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ro
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a
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ntr
o
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l.
18
,
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.
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,
Dec
em
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o
f
th
e
p
a
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ll
e
l
ro
b
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u
sin
g
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n
e
c
k
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d
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t.
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e
m
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o
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ten
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th
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p
a
p
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is
to
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e
th
e
i
n
v
e
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rs
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se
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r
p
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ra
ll
e
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r
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b
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m
a
n
i
p
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s.
F
i
n
a
ll
y
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n
u
m
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rica
l
sim
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latio
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o
f
t
h
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ic
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3
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RRR
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lt
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ip
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is p
re
se
n
te
d
a
s
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n
il
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stra
ti
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x
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m
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le.
K
ey
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:
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n
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ics co
n
tr
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ller
Kr
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n
ec
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er
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r
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ct
Nu
m
er
ical
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Par
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b
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t m
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tr
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C
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p
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A
uth
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r
:
Ng
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Ho
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,
T
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Ng
u
y
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n
Un
iv
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s
ity
o
f
T
e
ch
n
o
lo
g
y
,
No
.
6
6
6
,
3
/2
Stre
et,
T
ic
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L
u
o
n
g
W
ar
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Ng
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C
ity
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Vietn
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.
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m
ail:
q
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.
n
g
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y
en
h
o
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@
tn
u
t.e
d
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
I
n
th
e
p
ast
th
r
ee
d
e
ca
d
es,
th
e
th
eo
r
y
o
n
d
y
n
am
ics
o
f
c
o
n
s
tr
ain
ed
m
u
ltib
o
d
y
s
y
s
tem
s
h
as
b
ee
n
d
ev
elo
p
e
d
to
a
h
ig
h
d
eg
r
ee
o
f
m
atu
r
ity
[
1
-
4
]
.
T
h
e
p
ar
all
el
r
o
b
o
t
m
a
n
ip
u
lato
r
s
ar
e
c
o
n
s
tr
ain
ed
m
u
ltib
o
d
y
s
tr
u
ctu
r
es
[
5
-
7
]
.
T
h
e
eq
u
atio
n
s
o
f
m
o
tio
n
f
o
r
a
m
u
ltib
o
d
y
s
y
s
tem
ar
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o
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tain
e
d
as
th
e
en
d
r
esu
lt
o
f
a
s
eq
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e
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ce
o
f
m
ath
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atica
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o
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er
ato
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s
.
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n
g
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al,
th
e
k
n
o
wn
m
eth
o
d
s
to
d
er
iv
e
th
e
eq
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atio
n
s
o
f
m
o
tio
n
o
f
m
u
ltib
o
d
y
s
y
s
tem
s
ar
e
L
ag
r
a
n
g
e’
s
e
q
u
atio
n
s
,
New
to
n
–
E
u
ler
e
q
u
ati
o
n
s
,
Kan
e’
s
eq
u
atio
n
s
.
Am
o
n
g
th
ese
m
eth
o
d
s
,
th
e
ap
p
r
o
ac
h
u
s
in
g
L
ag
r
an
g
e’
s
eq
u
atio
n
s
with
m
u
ltip
lie
r
s
h
as
b
ec
o
m
e
an
attr
ac
tiv
e
m
eth
o
d
to
d
er
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e
th
e
eq
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atio
n
s
o
f
m
o
tio
n
o
f
co
n
s
tr
ain
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d
m
u
ltib
o
d
y
s
y
s
tem
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.
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h
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s
ap
p
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h
p
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v
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es
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well
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o
r
d
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ly
s
tr
u
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r
e
th
at
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v
er
y
u
s
ef
u
l f
o
r
co
n
tr
o
l p
u
r
p
o
s
es.
T
h
e
co
n
t
r
o
l
o
f
tr
ee
lik
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m
u
ltib
o
d
y
s
y
s
tem
s
is
o
f
in
te
r
est
to
a
n
u
m
b
er
o
f
r
esear
ch
c
o
m
m
u
n
ities
in
a
v
e
r
y
o
f
ap
p
licatio
n
s
ar
ea
s
.
Ma
n
y
a
d
v
an
ce
d
m
eth
o
d
s
f
o
r
co
n
tr
o
l
o
f
r
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b
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t
m
an
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lato
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s
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ased
o
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th
e
L
ag
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a
n
g
e’
s
eq
u
atio
n
s
h
av
e
b
ee
n
d
ev
elo
p
e
d
[
8
-
19
]
.
T
h
e
ap
p
licatio
n
o
f
m
o
d
er
n
co
n
tr
o
l
m
eth
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ch
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eth
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d
,
th
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al
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et
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ig
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o
f
th
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lik
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o
b
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m
an
ip
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lat
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r
s
is
p
r
esen
ted
in
th
e
wo
r
k
s
[
2
0
-
3
0
]
.
I
n
c
o
n
tr
ast
to
th
e
r
a
p
id
p
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o
g
r
ess
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co
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tr
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m
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e
d
ev
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m
en
t
o
f
th
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co
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r
p
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r
allel
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till
lim
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d
er
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co
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tr
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l
m
eth
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d
s
h
a
v
e
also
b
ee
n
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s
ed
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th
e
co
n
tr
o
l
p
r
o
b
lem
o
f
p
lan
e
p
a
r
allel
m
an
ip
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lato
r
s
[
3
1
-
3
4
]
.
On
e
h
as
u
s
ed
t
h
e
co
n
tr
o
l
m
eth
o
d
s
s
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ch
as
th
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p
r
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p
o
r
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d
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PD
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co
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tr
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l
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d
p
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p
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tio
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al
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te
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d
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PID
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co
n
tr
o
l
f
o
r
d
esig
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i
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g
s
o
m
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co
n
tr
o
ller
s
o
f
s
p
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p
a
r
allel
r
o
b
o
t
m
an
ip
u
lato
r
s
[
3
5
-
3
8
]
.
Ho
wev
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r
,
th
e
ap
p
licatio
n
o
f
m
o
d
er
n
co
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tr
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n
eu
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etw
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co
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d
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p
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tial
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b
lem
th
at
h
as
n
o
t
b
ee
n
in
v
esti
g
ated
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
3
1
9
1
-
320
1
3192
R
ec
en
tly
,
N.
