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[
1
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[
3
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izatio
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[
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4
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p
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[
5
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,
[
6
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Seq
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p
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m
m
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SQP
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m
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t
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tech
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er
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x
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tr
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ts
[
5
]
.
R
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s
t
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h
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also
in
te
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tech
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Kal
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in
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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6
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6930
T
E
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KOM
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A
T
elec
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m
u
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C
o
m
p
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t E
l
C
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,
Vo
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24
,
No
.
3
,
J
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20
26
:
1
037
-
1
0
4
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1038
r
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[
6
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[
7
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ai
n
tai
n
f
o
r
m
at
io
n
,
av
o
id
o
b
s
tacle
s
,
an
d
tr
ac
k
t
h
e
v
ir
t
u
al
lead
er
tr
aj
ec
to
r
y
e
f
f
icie
n
tl
y
.
E
x
p
er
i
m
e
n
t
al
r
es
u
lt
s
d
e
m
o
n
s
tr
ate
t
h
at
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
s
ig
n
i
f
ica
n
tl
y
i
m
p
r
o
v
es
co
n
tr
o
l
p
er
f
o
r
m
a
n
ce
,
r
ed
u
ce
s
co
llis
io
n
s
,
an
d
m
ai
n
tai
n
s
f
o
r
m
a
tio
n
ac
cu
r
ac
y
i
n
co
m
p
le
x
en
v
ir
o
n
m
en
ts
o
p
en
i
n
g
u
p
n
e
w
d
ir
ec
ti
o
n
s
f
o
r
f
u
t
u
r
e
m
o
b
ile
r
o
b
o
tic
s
y
s
te
m
s
.
T
h
e
r
em
ain
d
er
o
f
th
i
s
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
.
Sectio
n
2
p
r
esen
ts
th
e
s
y
s
te
m
m
o
d
el,
in
cl
u
d
in
g
r
o
b
o
t
k
in
e
m
atic
s
an
d
t
h
e
h
i
er
ar
ch
ical
v
ir
t
u
al
-
lead
er
co
m
m
u
n
icat
io
n
s
tr
u
ct
u
r
e.
Sectio
n
3
d
escr
ib
es
th
e
f
o
r
m
u
latio
n
o
f
t
h
e
DM
P
C
co
s
t
f
u
n
ct
io
n
an
d
th
e
SQP
-
b
as
ed
o
p
tim
izatio
n
f
r
a
m
e
w
o
r
k
an
d
i
m
p
le
m
e
n
tat
io
n
d
etails.
Sectio
n
4
p
r
o
v
id
es
s
i
m
u
latio
n
r
es
u
lt
s
th
at
ev
al
u
a
te
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
in
ter
m
s
o
f
f
o
r
m
a
tio
n
ac
cu
r
ac
y
a
n
d
o
b
s
tacle
av
o
id
an
ce
u
n
d
er
m
ea
s
u
r
e
m
e
n
t
n
o
i
s
e.
Fin
al
l
y
,
s
ec
t
io
n
5
in
cl
u
d
es
co
n
clu
s
io
n
s
an
d
d
is
cu
s
s
io
n
o
f
f
u
t
u
r
e
r
esear
ch
d
ir
ec
tio
n
s
i
n
v
o
l
v
i
n
g
d
y
n
a
m
ic
o
b
s
tacle
s
ce
n
ar
io
s
.
2.
P
RE
L
I
M
I
NARIE
S
2
.
1
.
Ro
bo
t
m
o
del
I
n
th
is
s
t
u
d
y
,
w
e
co
n
s
id
er
o
m
n
id
ir
ec
tio
n
al
m
o
b
ile
r
o
b
o
ts
o
p
er
atin
g
i
n
a
t
w
o
-
d
i
m
e
n
s
io
n
al
p
lan
e.
E
ac
h
r
o
b
o
t
is
eq
u
ip
p
ed
w
i
th
o
m
n
i
o
r
m
ec
an
u
m
w
h
ee
ls
,
w
h
ic
h
all
o
w
i
n
s
ta
n
ta
n
eo
u
s
m
o
tio
n
i
n
a
n
y
d
ir
ec
tio
n
w
it
h
o
u
t
th
e
n
ee
d
to
r
eo
r
ien
t th
e
b
o
d
y
.
