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1.
I
NT
RO
D
UCT
I
O
N
T
h
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ar
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m
an
y
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v
a
n
ta
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f
co
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tr
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llin
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m
u
lt
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b
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u
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1
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Usi
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2
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3
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ated
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[
6
].
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A
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d
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o
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g
an
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s
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ti
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2
,
a
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e
r
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w
ab
o
u
t
f
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m
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co
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tr
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g
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s
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d
if
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ta
s
k
s
to
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i
th
m
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b
ile
r
o
b
o
ts
ar
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m
p
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s
iz
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.
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3
d
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ls
w
it
h
m
o
d
el
s
o
f
a
m
o
b
ile
r
o
b
o
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.
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a
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atic
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ted
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ic
m
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m
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I
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Sectio
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4
,
t
w
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f
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m
a
tio
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co
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tr
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b
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lead
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p
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ased
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I
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2089
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4856
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L
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7
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w
n
as
tr
aj
ec
to
r
y
tr
ac
k
in
g
.
An
o
t
h
er
m
o
tio
n
ta
s
k
is
to
ac
h
ie
v
e
g
r
o
u
p
f
o
r
m
atio
n
.
T
h
er
eb
y
,
t
h
e
g
o
al
i
s
to
ch
a
n
g
e
th
e
p
o
s
itio
n
o
f
ea
ch
r
o
b
o
t
i
n
o
r
d
er
to
g
e
n
er
ate
a
g
r
o
u
p
f
o
r
m
at
io
n
[
8
]
.
T
h
is
f
o
r
m
atio
n
c
o
n
tr
o
l
co
u
ld
b
e
co
n
s
id
er
ed
as
an
ex
te
n
s
io
n
to
th
e
tr
aj
ec
t
o
r
y
tr
ac
k
i
n
g
p
r
o
b
le
m
w
h
er
e
r
o
b
o
ts
f
o
llo
w
a
g
iv
e
n
tr
aj
ec
to
r
y
w
h
ile
p
er
f
o
r
m
i
n
g
a
f
o
r
m
atio
n
.
T
h
e
tr
aj
ec
to
r
y
tr
ac
k
in
g
p
r
o
b
lem
w
a
s
s
o
l
v
ed
in
[
9
]
b
y
u
s
i
n
g
a
ti
m
e
-
v
ar
y
i
n
g
co
n
tr
o
l la
w
a
s
a
f
ee
d
b
ac
k
.
An
o
th
er
w
a
y
to
s
o
l
v
e
t
h
i
s
p
r
o
b
le
m
i
s
t
h
r
o
u
g
h
th
e
u
s
e
o
f
d
y
n
a
m
ic
f
ee
d
b
ac
k
li
n
ea
r
izatio
n
[
10
]
,
[
11
]
an
d
[
1
2
]
.
I
n
[
13
]
an
d
[
1
4
]
th
e
tech
n
iq
u
e
o
f
b
ac
k
s
tep
p
in
g
is
u
s
ed
f
o
r
tr
aj
ec
to
r
y
tr
ac
k
i
n
g
o
f
n
o
n
h
o
lo
n
o
m
ic
s
y
s
te
m
s
.
T
h
e
ap
p
r
o
ac
h
in
[
15
]
tak
es a
d
v
an
ta
g
e
o
f
t
h
e
ca
s
ca
d
e
s
tr
u
ct
u
r
e
o
f
t
h
e
r
o
b
o
t m
o
d
el.
T
h
e
g
r
o
u
p
f
o
r
m
atio
n
co
n
tr
o
l
is
co
n
s
id
er
ed
as
a
co
n
tr
o
l
la
w
w
h
ic
h
co
n
tr
o
ls
t
h
e
m
o
b
ile
r
o
b
o
ts
in
a
ce
r
tain
f
o
r
m
atio
n
.
I
n
[
16
]
,
th
e
au
t
h
o
r
s
p
r
o
p
o
s
ed
an
ap
p
r
o
ac
h
to
ac
h
ie
v
e
t
h
i
s
g
o
al
b
y
a
ti
m
e
-
v
ar
y
in
g
f
ee
d
b
ac
k
co
n
tr
o
l.
Z
h
i
y
u
n
et
a
l.
g
i
v
e
n
e
ce
s
s
ar
y
an
d
s
u
f
f
i
cie
n
t
g
r
ap
h
ic
al
co
n
d
itio
n
s
f
o
r
t
h
e
f
o
r
m
atio
n
s
tab
ilizatio
n
to
a
p
o
in
t a
n
d
to
m
o
r
e
g
en
er
al
g
eo
m
etr
ic
p
atter
n
[
17
].
T
h
er
e
ar
e
v
ar
io
u
s
ap
p
r
o
ac
h
es
to
f
o
r
m
a
tio
n
tr
ac
k
i
n
g
,
lik
e
th
e
b
eh
av
io
r
-
b
ased
m
et
h
o
d
[
18
]
,
th
e
v
ir
t
u
al
s
tr
u
ct
u
r
e
s
tr
a
te
g
y
[
19
]
an
d
th
e
lead
er
-
f
o
llo
w
er
ap
p
r
o
ac
h
[
20
]
,
[
21
]
an
d
[
22
]
.
T
h
e
b
eh
av
i
o
r
-
b
ased
ap
p
r
o
ac
h
de
fi
n
e
s
a
d
esire
d
b
eh
av
io
r
f
o
r
ea
ch
r
o
b
o
t.
I
n
o
r
d
er
to
d
er
iv
e
th
e
co
n
tr
o
l
la
w
,
th
e
r
elativ
e
i
m
p
o
r
ta
n
ce
o
f
ea
ch
b
eh
av
io
r
is
w
ei
g
h
ted
[
23
]
.