H.
Q
u
an
g
[
3
9
-
4
1
]
p
r
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p
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s
ed
a
co
n
tr
o
l
m
eth
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d
u
s
in
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o
d
el
p
r
e
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p
r
o
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h
.
AL
-
Azz
awi
[
4
2
]
ad
d
r
ess
th
e
co
n
tr
o
l
p
r
o
b
lem
f
o
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ased
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r
f
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d
b
ac
k
co
n
tr
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l
s
tr
ateg
ies.
S.
R
iach
e
[
4
3
]
p
r
o
p
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s
ed
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p
tiv
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n
o
n
s
in
g
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la
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n
tr
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ller
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o
f
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y
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r
id
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o
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a
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o
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in
g
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lar
ter
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tr
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a
n
d
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s
u
p
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g
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Simu
latio
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s
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n
o
n
s
in
g
u
lar
ter
m
in
al
s
u
p
er
-
twis
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g
co
n
tr
o
l
to
p
r
o
v
e
th
e
s
u
p
er
i
o
r
ity
an
d
t
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
I
n
[
4
4
]
,
a
n
ew
co
m
p
o
u
n
d
h
ier
ar
c
h
ical
s
lid
in
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m
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as b
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atch
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r
c
o
n
tr
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ller
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esig
n
o
f
s
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allel
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o
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o
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m
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s
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,
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y
s
tem
s
to
estab
li
s
h
a
n
ew
ex
p
r
ess
io
n
f
o
r
ca
lcu
l
atio
n
o
f
th
e
d
r
i
v
in
g
t
o
r
q
u
es
o
f
p
ar
allel
r
o
b
o
ts
will
b
e
d
is
cu
s
s
ed
.
T
h
e
in
v
er
s
e
d
y
n
am
ics
co
n
tr
o
ller
f
o
r
th
e
p
ar
all
el
r
o
b
o
t
m
a
n
ip
u
lato
r
is
co
n
s
id
er
ed
in
th
e
s
ec
tio
n
3
.
I
n
th
e
s
ec
tio
n
4
,
n
u
m
er
ical
s
im
u
latio
n
o
f
th
e
in
v
e
r
s
e
d
y
n
a
m
ics
co
n
tr
o
ller
f
o
r
a
3
-
RRR
d
elta
p
ar
al
lel
s
p
atial
r
o
b
o
t m
an
ip
u
lato
r
is
p
r
esen
ted
a
s
an
illu
s
tr
ativ
e
ex
am
p
le.
2.
I
NVE
RS
E
DYNA
M
I
C
S O
F
CO
NST
R
AIN
E
D
M
UL
T
I
B
O
DY
SYS
T
E
M
S
L
et
u
s
co
n
s
id
er
a
s
cler
o
n
o
m
ic
m
u
ltib
o
d
y
s
y
s
tem
o
f
a
fn
d
eg
r
ee
o
f
f
r
ee
d
o
m
co
n
tain
in
g
r
ig
id
-
b
o
d
ies
with
r
h
o
lo
n
o
m
ic
c
o
n
s
tr
ain
ts
.
L
et
=
[
1
,
2
,
.
.
.
,
]
b
e
th
e
v
ec
t
o
r
o
f
g
e
n
er
alize
d
co
o
r
d
i
n
ates,
th
e
m
o
tio
n
e
q
u
atio
n
s
o
f
co
n
s
tr
ain
ed
h
o
l
o
n
o
m
ic
m
u
ltib
o
d
y
s
y
s
tem
s
ca
n
b
e
wr
itten
as:
(
)
̈
+
(
,
̇
)
̇
+
(
)
+
(
)
+
(
,
̇
)
=
(
1
)
(
)
=
0
(
2
)
wh
er
e
(
)
is
th
e
nn
m
ass
m
atr
ix
,
(
,
̇
)
i
s
th
e
nn
co
r
io
lis
/cen
tr
ip
etal
m
at
r
ix
,
is
1
r
v
ec
to
r
o
f
co
n
s
tr
ain
t
eq
u
atio
n
s
,
(
)
is
th
e
rn
J
ac
o
b
ian
m
atr
ix
o
f
t
h
e
v
e
cto
r
,
d
i
s
th
e
1
n
v
ec
to
r
o
f
f
r
ictio
n
f
o
r
ce
an
d
d
is
tu
r
b
a
n
ce
,
is
th
e
1
n
v
ec
to
r
o
f
d
r
iv
i
n
g
f
o
r
ce
s
/to
r
q
u
e
s
,
is
th
e
1
r
v
ec
to
r
o
f
L
ag
r
a
n
g
ian
m
u
ltip
lier
s
.
T
h
e
C
o
r
io
lis
/C
en
tr
ip
etal
m
atr
ix
(
,
̇
)
is
d
eter
m
in
ed
f
r
o
m
th
e
m
ass
m
atr
ix
ac
c
o
r
d
in
g
th
e
f
o
llo
win
g
f
o
r
m
u
la
[
4
5
,
4
6
]
.
(
,
̇
)
=
(
)
(
⊗
̇
)
−
1
2
[
(
)
(
̇
⊗
)
]
(
3
)
T
h
e
J
ac
o
b
ian
m
atr
i
x
(
)
o
f
th
e
co
n
s
tr
ain
ed
eq
u
atio
n
s
is
d
eter
m
in
e
d
b
y
th
e
f
o
llo
win
g
f
o
r
m
u
la
;
=
=
[
1
1
.
.
.
1
.
.
.
.
.
.
.
.
.
1
.
.
.
]
(
4
)
Firstl
y
,
th
e
g
en
er
alize
d
co
o
r
d
in
ates
in
v
ec
to
r
s
ar
e
d
iv
id
ed
in
t
o
two
s
u
b
g
r
o
u
p
s
:
in
d
ep
en
d
en
t
c
o
o
r
d
in
ates
,
an
d
r
ed
u
n
d
an
t c
o
o
r
d
in
ates
.
T
h
en
we
h
av
e
;
=
[
]
,
1
1
,
.
.
.
.
