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3
,
Sep
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201
6
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p
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182
~
189
I
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N:
2089
-
4856
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[
1
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2
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[
5
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A
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[
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7
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8
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9
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,
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1
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I
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4
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Lo
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183
2.
L
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-
[
(
t)
-
*
(
t)
]
h
er
e,
(
t)
is
cu
r
r
en
t
d
ir
ec
t
io
n
al
an
g
le
o
f
r
o
b
o
t,
*
(
t)
is
d
esira
b
le
d
ir
ec
tio
n
an
g
le,
i
s
a
p
o
s
itiv
e
co
n
s
ta
n
t.
Sev
er
al
ap
p
r
o
ac
h
es
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
th
e
li
ter
atu
r
e
in
t
h
e
p
ast
to
s
o
l
v
e
t
h
e
p
ath
p
lan
n
i
n
g
p
r
o
b
lem
i
n
a
n
u
n
k
n
o
w
n
r
e
g
io
n
.
O
n
e
o
f
th
e
w
id
el
y
u
s
ed
s
c
h
e
m
es
th
at
ex
te
n
s
iv
e
l
y
d
i
s
cu
s
s
e
d
in
t
h
e
liter
at
u
r
e
i
s
„
B
u
g
alg
o
r
it
h
m
s
‟
,
th
e
s
e
n
s
o
r
-
b
ased
p
ath
p
lan
n
i
n
g
ap
p
r
o
ac
h
.
T
w
o
alg
o
r
ith
m
s
n
a
m
el
y
B
u
g
1
an
d
B
u
g
2
w
er
e
p
r
o
p
o
s
ed
b
y
L
u
m
els
k
y
et
al
[
3
]
.
T
h
is
alg
o
r
ith
m
o
p
er
ates
s
w
itc
h
in
g
b
et
w
ee
n
t
w
o
s
i
m
p
l
e
b
eh
av
io
r
s
:
(
i)
th
e
m
o
v
e
m
e
n
t
to
w
ar
d
s
t
h
e
g
o
al
an
d
(
ii)
th
e
m
o
v
e
m
en
t
ar
o
u
n
d
an
o
b
s
tacle
.
Sev
er
al
v
er
s
io
n
s
o
f
B
u
g
alg
o
r
it
h
m
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
s
in
ce
th
e
n
.
T
h
e
m
o
s
t
co
m
m
o
n
l
y
u
s
ed
an
d
r
ef
er
r
ed
in
m
o
b
ile
r
o
b
o
t
p
ath
p
lan
n
in
g
ar
e
B
u
g
1
an
d
B
u
g
2
,
Vi
s
B
u
g
,
Dis
t
B
u
g
a
n
d
T
an
g
en
tB
u
g
.
Oth
e
r
s
b
u
g
al
g
o
r
ith
m
s
ar
e
A
l
g
1
an
d
A
l
g
2
C
lass
,
R
e
v
an
d
R
ev
2
,
On
eB
u
g
a
n
d
L
ea
v
eB
u
g
[
4
]
.
L
u
m
e
ls
k
y
a
n
d
Sk
e
w
i
s
p
r
o
p
o
s
e
d
an
im
p
r
o
v
e
m
e
n
t
in
t
h
e
B
u
g
2
w
ith
t
h
e
Vis
B
u
g
in
co
r
p
o
r
atin
g
a
r
an
g
e
s
en
s
o
r
,
w
h
ic
h
is
a
n
en
h
a
n
ce
m
en
t
to
th
e
co
n
d
itio
n
t
h
at
th
e
r
o
b
o
t
u
s
es
to
s
to
p
co
n
to
u
r
i
n
g
an
o
b
s
tacle
a
n
d
r
esu
m
e
t
h
e
m
o
v
e
m
e
n
t
to
th
e
g
o
al,
th
e
s
o
ca
l
led
leav
in
g
co
n
d
itio
n
.
Su
c
h
i
m
p
r
o
v
e
m
e
n
t
g
e
n
er
ates
s
h
o
r
t
c
u
t
s
i
n
th
e
p
ath
[
2
]
.
Ka
m
o
n
a
n
d
R
i
v
li
n
cr
ea
ted
th
e
Dis
tB
u
g
w
h
ich
i
s
ch
ar
ac
ter
i
ze
d
b
y
an
o
t
h
er
alter
atio
n
i
n
t
h
e
leav
in
g
co
n
d
itio
n
.
Un
d
er
ce
r
tain
s
p
ec
ial
co
n
d
itio
n
s
t
h
e
co
n
v
er
g
e
n
c
e
o
f
th
e
Dis
tB
u
g
ca
n
b
e
p
r
o
v
ed
.
T
h
e
Dis
tB
u
g
alg
o
r
ith
m
in
co
r
p
o
r
ate
s
,
b
asic
all
y
,
t
w
o
co
n
tr
ib
u
tio
n
s
i
n
r
el
atio
n
to
th
e
ea
r
lier
al
g
o
r
ith
m
s
:
(
i)
a
r
o
u
ti
n
e
t
h
at
k
ee
p
s
t
h
e
co
m
p
u
tatio
n
co
s
t
i
n
r
an
g
e
b
u
t
o
f
f
er
s
m
o
r
e
a
g
g
r
ess
iv
e
leav
in
g
co
n
d
itio
n
a
n
d
(
ii)
a
m
et
h
o
d
to
d
eter
m
in
e
w
h
ic
h
s
id
e
o
f
t
h
e
o
b
s
tacle
s
h
o
u
ld
b
e
co
n
-
to
u
r
ed
.
I
t r
e
q
u
ir
es its
o
w
n
p
o
s
itio
n
b
y
ap
p
ly
i
n
g
o
d
o
m
etr
y
,
d
esti
n
atio
n
an
d
s
en
s
o
r
d
ata.