T
h
is
ap
p
r
o
ac
h
is
u
s
ed
,
f
o
r
ex
a
m
p
le,
to
ap
p
ly
th
e
s
o
cial
ch
ar
a
cter
is
tics
o
f
in
s
ec
ts
an
d
an
i
m
al
s
to
m
u
ltiro
b
o
t
s
y
s
te
m
s
[
24
]
.
T
h
e
v
ir
tu
al
s
tr
u
ct
u
r
e
m
eth
o
d
tr
ea
ts
t
h
e
en
tire
f
o
r
m
atio
n
a
s
a
s
i
n
g
le
en
tit
y
.
T
o
d
er
iv
e
th
e
co
n
tr
o
l
la
w
f
o
r
ea
ch
r
o
b
o
t,
th
e
m
o
tio
n
o
f
th
e
v
ir
tu
al
s
tr
u
ct
u
r
e
is
c
o
n
s
id
er
ed
an
d
tr
an
s
f
o
r
m
ed
in
to
t
h
e
m
o
tio
n
o
f
th
e
r
o
b
o
t [
25
]
an
d
[
26
].
I
n
th
i
s
p
ap
er
,
w
e
f
o
cu
s
o
n
t
h
e
lead
er
-
f
o
llo
w
er
ap
p
r
o
ac
h
.
T
o
ac
co
m
p
li
s
h
th
e
lead
er
-
f
o
llo
wer
s
tr
ateg
y
th
er
e
ar
e
s
e
v
er
al
ap
p
r
o
ac
h
es.
L
ei
a
n
d
A
n
ts
a
k
lis
m
ad
e
u
s
e
o
f
th
e
ca
s
ca
d
e
ap
p
r
o
ac
h
as
i
n
[
15
]
to
ac
h
iev
e
a
co
n
s
en
s
u
s
-
b
ased
co
n
tr
o
ller
[
27
]
.
Desai
et
al.
ap
p
lied
f
ee
d
b
ac
k
lin
ea
r
izatio
n
to
ex
p
o
n
e
n
tiall
y
s
tab
il
ize
th
e
d
is
tan
ce
an
d
th
e
o
r
ien
tatio
n
b
et
w
ee
n
th
e
lead
er
an
d
th
e
f
o
ll
o
w
er
[
20
]
.
I
n
ad
d
itio
n
to
t
h
ese
ap
p
r
o
ac
h
es,
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
MP
C
)
h
as
b
ec
o
m
e
an
ac
ce
p
ted
m
et
h
o
d
i
n
s
o
lv
i
n
g
t
h
e
f
o
r
m
atio
n
co
n
tr
o
l
p
r
o
b
lem
.
I
n
[
28
]
,
a
n
o
n
li
n
ea
r
MP
C
is
ap
p
lied
.
S
in
ce
t
h
e
co
m
p
u
tatio
n
al
e
o
r
t
i
s
h
i
g
h
er
th
a
n
ap
p
l
y
i
n
g
a
l
in
ea
r
MP
C
,
Ka
m
el
an
d
Yo
u
m
in
u
s
e
a
l
in
ea
r
MP
C
i
n
co
m
b
i
n
atio
n
w
it
h
an
in
p
u
t
-
o
u
tp
u
t
f
ee
d
b
ac
k
li
n
ea
r
izatio
n
t
o
ac
h
iev
e
a
lead
er
-
f
o
llo
w
er
f
o
r
m
atio
n
co
n
tr
o
l [
29
].
R
elated
wo
r
k
s
,
wh
er
e
an
im
p
le
m
en
tatio
n
o
f
a
f
o
r
m
atio
n
c
o
n
tr
o
ller
tak
es
p
lace
ar
e
[
30
]
,
[
31
]
,
[
32
]
an
d
[
33
]
.
I
n
th
ese
p
ap
er
s
s
i
m
u
lati
o
n
r
esu
lt
s
o
f
t
h
e
f
o
r
m
atio
n
c
o
n
tr
o
ller
ar
e
p
r
esen
te
d
.
Ho
w
ev
er
,
n
o
n
e
o
f
th
e
m
co
n
s
id
er
s
a
d
y
n
a
m
ic
m
o
d
el,
u
n
ce
r
tain
ties
o
f
th
e
s
e
n
s
o
r
s
o
r
t
h
e
co
m
m
u
n
icatio
n
s
tr
u
ct
u
r
e.
T
h
er
ef
o
r
e,
th
is
w
o
r
k
tak
es
a
n
ex
ten
d
ed
m
o
d
el
o
f
th
e
r
o
b
o
t
in
to
ac
co
u
n
t
a
n
d
p
er
f
o
r
m
s
f
u
r
th
er
s
i
m
u
latio
n
s
.
I
n
Fi
g
u
r
e
2
is
t
h
e
co
n
s
id
er
ed
r
o
b
o
t w
it
h
th
e
r
ele
v
an
t p
ar
a
m
eter
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
J
R
A
,
Vo
l.
7
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
1
8
–
3
8
20
Fig
u
r
e
2
.
T
h
is
Fig
u
r
e
s
h
o
w
s
th
e
co
n
s
id
er
ed
r
o
b
o
t
w
it
h
th
e
r
el
ev
an
t p
ar
a
m
eter
s
3.
M
O
DE
L
S
E
T
UP
I
n
th
i
s
s
ec
tio
n
,
a
k
i
n
e
m
atic
a
n
d
a
d
y
n
a
m
ic
m
o
d
el
is
i
n
tr
o
d
u
ce
d
.
T
h
e
k
in
e
m
atic
m
o
d
el
d
es
cr
ib
es
th
e
m
o
tio
n
o
f
t
h
e
m
o
b
ile
r
o
b
o
t
w
it
h
t
h
e
v
elo
cit
y
a
n
d
an
g
u
lar
v
elo
cit
y
a
s
an
i
n
p
u
t.
T
h
is
m
o
d
el
is
u
s
ed
f
o
r
th
e
co
n
tr
o
ller
d
esig
n
.
