c
os(
)
.
c
os(
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3
1
1
1
1
1
.
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n(
)
.
si
n(
)
3
1
1
1
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1
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si
n(
30
)
3
3
.
c
os(
)
.
c
os(
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.
c
os(
30
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1
1
1
1
1
3
3
.
si
n(
)
.
si
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)
.
si
n(
30
)
1
1
1
1
1
3
h
x
ab
y
a
b
h
h
x
a
b
h
y
a
b
(
4
)
W
h
en
k
i
n
e
m
atic
p
r
o
b
lem
is
s
t
r
u
ctu
r
ed
b
ased
o
n
(
2
)
,
v
alu
e
o
f
j
o
in
t
v
ar
iab
les
11
,
is
d
eter
m
in
e
d
s
o
th
at
p
o
s
itio
n
er
r
o
r
11
,
OO
xy
an
d
o
r
ien
tatio
n
er
r
o
r
o
f
th
e
en
d
ef
f
ec
to
r
r
ea
ch
m
i
n
i
m
u
m
v
al
u
e.
T
h
er
ef
o
r
e,
o
b
j
ec
tiv
e
f
u
n
ctio
n
T
d
escr
ib
in
g
d
ev
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o
f
p
o
s
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n
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n
d
o
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tatio
n
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h
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e
n
d
e
f
f
ec
to
r
is
d
eter
m
in
ed
a
s
f
o
llo
w
s
:
01
01
3
2
[
(
.
c
o
s
(
)
.
c
o
s
(
)
.
c
o
s
(
3
0)
)
]
+
1
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[
(
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in
(
)
.
s
in
(
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3
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)
]
1
1
1
1
1
3
h
T
x
a
b
h
y
a
b
m
in
im
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(
5
)
Ob
v
io
u
s
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,
(
5
)
is
al
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s
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0
,
th
u
s
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m
ize
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.
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(
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h
as
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m
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lled
R
o
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en
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r
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-
B
an
a
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f
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[
1
1
]
,
th
e
m
o
s
t
ap
p
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o
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r
iate
alg
o
r
ith
m
to
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Ge
n
er
alize
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R
ed
u
ce
d
Gr
ad
ien
t (
GR
G)
al
g
o
r
ith
m
[
9
,
1
2
]
.
3
.
2
.
Ass
o
cia
t
ed
equa
t
io
n w
he
n d
riv
en
by
pris
m
a
t
ic
j
o
int
s
C
o
n
s
id
er
d
etailed
d
iag
r
am
o
f
o
n
e
li
m
b
O
A
3
B
3
P
o
f
p
ar
allel
r
o
b
o
t w
it
h
3
R
P
S st
r
u
ct
u
r
e
(
Fig
u
r
e
2
)
.
Fig
u
r
e
2
.
P
ar
allel
r
o
b
o
t w
it
h
3
R
P
S st
r
u
ct
u
r
e
Ass
o
ciate
d
v
ec
to
r
eq
u
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n
h
a
s
th
e
f
o
llo
w
in
g
f
o
r
m
:
.
i
i
R
P
Y
i
d
a
P
R
b
(6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
A
Tech
n
iq
u
es to
Do
w
n
g
r
a
d
e
Do
w
n
g
r
a
d
e
Ob
jective
F
u
n
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n
in
P
a
r
a
llel R
o
b
o
t
…
(
Tr
a
n
g
Th
a
n
h
Tr
u
n
g
)
189
T
h
e
len
g
t
h
o
f
i
th
li
m
b
th
at
is
th
e
d
is
ta
n
ce
b
et
w
ee
n
t
w
o
en
d
s
o
f
v
ec
to
r
i
c
an
d
i
a
is
d
eter
m
in
e
d
as
f
o
llo
w
s
:
2
2
2
(
)
(
)
(
)
(
)
(
)
d
c
a
c
a
c
a
c
a
c
a
i
i
x
i
x
i
y
i
y
i
z
i
z
i
i
i
i
(
7
)
W
h
en
t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
i
s
s
tr
u
ct
u
r
ed
b
ased
o
n
(
2
)
,
s
im
i
lar
to
s
ec
tio
n
A
,
o
b
j
ec
tiv
e
f
u
n
ctio
n
is
i
n
th
e
f
o
r
m
o
f
q
u
ater
n
ar
y
f
u
n
ctio
n
d
u
e
to
th
e
p
r
esen
ce
o
f
p
r
is
m
atic
j
o
in
t v
ar
iab
les
d
i
:
2
2
2
2
2
(
)
(
)
(
)
1
m
i
n
i
m
i
z
e
n
T
c
a
c
a
c
a
d
i
x
i
x
i
y
i
y
i
z
i
z
i
i
(
8
)
4.