T
o
en
s
u
r
e
co
n
v
er
g
en
ce
to
th
e
g
o
al,
th
e
Dis
tB
u
g
al
g
o
r
ith
m
n
e
ed
s
a
litt
le
am
o
u
n
t
o
f
g
lo
b
al
in
f
o
r
m
atio
n
f
o
r
m
o
d
if
y
i
n
g
d
m
in
(
d
is
ta
n
ce
f
r
o
m
r
o
b
o
t
to
d
esti
n
atio
n
)
an
d
f
o
r
d
eter
m
in
i
n
g
th
at
t
h
e
r
o
b
o
t
f
in
i
s
h
ed
a
lo
o
p
a
r
o
u
n
d
an
o
b
s
tacle
.
T
h
e
v
alu
e
o
f
d
m
in
ca
n
b
e
ex
tr
ac
ted
d
ir
ec
t
l
y
f
r
o
m
t
h
e
v
is
u
a
l
in
f
o
r
m
atio
n
.
T
h
is
co
n
v
er
g
e
n
c
e
u
s
in
g
u
p
d
ati
n
g
d
m
in
v
al
u
e
m
ak
es
p
r
o
b
lem
i
n
d
eter
m
in
in
g
ac
cu
r
ac
y
b
ec
au
s
e
t
h
e
v
alu
e
o
f
d
m
i
n
is
ta
k
en
d
ir
ec
t
ly
f
r
o
m
u
s
er
.
T
h
e
T
an
g
en
tB
u
g
i
m
p
r
o
v
e
s
t
h
e
Dis
tB
u
g
a
n
d
B
u
g
2
al
g
o
r
ith
m
b
y
i
n
te
g
r
ati
n
g
r
a
n
g
e
s
en
s
o
r
s
f
r
o
m
ze
r
o
to
in
f
i
n
it
y
to
d
etec
t
o
b
s
tacle
s
.
R
o
b
o
t
w
ill
s
tar
t
m
o
v
i
n
g
ar
o
u
n
d
th
e
o
b
s
tacle
o
n
d
etec
tio
n
o
f
an
o
b
s
tacle
an
d
as
s
o
o
n
as
it
clea
r
s
t
h
e
o
b
s
tacle
w
il
l
co
n
ti
n
u
e
m
o
tio
n
to
w
ar
d
t
ar
g
et
p
o
in
t.
Du
r
i
n
g
f
o
llo
w
i
n
g
b
o
u
n
d
ar
y
,
it
r
ec
o
r
d
s
th
e
m
i
n
i
m
al
d
is
ta
n
ce
to
tar
g
et
d
m
in
w
h
ich
d
eter
m
i
n
es
o
b
s
tacle
leav
i
n
g
a
n
d
r
ea
ch
i
n
g
c
o
n
d
itio
n
.
T
h
e
r
o
b
o
t
co
n
s
tr
u
ct
s
a
lo
ca
l
ta
n
g
en
t
g
r
a
p
h
(
L
T
G)
b
ased
o
n
its
s
e
n
s
o
r
s
‟
i
m
m
ed
iate
r
ea
d
in
g
s
.
T
o
d
ec
i
d
e
th
e
n
e
x
t
m
o
tio
n
r
o
b
o
t
co
n
tin
u
o
u
s
l
y
m
o
d
i
f
ied
L
T
G
an
d
u
s
e
it
.
T
h
e
d
is
ad
v
an
tag
e
o
f
t
h
is
al
g
o
r
ith
m
is
a
co
m
p
lete
360
0
s
ca
n
is
r
eq
u
ir
ed
b
y
r
o
b
o
t
in
m
a
k
in
g
d
ec
is
io
n
to
m
o
v
e
to
th
e
n
ex
t ta
r
g
et.
An
o
th
er
v
ar
iatio
n
o
f
B
u
g
al
g
o
r
ith
m
is
P
o
in
tB
u
g
alg
o
r
it
h
m
[
4
]
w
h
ic
h
i
m
p
r
o
v
es
t
h
e
T
an
g
e
n
tB
u
g
alg
o
r
ith
m
.
T
h
is
alg
o
r
it
h
m
tr
ie
s
to
m
i
n
i
m
ize
m
o
v
i
n
g
ar
o
u
n
d
o
f
a
n
o
b
s
tacle
(
o
b
s
tacle
b
o
r
d
er
)
b
y
co
n
s
id
er
i
n
g
p
o
in
ts
o
n
t
h
e
o
u
ter
p
er
i
m
eter
o
f
o
b
s
tacle
ar
ea
as
a
r
o
tatin
g
p
o
s
itio
n
to
g
o
al
an
d
f
in
al
l
y
cr
ea
t
e
a
n
en
tire
p
at
h
f
r
o
m
s
o
u
r
ce
to
o
b
j
ec
tiv
e.
T
h
e
m
ai
n
id
ea
i
s
f
e
w
er
u
s
e
o
f
o
u
te
r
p
er
im
e
ter
o
f
o
b
s
tac
le
ar
ea
m
in
i
m
izes
to
tal
p
at
h
len
g
th
ta
k
en
b
y
a
m
o
b
ile
r
o
b
o
t.
A
s
r
o
b
o
t
c
o
n
s
id
er
s
h
er
e
th
e
r
ig
h
t
m
o
s
t
s
u
d
d
en
p
o
in
t
f
ir
s
t,
s
o
th
is
alg
o
r
ith
m
m
a
y
ta
k
e
f
e
w
ex
tr
a
ti
m
es
if
m
o
r
e
th
a
n
o
n
e
s
u
d
d
en
p
o
in
t
ex
is
t
s
i
n
an
o
b
s
tacle
.
Fi
g
.
1
s
h
o
w
s
t
h
e
d
i
f
f
er
e
n
t
tr
aj
ec
to
r
ies g
en
er
ated
b
y
B
u
g
2
,
Vis
B
u
g
,
Di
s
tB
u
g
,
T
an
g
en
tB
u
g
a
n
d
P
o
in
t B
u
g
.
Fig
u
r
e
1
.
T
r
aj
ec
t
o
r
ies Fo
r
m
ed
b
y
d
i
f
f
er
en
t B
u
g
A
l
g
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
5
,
No
.
3
,
Sep
tem
b
er
201
6
:
1
8
2
–
1
8
9
184
3.