Op
p
o
s
ed
to
th
e
k
i
n
e
m
atic
m
o
d
el,
th
e
d
y
n
a
m
ic
m
o
d
el
d
escr
ib
es
th
e
m
o
tio
n
o
f
th
e
m
o
b
ile
r
o
b
o
t
b
ased
o
n
th
e
ac
t
in
g
f
o
r
ce
s
.
T
h
e
d
y
n
a
m
ic
m
o
d
el
is
to
o
d
etailed
to
u
s
e
f
o
r
th
e
co
n
tr
o
ll
er
d
esig
n
b
u
t
it
ca
n
b
e
u
s
ed
to
v
alid
ate
th
e
d
esi
g
n
e
d
co
n
tr
o
ller
.
3
.
1
.
K
ine
m
a
t
ic
M
o
del
I
n
th
i
s
w
o
r
k
,
di
ff
er
en
tiall
y
d
r
iv
en
w
h
ee
led
m
o
b
ile
r
o
b
o
ts
ar
e
co
n
s
id
er
ed
.
E
ac
h
r
o
b
o
t
h
as
tw
o
w
h
ee
l
s
th
at
ca
n
b
e
ac
t
u
ated
i
n
d
ep
en
d
en
tl
y
.
T
h
e
d
escr
ip
tio
n
o
f
a
r
o
b
o
t
in
a
t
w
o
-
d
i
m
e
n
s
io
n
al
s
p
ac
e
ca
n
b
e
d
o
n
e
b
y
t
h
e
cu
r
r
en
t
p
o
s
itio
n
(
x
;
y
)
a
n
d
th
e
o
r
ien
tatio
n
an
g
le
.
Hen
ce
,
th
e
s
tate
v
ec
to
r
r
es
u
lts
to
.
T
h
e
k
in
e
m
atic
eq
u
atio
n
s
o
f
t
h
e
r
o
b
o
t a
r
e
r
ep
r
esen
ted
in
E
q
u
atio
n
(
1
)
,
(
1
)
w
it
h
t
h
e
v
elo
cit
y
v
an
d
t
h
e
an
g
u
lar
v
elo
cit
y
as
an
in
p
u
t
.
T
h
e
co
n
n
ec
ted
n
es
s
o
f
th
e
v
e
l
o
cit
y
an
d
an
g
u
lar
v
elo
cit
y
o
f
th
e
r
o
b
o
t to
th
e
an
g
u
lar
v
elo
cit
y
o
f
b
o
th
w
h
ee
ls
is
g
iv
e
n
b
y
(
2
)
w
it
h
r
b
ein
g
th
e
r
ad
iu
s
o
f
a
w
h
ee
l
.
3
.
2
.
D
y
na
m
ic
M
o
del
3
.
2
.
1
.
U
nreduced
M
o
del
T
h
e
g
eo
m
etr
ic
p
ar
a
m
eter
s
o
f
a
m
o
b
ile
r
o
b
o
t
ar
e
s
h
o
w
n
in
Fig
u
r
e
2
w
h
er
e
B
is
t
h
e
w
h
ee
l
b
aselin
e
ce
n
ter
,
G
is
th
e
ce
n
ter
o
f
g
r
av
i
t
y
,
C
i
s
t
h
e
p
o
s
it
io
n
o
f
t
h
e
ca
s
t
o
r
,
L
is
th
e
p
o
s
itio
n
o
f
th
e
le
f
t
w
h
ee
l a
n
d
R
is
th
e
p
o
s
itio
n
o
f
th
e
r
i
g
h
t
w
h
ee
l.
T
h
e
g
eo
m
etr
ic
d
is
ta
n
ce
s
ar
e
ex
p
r
ess
ed
b
y
b
,
c
an
d
d
.
T
h
e
d
y
n
a
m
ic
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o
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el
o
f
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b
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is
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er
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ed
in
[
34
]
.
T
h
e
f
u
ll
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ic
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f
[
3
4
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Eq
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3
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,
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m
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is
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an
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
A
I
SS
N:
2089
-
4856
I
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2
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educed
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r
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cle
o
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th
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p
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ls
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-
w
id
t
h
m
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d
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latio
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(
P
W
M)
s
ig
n
al.
Si
n
ce
t
h
e
m
o
d
el
i
n
E
q
u
atio
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(
3
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is
u
s
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n
g
t
h
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cu
r
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p
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i
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ch
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r
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lic
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th
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v
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t
h
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m
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to
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h
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s
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as
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T
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n
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d
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D
C
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i
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E
q
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atio
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5
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(
5
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R
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at
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E
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tial e
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t
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m
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in
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(
5
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ar
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ig
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ca
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t
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f
aste
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ic
in
E
q
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atio
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.
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m
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ted
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o
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w
in
g
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q
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(
6
)
an
d
E
q
u
atio
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(
7
)
(
6
)
w
it
h
t
h
ese
s
i
m
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s
,
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h
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ce
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(
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3
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2
.
3
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M
o
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I
denti
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ca
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T
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g
o
al
o
f
th
e
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o
d
el
id
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f
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tio
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eter
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e
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n
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o
w
n
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ar
a
m
eter
s
in
E
q
u
atio
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(
7
)
.
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ce
in
E
q
ua
tio
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(
7
)
p
ar
am
e
ter
s
o
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l
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cc
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th
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g
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t h
a
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d
th
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o
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y
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E
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ar
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ld
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p
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Fi
g
u
r
e
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
J
R
A
,
Vo
l.
7
,
No
.
1
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Ma
r
ch
2
0
1
8
:
1
8
–
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8
22
(
8
)
Fig
u
r
e
3
.
Si
m
u
latio
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m
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w
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f
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Fo
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a
r
e
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r
ee
e
x
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m
e
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ts
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n
s
id
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ed
.