E
Q
UIVA
L
E
NT
A
L
T
E
RN
A
T
I
V
E
K
I
N
E
M
AT
I
C
M
O
DE
L
Fro
m
s
ec
t
io
n
3
,
it
ca
n
b
e
s
ee
n
th
at
f
o
r
th
e
p
ar
allel
r
o
b
o
t
d
r
iv
en
b
y
th
e
p
r
is
m
atic
j
o
in
ts
,
t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
o
f
t
h
e
p
ar
allel
r
o
b
o
t
k
in
e
m
at
ics
p
r
o
b
le
m
al
w
a
y
s
i
s
in
q
u
ater
n
ar
y
f
o
r
m
,
t
h
u
s
G
R
G
al
g
o
r
ith
m
is
n
o
lo
n
g
er
ap
p
r
o
p
r
iate
to
s
o
lv
e
th
is
f
o
r
m
o
f
f
u
n
ctio
n
.
T
o
s
o
lv
e
o
b
j
e
ctiv
e
f
u
n
ctio
n
co
n
t
ain
i
n
g
f
o
u
r
t
h
o
r
d
er
v
ar
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les,
th
er
e
ar
e
s
o
m
e
ap
p
r
o
p
r
iate
m
et
h
o
d
s
s
u
ch
a
s
Ne
w
t
o
n
R
ap
h
s
o
n
,
Ho
o
k
-
J
ee
v
es,
Fle
tch
er
P
o
w
ell
[
1
0
]
.
I
n
o
r
d
er
to
s
i
m
p
lify
a
n
d
to
u
s
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o
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l
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et
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alg
o
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h
m
to
s
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v
e
th
e
q
u
ater
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b
j
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e
f
u
n
ctio
n
i
n
p
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allel
r
o
b
o
t
k
in
e
m
atic
s
p
r
o
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lem
.
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h
is
ar
ticle
p
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ts
a
m
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o
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o
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g
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th
e
o
b
j
ec
tiv
e
f
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n
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ased
o
n
eq
u
i
v
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lter
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m
at
ic
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n
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8
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IJ
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IJ
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191
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RE
F
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NC
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S
[1
]
Y.D.
P
a
tel,
P
.
M
.
G
e
o
rg
e
,
P
a
ra
ll
e
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En
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g
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v
o
l.
2,
p
p
.
57
-
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4
,
2
0
1
2
.
[2
]
T
a
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K.T
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n
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v
.
Kin
e
m
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s
o
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1
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-
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1
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6
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e
p
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r
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[3
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r
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c
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Kin
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s,
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in
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larity
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terit
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n
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ip
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se
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o
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.
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-
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2
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.
[4
]
K
a
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g
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B.
;
Ch
u
,
J.
&
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il
ls,
J.
K
.
De
sig
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lan
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IEE
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In
ter
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s
a
n
d
Au
t
o
ma
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o
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Ko
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a
,
pp.
2
7
2
3
-
2
7
2
8
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2
0
0
1
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[5
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L
u
c
Ro
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m
a
ti
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p
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9
5
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5
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2
0
0
5
.
[6
]
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tern
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J.
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2
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p
p
li
c
a
ti
o
n
a
n
d
in
d
u
str
ializa
ti
o
n
o
f
n
e
w
tec
h
n
o
lo
g
ies
f
o
r
CNC
m
a
c
h
in
in
g
c
e
n
ter
is
t
o
p
ro
m
o
te.
Op
ti
c
a
l
-
m
e
c
h
a
n
ica
l
-
e
lec
tri
c
a
l
in
teg
ra
ti
o
n
re
s
u
lt
s
o
f
th
e
a
v
iatio
n
i
n
d
u
stry
,
sc
ien
ti
f
ic
a
n
d
tec
h
n
o
lo
g
ica
l
p
ro
g
re
ss
Aw
a
rd
1
9
9
5
,
CNC
tec
h
n
o
l
o
g
y
,
G
u
a
n
g
d
o
n
g
P
r
o
v
in
c
ial
S
c
ien
c
e
a
n
d
tec
h
n
o
lo
g
y
p
ro
g
re
ss
a
w
a
rd
o
f
G
u
a
n
g
d
o
n
g
e
x
c
e
ll
e
n
t
n
e
w
p
ro
d
u
c
t
Aw
a
rd
.