T
h
e
co
n
f
ig
u
r
atio
n
(
p
o
s
e)
o
f
r
o
b
o
t i
is
d
escr
ib
ed
b
y
th
e
s
tate
v
ec
to
r
:
=
[
]
⊺
(
1
)
w
h
er
e
(
,
)
∈
ℝ
d
en
o
tes
t
h
e
p
o
s
itio
n
c
o
o
r
d
in
ates
in
t
h
e
g
lo
b
al
r
ef
er
e
n
ce
f
r
a
m
e,
a
n
d
∈
ℝ
is
th
e
h
ea
d
i
n
g
an
g
le
o
f
th
e
r
o
b
o
t e
x
p
r
ess
ed
i
n
r
ad
ian
s
.
T
h
e
co
r
r
esp
o
n
d
in
g
co
n
tr
o
l i
n
p
u
t v
ec
to
r
is
g
i
v
en
b
y
:
=
[
,
,
]
⊺
(
2
)
w
h
er
e
,
,
,
ar
e
th
e
lin
ea
r
v
elo
citi
es
alo
n
g
t
h
e
b
o
d
y
-
f
r
a
m
e
a
x
es
o
f
th
e
r
o
b
o
t,
an
d
is
th
e
a
n
g
u
la
r
v
elo
cit
y
ar
o
u
n
d
th
e
v
er
tical
ax
i
s
.
T
h
e
k
in
e
m
atic
m
o
d
el
o
f
ea
c
h
o
m
n
id
ir
ec
tio
n
al
m
o
b
ile
r
o
b
o
t is th
e
n
g
i
v
e
n
b
y
:
̇
[
̇
̇
̇
]
=
[
−
0
0
0
0
1
]
⏟
(
)
[
,
,
]
(
3
)
w
h
er
e
(
)
is
th
e
r
o
tatio
n
m
atr
i
x
t
h
at
m
ap
s
t
h
e
co
n
tr
o
l
i
n
p
u
ts
f
r
o
m
th
e
b
o
d
y
f
r
a
m
e
to
th
e
w
o
r
ld
f
r
a
m
e.
T
h
e
f
ir
s
t
t
w
o
r
o
w
s
d
escr
ib
e
th
e
tr
an
s
lat
io
n
al
m
o
tio
n
in
th
e
g
lo
b
al
x
-
y
p
lan
e,
w
h
ile
th
e
th
ir
d
r
o
w
d
ir
ec
tly
r
elate
s
th
e
an
g
u
lar
r
ate
to
th
e
h
ea
d
i
n
g
d
y
n
a
m
ics
̇
,
w
id
el
y
u
s
ed
i
n
o
m
n
i
-
d
ir
ec
tio
n
al
r
o
b
o
t m
o
d
elin
g
[
8
]
-
[
1
0
]
.
Fo
r
th
e
s
u
b
s
eq
u
e
n
t
p
r
ed
ictiv
e
co
n
tr
o
l
f
o
r
m
u
latio
n
,
th
e
co
n
ti
n
u
o
u
s
-
ti
m
e
m
o
d
el
(
3
)
is
d
is
cr
etize
d
w
i
t
h
a
s
a
m
p
li
n
g
t
i
m
e
u
s
i
n
g
a
f
o
r
war
d
E
u
ler
s
ch
e
m
e
:
(
ℎ
+
1
)
=
(
ℎ
)
+
(
(
ℎ
)
,
(
ℎ
)
)
,
ℎ
=
0
,
1
,
…
,
−
1
(
4
)
w
h
er
e
(
∙
)
is
o
b
tain
ed
f
r
o
m
t
h
e
r
ig
h
t
-
h
a
n
d
s
id
e
o
f
(
3
)
,
an
d
H
d
e
n
o
tes
th
e
p
r
ed
ictio
n
h
o
r
izo
n
.
T
h
r
o
u
g
h
o
u
t
th
e
p
ap
er
,
all
in
ter
n
al
co
m
p
u
tati
o
n
s
u
s
e
in
r
ad
ian
s
;
h
ea
d
in
g
er
r
o
r
s
s
h
o
w
n
i
n
t
h
e
s
i
m
u
l
atio
n
f
ig
u
r
es
ar
e
co
n
v
er
ted
to
d
eg
r
ee
s
o
n
l
y
f
o
r
v
is
u
aliza
t
io
n
.
T
h
e
s
i
g
n
ed
h
ea
d
in
g
er
r
o
r
is
w
r
ap
p
ed
to
th
e
i
n
t
er
v
al
[
−
,
]
u
s
in
g
a
s
tan
d
ar
d
w
r
ap
-
to
-
o
p
er
atio
n
an
d
is
later
u
s
ed
in
t
h
e
DM
P
C
co
s
t f
u
n
ctio
n
.
2
.
2
.