T
h
e
in
p
u
t
s
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g
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al
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s
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h
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e
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a
s
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s
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f
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n
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i
m
en
t
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n
al
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T
h
ese
ex
p
er
i
m
e
n
ts
ar
e
ch
o
s
en
as
t
y
p
ical
m
o
v
e
m
e
n
ts
o
f
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e
r
o
b
o
t.
T
h
e
fi
r
s
t
ex
p
er
i
m
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t
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aig
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t
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d
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a
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.
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n
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to
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e
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ar
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m
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s
,
t
h
e
m
o
d
el
ac
co
r
d
in
g
to
E
q
u
at
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n
(
8
)
is
s
i
m
u
lated
w
it
h
a
p
ar
a
m
e
ter
v
ec
to
r
.
T
h
e
v
elo
cit
y
an
d
t
h
e
an
g
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lar
v
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cit
y
f
r
o
m
t
h
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m
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r
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m
en
t
s
ar
e
ca
lcu
lated
in
p
ar
allel.
T
h
e
o
u
t
p
u
t
o
f
th
e
m
o
d
el
an
d
th
e
o
u
tp
u
t
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f
th
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m
ea
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r
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t
s
ar
e
co
n
s
id
er
ed
in
a
co
s
t f
u
n
cti
o
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.
(
9
)
T
h
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y
M
is
th
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q
u
a
n
tit
y
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f
m
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r
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le
x
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c
h
m
et
h
o
d
is
u
s
ed
[
35
]
.
3
.
2
.
4
.
Sp
ee
d
C
o
ntr
o
ller
T
h
e
f
o
r
m
atio
n
co
n
tr
o
ller
,
w
h
i
ch
is
co
n
s
id
er
ed
in
th
i
s
w
o
r
k
,
u
s
e
s
th
e
k
i
n
e
m
atic
m
o
d
el
in
E
q
u
atio
n
(
1
)
to
o
b
tain
th
e
co
n
tr
o
l
la
w
f
o
r
e
ac
h
r
o
b
o
t.
Sin
ce
th
e
i
n
p
u
t
o
f
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b
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e
d
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t
y
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cle
o
f
th
e
P
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M
s
ig
n
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f
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ch
w
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l,
it
is
n
o
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g
u
ar
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teed
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at
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r
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ch
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h
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th
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esire
d
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.
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it
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s
ar
y
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m
p
le
m
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r
th
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r
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s
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m
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l
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P
I
D
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n
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o
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n
s
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.
T
h
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in
p
u
t
o
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co
n
tr
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th
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er
r
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b
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w
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n
th
e
d
es
ir
ed
s
p
ee
d
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d
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h
e
c
u
r
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t
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p
ee
d
o
f
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c
h
w
h
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l.
E
q
u
a
tio
n
(
2
)
ca
n
b
e
r
e
ar
r
an
g
ed
to
o
b
tain
th
e
d
esire
d
s
p
ee
d
f
r
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m
t
h
e
v
elo
cit
y
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d
an
g
u
lar
v
elo
cit
y
o
f
th
e
r
o
b
o
t.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
t
h
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n
ti
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u
s
-
ti
m
e
P
I
D
co
n
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o
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g
i
v
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(
1
0
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w
it
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m
ize
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teg
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q
u
ar
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
A
I
SS
N:
2089
-
4856
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w
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s
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Fig
u
r
e
4
.
I
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l c
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ac
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g
to
[
20
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4.
F
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RM
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I
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.
1
.
Co
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T
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[
1
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u
r
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4
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ip
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atio
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ip
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ac
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[
20
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,
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:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
J
R
A
,
Vo
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7
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No
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1
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1
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1
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1
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ac
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[
20
]
.
I
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2
an
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p
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.
Fro
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ed
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4
.
2
.
Co
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T
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co
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tr
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s
ed
in
[
20
]
.
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h
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co
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tr
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th
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f
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f
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llo
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er
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d
th
e
t
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s
.
Fig
u
r
e
5
illu
s
tr
ates t
h
e
t
w
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lea
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s
(
R
o
b
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t 1
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d
R
o
b
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2
)
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R
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)
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13
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23
.
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s
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th
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g
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as
.
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13
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th
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t
w
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lead
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s
[
20
].
T
h
e
k
in
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m
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r
elatio
n
s
h
ip
s
f
o
r
th
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lead
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o
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h
o
w
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i
n
Fig
u
r
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5
ar
e
g
i
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b
y
E
q
u
atio
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(
1
)
.
T
h
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k
in
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r
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s
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ip
s
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llo
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n
b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
A
I
SS
N:
2089
-
4856
I
n
ve
s
tig
a
tio
n
o
f F
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r
ma
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C
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tr
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l A
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p
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o
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A
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(
Ha
n
n
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25
(
1
8
)
ac
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g
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[
20
]
,
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.
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llo
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g
co
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l la
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f
o
r
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e
f
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llo
w
er
Fig
u
r
e
5
.
I
llu
s
tr
atio
n
o
f
th
e
lea
d
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f
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llo
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tel
latio
n
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f
t
h
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co
n
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ac
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to
[
20
]
(
1
9
)
w
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h
ese
i
n
p
u
t
s
th
e
v
ar
iab
les
b
ec
o
m
e
(
2
0
)
w
h
er
eb
y
E
q
u
a
tio
n
(
1
9
)
an
d
E
q
u
atio
n
(
2
0
)
d
e
fi
n
ed
ac
co
r
d
in
g
to
[
20
]
.
T
h
e
c
alcu
latio
n
o
f
t
h
e
c
u
r
r
en
t
le
n
g
t
h
a
nd
f
o
llo
w
s
E
q
u
at
io
n
(
1
6
)
.