CRIT
I
CA
L
-
P
O
I
NT
B
U
G
A
L
G
O
R
I
T
H
M
T
h
is
alg
o
r
ith
m
h
e
lp
s
to
n
av
i
g
ate
a
r
o
b
o
t
in
a
p
lan
e
f
illed
w
it
h
s
ta
tic
o
b
s
tacle
s
o
f
u
n
k
n
o
w
n
s
h
ap
e,
s
ize
an
d
lo
ca
tio
n
.
T
h
e
r
o
b
o
t
u
s
es
r
an
g
e
s
e
n
s
o
r
to
d
etec
t
ab
r
u
p
t
ch
an
g
e
i
n
d
is
tan
ce
to
d
etec
t
o
b
s
tacle
p
o
s
itio
n
s
.
Dep
en
d
in
g
o
n
t
h
e
o
b
s
tacle
p
o
s
itio
n
s
it
ca
lc
u
lat
e
s
an
d
d
eter
m
i
n
es
t
h
e
n
ex
t
p
o
in
t
to
m
o
v
e
f
r
o
m
c
u
r
r
en
t
p
o
in
t
to
r
ea
ch
th
e
tar
g
et.
W
e
co
n
s
id
er
a
p
o
s
s
ib
ly
u
n
b
o
u
n
d
ed
s
p
ac
e
Q
⊂
R
2
w
h
ich
i
s
o
cc
u
p
ied
b
y
a
s
e
t
o
f
b
o
u
n
d
ed
s
tatic
o
b
s
tacle
s
O
=
{O
1
,O
2
,
.
.
.
,
O
K
}.
W
e
co
n
s
id
er
a
w
h
ee
le
d
r
o
b
o
t
w
h
ic
h
is
eq
u
ip
p
ed
w
it
h
s
e
n
s
o
r
s
to
d
etec
t
o
b
s
tacle
s
.
T
h
e
r
o
b
o
t
h
as
its
i
n
itial
co
o
r
d
in
ates
w
it
h
r
ef
er
e
n
ce
to
a
g
lo
b
al
f
r
a
m
e
o
f
r
ef
e
r
en
ce
.
W
e
s
o
lv
e
th
e
p
r
o
b
lem
in
t
h
e
co
n
f
i
g
u
r
at
io
n
s
p
ac
e
w
h
er
e
t
h
e
r
o
b
o
t is r
ep
r
es
en
ted
as a
p
o
in
t.
B
ef
o
r
e
p
r
o
ce
ed
in
g
to
t
h
e
d
e
s
cr
ip
tio
n
o
f
t
h
e
al
g
o
r
i
th
m
s
,
w
e
m
a
k
e
s
o
m
e
n
ec
ess
ar
y
a
n
d
u
s
e
f
u
l
ass
u
m
p
tio
n
s
a
n
d
d
ef
in
i
tio
n
s
f
o
r
th
is
al
g
o
r
ith
m
.
3.
1
.
Ass
u
m
ptio
ns
A
1
.
Her
e,
th
e
R
o
b
o
t is co
n
s
id
er
ed
as P
o
in
t Ro
b
o
t
A
2
.
W
o
r
ld
c
o
-
o
r
d
in
ate
s
y
s
te
m
is
u
s
ed
A
3
.
A
ll p
o
in
ts
(
in
c
lu
d
i
n
g
s
o
u
r
ce
a
n
d
d
esti
n
at
io
n
)
ar
e
in
f
ir
s
t q
u
a
d
r
an
t
A
4
.
T
h
e
v
elo
cit
y
an
d
a
n
g
u
lar
v
elo
cit
y
is
co
n
s
ta
n
t i
n
ev
er
y
m
o
v
e
m
en
t a
n
d
r
o
tatio
n
r
esp
ec
tiv
e
l
y
A
5
.
Su
r
f
ac
e
is
s
m
o
o
th
a
n
d
in
s
a
m
e
altitu
d
e
A
6
.
A
ll t
h
e
o
b
s
tacle
s
ar
e
s
ta
tio
n
ar
y
an
d
o
f
a
n
y
s
h
ap
e
an
d
s
ize
A
7
.
T
h
e
m
o
b
ile
r
o
b
o
t m
o
v
es i
n
a
t
w
o
-
d
i
m
e
n
s
io
n
al
s
p
ac
e
3
.
2
.
Su
b G
o
a
l P
o
int
a
nd
Crit
ica
l P
o
int
T
h
e
m
as
s
iv
e
ch
a
n
g
e
o
f
d
is
ta
n
ce
r
ea
d
in
g
f
r
o
m
r
an
g
e
s
e
n
s
o
r
o
u
tp
u
t
ei
th
er
i
n
i
n
cr
ea
s
i
n
g
o
r
d
ec
r
ea
s
in
g
m
o
d
e
i
s
co
n
s
id
er
ed
f
o
r
f
in
d
i
n
g
S
u
b
g
o
al
p
o
in
t
.
I
t
ca
n
b
e
f
r
o
m
i
n
f
in
i
t
y
to
a
d
ef
i
n
ite
v
al
u
e
o
r
a
d
ef
in
ite
v
al
u
e
to
in
f
in
it
y
o
r
d
ef
in
i
te
v
a
l
u
e
to
a
d
ef
in
ite
v
a
lu
e
w
h
er
e
th
e
d
if
f
er
en
ce
v
a
lu
e,
Δ
d
is
d
ef
i
n
ed
.
A
n
y
r
ea
d
in
g
f
r
o
m
r
an
g
e
s
e
n
s
o
r
f
r
o
m
in
ter
v
al
t
i
m
e,
t
n
to
t
n
+
1
w
h
ic
h
d
etec
t
s
t
h
is
m
as
s
i
v
e
c
h
an
g
e
in
r
an
g
e
i
s
co
n
s
id
er
ed
a
s
S
u
b
g
o
al
P
o
in
t.
T
h
e
r
o
b
o
t
m
a
y
s
ca
n
th
e
s
u
r
r
o
u
n
d
i
n
g
s
b
y
r
an
g
e
s
e
n
s
o
r
f
r
o
m
0
0
to
3
6
0
0
.
T
h
e
in
itiall
y
th
e
r
o
b
o
t
f
ac
ed
s
tr
aig
h
t to
w
ar
d
s
g
o
al
p
o
in
t a
n
d
th
en
it s
tar
ts
s
ca
n
n
in
g
f
o
r
s
u
b
g
o
al
p
o
in
t.