V
-
f
o
rm
a
t
io
n a
nd
co
mm
un
ica
t
io
n str
uct
ure
I
n
th
e
p
r
o
p
o
s
ed
m
o
d
el,
th
e
o
m
n
id
ir
ec
tio
n
al
m
o
b
ile
r
o
b
o
ts
ar
e
o
r
g
an
ized
i
n
to
a
V
-
s
h
ap
ed
f
o
r
m
atio
n
,
co
n
s
is
tin
g
o
f
a
s
i
n
g
le
lead
in
g
r
o
b
o
t
an
d
m
u
l
tip
le
f
o
llo
w
er
r
o
b
o
ts
s
y
m
m
e
tr
icall
y
d
i
s
tr
ib
u
ted
o
n
b
o
th
s
id
es.
T
h
e
V
-
f
o
r
m
atio
n
is
o
r
g
an
ized
with
a
lead
er
at
th
e
ap
e
x
f
o
llo
w
i
n
g
a
p
r
ed
ef
i
n
ed
tr
aj
ec
to
r
y
,
a
n
d
f
o
llo
w
er
s
Evaluation Warning : The document was created with Spire.PDF for Python.
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[
1
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[
1
3
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:
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(
,
ℰ
,
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(
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L
et
=
{
1
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}
d
en
o
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e
s
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o
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r
ep
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b
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e
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ed
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e
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,
in
d
icate
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h
at
r
o
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o
t i
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o
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m
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r
o
m
r
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C
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ies
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ch
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[
1
4
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e
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i
n
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m
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n
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ch
a
n
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ed
v
ar
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tio
n
s
tr
u
ct
u
r
e
is
d
esi
g
n
ed
to
s
a
tis
f
y
t
h
e
f
o
llo
w
i
n
g
cr
iter
ia:
e
n
s
u
r
e
g
lo
b
al
co
n
n
ec
t
iv
i
t
y
o
f
th
e
n
et
w
o
r
k
;
m
i
n
i
m
ize
co
m
p
u
tat
io
n
al
a
n
d
co
m
m
u
n
icat
i
o
n
lo
ad
,
w
h
ich
i
s
es
s
en
tial
f
o
r
d
is
tr
ib
u
ted
co
n
tr
o
l
s
ch
e
m
es;
s
u
p
p
o
r
t
th
e
im
p
le
m
e
n
tatio
n
o
f
DM
P
C
,
w
h
er
e
ea
ch
r
o
b
o
t
s
o
lv
es
a
l
o
ca
l
o
p
tim
izat
io
n
p
r
o
b
lem
b
ased
o
n
in
f
o
r
m
atio
n
f
r
o
m
it
s
n
ei
g
h
b
o
r
s
.
T
h
is
s
p
ar
s
e
an
d
d
ir
ec
ted
to
p
o
lo
g
y
r
ed
u
ce
s
d
ep
en
d
en
c
e
o
n
ce
n
tr
alize
d
o
r
f
u
ll
y
-
co
n
n
ec
ted
co
m
m
u
n
icati
o
n
,
w
h
ic
h
m
a
y
h
elp
m
ai
n
tai
n
co
o
r
d
in
ated
b
eh
av
io
r
ev
e
n
w
h
e
n
o
n
l
y
lo
ca
l
n
eig
h
b
o
r
in
f
o
r
m
atio
n
is
av
a
ila
b
le.
3.
P
RO
P
O
SE
D
M
E
T
H
O
D
3
.
1
.
D
M
P
C
co
s
t
f
un
ct
io
n
I
n
th
e
DM
P
C
f
r
a
m
e
w
o
r
k
,
ea
ch
r
o
b
o
t
in
th
e
s
y
s
te
m
i
n
d
ep
en
d
en
tl
y
o
p
ti
m
izes
a
lo
ca
l
o
b
j
ec
tiv
e
f
u
n
ctio
n
at
ev
er
y
ti
m
e
s
tep
,
b
a
s
ed
o
n
its
cu
r
r
en
t
s
tate
an
d
in
f
o
r
m
at
io
n
r
ec
eiv
ed
f
r
o
m
n
ei
g
h
b
o
r
in
g
r
o
b
o
ts
.
T
h
e
o
p
tim
izatio
n
p
r
o
b
le
m
is
s
o
l
v
ed
in
a
r
ec
ed
in
g
h
o
r
izo
n
m
an
n
er
,
en
s
u
r
i
n
g
b
o
th
f
ea
s
i
b
ilit
y
an
d
s
tab
ilit
y
th
r
o
u
g
h
o
u
t th
e
co
n
tr
o
l p
r
o
ce
s
s
.