T
o
ca
lcu
late
t
h
e
co
n
tr
o
l
la
w
i
n
t
h
e
f
o
llo
w
er
r
o
b
o
t,
th
e
w
h
o
le
s
tate
o
f
th
e
t
w
o
lead
er
s
q
1
an
d
q
2
,
th
e
w
h
o
le
s
tate
o
f
t
h
e
f
o
llo
w
er
q
3
a
n
d
th
e
v
elo
cit
y
o
f
t
h
e
lead
er
s
v
1
a
n
d
v
2
ar
e
r
eq
u
ir
ed
a
s
w
ell
as
t
h
e
an
g
u
lar
v
e
lo
cit
y
o
f
th
e
f
o
llo
w
er
.
C
o
n
s
id
er
in
g
th
is
in
f
o
r
m
at
io
n
,
th
e
co
m
m
u
n
icatio
n
ca
n
b
e
d
eter
m
in
ed
.
4
.
3
.
Co
llis
io
n Av
o
ida
nce
Co
ntr
o
ller
Fo
llo
w
i
n
g
,
an
e
x
ten
s
io
n
o
f
t
h
e
co
n
tr
o
ller
f
r
o
m
Sectio
n
4
.
1
is
p
r
o
p
o
s
ed
.
T
h
e
g
o
al
o
f
th
is
ex
ten
s
io
n
co
n
ce
r
n
s
th
e
co
lli
s
i
o
n
av
o
id
an
ce
b
ased
o
n
lo
ca
l
s
en
s
o
r
s
.
First
o
f
a
ll,
s
tatic
o
b
s
tacle
s
s
h
o
u
ld
b
e
r
ec
o
g
n
ized
b
y
th
e
lo
ca
l
P
SD
s
en
s
o
r
s
.
Usi
n
g
t
h
is
m
ea
s
u
r
e
m
en
t,
a
d
e
fi
n
ed
s
af
e
t
y
d
i
s
ta
n
ce
to
a
s
tatic
o
b
s
tacle
s
h
o
u
ld
b
e
m
a
in
ta
in
ed
.
F
u
r
th
er
m
o
r
e,
a
co
llis
io
n
w
it
h
o
th
er
r
o
b
o
ts
in
th
e
f
o
r
m
atio
n
n
ee
d
s
to
b
e
av
o
id
ed
.
Fo
r
th
e
co
llis
io
n
a
v
o
id
an
ce
c
o
n
tr
o
ller
,
a
f
o
r
m
atio
n
w
i
th
o
n
e
lead
er
an
d
N
f
o
llo
w
er
s
i
s
c
o
n
s
id
er
ed
.
T
h
is
f
o
r
m
atio
n
is
co
n
tr
o
lled
b
y
a
co
n
tr
o
ller
.
T
o
b
e
ab
le
to
a
v
o
id
a
co
llis
io
n
,
t
h
e
d
e
s
ir
ed
co
n
tr
o
l
v
alu
e
s
an
d
ar
e
ch
an
g
ed
i
n
a
n
ap
p
r
o
p
r
iated
m
an
n
er
.
T
h
is
i
m
p
lies
th
at
th
e
d
esire
d
v
alu
e
s
ar
e
ti
m
e
d
ep
en
d
en
t.
T
h
er
ef
o
r
e,
th
e
f
o
llo
w
i
n
g
al
g
o
r
ith
m
f
o
r
c
h
an
g
i
n
g
t
h
e
d
e
s
ir
ed
v
al
u
es
a
n
d
h
e
n
ce
th
e
f
o
r
m
atio
n
i
s
p
r
o
p
o
s
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
0
8
9
-
4856
I
J
R
A
,
Vo
l.
7
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
1
8
–
3
8
26
(
2
1
)
w
it
h
(
2
2
)
w
h
er
e
s
u
b
s
cr
ip
t
L
,
R
a
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d
F
r
e
f
er
to
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lef
t
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id
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e
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ig
h
t
s
id
e
an
d
t
h
e
f
r
o
n
t,
r
e
s
p
ec
tiv
el
y
.
T
h
e
s
y
m
b
o
l
P
SD
d
en
o
tes
t
h
e
v
a
lu
e
o
f
t
h
e
P
SD
s
en
s
o
r
an
d
s
p
ec
i
fi
es
th
e
th
r
e
s
h
o
ld
.
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h
e
v
al
u
e
o
f
th
e
m
ea
s
u
r
e
m
e
n
t
f
r
o
m
th
e
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SD
s
en
s
o
r
s
is
r
elate
d
to
th
e
d
is
tan
ce
,
i.e
.
,
if
th
e
v
al
u
e
is
b
ey
o
n
d
a
th
r
esh
o
ld
,
n
o
th
r
ea
t
co
n
ce
r
n
i
n
g
a
co
llis
io
n
ex
is
t
s
.
5.
SI
M
UL
AT
I
VE
I
NVE
ST
I
G
AT
I
O
N
S AN
D
R
E
SU
L
T
S
I
n
th
is
s
ec
tio
n
,
t
h
e
t
h
r
ee
f
o
r
m
atio
n
co
n
tr
o
ller
s
f
r
o
m
Sectio
n
4
ar
e
in
v
e
s
ti
g
ated
f
o
r
t
h
e
p
u
r
p
o
s
e
o
f
a
p
o
s
s
ib
le
i
m
p
le
m
e
n
tatio
n
o
n
t
h
e
g
i
v
en
r
o
b
o
ts
.
Sp
ec
i
fi
ca
ll
y
,
s
ev
er
al
s
i
m
u
latio
n
s
o
f
ea
c
h
f
o
r
m
at
io
n
co
n
tr
o
ller
ar
e
ca
r
r
ied
o
u
t
w
ith
d
if
f
er
en
t
m
o
d
el
s
o
f
th
e
r
o
b
o
t.
T
h
ese
m
o
d
els
ar
e
ch
an
g
ed
i
n
a
n
ap
p
r
o
p
r
iated
m
a
n
n
er
to
ac
h
iev
e
a
m
o
r
e
d
etailed
m
o
d
el
o
f
th
e
r
ea
l
r
o
b
o
ts
.