He
h
a
s
w
o
n
m
o
re
th
a
n
3
0
n
a
ti
o
n
a
l
in
v
e
n
ti
o
n
p
a
ten
t
a
n
d
u
ti
l
it
y
m
o
d
e
l
p
a
ten
ts.
In
re
c
e
n
t
y
e
a
rs,
h
e
h
a
s m
o
re
th
a
n
1
0
0
p
a
p
e
rs p
u
b
l
ish
e
d
i
n
n
a
ti
o
n
a
l
a
n
d
i
n
tern
a
ti
o
n
a
l
a
c
a
d
e
m
ic
p
a
p
e
rs,
e
d
it
o
rs
p
u
b
l
ish
e
d
a
m
o
d
e
rn
m
a
n
u
f
a
c
tu
rin
g
te
c
h
n
o
l
o
g
y
(
m
e
c
h
a
n
ica
l
in
d
u
stry
p
u
b
li
sh
i
n
g
h
o
u
se
),
m
e
c
h
a
n
ica
l
c
o
n
tro
l
F
o
u
n
d
a
ti
o
n
(b
il
in
g
u
a
l
t
u
to
rial)
(W
u
h
a
n
Un
iv
e
rsity
o
f
tec
h
n
o
l
o
g
y
p
re
ss
),
th
e
m
a
c
h
in
e
ry
a
n
d
e
q
u
ip
m
e
n
t
o
f
CNC
tec
h
n
o
lo
g
y
(n
a
ti
o
n
a
l
d
e
f
e
n
se
in
d
u
stry
p
re
ss
)
a
n
d
3
tex
tb
o
o
k
s.
Ph
a
m
T
h
a
n
h
Lo
n
g
w
a
s
b
o
rn
in
V
in
h
P
h
u
,
Vie
t
Na
m
in
1
9
7
7
.
He
re
c
e
iv
e
d
th
e
B.
S
,
M
.
S
.
a
n
d
P
h
.
D.
d
e
g
re
e
in
m
e
c
h
a
n
ica
l
e
n
g
i
n
e
e
rin
g
f
ro
m
F
a
c
u
lt
y
o
f
M
e
c
h
a
n
ica
l
En
g
in
e
e
rin
g
,
T
h
a
i
Ng
u
y
e
n
Un
iv
e
rsit
y
o
f
Tec
h
n
o
lo
g
y
,
V
iet
N
a
m
in
1
9
9
5
,
2
0
0
1
,
2
0
0
6
,
re
sp
e
c
ti
v
e
l
y
.
F
ro
m
2
0
0
0
t
o
2
0
0
8
,
h
e
w
a
s a lec
t
u
re
r
a
t
F
a
c
u
lt
y
o
f
M
e
c
h
a
n
ica
l
En
g
in
e
e
rin
g
,
T
h
a
i
Ng
u
y
e
n
Un
iv
e
rsit
y
o
f
Tec
h
n
o
lo
g
y
,
V
iet
N
a
m
.
F
ro
m
2
0
0
8
to
2
0
1
5
,
h
e
w
a
s t
h
e
h
e
a
d
o
f
De
p
a
rt
m
e
n
t
o
f
M
e
c
h
a
tro
n
ics
,
T
h
a
i
Ng
u
y
e
n
Un
iv
e
rsit
y
o
f
Tec
h
n
o
lo
g
y
.
His res
e
a
r
c
h
in
tere
st co
v
e
rs
m
e
c
h
a
tro
n
ics
,
ro
b
o
ti
c
s,
a
u
t
o
m
a
ti
o
n
in
m
a
n
u
f
a
c
tu
rin
g
,
CA
D/CA
M
/CNC t
e
c
h
n
o
lo
g
y
.
He
h
a
s
m
o
re
th
a
n
1
7
p
a
p
e
rs
p
u
b
li
sh
e
d
in
n
a
ti
o
n
a
l
a
n
d
i
n
tern
a
t
io
n
a
l
a
c
a
d
e
m
ic p
a
p
e
rs,
0
3
tex
tb
o
o
k
s,
a
n
d
p
a
rti
c
i
p
a
ted
i
n
7
re
se
a
rc
h
to
p
ics
in
V
iet
n
a
m
.
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