A
s
u
b
g
o
al
p
o
in
t
ch
o
s
e
n
b
y
t
h
e
r
o
b
o
t
f
o
r
n
ex
t
p
o
in
t
to
m
o
v
e
is
C
r
itica
l
p
o
in
t.
Gen
er
all
y
th
is
p
o
in
t
h
as t
h
e
lo
w
est d
is
ta
n
ce
f
r
o
m
d
est
in
a
tio
n
w
it
h
i
n
t
h
e
s
et
o
f
s
u
b
g
o
al
an
d
is
n
o
t tr
a
v
er
s
ed
y
et.
W
e
co
n
s
id
er
,
T=
{(
x
1
,y
1
)
,
(
x
2
,y
2
)
,
.
.
.
,
(
x
i
,y
i
)
}
as
a
s
et
of
p
o
in
t
s
tr
av
er
s
ed
b
y
th
e
r
o
b
o
t
w
h
er
e
(
x
i
,
y
i
)
r
ep
r
esen
ts
t
h
e
co
o
r
d
in
ate
v
alu
e
s
SG=
{(
α
a
,d
a
)
,
(
α
b
,d
b
)
,
.
.
.
.
,
(
α
k
,d
k
)
}
as
a
s
et
o
f
n
e
x
t
s
u
b
g
o
al
p
o
in
ts
d
etec
ted
b
y
t
h
e
s
e
n
s
o
r
w
h
er
e
α
an
d
d
r
ep
r
esen
ts
th
e
a
n
g
les
&
d
is
ta
n
ce
s
o
f
s
u
b
g
o
als
f
r
o
m
t
h
e
r
o
b
o
t r
esp
ec
tiv
el
y
D=
{(
(
x
i
,y
i
)
,
δ
i
)
,
….
.
,
(
(
x
j
,y
j
)
,
δ
j
)
}
as a
s
et
o
f
s
u
b
g
o
al
p
o
in
ts
a
n
d
d
is
tan
ce
f
r
o
m
d
esti
n
atio
n
o
f
t
h
at
p
o
in
t
Her
e
d
m
in
is
t
h
e
d
is
ta
n
ce
f
r
o
m
th
e
r
o
b
o
t to
tar
g
et
p
o
in
t a
n
d
is
th
e
d
ir
ec
tio
n
o
f
th
e
s
a
m
e.
Fig
u
r
e
2
.
Ob
s
tacle
s
d
etec
ted
b
y
R
a
n
g
e
s
en
s
o
r
(
R
)
T
h
e
alg
o
r
ith
m
i
s
as
f
o
llo
w
s
:
1.
R
o
b
o
t Star
t
2.
T
ak
e
in
p
u
t
o
f
t
h
e
p
o
s
itio
n
co
-
o
r
d
in
ates o
f
s
o
u
r
ce
a
n
d
d
esti
n
atio
n
3.
C
alcu
late
th
e
d
is
tan
ce
a
n
d
d
ir
ec
tio
n
f
r
o
m
s
o
u
r
ce
to
d
esti
n
a
tio
n
d
m
in
a
n
d
r
esp
ec
ti
v
el
y
4.
W
HI
L
E
n
o
t D
esti
n
atio
n
5.
I
F o
b
s
tacle
in
d
ir
ec
tio
n
6.
Fin
d
o
u
t t
h
e
s
u
b
g
o
al
p
o
in
ts
u
s
in
g
d
i
s
tan
ce
a
n
d
an
g
le
o
f
r
o
tat
io
n
r
eq
u
ir
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Lo
ca
l P
a
th
P
la
n
n
in
g
o
f Mo
b
il
e
R
o
b
o
t U
s
in
g
C
r
itica
l
-
P
o
in
tB
u
g
A
lg
o
r
ith
m
A
vo
i
d
in
g
(
A
jo
y
K
u
ma
r
Du
tta
)
1
85
7.
C
alcu
late
th
e
co
o
r
d
in
ate
s
o
f
s
u
b
g
o
als
f
r
o
m
SG a
n
d
s
av
e
i
t i
n
s
et
D
8.
C
al
cu
late
d
is
ta
n
ce
o
f
ea
ch
s
u
b
g
o
al
an
d
s
av
e
i
t in
s
e
t D
9.
Select
th
e
co
o
r
d
in
ate
h
a
v
i
n
g
t
h
e
lo
w
e
s
t d
is
ta
n
ce
10.
I
F th
e
p
o
in
t e
x
is
t
s
in
T
r
av
er
s
e
p
o
in
t set T
11.
Dis
ca
r
d
th
e
p
o
in
t
12.
Select
th
e
n
ex
t lo
w
e
s
t d
is
ta
n
ce
f
r
o
m
D
13.
Fo
llo
w
s
tep
7
14.
E
L
SE
Sa
v
e
t
h
e
co
o
r
d
in
ate
in
t
r
av
er
s
e
p
o
in
t set T
15.
C
alcu
late
an
g
le
o
f
r
o
tatio
n
16.
Mo
v
e
to
w
ar
d
s
s
u
b
g
o
al
17.
Get
d
ir
ec
tio
n
18.
E
L
SE
19.
C
alcu
late
th
e
co
o
r
d
in
ate
at
r
ad
iu
s
to
w
ar
d
s
t
h
e
d
ir
ec
tio
n
20.
Sav
e
t
h
e
co
o
r
d
in
ate
in
T
21.
Mo
v
e
u
p
to
r
ad
iu
s
o
f
v
is
io
n
to
w
ar
d
s
d
ir
ec
tio
n
22.
E
ND
I
F
23.
E
ND
W
HI
L
E
24.
R
o
b
o
t
Sto
p
Fig
u
r
e
2
.
S
h
o
w
s
h
o
w
a
r
a
n
g
e
s
e
n
s
o
r
s
ca
n
n
in
g
o
b
s
tacle
s
w
i
th
i
ts
m
a
x
i
m
u
m
r
ad
iu
s
.