A
cc
o
r
d
in
g
to
th
e
r
es
u
lts
o
f
t
h
e
s
e
s
i
m
u
l
atio
n
s
,
a
co
n
cl
u
s
io
n
is
g
i
v
e
n
r
eg
ar
d
in
g
th
e
p
o
s
s
ib
il
it
y
o
f
i
m
p
le
m
en
tin
g
a
f
o
r
m
ati
o
n
co
n
tr
o
ller
o
n
th
e
r
o
b
o
ts
.
5.
1
.
Co
ns
idered
Si
m
u
la
t
io
n M
o
dels
B
ef
o
r
e
th
e
s
i
m
u
la
tio
n
s
ta
k
e
p
lace
,
th
e
d
if
f
er
en
t
m
o
d
e
ls
f
o
r
th
e
s
i
m
u
latio
n
a
n
d
d
if
f
er
e
n
t
s
i
m
u
lat
io
n
e
n
v
ir
o
n
m
e
n
t
s
ar
e
in
tr
o
d
u
ce
d
.
T
h
e
m
o
d
els
ar
e
c
h
an
g
ed
f
r
o
m
an
ea
s
y
k
i
n
e
m
atic
m
o
d
el
to
a
v
er
y
d
etailed
m
o
d
el
w
h
ich
also
co
n
s
id
e
r
s
c
o
m
m
u
n
icatio
n
.
W
ith
th
e
s
e
d
i
f
f
er
en
t
m
o
d
els
it
i
s
p
o
s
s
ib
le
to
g
u
r
e
o
u
t
t
h
e
cr
u
cial
p
ar
ts
o
f
th
e
w
h
o
le
s
y
s
te
m
co
n
ce
r
n
i
n
g
an
i
m
p
le
m
e
n
tatio
n
o
f
th
e
f
o
r
m
a
tio
n
co
n
tr
o
ller
s
o
n
th
e
r
ea
l
r
o
b
o
ts
.
T
h
ese
m
o
d
els
ar
e
m
o
d
elled
a
n
d
s
i
m
u
lated
i
n
Ma
tlab
/
Si
m
u
l
in
k
.
A
s
a
f
u
r
t
h
er
s
i
m
u
latio
n
en
v
ir
o
n
m
e
n
t,
E
y
e
Si
m
is
in
tr
o
d
u
ce
d
[
36
]
,
[
37
].
As
alr
ea
d
y
m
en
tio
n
ed
,
th
e
fi
r
s
t
m
o
d
el
w
ill
b
e
a
k
in
e
m
ati
c
m
o
d
el
as
in
t
r
o
d
u
ce
d
in
(
1
)
.
T
h
e
fi
r
s
t
i
m
p
r
o
v
e
m
en
t
o
n
t
h
e
s
i
m
u
latio
n
m
o
d
el
co
n
ce
r
n
s
t
h
e
m
o
d
el
o
f
t
h
e
r
o
b
o
t.
I
n
s
tead
o
f
u
s
i
n
g
t
h
e
k
i
n
e
m
at
ic
m
o
d
el
o
f
th
e
r
o
b
o
t
o
n
w
h
ic
h
th
e
co
n
tr
o
l
d
esig
n
i
s
b
ased
,
a
d
y
n
a
m
ical
m
o
d
el
is
u
s
ed
.
T
h
er
ef
o
r
e,
th
e
m
o
d
el
E
q
u
atio
n
(
7
)
o
f
Sectio
n
3
.
2
.
2
w
it
h
th
e
id
e
n
ti
f
i
ed
p
ar
a
m
ete
r
s
is
u
s
ed
.
Si
n
ce
th
e
v
elo
cit
y
v
an
d
th
e
an
g
u
lar
v
elo
cit
y
a
r
e
n
o
t
co
n
tr
o
lled
in
E
q
u
atio
n
(
7
)
,
th
e
s
p
ee
d
co
n
tr
o
ller
o
f
Sectio
n
3
.
2
.
4
is
ap
p
lied
.
T
h
er
ef
o
r
e,
n
o
t
o
n
l
y
t
h
e
o
p
ti
m
ized
co
n
tr
o
l
p
ar
a
m
eter
s
o
f
t
h
e
P
I
D
co
n
tr
o
ller
ar
e
u
s
ed
.
W
ith
th
e
ch
a
n
g
e
o
f
th
e
s
e
p
ar
a
m
eter
s
an
d
th
er
e
f
o
r
e
th
e
c
h
an
g
e
o
f
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
v
elo
c
it
y
co
n
tr
o
ller
,
s
o
m
e
r
eq
u
ir
e
m
en
ts
o
n
th
e
s
p
ee
d
co
n
tr
o
ller
ca
n
b
e
f
o
r
m
u
lated
.
T
o
im
p
r
o
v
e
th
e
d
y
n
a
m
ic
m
o
d
el,
a
f
u
r
th
er
ch
ar
ac
ter
is
t
ic
o
f
th
e
r
o
b
o
t
is
in
clu
d
ed
.
A
cr
u
cial
asp
ec
t
f
r
o
m
i
m
p
le
m
e
n
ti
n
g
a
co
n
tr
o
ller
in
h
ar
d
w
ar
e
is
t
h
e
d
is
cr
etiza
tio
n
.
Du
e
to
t
h
e
c
h
ar
ac
ter
is
tic
o
f
a
m
icr
o
co
n
tr
o
ller
,
it
is
n
o
t
p
o
s
s
i
b
le
to
ac
h
iev
e
a
co
n
ti
n
u
o
u
s
o
u
tp
u
t
s
ig
n
al
o
f
t
h
e
co
n
tr
o
ller
.
T
h
e
co
n
tr
o
l
o
u
tp
u
t
w
il
l th
er
e
f
o
r
e
b
e
a
d
is
cr
ete
s
ig
n
al.