.
.
T
r
T
af
zz
qq
qz
,
=
+
(
5
)
B
y
d
i
f
f
e
r
e
n
t
i
a
t
i
n
g
in
(
2
)
w
i
t
h
r
e
s
p
e
c
t
t
o
v
e
c
t
o
r
s
,
,
,
r
e
s
p
e
c
t
i
v
e
l
y
,
w
e
o
b
t
a
i
n
t
h
e
f
o
l
l
o
w
i
n
g
J
a
c
o
b
i
a
n
m
a
t
r
i
c
e
s
,
,
,
r
n
r
r
r
f
s
z
a
a
f
f
f
s
z
q
,
=
[
]
(
6
)
B
y
in
tr
o
d
u
cin
g
th
e
p
r
o
jectio
n
m
atr
ix
[
4
7
]
:
(
)
=
[
−
−
1
]
∈
×
(
7
)
o
n
e
h
as:
(
)
(
)
=
0
,
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
R
a
d
ia
l b
a
s
is
fu
n
ctio
n
n
eu
r
a
l
n
etw
o
r
k
co
n
tr
o
l fo
r
p
a
r
a
llel sp
a
tia
l ro
b
o
t
(
N
g
u
ye
n
Ho
n
g
Qu
a
n
g
)
3193
wh
er
e
E
is
th
e
×
id
en
tity
m
atr
ix
.
L
ef
t
m
u
ltip
licatio
n
o
f
th
e
m
o
tio
n
i
n
(
1
)
with
th
e
m
atr
ix
T
Rs
y
ield
s
,
[
(
)
̈
+
(
,
̇
)
̇
+
(
)
+
(
)
+
(
,
̇
)
]
=
[
]
=
[
[
−
1
(
)
]
]
[
]
=
−
[
−
1
(
)
]
(
9
)
w
h
e
r
e
a
i
s
t
h
e
v
e
c
t
o
r
o
f
t
h
e
d
r
i
v
i
n
g
f
o
r
c
e
s
/
t
o
r
q
u
e
s
i
n
a
c
t
i
v
e
j
o
i
n
t
s
a
n
d
i
s
t
h
e
v
e
c
t
o
r
o
f
t
h
e
f
o
r
c
e
s
/
t
o
r
q
u
e
s
i
n
p
a
s
s
i
v
e
j
o
i
n
t
s
.
M
a
k
i
n
g
u
s
e
o
f
in
(
8
)
a
n
d
a
s
s
u
m
i
n
g
t
h
a
t
=
0
,
t
h
e
d
r
i
v
i
n
g
t
o
r
q
u
e
s
c
a
n
b
e
d
e
d
u
c
e
d
f
r
o
m
(
9
)
a
s
,
=
[
(
)
̈
+
(
,
̇
)
̇
+
(
)
+
(
,
̇
)
]
(
1
0
)
3.
ADAP
T
I
VE
R
B
F
NE
URA
L
NE
T
WO
RK
CO
NT
RO
L
B
A
SE
D
O
N
I
N
VE
R
SE
D
YNA
M
I
C
S F
O
R
P
ARAL
L
E
L
RO
B
O
T
S
3
.
1
.
T
ra
ns
f
o
r
m
a
t
io
n
o
f
m
o
t
io
n e
qu
a
t
io
ns
To
s
t
u
d
y
t
h
e
s
t
a
b
i
l
i
t
y
o
f
t
h
e
c
o
n
t
r
o
l
a
l
g
o
r
i
t
h
m
s
,
t
h
e
m
o
t
i
o
n
e
q
u
a
t
i
o
n
s
o
f
p
a
r
a
l
l
e
l
r
o
b
o
t
s
a
r
e
t
r
a
n
s
f
o
r
m
e
d
i
n
t
o
a
s
u
i
t
a
b
l
e
f
o
r
m
.
L
e
t
u
s
c
o
n
s
i
d
e
r
a
s
c
l
e
r
o
n
o
m
i
c
c
o
n
s
t
r
a
i
n
e
d
m
u
l
t
i
b
o
d
y
s
y
s
t
e
m
.
F
r
o
m
t
h
e
c
o
n
s
t
r
a
i
n
e
d
in
(
2
)
w
e
g
e
t
;
(
)
(
,
)
,
a
a
a
z
f
s
f
q
z
0
f
q
z
0
(
1
1
)
Ass
u
m
in
g
th
at
th
e
J
ac
o
b
ian
m
atr
ix
is
n
o
n
s
in
g
u
lar
,
d
et
(
)
0
.
Fro
m
(
1
1
)
o
n
e
m
ay
o
b
tain
,
̇
=
−
−
1
̇
(
1
2
)
I
t is n
o
ted
th
at
,
=
(
1
3
)
C
o
m
b
in
in
g
(
1
2
)
with
(
1
3
)
y
iel
d
s
th
e
f
o
llo
win
g
d
if
f
er
e
n
tial e
q
u
ati
on
:
̇
=
(
)
̇
(
1
4
)
Dif
f
er
en
tiatin
g
in
(
1
4
)
with
r
e
s
p
ec
t to
tim
e
g
iv
es th
e
ac
ce
ler
atio
n
r
elatio
n
as
;
̈
=
(
)
̈
+
̇
(
,
̇
)
̇
=
(
)
̈
+
(
)
(
⊗
̇
)
̇
(
1
5
)
Su
b
s
titu
tin
g
in
(
1
4
)
an
d
(
1
5
)
i
n
to
to
(
9
)
y
ield
s
;
()
(
)
(
(
)
(
)
)
(
)
+
(
,
)
,
a
p
a
a
a
T
s
s
s
q
E
s
q
s
q
d
s
s
s
R
R
M
s
R
C
s
s
R
g
s
(
1
6
)
T
o
s
im
p
lify
th
e
d
escr
ip
tio
n
,
w
e
d
ef
in
e
;
̄
(
)
≔
(
)
(
)
(
)
̄
(
,
̇
)
≔
(
)
[
(
)
(
)
(
⊗
̇
)
+
(
,
̇
)
(
)
]
̄
(
)
:
=
(
)
(
)
̄
(
,
̇
)
:
=
(
)
(
,
̇
)
(
17
)
I
n
(9
)
an
d
(
1
1
)
n
o
w
ca
n
b
e
r
e
wr
itten
as f
o
llo
ws
;
̄
(
)
̈
+
̄
(
,
̇
)
̇
+
̄
(
)
+
̄
(
,
̇
)
=
(
1
8
)
(
)
=
0
(
1
9
)
T
h
e
m
o
tio
n
eq
u
atio
n
s
o
f
p
ar
all
el
r
o
b
o
ts
(
1
8
)
an
d
(
1
9
)
ar
e
ca
ll
ed
th
e
m
o
tio
n
eq
u
atio
n
s
in
m
ix
tu
r
e
f
o
r
m
.