B
ased
o
n
th
e
ex
c
h
a
n
g
ed
s
ta
te
in
f
o
r
m
atio
n
b
et
w
ee
n
r
o
b
o
ts
,
w
e
co
n
s
tr
u
c
t
a
co
s
t
f
u
n
ctio
n
c
o
m
p
r
i
s
in
g
th
e
f
o
llo
w
in
g
co
m
p
o
n
en
ts
:
f
o
r
m
atio
n
-
k
ee
p
in
g
r
elati
v
e
to
t
h
e
lead
er
o
r
v
ir
tu
al
lead
er
;
co
n
s
en
s
u
s
o
n
p
o
s
it
io
n
an
d
h
ea
d
in
g
w
i
th
n
ei
g
h
b
o
r
in
g
r
o
b
o
ts
;
co
llis
io
n
av
o
id
an
ce
;
co
n
tr
o
l
ef
f
o
r
t
m
i
n
i
m
izatio
n
,
an
d
ter
m
i
n
al
co
s
t
t
o
en
s
u
r
e
lo
n
g
-
ter
m
s
tab
il
it
y
[
1
1
]
,
[
1
5
]
-
[
1
7
]
.
T
h
e
g
en
er
al
f
o
r
m
o
f
th
e
co
s
t
f
u
n
ctio
n
is
d
ef
in
ed
as:
=
∑
[
[
ℎ
]
+
[
ℎ
]
+
[
ℎ
]
+
[
ℎ
]
+
]
−
1
ℎ
=
0
(
6
)
3
.
1
.
1
.
F
o
rm
a
t
io
n
-
k
ee
p
ing
co
s
t
I
f
t
h
e
lead
er
(
o
r
v
ir
t
u
al
lead
e
r
)
is
i
n
cl
u
d
ed
in
th
e
n
ei
g
h
b
o
r
s
et
,
r
o
b
o
t
i
m
ai
n
tai
n
s
a
d
esire
d
r
elativ
e
o
f
f
s
et
,
ex
p
r
ess
ed
in
t
h
e
lead
er
’
s
b
o
d
y
f
r
a
m
e
[
1
4
]
:
[
ℎ
]
=
{
.
‖
[
ℎ
]
−
(
[
ℎ
]
+
(
[
ℎ
]
.
,
)
)
‖
2
0
,
(
7
)
w
h
er
e
=
[
,
]
⊺
is
t
h
e
r
o
b
o
t p
o
s
itio
n
,
an
d
>
0
is
th
e
f
o
r
m
atio
n
.
I
f
t
h
e
lea
d
er
is
n
o
t a
n
eig
h
b
o
r
(
e.
g
.
,
s
ec
o
n
d
-
la
y
er
f
o
llo
w
er
)
,
w
e
s
e
t
=
0
.
3
.
1
.
2
.
Co
ns
ens
u
s
co
s
t
w
it
h neig
hb
o
ring
ro
bo
t
s
R
o
b
o
ts
m
ai
n
tai
n
co
h
esio
n
b
y
r
eg
u
la
tin
g
p
o
s
itio
n
an
d
h
ea
d
i
n
g
d
if
f
er
en
ce
s
r
elativ
e
to
n
eig
h
b
o
r
s
[
1
8
]
:
[
ℎ
]
=
∑
[
(
‖
[
ℎ
]
−
[
ℎ
]
‖
−
,
)
2
+
(
[
ℎ
]
−
[
ℎ
]
)
2
]
∈
,
(
8
)
w
h
er
e
,
is
t
h
e
d
esire
d
in
ter
-
r
o
b
o
t sp
ac
in
g
,
,
>
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
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elec
o
m
m
u
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C
o
m
p
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C
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tr
o
l
,
Vo
l.
24
,
No
.
3
,
J
u
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20
26
:
1
037
-
1
0
4
7
1040
3
.
1
.
3
.
O
bs
t
a
cle
a
v
o
ida
nce
co
s
t
(
ba
rr
ier
f
un
ct
io
n)
L
et
,
d
en
o
te
th
e
p
o
s
itio
n
o
f
th
e
m
-
t
h
o
b
s
tacle
ce
ll
in
t
h
e
g
r
id
m
ap
,
an
d
let
[
ℎ
]
=
‖
[
ℎ
]
−
,
‖
b
e
th
e
d
is
tan
ce
b
et
w
ee
n
r
o
b
o
t
i
an
d
o
b
s
tacle
m
.
T
o
s
tr
o
n
g
l
y
p
en
alize
d
is
tan
ce
s
ap
p
r
o
ac
h
in
g
a
s
af
et
y
m
ar
g
i
n
,
w
e
ad
o
p
t a
s
m
o
o
t
h
b
ar
r
ier
f
u
n
ctio
n
[
1
9
]
-
[
2
1
]
:
[
ℎ
]
=
∑
1
(
[
ℎ
]
−
)
2
=
1
,
(
9
)
w
h
er
e
>
0
.