Du
e
to
th
e
f
ac
t
t
h
at
t
h
ese
f
o
r
m
atio
n
co
n
tr
o
ller
s
n
ee
d
co
m
m
u
n
icat
io
n
,
th
e
m
et
h
o
d
an
d
i
m
p
ac
t
o
f
co
m
m
u
n
icatio
n
is
i
n
v
e
s
ti
g
ated
.
Fo
r
th
is
w
o
r
k
,
t
w
o
t
y
p
es
o
f
e
r
r
o
r
ca
u
s
es
ar
e
co
n
s
id
er
ed
.
T
h
e
fi
r
s
t
er
r
o
r
r
esu
lts
f
r
o
m
n
et
w
o
r
k
d
ela
y
s
.
T
h
er
e
ar
e
m
an
y
ca
u
s
e
s
f
o
r
t
h
ese
d
ela
y
s
e.
g
.
t
h
e
li
m
ited
n
et
w
o
r
k
tr
an
s
f
er
r
ate
o
r
s
en
d
i
n
g
p
ac
k
ag
es
t
h
r
o
u
g
h
s
e
v
er
al
la
y
e
r
s
.
I
n
s
u
m
m
ar
y
all
th
e
s
e
d
ela
y
s
ca
n
b
e
co
n
s
id
er
ed
as
an
ad
d
itio
n
al
a
m
o
u
n
t
o
f
ti
m
e
i
n
t
h
e
s
a
m
p
l
in
g
ti
m
e.
T
h
e
s
ec
o
n
d
co
n
s
id
er
ed
er
r
o
r
co
n
ce
r
n
s
t
h
e
co
m
m
u
n
icatio
n
p
r
o
to
co
l
UDP
,
w
h
ic
h
i
s
u
s
ed
f
o
r
tr
an
s
m
itti
n
g
d
ata.
T
h
is
p
r
o
to
co
l
is
u
n
r
eliab
le
an
d
t
h
er
e
is
n
o
g
u
ar
an
tee
o
f
d
eliv
er
y
.
T
h
er
ef
o
r
e,
th
e
m
o
d
el
o
f
t
h
e
s
y
s
te
m
i
s
e
x
ten
d
ed
to
co
v
er
th
e
o
cc
u
r
r
en
ce
o
f
p
ac
k
ag
e
lo
s
s
i
n
t
h
e
n
et
w
o
r
k
.
T
h
e
ev
en
t
o
f
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
A
I
SS
N:
2089
-
4856
I
n
ve
s
tig
a
tio
n
o
f F
o
r
ma
tio
n
C
o
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tr
o
l A
p
p
r
o
a
ch
es C
o
n
s
id
erin
g
th
e
A
b
ilit
y
o
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…
(
Ha
n
n
es W
in
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)
27
p
ac
k
ag
e
lo
s
s
i
s
ass
u
m
ed
to
b
e
u
n
i
f
o
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m
l
y
d
is
tr
ib
u
ted
an
d
i
f
o
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e
p
ac
k
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e
is
lo
s
t,
t
h
e
w
h
o
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e
ca
lcu
latio
n
o
f
t
h
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co
n
tr
o
ller
is
s
k
ip
p
ed
in
t
h
is
s
a
m
p
le
.
E
y
eSi
m
is
u
s
ed
as
a
s
ec
o
n
d
en
v
ir
o
n
m
e
n
t
f
o
r
s
i
m
u
lat
in
g
t
h
e
f
o
r
m
a
tio
n
co
n
tr
o
ller
[
36
]
,
[
37
]
.
T
h
is
p
r
o
g
r
am
is
a
s
i
m
u
la
tio
n
en
v
ir
o
n
m
e
n
t
f
o
r
m
u
ltip
le
m
o
b
ile
r
o
b
o
ts
w
h
ic
h
p
r
o
v
id
es
th
e
p
o
s
s
ib
ilit
y
to
s
i
m
u
la
te
di
ff
er
e
n
t
k
in
d
o
f
r
o
b
o
ts
[
36
]
,
[
37
]
.
On
e
o
f
th
o
s
e
r
o
b
o
ts
is
s
i
m
ilar
to
th
e
r
o
b
o
ts
th
is
p
ap
er
tak
es
as
a
b
as
is
.
An
ad
v
an
ta
g
e
o
f
E
y
e
Si
m
is
th
e
a
p
p
licatio
n
p
r
o
g
r
a
m
m
er
in
ter
f
a
ce
(
A
P
I
)
w
h
i
c
h
i
s
t
h
e
s
a
m
e
a
s
th
e
A
P
I
o
f
th
e
r
ea
l
r
o
b
o
t.
T
h
is
m
ea
n
s
th
e
w
h
o
le
f
u
n
ct
io
n
alit
y
o
f
t
h
e
h
i
g
h
le
v
el
i
s
p
r
o
v
id
ed
in
E
y
eSi
m
.
T
h
e
r
elev
an
t
f
u
n
c
tio
n
ali
t
y
f
o
r
th
i
s
p
u
r
p
o
s
e
is
l
i
m
ited
to
m
an
ip
u
lati
n
g
t
h
e
s
p
ee
d
o
f
t
h
e
r
o
b
o
t,
th
e
co
m
m
u
n
icatio
n
b
et
w
ee
n
r
o
b
o
ts
an
d
th
e
r
etr
iev
in
g
o
f
th
e
s
e
n
s
o
r
d
ata.
T
h
e
u
s
e
o
f
E
y
eSi
m
is
also
a
g
o
o
d
o
p
p
o
r
tu
n
it
y
to
ch
ec
k
th
e
co
n
tr
o
l
la
w
in
co
m
b
i
n
atio
n
w
it
h
t
h
e
h
ig
h
l
ev
el
f
u
n
ctio
n
alit
y
.