T
h
e
c
ir
cle
is
th
e
s
ca
n
n
ed
ar
ea
at
an
y
p
o
in
t
o
f
ti
m
e.
O
1
,
O
2
,
O
3
,
O
4
,
O
5
ar
e
th
e
o
b
s
tacle
s
.
T
h
in
b
lack
lin
e
s
h
o
w
s
t
h
e
ex
i
s
te
n
ce
o
f
o
b
s
tacle
s
d
etec
ted
b
y
t
h
e
s
en
s
o
r
w
ith
in
it
s
r
ad
iu
s
.
T
h
e
e
n
d
p
o
in
ts
o
f
t
h
e
ea
ch
b
lac
k
lin
e
ca
n
b
e
tr
ea
ted
as
s
u
b
g
o
al
p
o
in
ts
w
it
h
d
is
ta
n
ce
an
d
s
en
s
o
r
an
g
le.
3
.
3
.
Crit
ica
l
-
P
o
intbug
Alg
o
rit
h
m
Ana
ly
s
is
L
et
u
s
co
n
s
id
er
a
m
o
b
ile
r
o
b
o
t
as
s
h
o
w
n
in
F
ig
u
r
e
5
,
w
it
h
it
s
s
tar
ti
n
g
p
o
s
itio
n
(
x
0
,y
0
)
.
T
h
e
f
o
r
m
u
latio
n
co
n
s
id
er
s
e
v
alu
a
ti
o
n
o
f
n
e
x
t
o
b
s
tacle
f
r
ee
co
-
o
r
d
in
ate
p
o
s
itio
n
o
f
t
h
e
r
o
b
o
t.
T
h
e
r
o
b
o
t
k
n
o
w
s
it
s
g
o
al
p
o
s
itio
n
.
Du
r
i
n
g
its
m
o
ti
o
n
at
an
y
i
n
s
tan
ce
o
f
ti
m
e:
L
et,
(x
i
,y
i
)
–
T
h
e
cu
r
r
en
t p
o
s
itio
n
o
f
th
e
r
o
b
o
t
(x
i+
1
,y
i+
1
)
–
T
h
e
n
ex
t
p
o
s
s
ib
le
p
o
s
itio
n
to
m
o
v
e
b
y
t
h
e
r
o
b
o
t
α
–
An
g
le
w
h
er
e
s
u
b
g
o
al
p
o
in
t
is
d
etec
ted
b
y
s
e
n
s
o
r
β
–
R
o
b
o
t
r
o
tatio
n
an
g
le
w
i
th
r
esp
ec
t
to
th
e
lin
e
p
ar
allel
to
x
-
ax
is
an
d
p
ass
i
n
g
th
r
o
u
g
h
(
x
i
,y
i
)
b
ef
o
r
e
m
o
v
e
m
e
n
t
θ
–
A
n
g
le
g
e
n
er
ated
b
y
β
w
it
h
r
esp
ec
t to
th
e
lin
e
p
ar
allel
to
x
-
a
x
i
s
f
o
r
s
u
b
g
o
a
l p
o
in
t c
o
o
r
d
in
ates c
alc
u
latio
n
d
k
–
Dis
ta
n
ce
o
f
a
s
u
b
g
o
al
p
o
in
t f
r
o
m
c
u
r
r
en
t lo
ca
tio
n
v
–
Velo
cit
y
o
f
t
h
e
r
o
b
o
t
–
A
n
g
u
lar
v
elo
cit
y
o
f
t
h
e
r
o
b
o
t
Fo
u
r
k
in
d
s
o
f
m
o
v
e
m
e
n
t
ar
e
p
o
s
s
ib
le
f
o
r
th
e
r
o
b
o
t.
T
h
ese
ar
e:
1
.
L
ef
t
UP
,
2
.
R
ig
h
t
UP
,
3
.
L
ef
t
Do
w
n
,
4
R
ig
h
t
Do
w
n
.
Dep
en
d
in
g
u
p
o
n
s
u
b
g
o
al
e
ac
h
f
o
u
r
m
o
v
e
m
en
t
ca
n
m
ak
e
r
o
tatio
n
o
f
r
o
b
o
t.
T
h
is
r
o
tatio
n
f
o
r
n
ex
t p
o
s
s
ib
le
m
o
v
e
m
en
t
ca
n
b
e
class
if
ied
in
to
f
o
u
r
s
u
b
k
in
d
w
h
ic
h
ca
n
b
e
d
escr
ib
ed
p
icto
r
iall
y
Fig
u
r
e
3
r
ep
r
esen
ts
th
e
v
ar
io
u
s
t
y
p
e
s
o
f
m
o
v
e
m
en
t
a
n
d
F
ig
u
r
e
4
s
h
o
w
s
h
o
w
r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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0
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IJ
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ates
Fig
u
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3
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Dif
f
er
en
t
k
in
d
s
o
f
r
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b
o
t m
o
v
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m
e
n
t
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d
r
o
tatio
n
Fig
u
r
e
4
.
C
u
r
r
en
t a
n
d
n
e
x
t p
o
s
itio
n
o
f
t
h
e
r
o
b
o
t
Fig
u
r
e
5
.
T
r
aj
ec
t
o
r
y
o
f
a
r
o
b
o
t u
s
i
n
g
C
r
itical
-
P
o
in
tB
u
g
A
l
g
o
r
ith
m
Fig
u
r
e
5
s
h
o
w
s
h
o
w
a
r
o
b
o
t c
an
r
ea
ch
to
it
s
d
est
in
atio
n
.
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m
s
o
u
r
ce
p
o
in
t
it
g
et
s
t
w
o
s
u
b
g
o
al
p
o
in
t
A
&
B
.
I
t se
lects
A
a
s
C
r
itical
P
o
in
t (
A
s
th
e
d
is
ta
n
ce
f
r
o
m
A
is
lo
w
er
th
a
n
B
)
.
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t
it
s
elec
ts
C
f
r
o
m
n
e
x
t
s
u
b
g
o
als C
&
D
f
o
r
th
e
s
a
m
e
r
ea
s
o
n
.
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n
th
i
s
w
a
y
i
t r
ea
ch
es
E
,
F,
G,
H
an
d
f
in
a
ll
y
d
es
tin
at
io
n
.