T
h
is
ter
m
g
r
o
w
s
r
ap
id
l
y
as
[
ℎ
]
→
,
en
s
u
r
i
n
g
co
lli
s
io
n
-
f
r
ee
tr
aj
ec
to
r
ies.
3
.
1
.
4
C
o
ntr
o
l e
f
f
o
rt
m
i
ni
m
i
z
a
t
io
n
S
m
o
o
th
i
n
p
u
t b
e
h
av
io
r
is
e
n
co
u
r
ag
ed
b
y
p
en
aliz
in
g
t
h
e
E
u
cli
d
ea
n
n
o
r
m
o
f
t
h
e
co
n
tr
o
l v
ec
t
o
r
:
[
ℎ
]
=
.
‖
[
ℎ
]
‖
2
(
1
0
)
w
it
h
>
0
.
3
.
1
.
5
.
T
er
m
i
na
l c
o
s
t
A
ter
m
i
n
al
-
s
tate
p
en
al
t
y
i
s
i
m
p
o
s
ed
at
th
e
en
d
o
f
t
h
e
p
r
ed
ictio
n
h
o
r
izo
n
to
i
m
p
r
o
v
e
lo
n
g
-
ter
m
s
tab
ilit
y
:
=
‖
(
)
−
,
(
)
‖
2
,
(
1
1
)
w
h
er
e
≥
0
is
a
p
o
s
itiv
e
s
e
m
id
ef
i
n
i
te
ter
m
i
n
al
w
ei
g
h
t
m
atr
i
x
,
an
d
,
(
)
is
th
e
ter
m
in
al
r
e
f
er
en
ce
s
tate
.
3
.
2
.
D
M
P
C
-
SQ
P
f
ra
m
ew
o
rk
I
n
th
e
d
is
tr
ib
u
ted
f
r
a
m
e
w
o
r
k
,
ea
ch
r
o
b
o
t
i
s
o
lv
es
a
lo
ca
l
o
p
t
i
m
al
co
n
tr
o
l
p
r
o
b
lem
at
ev
er
y
ti
m
e
s
tep
o
v
er
a
p
r
ed
ictio
n
h
o
r
izo
n
o
f
len
g
t
h
H
.
T
h
e
v
ar
iab
le
o
f
t
h
e
d
ec
is
io
n
is
t
h
e
co
n
tr
o
l seq
u
en
ce
:
=
{
[
0
]
,
[
1
]
,
…
,
[
−
1
]
}
an
d
th
e
o
b
j
ec
tiv
e
is
to
m
i
n
i
m
ize
t
h
e
co
s
t
f
u
n
ct
io
n
(
)
d
ef
in
ed
in
(
6
)
-
(
1
1
)
,
w
h
ic
h
a
g
g
r
e
g
ates
f
o
r
m
atio
n
-
k
ee
p
in
g
,
co
n
s
e
n
s
u
s
,
o
b
s
tacle
a
v
o
id
an
ce
,
co
n
tr
o
l e
f
f
o
r
t,
an
d
ter
m
in
a
l p
en
altie
s
.
3
.
2
.
1
.
Dis
cr
et
e
-
t
i
m
e
k
i
ne
m
a
t
i
cs a
nd
inp
ut
co
ns
t
ra
ints
T
h
e
co
n
tin
u
o
u
s
-
ti
m
e
k
in
e
m
at
i
c
m
o
d
el
o
f
th
e
o
m
n
id
ir
ec
tio
n
a
l
m
o
b
ile
r
o
b
o
t
is
g
iv
en
in
(
3
)
.
Ov
er
th
e
p
r
ed
ictio
n
h
o
r
izo
n
,
it is
d
is
cr
et
ized
w
it
h
s
a
m
p
li
n
g
p
er
io
d
as
:
[
ℎ
+
1
]
=
[
ℎ
]
+
[
c
os
[
ℎ
]
−
s
in
[
ℎ
]
0
s
in
[
ℎ
]
c
os
[
ℎ
]
0
0
0
1
]
[
ℎ
]
,
ℎ
=
0
,
…
,
−
1
,
(
1
2
)
w
h
er
e
[
ℎ
]
=
[
[
ℎ
]
,
[
ℎ
]
,
[
ℎ
]
]
an
d
[
ℎ
]
=
[
,
[
ℎ
]
,
,
[
ℎ
]
,
[
ℎ
]
]
.