W
h
er
e
s
is
th
e
v
ec
to
r
o
f
r
ed
u
n
d
an
t
g
en
e
r
alize
d
co
o
r
d
in
ates
a
n
d
is
th
e
v
ec
to
r
o
f
in
d
ep
en
d
e
n
t
co
o
r
d
in
ates.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
3
1
9
1
-
320
1
3194
W
e
wil
l
u
s
e
th
is
eq
u
atio
n
as
th
e
b
asis
f
o
r
d
esig
n
in
g
th
e
co
n
tr
o
ller
f
o
r
p
ar
allel
r
o
b
o
ts
.
Fo
r
th
is
p
u
r
p
o
s
e,
we
p
r
o
v
e
th
e
f
o
llo
win
g
p
r
o
p
er
ties
[
3
3
]
:
−
̄
is
a
s
y
m
m
etr
ic
p
o
s
itiv
e
d
ef
in
i
te
m
atr
ix
:
̄
=
̄
,
−
̄
̇
−
2
̄
is
a
s
k
ew
-
s
y
m
m
etr
ic
m
atr
ix
:
(
̄
̇
−
2
̄
)
=
−
(
̄
̇
−
2
̄
)
.
Du
e
to
th
e
s
y
m
m
etr
y
o
f
th
e
m
atr
ix
M
is
s
y
m
m
etr
ic,
o
n
e
h
as
;
̄
(
)
=
[
(
)
(
)
(
)
]
=
(
)
(
)
(
)
=
̄
(
)
Sin
ce
(
)
is
p
o
s
itiv
e
d
ef
in
ite,
̄
(
)
is
also
a
p
o
s
itiv
e
d
ef
in
ite
m
atr
ix
.
Usi
n
g
th
e
(
1
7
)
,
o
n
e
o
b
tain
s
;
̄
̇
(
)
−
2
̄
(
,
̇
)
=
̇
+
̇
+
̇
−
2
(
̇
+
)
=
̇
+
̇
−
̇
−
2
=
(
̇
−
2
)
−
̇
+
̇
(
2
0
)
Sin
ce
̇
−
2
is
s
k
ew
-
s
y
m
m
etr
ic
[
8
]
,
f
r
o
m
in
(
2
0
)
o
n
e
h
as
;
[
̄
̇
(
)
−
2
̄
(
,
̇
)
]
=
[
(
̇
−
2
)
]
−
(
̇
)
+
(
̇
)
=
−
(
̇
−
2
)
−
̇
+
̇
=
−
[
̄
̇
(
)
−
2
̄
(
,
̇
)
]
(
2
1
)
T
h
u
s
,
̄
̇
(
)
−
2
̄
(
,
̇
)
is
a
s
k
ew
s
y
m
m
etr
ic
m
atr
ix
.
3
.
2
.
RB
F
neura
l net
wo
rk
c
o
n
t
ro
l la
w
a
nd
s
t
a
bil
it
y
a
na
ly
s
is
I
n
p
r
ac
tice,
th
e
p
e
r
f
ec
t
r
o
b
o
t m
o
d
el
co
u
ld
b
e
d
if
f
ic
u
lt
to
o
b
tain
,
an
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
ar
e
alwa
y
s
p
r
esen
t
in
p
r
ac
tice.
T
h
e
u
n
ce
r
tain
m
o
tio
n
eq
u
atio
n
s
o
f
p
ar
a
llel
r
o
b
o
ts
with
a
nf
ac
tiv
e
jo
in
ts
(
1
8
)
ca
n
b
e
d
escr
i
b
ed
in
th
e
f
o
llo
win
g
f
o
r
m
;
̂
(
)
̈
+
̂
(
,
̇
)
̇
+
̂
(
)
+
̂
(
,
̇
)
=
(
2
2
)
wh
er
e
̂
(
)
is
an
ff
in
er
tia
m
atix
,
̂
(
,
̇
)
is
an
ff
m
atr
ix
c
o
n
tain
in
g
th
e
ce
n
tr
if
u
g
al
an
d
C
o
r
io
lis
ter
m
s
,
ˆ
()
gs
is
an
1
f
v
ec
to
r
co
n
tain
in
g
g
r
a
v
itatio
n
al
f
o
r
ce
s
an
d
to
r
q
u
es,
s
is
th
e
v
ec
to
r
o
f
g
en
er
alize
d
co
o
r
d
in
ates
,
a
q
is
ac
tiv
e
jo
in
t c
o
o
r
d
in
ates,
an
d
ˆ
d
d
en
o
tes d
is
tu
r
b
an
ce
s
.
I
t is su
p
p
o
s
ed
t
h
at
,
̂
(
)
=
̄
(
)
+
̄
(
)
̂
(
,
̇
)
=
̄
(
,
̇
)
+
̄
(
,
̇
)
(
2
3
)
̂
(
)
=
̄
(
)
+
̄
(
)
̂
(
,
̇
)
=
̄
(
,
̇
)
+
̄
(
,
̇
)
wh
er
e
,
,
,
M
C
g
d
ar
e
th
e
p
r
io
r
-
k
n
o
wn
co
m
p
o
n
en
ts
an
d
,
,
,
M
C
g
d
ar
e
m
o
d
elin
g
er
r
o
r
s
o
f
ˆˆ
ˆ
,
,
M
C
g
an
d
ˆ
d
r
esp
ec
tiv
ely
.