P
ath
: so
u
r
ce
A
C
E
F
G
H
d
esti
n
atio
n
Fig
u
r
e
6
s
h
o
w
s
C
r
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ical
-
P
o
in
tB
u
g
a
lg
o
r
it
h
m
ca
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e
u
s
ed
to
h
a
n
d
le
lo
ca
l
m
i
n
i
m
a
p
r
o
b
le
m
.
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h
e
r
h
o
m
b
u
s
m
ar
k
s
s
h
o
w
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al
p
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ts
th
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it f
o
llo
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s
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e
p
r
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ce
s
s
as
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escr
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ef
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r
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u
r
e
6
.
C
r
itical
-
P
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in
tB
u
g
Al
g
o
r
ith
m
s
o
l
v
in
g
t
h
e
L
o
ca
l M
in
i
m
a
P
r
o
b
lem
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
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N:
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Lo
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187
3
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4
.
T
o
t
a
l Ti
m
e
And P
a
t
h L
e
ng
t
h Ca
lcula
t
io
n
Du
r
in
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ea
c
h
m
o
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e
m
e
n
t E
u
clid
ian
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is
ta
n
ce
tr
av
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s
ed
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y
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h
e
r
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r
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(
x
i
,y
i
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(
x
i
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is
√
I
f
th
e
r
o
b
o
t ta
k
es n
i
n
ter
v
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r
ea
ch
its
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esti
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at
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co
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ter
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n
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h
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la
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ai
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im
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u
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2
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im
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ta
k
en
to
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th
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t f
o
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p
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t b
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leav
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x
t p
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t.
1.
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im
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ta
k
en
i
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m
o
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i
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:
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f
d
i
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d
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ar
e
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is
ta
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ce
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ed
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d
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it
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it
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ter
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h
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ith
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en
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o
tal
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n
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⁄
2.
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im
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en
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n
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g
t
h
e
r
o
b
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ac
h
in
ter
v
al
:
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f
i
i
s
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e
d
etec
tio
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g
le
o
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o
in
t
an
d
i
is
th
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a
n
g
u
lar
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h
en
t
i
m
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ta
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n
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o
r
r
o
tatio
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at
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h
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ter
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l is
⁄
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tal
ti
m
e
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o
tatio
n
is
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⁄
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er
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o
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e
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t f
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ctio
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ll b
e
s
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e.
m
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e:
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⁄
∑
⁄
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⁄
Fig
u
r
e
7
.
P
ath
Gen
er
ated
b
y
T
ab
g
en
tB
u
g
,
P
o
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u
g
an
d
C
r
itical
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P
o
in
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u
g
alg
o
r
it
h
m
w
it
h
r
ef
er
e
n
ce
to
liter
atu
r
e
[
4
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
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5
,
No
.
3
,
Sep
tem
b
er
201
6
:
1
8
2
–
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188
4.
SI
M
UL
AT
I
O
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A
ND
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L
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h
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s
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m
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la
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s
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d
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Flas
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lated
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e
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ir
o
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en
t
w
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th
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t
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n
d
o
f
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li
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e
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Fig
u
r
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ese
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ted
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at
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ated
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g
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s
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h
e
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r
a
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ec
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ies
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r
o
d
u
ce
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r
itical
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o
in
t
a
n
d
o
th
er
al
g
o
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ith
m
s
ar
e
p
lo
tted
in
d
i
f
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er
e
n
t
co
lo
r
s
.
T
h
e
s
u
b
g
o
al
an
d
cr
it
ical
p
o
in
t
s
ar
e
also
p
lo
tted
u
s
i
n
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s
p
ec
i
f
i
c
s
y
m
b
o
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n
d
co
lo
r
s
.
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g
.
7
s
h
o
w
s
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f
f
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lik
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en
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ir
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n
m
e
n
t
A
w
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th
d
if
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t
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ap
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it
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t
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s
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i
s
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r
ef
er
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ce
is
ta
k
en
f
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m
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ter
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r
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[
4
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Fig
u
r
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8
p
r
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t
s
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f
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k
e
en
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ir
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B
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t
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h
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o
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ith
m
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m
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ate
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at
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n
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.
5
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ch
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ates
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h
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s
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b
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al
B
as
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itical
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o
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m
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e
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ate
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ath
o
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ter
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e
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ated
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y
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it
h
m
in
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f
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e
n
v
ir
o
n
m
en
t
B
5.
CO
NCLU
SI
O
NS A
ND
F
UT
URE WO
RK
W
e
p
r
esen
ted
a
s
i
m
p
le
s
e
n
s
o
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ased
p
ath
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n
in
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ith
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ata.
T
h
er
e
m
a
y
n
o
t
b
e
d
if
f
er
e
n
ce
in
ti
m
e
i
f
en
v
ir
o
n
m
e
n
t
w
it
h
le
s
s
co
m
p
le
x
it
y
,
p
r
ec
is
el
y
,
w
it
h
f
e
w
o
b
s
tacle
s
an
d
n
o
t
m
a
n
y
b
if
u
r
ca
tio
n
s
.
T
h
e
al
g
o
r
ith
m
co
n
s
i
d
er
s
o
n
l
y
t
h
o
s
e
o
b
s
tacle
s
‟
v
e
r
tices
t
h
at
g
en
er
at
e
co
llis
io
n
s
.
Am
o
n
g
s
t
th
e
ad
v
an
ta
g
es
o
f
th
e
C
r
itical
-
P
o
in
t
B
u
g
a
lg
o
r
it
h
m
s
w
h
e
n
co
m
p
ar
ed
to
th
e
o
th
er
m
et
h
o
d
s
ar
e:
(
i)
little
iter
atio
n
r
eq
u
ir
ed
to
fi
n
d
t
h
e
g
o
al.
(
ii)
T
h
er
e
is
n
o
n
ee
d
to
h
av
e
k
n
o
w
led
g
e
ab
o
u
t
t
h
e
en
v
ir
o
n
m
e
n
t.