T
o
en
s
u
r
e
f
ea
s
ib
le
an
d
s
af
e
m
o
tio
n
,
t
h
e
co
n
tr
o
l in
p
u
ts
ar
e
b
o
u
n
d
by
:
‖
[
,
[
ℎ
]
,
,
[
ℎ
]
]
‖
≤
,
|
[
ℎ
]
|
≤
,
ℎ
=
0
,
…
,
−
1
(
1
3
)
3
.
2
.
2
.
No
nli
nea
r
o
pti
m
a
l
co
n
t
ro
l pro
ble
m
Usi
n
g
t
h
e
co
s
t
(
6
)
-
(
1
1
)
an
d
th
e
p
r
ed
ictio
n
m
o
d
el
(
1
2
)
,
th
e
l
o
ca
l
DM
P
C
p
r
o
b
lem
f
o
r
r
o
b
o
t
iii
ca
n
b
e
w
r
itte
n
as
:
min
(
)
(
1
4
)
w
h
er
e
th
e
s
tate
tr
aj
ec
to
r
y
{
[
ℎ
]
}
ℎ
=
0
i
s
g
en
er
ated
b
y
(
1
2
)
s
tar
tin
g
f
r
o
m
th
e
c
u
r
r
en
t
s
tate
[
0
]
,
an
d
th
e
co
n
tr
o
ls
s
atis
f
y
t
h
e
b
o
u
n
d
s
(
1
3
)
f
o
r
all
h
.
Neig
h
b
o
r
in
f
o
r
m
atio
n
en
ter
s
(
∙
)
th
r
o
u
g
h
th
e
f
o
r
m
atio
n
an
d
co
n
s
en
s
u
s
ter
m
s
as d
escr
ib
ed
in
s
ec
tio
n
3
.
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
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C
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tr
o
l
La
ye
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ed
virt
u
a
l le
a
d
er DMP
C
w
ith
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QP
fo
r
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ca
la
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le
V
fo
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n
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o
f
…
(
Tu
a
n
P
h
u
Du
o
n
g
)
1041
3
.
2
.
3
.
L
a
g
ra
ng
ia
n a
nd
SQ
P
f
o
r
m
u
la
t
io
n
T
o
s
o
lv
e
th
e
n
o
n
lin
ea
r
co
n
s
tr
ain
ed
p
r
o
b
lem
(
1
4
)
ef
f
icie
n
tl
y
a
t
ea
ch
s
a
m
p
lin
g
i
n
s
ta
n
t,
w
e
e
m
p
lo
y
SQP
,
a
s
ec
o
n
d
-
o
r
d
er
m
et
h
o
d
w
id
el
y
u
s
ed
i
n
n
o
n
li
n
ea
r
MP
C
[
5
]
,
[
1
5
]
,
[
1
6
]
,
[
2
2
]
.
T
h
e
L
ag
r
an
g
ia
n
o
f
t
h
e
lo
ca
l
p
r
o
b
lem
is
d
ef
in
ed
as
:
ℒ
(
,
,
)
=
(
)
+
(
)
+
(
)
(
1
5
)
w
h
er
e
(
)
co
llects
t
h
e
d
is
cr
etize
d
d
y
n
a
m
ics
co
n
s
tr
ain
t
s
(
1
2
)
alo
n
g
th
e
h
o
r
izo
n
,
a
n
d
(
)
r
ep
r
esen
ts
th
e
in
p
u
t b
o
u
n
d
s
(
1
3
)
.
Vec
to
r
s
an
d
ar
e
th
e
co
r
r
esp
o
n
d
in
g
L
ag
r
an
g
e
m
u
lt
ip
lier
s
.
A
t
iter
atio
n
k
,
t
h
e
L
a
g
r
an
g
ia
n
i
s
ap
p
r
o
x
i
m
ated
ar
o
u
n
d
t
h
e
cu
r
r
en
t
co
n
tr
o
l
s
eq
u
en
ce
u
s
i
n
g
a
s
ec
o
n
d
-
o
r
d
er
T
ay
lo
r
ex
p
an
s
io
n
:
ℒ
(
+
)
≈
ℒ
(
)
+
∇
ℒ
(
)
+
1
2
(
1
6
)
w
h
er
e
,
is
th
e
s
ea
r
ch
d
ir
ec
t
io
n
an
d
is
a
p
o
s
itiv
e
-
d
ef
i
n
ite
ap
p
r
o
x
i
m
atio
n
o
f
th
e
Hess
ia
n
o
f
th
e
L
a
g
r
an
g
ian
,
u
p
d
ated
b
y
a
B
F
GS
-
t
y
p
e
f
o
r
m
u
la.