Fi
g
u
r
e
6
is
v
is
u
aliza
tio
n
o
f
t
h
e
co
n
tr
o
ller
w
it
h
a
k
in
e
m
at
ic
m
o
d
el
.
T
h
e
R
o
b
o
t 1
is
d
en
o
ted
as +
,
R
o
b
o
t
2
as o
an
d
R
o
b
o
t 3
is
d
en
o
ted
as
*.
Fig
u
r
e
6
.
Vis
u
al
izatio
n
o
f
t
h
e
co
n
tr
o
ller
w
it
h
a
k
i
n
e
m
atic
m
o
d
el
5
.
2
.
Si
m
ula
t
io
ns
o
f
t
he
Co
ntr
o
ller
I
n
th
i
s
s
u
b
s
ec
tio
n
,
s
e
v
er
al
s
i
m
u
latio
n
s
fi
r
s
tl
y
w
it
h
Ma
t
lab
/Si
m
u
li
n
k
an
d
s
ec
o
n
d
l
y
w
it
h
E
y
eSi
m
ar
e
ca
r
r
ied
o
u
t.
Fin
all
y
,
t
h
e
ap
p
licab
ilit
y
to
i
m
p
le
m
e
n
t t
h
is
co
n
tr
o
ller
is
d
is
cu
s
s
ed
.
5
.
2
.
1
.
Si
m
ula
t
io
n in M
a
t
l
a
b/S
i
m
ul
in
k
T
h
e
fi
r
s
t
s
i
m
u
latio
n
o
f
t
h
e
co
n
tr
o
ller
is
d
o
n
e
w
it
h
t
h
e
k
in
e
m
atic
m
o
d
el
to
i
n
v
esti
g
at
e
its
b
eh
av
io
r
.
T
h
er
ef
o
r
e,
a
co
n
s
te
llatio
n
w
it
h
o
n
e
lead
er
an
d
t
w
o
f
o
llo
w
er
s
is
co
n
s
id
er
ed
.
T
h
e
lead
er
d
r
iv
es
a
cu
r
v
e
w
i
th
t
h
e
i
n
p
u
t
v
al
u
es
v
r
=
0
.
1
an
d
.
T
h
e
f
o
r
m
atio
n
s
p
e
ci
fi
ca
tio
n
f
o
r
th
e
fi
r
s
t
f
o
llo
w
er
is
d
e
fi
n
ed
as
an
d
f
o
r
th
e
s
ec
o
n
d
f
o
llo
w
e
r
th
e
d
es
ir
ed
co
n
tr
o
l
v
a
lu
e
s
ar
e
.
T
h
e
in
itial
p
o
s
e
f
o
r
ea
ch
r
o
b
o
t is
t
h
e
co
n
tr
o
l p
ar
a
m
eter
s
ar
e
c
h
o
s
e
n
as
an
d
as s
h
o
w
n
i
n
E
q
u
atio
n
(
2
3
)
.
(
2
3
)
T
h
e
r
esu
lts
o
f
th
e
s
i
m
u
la
tio
n
w
it
h
t
h
e
k
in
e
m
atic
m
o
d
el
c
an
b
e
s
ee
n
i
n
F
ig
u
r
e
6
.
Af
te
r
an
in
it
ial
co
n
v
er
g
e
n
ce
o
f
t
h
e
t
w
o
f
o
ll
o
w
er
s
it
ca
n
b
e
o
b
s
er
v
ed
th
at
th
e
d
esire
d
len
g
th
a
n
d
th
e
d
esire
d
an
g
le
ar
e
m
ai
n
tai
n
ed
.
T
h
e
f
o
llo
w
er
r
o
b
o
t f
o
llo
w
s
t
h
e
lead
er
w
it
h
t
h
e
s
p
ec
i
fi
ed
p
ar
am
e
ter
s
.
T
h
e
s
ec
o
n
d
s
i
m
u
latio
n
is
ca
r
r
ied
o
u
t
w
it
h
a
d
y
n
a
m
ic
m
o
d
el
as
m
e
n
tio
n
ed
i
n
5
.
1
.
T
h
e
r
e
ar
e
t
w
o
cr
u
cial
o
u
tco
m
es
o
f
t
h
ese
s
i
m
u
latio
n
s
.
Firstl
y
,
t
h
e
s
p
ee
d
co
n
tr
o
ller
p
lay
s
an
i
m
p
o
r
tan
t
r
o
le
in
th
e
w
h
o
le
s
y
s
te
m
.
I
f
t
h
e
v
elo
cit
y
v
a
n
d
t
h
e
an
g
u
lar
v
elo
cit
y
o
f
ea
c
h
r
o
b
o
t
d
o
n
o
t
co
n
v
er
g
e
to
th
e
r
eq
u
ir
ed
v
al
u
e,
th
e
b
eh
av
io
r
o
f
th
e
d
y
n
a
m
ic
m
o
d
el
is
d
i
ff
er
e
n
t
f
r
o
m
t
h
e
k
i
n
e
m
atic
m
o
d
el.
I
n
ad
d
itio
n
to
th
is
,
th
e
len
g
t
h
l
1i
an
d
th
e
an
g
le
(
w
h
er
e
i
is
th
e
n
u
m
b
er
o
f
t
h
e
f
o
llo
w
er
)
d
o
n
o
t
co
n
v
er
g
e
to
th
e
d
esire
d
v
a
lu
es,
if
t
h
e
lead
er
r
o
b
o
t
c
o
n
v
er
g
es
to
t
h
e
k
i
n
e
m
a
tic
m
o
d
el
an
d
th
e
f
o
llo
w
er
s
d
o
n
o
t
co
n
v
er
g
e.
T
o
ac
h
iev
e
th
is
g
o
al,
th
e
i
n
te
g
r
al
Evaluation Warning : The document was created with Spire.PDF for Python.