Ass
u
m
e
th
at
th
e
m
o
d
elin
g
er
r
o
r
s
ar
e
b
o
u
n
d
e
d
b
y
s
o
m
e
f
in
ite
co
n
s
tan
ts
as
;
0
0
0
0
,
,
d
,
m
c
g
M
C
g
d
(
2
4
)
wh
er
e
0
0
0
0
,
,
,
mg
d
c
ar
e
k
n
o
wn
c
o
n
s
tan
t
s
.
Su
b
s
titu
tin
g
in
(
2
3
)
in
t
o
to
(
2
2
)
y
ield
s
.
(
̄
+
̄
)
̈
+
(
̄
+
̄
)
̇
+
̄
+
̄
+
̄
+
̄
=
(
2
5
)
Fro
m
(
2
5
)
o
n
e
h
as
;
̄
(
)
̈
+
̄
(
,
̇
)
̇
+
̄
(
)
+
̄
(
,
̇
)
+
ℎ
̄
(
,
̇
)
=
(
2
6
)
wh
er
e
ℎ
̄
(
,
̇
)
is
th
e
s
u
m
o
f
u
n
k
n
o
wn
ter
m
s
o
f
th
e
d
y
n
am
ic
s
y
s
tem
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
R
a
d
ia
l b
a
s
is
fu
n
ctio
n
n
eu
r
a
l
n
etw
o
r
k
co
n
tr
o
l fo
r
p
a
r
a
llel sp
a
tia
l ro
b
o
t
(
N
g
u
ye
n
Ho
n
g
Qu
a
n
g
)
3195
ℎ
̄
(
,
̇
)
=
̄
̈
+
̄
̇
+
̄
+
̄
(
2
7
)
Ass
u
m
e
th
at
‖
ℎ
̄
(
,
̇
)
‖
≤
ℎ
0
.
T
h
e
s
lid
in
g
m
o
d
e
f
u
n
ctio
n
is
s
elec
ted
as
;
(
)
=
̇
(
)
+
(
)
(
2
8
)
wh
er
e
is
th
e
p
o
s
itiv
e
d
iag
o
n
al
m
atr
ix
.
1
2
n
a
i
d
i
a
g
,
,
,
,
0
;
1
,
2
,
,
a
in
(
2
9
)
I
n
(
2
8
)
we
d
e
f
in
e
,
d
a
a
a
t
t
t
e
q
q
(
3
0
)
wh
er
e
(
)
is
th
e
v
ec
to
r
o
f
d
esire
d
tr
ajec
to
r
y
an
d
(
)
is
th
e
v
ec
to
r
o
f
r
ea
l
tr
ajec
to
r
y
.
T
h
e
f
u
n
c
tio
n
ℎ
̄
(
,
̇
)
ca
n
b
e
r
ewr
itten
as:
ℎ
̄
(
)
:
=
ℎ
̄
(
,
̇
)
(
3
1
)
T
h
e
f
u
n
ctio
n
ℎ
̄
(
)
is
th
e
m
ain
r
ea
s
o
n
f
o
r
t
h
e
d
e
g
r
ad
atio
n
o
f
th
e
co
n
tr
o
l
q
u
ality
.
I
f
t
h
is
ef
f
ec
t
i
s
co
m
p
en
s
ated
,
th
e
co
n
tr
o
l
ac
cu
r
ac
y
ca
n
th
e
n
b
e
im
p
r
o
v
ed
.
Acc
o
r
d
i
n
g
to
St
o
n
e
-
W
eier
s
tr
ass
th
eo
r
em
[
2
3
-
24]
o
n
e
ca
n
ch
o
o
s
e
an
ap
p
r
o
p
r
iate
a
r
tific
al
n
eu
r
a
l
n
etwo
r
k
(
ANN)
with
a
lim
i
ted
n
u
m
b
er
o
f
n
e
u
r
als
th
at
c
an
ap
p
r
o
x
im
ate
a
n
u
n
k
n
o
wn
n
o
n
lin
ea
r
f
u
n
ctio
n
with
a
g
i
v
en
ac
cu
r
ac
y
.
Fo
r
ap
p
r
o
x
im
atin
g
f
u
n
ctio
n
ℎ
̄
(
)
we
c
h
o
o
s
e
th
e
f
o
llo
win
g
s
im
p
le
s
tr
u
ctu
r
e
ANN:
ℎ
̄
(
)
=
+
=
ℎ
̂
(
)
+
(
3
2
)
wh
er
e
is
th
e
×
m
atr
ix
,
ℎ
̂
(
)
=
[
ℎ
̂
1
,
ℎ
̂
2
,
.
.
,
ℎ
̂
]
=
is
th
e
ap
p
r
o
x
im
atio
n
o
f
ℎ
̄
(
)
,
i
s
th
e
a
p
p
r
o
x
im
atio
n
er
r
o
r
.
I
f
‖
ℎ
̄
(
)
‖
≤
ℎ
0
,
we
h
av
e
‖
‖
≤
0
.
Ass
u
m
in
g
th
at
th
e
m
atr
ix
h
as
co
lu
m
n
v
ec
to
r
s
,
we
h
av
e
;
ℎ
̂
=
[
ℎ
̂
1
,
ℎ
̂
2
,
.
.
,
ℎ
̂
]
=
=
∑
=
1
(
3
3
)
I
n
th
is
p
a
p
er
,
th
e
r
ad
ial
b
asis
f
u
n
ctio
n
(
RBF
)
n
eu
r
al
n
etwo
r
k
was
u
s
e
d
as
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
is
s
tr
u
ctu
r
e
h
as
b
ee
n
p
r
o
v
e
d
to
s
atis
f
y
th
e
Sto
n
e
-
W
eier
s
tr
ass
th
eo
r
em
[
2
3
]
.