T
h
e
eq
u
ality
an
d
in
eq
u
alit
y
c
o
n
s
tr
ain
ts
ar
e
lin
ea
r
ized
at
,
l
ea
d
in
g
to
an
ap
p
r
o
x
im
ati
n
g
q
u
ad
r
atic
p
r
o
g
r
am
m
i
n
g
(
QP
)
s
u
b
p
r
o
b
le
m
o
f
t
h
e
f
o
r
m
.
min
∇
ℒ
(
)
+
1
2
,
.
(
)
+
∇
(
)
=
0
,
(
)
+
∇
(
)
≤
0
(
1
7
)
I
n
th
e
i
m
p
le
m
e
n
tatio
n
u
s
ed
i
n
t
h
is
w
o
r
k
,
t
h
e
d
y
n
a
m
ics
(
1
2
)
ar
e
em
b
ed
d
ed
in
t
h
e
p
r
ed
ictio
n
m
o
d
el
t
h
a
t
co
n
s
tr
u
ct
s
(
)
,
an
d
th
e
v
elo
cit
y
b
o
u
n
d
s
(
1
3
)
ar
e
h
an
d
led
as
s
i
m
p
le
b
o
x
co
n
s
tr
ain
t
s
.
I
n
th
at
c
ase,
(
1
7
)
r
ed
u
ce
s
to
a
Q
P
w
it
h
b
o
u
n
d
co
n
s
tr
ain
ts
o
n
+
;
its
o
b
j
ec
tiv
e
s
till
h
a
s
th
e
s
tan
d
ar
d
f
o
r
m
(
1
6
)
w
it
h
in
ter
p
r
eted
as a
n
ap
p
r
o
x
i
m
ate
Hess
ia
n
o
f
t
h
e
L
ag
r
a
n
g
ia
n
.
T
h
e
g
r
ad
ien
t
o
f
th
e
co
s
t
w
it
h
r
esp
ec
t
to
th
e
co
n
tr
o
l
v
ec
to
r
is
co
m
p
u
ted
n
u
m
er
ical
l
y
b
y
a
f
i
n
ite
-
d
if
f
er
e
n
ce
ap
p
r
o
x
i
m
atio
n
:
[
∇
(
)
]
≈
(
+
)
−
(
)
,
≪
1
,
(
1
8
)
w
h
er
e
,
is
th
e
u
n
it
v
ec
to
r
w
it
h
1
at
in
d
ex
j
an
d
0
else
w
h
er
e.
A
f
ter
s
o
lv
in
g
th
e
QP
,
th
e
c
o
n
tr
o
l
s
eq
u
en
ce
is
u
p
d
ated
as
:
+
1
=
+
,
(
1
9
)
w
h
er
e
,
∈
(
0
,
1
]
is
th
e
s
tep
s
ize
o
b
tai
n
ed
f
r
o
m
a
lin
e
-
s
ea
r
ch
p
r
o
ce
d
u
r
e
to
en
s
u
r
e
s
u
f
f
icie
n
t
d
ec
r
ea
s
e
o
f
a
s
u
itab
le
m
er
it
f
u
n
ctio
n
b
u
ilt
f
r
o
m
,
,
an
d
.
A
t
ea
c
h
s
a
m
p
l
in
g
ti
m
e,
o
n
l
y
t
h
e
f
ir
s
t
co
n
tr
o
l
in
p
u
t
i
n
+
1
is
ap
p
lied
t
o
th
e
r
o
b
o
t,
an
d
th
e
r
em
ai
n
i
n
g
p
ar
t
o
f
th
e
s
eq
u
e
n
ce
is
s
h
i
f
ted
an
d
u
s
ed
to
w
ar
m
-
s
tar
t
t
h
e
n
e
x
t
SQP
iter
atio
n
.
4.
SI
M
UL
AT
I
O
N
SE
T
UP
AN
D
RE
SU
L
T
S
A
ll
r
o
b
o
ts
i
n
th
e
f
o
r
m
at
io
n
(
b
o
th
lead
e
r
an
d
f
o
llo
w
er
s
)
s
h
ar
e
a
co
m
m
o
n
co
n
tr
o
l
s
tr
u
ctu
r
e
b
ased
o
n
a
DM
P
C
co
s
t
f
u
n
ctio
n
o
p
ti
m
iz
ed
u
s
i
n
g
SQP
.
T
h
e
co
s
t
f
u
n
ct
io
n
is
d
e
f
in
ed
b
y
(
5
)
-
(
1
1
)
.