(
ii
i)
O
n
l
y
t
h
o
s
e
o
b
s
tacle
s
w
i
ll
b
e
p
r
o
ce
s
s
ed
f
o
r
ca
lcu
lati
n
g
s
u
b
g
o
al
an
d
c
r
itical
p
o
in
t,
w
h
ic
h
m
a
y
p
r
o
d
u
ce
co
llis
io
n
.
(
iv
)
T
h
e
c
o
o
r
d
in
ate
p
o
in
ts
ca
n
ea
s
il
y
b
e
ca
lcu
lated
.
T
h
e
alg
o
r
ith
m
i
s
n
o
t
d
es
ig
n
ed
to
o
p
er
ate
in
d
y
n
a
m
ical
e
n
v
ir
o
n
m
e
n
ts
,
w
h
e
r
e
t
h
e
o
b
s
tacle
s
ch
an
g
e
its
p
o
s
itio
n
d
u
r
i
n
g
th
e
r
o
b
o
t
m
o
v
e
m
en
t.
F
u
t
u
r
e
w
o
r
k
i
n
cl
u
d
es
b
o
th
th
eo
r
etica
l
s
t
u
d
ies
a
n
d
p
r
ac
tical
w
o
r
k
i
n
t
h
i
s
p
ar
ti
cu
lar
ar
ea
.
RE
F
E
R
E
NC
E
S
[1
]
R.
A
b
i
y
e
v
,
D.
Ib
ra
h
im
,
B.
Eri
n
.
Na
v
ig
a
t
io
n
o
f
mo
b
il
e
ro
b
o
ts
i
n
t
h
e
p
re
se
n
c
e
o
f
o
b
st
a
c
les
.
Ad
v
a
n
c
e
s
in
E
n
g
i
n
e
e
rin
g
S
o
ft
w
a
re
.
2
0
1
0
;
4
1
:
1
1
7
9
–
1
1
8
6
.
[2
]
Rica
rd
o
A
.
L
a
n
g
e
r,
Lea
n
d
ro
S
.
C
o
e
lh
o
a
n
d
G
u
sta
v
o
H.
C.
Oliv
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ira
K
-
Bu
g
,
A
n
e
w
b
u
g
a
p
p
ro
a
c
h
f
o
r
mo
b
il
e
r
o
b
o
t
'
s
p
a
t
h
p
la
n
n
in
g
.
1
6
th
IEE
E
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
Co
n
tro
l
Ap
p
li
c
a
ti
o
n
s
Pa
rt
o
f
IEE
E
M
u
lt
i
-
c
o
n
fer
e
n
c
e
o
n
S
y
ste
ms
a
n
d
Co
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tro
l
S
i
n
g
a
p
o
re
.
2
0
0
7
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o
C
0
3
.
2
:
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0
3
-
4
0
8
[3
]
K.R.
G
u
ru
p
ra
sa
d
Eg
re
ss
Bu
g
:
A
Rea
l
T
ime
Pa
th
Pl
a
n
n
i
n
g
Al
g
o
rit
h
m
fo
r
a
M
o
b
il
e
Ro
b
o
t
i
n
a
n
Un
k
n
o
w
n
En
v
iro
n
me
n
t.
P
.
S
.
T
h
il
a
g
a
m
e
t
a
l.
(Ed
s.):
ADCONS
2
0
1
1
.
2
0
1
2
;
L
NCS
7
1
3
5
:
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2
8
–
2
3
6
.
[4
]
Bu
n
iy
a
m
in
N.,
W
a
n
Ng
a
h
W
.
A
.
J.,
S
a
ri
ff
N.,
M
o
h
a
m
a
d
Z.
A
S
imp
le
L
o
c
a
l
P
a
th
Pl
a
n
n
in
g
Al
g
o
rit
h
m
fo
r
Au
to
n
o
m
o
u
s
M
o
b
il
e
Ro
b
o
ts.
In
ter
n
a
ti
o
n
a
l
jo
u
rn
a
l
o
f
sy
ste
ms
a
p
p
li
c
a
ti
o
n
s,
e
n
g
i
n
e
e
rin
g
&
d
e
v
e
lo
p
me
n
t
.
2
0
1
1
;
5(
2
):
151
-
1
5
9
[5
]
P
re
e
th
a
Bh
a
tt
a
c
h
a
rjee
,
P
ra
ty
u
sh
a
Ra
k
sh
it
,
In
d
ra
n
i
G
o
s
w
a
m
i
(Ch
a
k
ra
b
o
rty
),
Am
it
Ko
n
a
r,
A
tu
ly
a
K.
Na
g
a
r
M
u
lt
i
-
Ro
b
o
t
P
a
th
-
Pl
a
n
n
i
n
g
Us
i
n
g
Arti
f
icia
l
Bee
Co
l
o
n
y
Op
ti
miza
ti
o
n
A
lg
o
rit
h
m
.
T
h
ird
W
o
rl
d
Co
n
g
re
ss
o
n
N
a
tu
re
a
n
d
Bi
o
lo
g
ica
ll
y
In
sp
ire
d
Co
m
p
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g
.
2
0
1
1
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IJ
RA
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N:
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-
4856
Lo
ca
l P
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th
P
la
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n
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ith
m
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vo
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g
(
A
jo
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u
ma
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tta
)
189
[6
]
Qin
g
b
a
o
Zh
u
,
Ju
n
Hu
,
W
e
n
b
in
Ca
i,
L
a
rr
y
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n
sc
h
e
n
.
A
n
e
w
ro
b
o
t
n
a
v
ig
a
ti
o
n
a
l
g
o
rit
h
m
fo
r
d
y
n
a
mic
u
n
k
n
o
w
n
e
n
v
iro
n
me
n
ts
b
a
se
d
o
n
d
y
n
a
mi
c
p
a
th
re
-
c
o
mp
u
t
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ti
o
n
a
n
d
a
n
imp
ro
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sc
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t
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ri
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.
A
p
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e
d
S
o
ft
Co
mp
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t
in
g
.
2
0
1
1
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11
:
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6
6
7
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6
7
6
[7
]
A
lp
a
Re
sh
a
m
wa
la,
De
e
p
ik
a
P
Vi
n
c
h
u
rk
a
r
.