I
f
we
c
h
o
o
s
e
th
e
Gau
s
s
ian
ac
t
iv
atio
n
f
u
n
ctio
n
ac
co
r
d
in
g
to
th
e
f
o
r
m
u
la
,
=
[
−
‖
−
‖
2
2
]
(
3
4
)
w
h
e
r
e
t
h
e
v
e
c
t
o
r
r
e
p
r
e
s
e
n
t
s
t
h
e
c
o
o
r
d
i
n
a
t
e
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l
u
e
o
f
t
h
e
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e
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ter
p
o
i
n
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o
f
t
h
e
G
a
u
s
s
i
a
n
f
u
n
c
t
io
n
o
f
n
e
u
r
a
l
n
e
t
,
a
n
d
i
s
d
e
r
i
v
a
ti
o
n
p
a
r
a
m
e
t
e
r
wh
i
c
h
i
s
f
r
e
el
y
c
h
o
o
s
e
n
,
t
h
e
f
u
n
ct
i
o
n
a
p
p
r
o
x
i
m
a
t
i
o
n
ˆ
h
h
a
s
t
h
e
f
o
l
lo
w
i
n
g
f
o
r
m
;
1
ˆ
,
1..
,
a
j
n
i
j
a
j
i
h
i
n
w
(
3
5
)
wh
er
e
ar
e
th
e
weig
h
ts
to
b
e
u
p
d
ated
o
f
th
e
ap
p
r
o
x
im
atin
g
n
eu
r
al
n
etwo
r
k
.
Fig
u
r
e
1
.
R
B
F n
eu
r
al
n
etwo
r
k
s
tr
u
ctu
r
e
1
ˆ
h
2
ˆ
h
ˆ
na
h
1
2
na
11
w
12
w
2
na
w
1
na
w
1
2
na
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
3
1
9
1
-
320
1
3196
T
h
e
co
n
tr
o
l
p
r
o
b
lem
is
n
o
w
t
o
f
in
d
th
e
co
n
t
r
o
l
to
r
q
u
e
u
an
d
l
ea
r
n
in
g
alg
o
r
ith
m
o
f
o
f
th
e
n
eu
r
al
n
etwo
r
k
s
o
th
at
→
0
an
d
p
o
s
itio
n
e
r
r
o
r
s
→
0
,
g
r
an
tin
g
(
)
→
(
)
.
T
h
eo
r
em
:
T
h
e
tr
ajec
to
r
y
(
)
o
f
d
y
n
am
ic
s
y
s
tem
d
ef
in
ed
b
y
(
3
.
3
4
)
with
R
FB
n
eu
r
al
n
et
wo
r
k
ac
co
r
d
in
g
to
(
3
.
6
0
)
,
(
3
.
6
2
)
,
a
n
d
th
e
s
lid
in
g
s
u
r
f
ac
e
(
3
.
4
0
)
will
tr
ac
k
th
e
d
esire
d
tr
ajec
to
r
y
(
)
with
er
r
o
r
(
)
=
(
)
−
(
)
→
0
if
th
e
co
n
t
r
o
l la
w
u
th
e
lear
n
in
g
alg
o
r
ith
m
i
w
ar
e
ch
o
s
en
as f
o
ll
o
ws
;
=
̄
(
)
̈
+
̄
(
,
̇
)
̇
+
̄
+
̄
−
̄
(
)
̇
−
̄
(
,
̇
)
−
−
‖
‖
+
(
1
+
)
(
3
6
)
̇
=
−
(
3
7
)
wh
er
e
is
a
×
s
y
m
m
etr
ic
p
o
s
itiv
e
m
atr
ix
,
an
d
>
0
,
>
0
.
No
tin
g
th
at
th
e
s
tates
,
̇
i
n
th
e
co
n
tr
o
l
law
(
3
6
)
ar
e
m
ea
s
u
r
ed
.
P
r
o
o
f
:
T
h
is
th
eo
r
em
ca
n
b
e
p
r
o
v
ed
u
s
in
g
th
e
L
y
a
p
u
n
o
v
d
i
r
ec
t
m
eth
o
d
.
W
e
ch
o
o
s
e
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
as
;
(
)
=
1
2
[
̄
+
∑
=
1
]
(
3
8
)
Sin
ce
̄
(
)
is
s
y
m
m
etr
ic
an
d
p
o
s
i
tiv
e
d
ef
in
ite
(
)
>
0
f
o
r
≠
0
,
≠
0
an
d
(
)
=
0
if
an
d
o
n
l
y
if
=
0
,
=
0
.
T
h
e
d
er
iv
ativ
e
o
f
th
e
f
u
n
ctio
n
(
)
is
,
̇
(
)
=
̄
̇
+
1
2
̄
̇
+
∑
=
1
̇
(
3
9
)
Usi
n
g
th
e
s
k
ew
-
s
y
m
m
etr
y
o
f
t
h
e
m
atr
ix
̄
(
)
−
2
̄
(
,
̇
)
,
we
h
av
e
(
̄
̇
−
2
̄
)
=
0
→
̄
̇
=
2
̄
(
4
0
)
Su
b
s
titu
tin
g
(
4
0
)
in
to
(
3
9
)
g
iv
es:
̇
(
)
=
(
̄
̇
+
̄
)
+
∑
=
1
̇
(
4
1
)
I
f
we
ch
o
o
s
e
a
u
,
f
r
o
m
(
3
8
)
a
n
d
(
2
6
)
o
n
e
h
as
,
̄
̇
+
̄
=
−
[
+
‖
‖
−
(
1
+
)
+
ℎ
̄
(
)
]
(
4
2
)
Su
b
s
titu
tin
g
in
(
4
2
)
in
to
to
(
4
1
)
y
ield
s
,
̇
(
)
=
[
−
−
|
|
|
|
+
−
]
+
∑
=
1
̇
(
4
3
)
Usi
n
g
th
e
lear
n
in
g
alg
o
r
ith
m
(
3
7
)
,
th
e
last
ter
m
in
(
4
3
)
h
as t
h
e
f
o
llo
win
g
f
o
r
m
,
∑
=
1
̇
=
−
∑
=
1
=
−
(
4
4
)
Su
b
s
titu
tin
g
(
4
4
)
in
to
to
(
4
3
)
y
ield
s
,
̇
(
)
=
−
−
‖
‖
−
(
4
5
)
I
f
we
s
elec
t
0
,
an
d
0
,
o
n
e
o
b
tain
s
:
̇
(
)
=
−
−
‖
‖
−
(
0
‖
‖
+
)
(
4
6
)
Sin
ce
‖
‖
<
0
,
̇
(
)
<
0
f
o
r
all
≠
0
,
an
d
̇
(
)
=
0
if
an
d
o
n
l
y
if
=
0
.
I
t
f
o
llo
ws
f
r
o
m
L
y
ap
u
n
o
v
’
s
th
eo
r
y
th
at
th
e
s
y
s
tem
is
asy
m
p
to
tically
s
tab
le,
o
r
→
0
as
→
∞
,
th
er
ef
o
r
e
,
t
d
a
a
a
tt
e
q
q
0
(
4
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
R
a
d
ia
l b
a
s
is
fu
n
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n
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eu
r
a
l
n
etw
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r
k
co
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tr
o
l fo
r
p
a
r
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llel sp
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l ro
b
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t
(
N
g
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n
g
Qu
a
n
g
)
3197
4.
SI
M
UL
A
T
I
O
N
E
XA
M
P
L
E
Fro
m
t
h
e
R
B
F n
eu
r
al
n
etwo
r
k
co
n
tr
o
l la
w
p
r
esen
te
d
in
th
e
a
b
o
v
e
s
ec
tio
n
,
th
e
r
esu
ltin
g
b
lo
ck
s
ch
em
e
is
illu
s
tr
ated
in
th
e
Fig
u
r
e
2
.
F
o
r
th
e
u
s
e
o
f
th
e
c
o
n
tr
o
l
law
u
b
ased
o
n
(
3
6
)
an
d
(
3
7
)
,
ac
tu
al
s
ig
n
als
,
̇
,
̈
ar
e
ass
u
m
ed
to
b
e
k
n
o
wn
.
T
h
er
ef
o
r
e,
o
n
e
ca
n
o
b
tain
ac
tu
al
v
alu
es
o
f
g
en
er
alize
d
co
o
r
d
in
ates,
v
elo
cities
an
d
ac
ce
ler
atio
n
s
,
̇
,
̈
.
T
h
e
n
u
m
er
ical
s
im
u
latio
n
m
a
y
b
e
a
p
o
s
s
ib
le
way
to
s
u
g
g
est
a
n
alter
n
ati
v
e
c
h
o
ice
f
o
r
ac
tu
al
v
alu
es
o
f
g
en
er
alize
d
co
o
r
d
in
a
tes,
v
e
lo
cities
an
d
ac
ce
ler
atio
n
s
.
C
o
n
s
id
er
in
g
th
e
d
y
n
a
m
ic
eq
u
atio
n
s
o
f
p
ar
allel
r
o
b
o
t
m
a
n
ip
u
lato
r
as;
(
)
̈
+
(
,
̇
)
̇
+
(
)
+
(
)
+
(
,
̇
)
=
(
4
8
)
(
)
=
0
(
4
9
)
wh
er
e
,
=
(
,
,
̇
,
,
̇
)
=
[
,
0
]
(
5
0
)
Dif
f
er
en
tiatin
g
in
(
4
9
)
with
r
e
s
p
ec
t to
tim
e
g
iv
es
,
̇
(
)
=
̇
=
̇
=
0
(
5
1
)
̈
(
,
̇
)
=
̈
+
̇
̇
=
0
(
5
2
)
wh
er
e
[
4
5
,
4
6
]
:
̇
(
)
=
(
⊗
̇
)
(
5
3
)
Def
in
e
,
1
(
,
̇
,
,
̇
,
)
=
−
(
,
̇
)
̇
−
(
)
−
(
,
̇
)
(
54)
2
(
,
̇
,
)
=
−
̇
(
)
̇
=
−
[
(
⊗
̇
)
]
̇
(
5
5
)
I
n
(
4
8
)
an
d
(
5
2
)
n
o
w
ca
n
b
e
w
r
itten
in
th
e
f
o
llo
win
g
f
o
r
m
,
(
)
̈
+
(
)
=
1
(
,
̇
,
,
̇
,
)
(
5
6
)
(
)
̈
=
2
(
,
̇
,
)
(
5
7
)
L
ef
t
m
u
ltip
licatio
n
o
f
(
5
6
)
wit
h
th
e
m
atr
ix
y
ield
s
,
(
)
(
)
̈
+
(
)
(
)
=
(
)
1
(
,
̇
,
)
(
5
8
)
Acc
o
r
d
in
g
t
o
(
8
)
,
(
5
8
)
b
ec
o
m
e
s
:
(
)
(
)
̈
=
(
)
1
(
,
̇
,
,
̇
,
)
(
5
9
)
I
n
(
5
9
)
is
a
s
y
s
tem
o
f
f
s
ec
o
n
d
-
o
r
d
er
d
if
f
er
e
n
tial e
q
u
atio
n
s
.
C
o
m
b
in
in
g
in
(
5
9
)
with
(
5
7
)
y
ie
ld
s
,
[
(
)
(
)
(
)
]
̈
=
[
(
)
1
2
]
(
6
0
)
I
f
th
e
m
atr
ix
,
(
)
=
[
(
)
(
)
(
)
]
(
6
1
)
is
n
o
n
s
ig
u
lar
,
f
r
o
m
(
6
0
)
o
n
e
o
b
tain
s
th
e
f
o
llo
w
in
g
d
if
er
e
n
tial e
q
u
atio
n
s
y
s
tem
,
̈
=
̈
(
,
̇
,
,
̇
,
)
(
6
2
)
T
h
en
,
s
o
lv
in
g
th
e
(
6
2
)
we
f
in
d
,
̇
[
4
8
]
.
T
h
er
ef
o
r
e
we
ca
n
ca
lcu
late
co
n
tr
o
l la
w
ac
co
r
d
in
g
t
o
(
3
6
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
3
1
9
1
-
320
1
3198
Fig
u
r
e
2
.
B
lo
ck
s
ch
em
e
o
f
j
o
in
t sp
ac
e
co
n
tr
o
l
A
3
-
R
R
R
s
p
atial
p
ar
allel
r
o
b
o
t
m
an
ip
u
lato
r
s
h
o
wn
in
Fig
u
r
e
3
is
u
tili
ze
d
in
th
is
s
tu
d
y
to
v
er
if
y
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
t
r
o
l
s
ch
em
e.