Ro
b
o
t
Pa
t
h
Pl
a
n
n
in
g
u
sin
g
A
n
An
t
Co
l
o
n
y
Op
t
imiza
ti
o
n
Ap
p
ro
a
c
h
:
A
S
u
rv
e
y
.
(
IJ
AR
AI)
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Ad
v
a
n
c
e
d
Res
e
a
rc
h
i
n
Ar
ti
fi
c
ia
l
I
n
telli
g
e
n
c
e
.
2
0
1
3
;
2
(
3
):
6
5
–
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1
[8
]
Na
re
n
d
ra
S
in
g
h
P
a
l,
S
a
n
jee
v
S
h
a
r
m
a
,
Ro
b
o
t
Pa
t
h
Pl
a
n
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in
g
u
sin
g
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wa
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In
telli
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e
:
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S
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rv
e
y
.
In
ter
n
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ti
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o
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l
o
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Co
m
p
u
ter
A
p
p
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ti
o
n
s (
0
9
7
5
–
8
8
8
7
)
.
2
0
1
3
;
83
(
12
):
5
–
12
[9
]
Ch
e
n
g
y
u
Hu
,
X
ian
g
n
in
g
W
u
,
Qi
n
g
z
h
o
n
g
L
ian
g
a
n
d
Yo
n
g
ji
W
a
n
g
.
Au
to
n
o
mo
u
s
Ro
b
o
t
P
a
t
h
P
la
n
n
in
g
Ba
se
d
o
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In
telli
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d
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tre
a
m
Fu
n
c
ti
o
n
s
.
S
p
rin
g
e
r
Ver
la
g
Be
rlin
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id
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lb
e
rg
ICES
2
0
0
7
,
L
N
CS
4
6
8
4
.
2
0
0
7
;
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NCS:
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7
7
–
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8
4
.
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0
]
W
e
sle
y
H.
Hu
a
n
g
,
Bre
tt
R.
F
a
jen
,
Jo
n
a
th
a
n
R.
F
in
k
,
W
il
li
a
m
H.
Warre
n
.
Vi
su
a
l
n
a
v
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a
ti
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a
n
d
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b
st
a
c
le
a
v
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a
n
c
e
u
sin
g
a
st
e
e
rin
g
p
o
ten
ti
a
l
fu
n
c
ti
o
n
.
R
o
b
o
ti
c
s a
n
d
Au
t
o
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mo
u
s S
y
st
e
ms
.
2
0
0
6
;
54
:
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8
8
–
2
9
9
[1
1
]
S
.
S
.
G
e
a
n
d
Y.
J.
C
u
i
.
Ne
w
P
o
ten
ti
a
l
F
u
n
c
ti
o
n
s
fo
r
M
o
b
il
e
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b
o
t
Pa
t
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P
la
n
n
i
n
g
.
IEE
E
T
r
a
n
s
a
c
ti
o
n
s
o
n
R
o
b
o
ti
c
s
a
n
d
Au
to
ma
ti
o
,
2
0
0
0
;
16
(
5
):6
1
5
–
6
2
0
[1
2
]
Du
sa
n
G
la
v
a
s
k
i,
M
a
rio
Vo
lf
,
M
irj
a
n
a
Bo
n
k
o
v
ic
.
M
o
b
il
e
ro
b
o
t
p
a
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p
l
a
n
n
in
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u
si
n
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x
a
c
t
c
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d
e
c
o
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io
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a
n
d
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ti
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fi
e
ld
me
th
o
d
s
.
W
S
EA
S
T
RA
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ACT
ION
S
o
n
CIRCUIT
S
a
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S
.
2
0
0
9
;
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9
):
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8
9
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0
0
[1
3
]
S
.
S
.
G
e
,
Y.J.
C
u
i
.
Dy
n
a
mic
M
o
ti
o
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Pl
a
n
n
in
g
f
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o
b
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e
R
o
b
o
ts
Us
i
n
g
Po
ten
ti
a
l
Fi
e
ld
M
e
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o
d
.
A
u
t
o
n
o
mo
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s R
o
b
o
ts
2
0
0
2
;
13
:
2
0
7
–
2
2
2
.
[1
4
]
M
.
De
n
g
,
A
.
In
o
u
e
,
K.S
e
k
ig
u
c
h
i
,
L
.
Jia
n
g
.
T
wo
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wh
e
e
led
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e
ro
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o
t
mo
ti
o
n
c
o
n
tr
o
l
in
d
y
n
a
mic
e
n
v
iro
n
me
n
ts
.
Ro
b
o
ti
c
s a
n
d
Co
mp
u
ter
-
In
teg
r
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te
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M
a
n
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fa
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.
2
0
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0
;
2
6
:
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6
8
–
272
.
[1
5
]
A
tsu
sh
i
F
u
ji
m
o
ri
,
P
e
t
e
r
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Nik
if
o
ru
k
,
M
a
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a
n
M
.
G
u
p
ta.
A
d
a
p
ti
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v
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a
ti
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o
f
M
o
b
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wit
h
Ob
st
a
c
le
Avo
id
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n
c
e
.
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ra
n
sa
c
ti
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n
s O
n
Ro
b
o
ti
c
s A
n
d
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u
to
m
a
ti
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n
,
1
9
9
7
;
13
(
4
):
5
9
6
-
6
0
2
.
BI
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
Dr.
A
jo
y
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m
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r
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tt
a
is
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y
a
P
ro
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De
p
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n
t
o
f
P
ro
d
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ti
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n
En
g
i
n
e
e
rin
g
,
Ja
d
a
v
p
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r
Un
i
v
e
rsit
y
,
IND
I
A
.
He
re
c
e
iv
e
d
h
is
B.
E.
&
M
.
E.
d
e
g
re
e
s
in
El
e
c
tro
n
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&
T
e
le
-
c
o
m
m
u
n
ica
ti
o
n
En
g
g
f
ro
m
J
a
d
a
v
p
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r
Un
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n
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9
8
3
&
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8
5
re
sp
e
c
ti
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e
l
y
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a
n
d
P
h
.
D.
(En
g
g
)
d
e
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e
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e
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re
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o
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o
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