T
h
e
m
ec
h
a
n
ical
m
o
d
el
f
o
r
th
e
3
-
RRR
d
elta
r
o
b
o
t
m
an
i
p
u
lato
r
is
a
s
y
s
tem
o
f
r
ig
id
b
o
d
ies
co
n
n
ec
ted
b
y
jo
in
ts
a
s
Fig
u
r
e
4
.
T
h
e
p
ar
allelo
g
r
am
m
ec
h
a
n
is
m
s
th
at
co
n
n
ec
t
th
e
d
r
iv
in
g
lin
k
s
to
th
e
m
o
b
ile
p
l
atf
o
r
m
ar
e
m
o
d
eled
as
h
o
m
o
g
en
eo
u
s
r
o
d
s
with
u
n
iv
er
s
al
an
d
s
p
h
er
ical
jo
in
ts
at
two
en
d
s
.
Fro
m
Fig
u
r
es
4
an
d
5
it
is
f
o
llo
wed
th
at
th
e
co
n
f
ig
u
r
atio
n
o
f
th
e
3
-
RRR
d
elta
s
p
atial
p
ar
allel
r
o
b
o
t
m
an
ip
u
lato
r
is
r
e
p
r
esen
ted
b
y
a
v
ec
to
r
o
f
g
e
n
er
alize
d
co
o
r
d
i
n
ates a
s
:
1
2
3
1
2
3
,
T
P
P
P
x
y
z
s
T
h
e
d
if
f
er
en
tial
-
alg
e
b
r
aic
e
q
u
atio
n
s
o
f
th
e
s
y
s
tem
ar
e
g
iv
e
n
in
th
e
Ap
p
en
d
ix
.
T
h
e
k
i
n
e
m
atic
an
d
d
y
n
am
ic
p
ar
am
eter
s
o
f
th
e
r
o
b
o
t
m
an
i
p
u
la
to
r
ar
e
g
iv
en
in
th
e
T
a
b
l
e
1.
I
n
th
e
s
im
u
latio
n
,
t
h
e
ce
n
ter
o
f
th
e
m
o
v
in
g
p
latf
o
r
m
will b
e
c
o
n
tr
o
lled
to
tr
ac
k
th
e
g
iv
e
n
tr
ajec
to
r
y
d
ef
i
n
ed
b
y
,
0
.
3
c
o
s
2
;
0
.
3
s
i
n
2
;
0
.
7
(
)
P
P
P
x
t
y
t
z
m
T
h
e
p
ar
am
eter
s
o
f
th
e
n
eu
r
al
n
etwo
r
k
co
n
t
r
o
l la
w
ar
e
ch
o
s
en
as f
o
llo
ws
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1
2
3
1
2
3
8
0
,
8
0
,
8
0
;
(
8
0
,
8
0
,
8
0
)
;
1
.
1
;
2
0
0
;
1
;
2
;
3
;
0
.
0
1
;
0
.
0
2
;
0
.
0
3
;
d
i
a
g
d
i
a
g
c
c
c
KL
Fig
u
r
e
3
.
Delta
r
o
b
o
t w
ith
th
r
e
e
p
ar
allelo
g
r
am
m
ec
h
an
is
m
s
Fig
u
r
e
4
.
Mo
d
el
o
f
3
-
R
R
R
De
lta
r
o
b
o
t
Fig
u
r
e
5
.
Po
s
itio
n
o
f
th
e
ii
BD
r
o
d
i
n
th
e
s
p
ac
e
In
v
e
r
s
e
k
i
n
e
m
a
ti
c
s
Co
n
tro
l
l
a
w
P
a
r
a
l
l
e
l
r
o
b
o
t
(
),
(t)
dd
t
ss
(
)
,
(
t
)
t
ss
()
t
u
()
d
t
x
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
R
a
d
ia
l b
a
s
is
fu
n
ctio
n
n
eu
r
a
l
n
etw
o
r
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co
n
tr
o
l fo
r
p
a
r
a
llel sp
a
tia
l ro
b
o
t
(
N
g
u
ye
n
Ho
n
g
Qu
a
n
g
)
3199
T
ab
le
1
.
T
h
e
p
ar
am
ete
r
s
o
f
th
e
Delta
r
o
b
o
t in
Fig
u
r
e
3
1
2
r
1
1
2
3
1
1
m
2
2
m
0
.
3
(
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8
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266
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2
(
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.
75
(
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I
n
th
is
p
ap
er
th
e
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er
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r
s
ar
e
ch
o
s
en
to
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e
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o
f
th
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io
r
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al
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o
f
th
e
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o
m
i
n
al
m
o
d
el
as
,
(
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=
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(
)
;
(
,
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)
=
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,
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;
(
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=
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(
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T
h
e
d
is
tu
r
b
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ce
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to
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is
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o
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en
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1
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6
6
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i
n
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o
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.
.
.
s
i
n
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o
s
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t
t
t
t
d
.
So
m
e
s
im
u
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n
r
esu
lts
ar
e
g
iv
en
in
th
e
Fig
u
r
es
f
r
o
m
6
t
o
9
.
T
h
e
p
o
s
itio
n
er
r
o
r
s
o
f
th
e
m
o
v
in
g
p
latf
o
r
m
ar
e
s
h
o
w
n
in
Fig
u
r
e
s
6
an
d
7
.
T
h
e
co
n
tr
o
l
to
r
q
u
e
s
ar
e
s
h
o
wn
in
Fig
u
r
e
s
8
an
d
9
.
T
h
e
s
tatio
n
ar
y
er
r
o
r
s
in
p
o
s
itio
n
o
f
th
e
p
la
tf
o
r
m
ar
e
k
e
p
t a
b
o
u
t 1
0
-
4
mm.
Fig
u
r
e
6
.
Po
s
itio
n
er
r
o
r
s
o
f
th
e
m
o
v
in
g
p
latf
o
r
m
with
o
u
t
t
h
e
m
o
d
elin
g
e
r
r
o
r
s
a
n
d
d
is
tu
r
b
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