T
h
is
f
u
n
ctio
n
e
n
s
u
r
es
k
e
y
o
p
er
atio
n
al
o
b
j
ec
tiv
es:
r
ef
er
en
ce
tr
aj
ec
to
r
y
tr
ac
k
i
n
g
,
co
llis
io
n
a
v
o
id
an
ce
,
f
o
r
m
at
io
n
s
h
ap
e
m
ai
n
ten
a
n
ce
,
an
d
s
tab
le
co
n
v
er
g
e
n
ce
.
T
h
e
s
e
ar
e
f
u
n
d
a
m
e
n
tal
g
o
al
s
an
d
co
m
m
o
n
ch
alle
n
g
e
s
th
at
an
y
r
o
b
o
t
f
o
r
m
atio
n
co
n
tr
o
l s
y
s
te
m
m
u
s
t a
d
d
r
ess
.
4
.
1
.
Si
m
ula
t
io
n set
up
4
.
1
.
1
.
F
o
rm
a
t
io
n t
o
po
lo
g
y
a
n
d r
ef
er
ence
t
ra
j
ec
t
o
r
y
T
h
e
tr
aj
ec
t
o
r
y
o
f
th
e
lead
er
r
o
b
o
t
is
o
b
tain
ed
as
t
h
e
r
esu
lt
o
f
a
p
ath
-
p
la
n
n
in
g
p
r
o
b
le
m
f
r
o
m
t
h
e
s
tar
t
p
o
in
t
to
t
h
e
g
o
al
p
o
in
t
o
n
a
2
D
en
v
ir
o
n
m
en
ta
l
m
ap
w
it
h
s
tatic
o
b
s
tacle
s
,
g
e
n
er
ated
b
y
th
e
∗
al
g
o
r
ith
m
co
m
b
i
n
ed
w
it
h
co
v
ar
ia
n
t
Ha
m
ilto
n
ian
o
p
ti
m
izatio
n
f
o
r
m
o
tio
n
p
lan
n
in
g
(
C
HOM
P
)
o
p
ti
m
izatio
n
[
2
3
]
.
T
h
is
tr
aj
ec
to
r
y
th
e
n
s
er
v
e
s
as
a
v
i
r
tu
al
r
ef
er
en
ce
p
at
h
.
T
h
e
lead
er
s
o
lv
es
an
o
p
ti
m
iza
tio
n
p
r
o
b
lem
to
tr
ac
k
t
h
e
g
en
er
ated
tr
aj
ec
to
r
y
w
h
ile
s
i
m
u
ltan
eo
u
s
l
y
tr
an
s
m
i
tti
n
g
its
p
r
ed
icte
d
s
tate
in
f
o
r
m
atio
n
to
its
n
ei
g
h
b
o
r
in
g
f
o
llo
w
er
r
o
b
o
ts
.
E
ac
h
n
e
ig
h
b
o
r
in
g
f
o
llo
w
er
also
s
o
lv
e
s
it
s
o
w
n
o
p
ti
m
izatio
n
p
r
o
b
le
m
to
tr
ac
k
it
s
v
ir
tu
al
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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1
6
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elec
o
m
m
u
n
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o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
24
,
No
.
3
,
J
u
n
e
20
26
:
1
037
-
1
0
4
7
1042
lead
er
an
d
s
u
b
s
eq
u
e
n
tl
y
s
h
ar
e
s
its
p
r
ed
icted
s
tate
i
n
f
o
r
m
ati
o
n
w
ith
th
e
n
e
x
t
f
o
llo
w
er
s
.
T
h
e
r
esu
lti
n
g
s
y
s
te
m
to
p
o
lo
g
y
f
o
r
m
s
a
tr
ee
-
li
k
e
co
m
m
u
n
icatio
n
s
tr
u
ctu
r
e
as i
llu
s
tr
ated
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
T
r
ee
s
y
s
te
m
to
p
o
lo
g
y
T
h
e
s
y
s
te
m
ad
o
p
ts
a
h
ier
ar
ch
ical
s
tr
u
ct
u
r
e,
w
h
er
e
r
o
b
o
t
1
s
er
v
es
as
a
v
ir
tu
al
lead
er
.
No
g
lo
b
al
b
r
o
ad
ca
s
tin
g
o
r
co
n
tr
o
l
s
ig
n
al
ex
ch
a
n
g
e
ex
is
ts
a
m
o
n
g
r
o
b
o
ts
,
en
s
u
r
i
n
g
a
f
u
ll
y
d
is
tr
ib
u
ted
a
r
ch
itect
u
r
e
s
u
itab
le
f
o
r
DM
P
C
.
T
h
e
p
h
y
s
ical
lead
er
f
o
llo
w
s
a
p
r
ed
ef
in
ed
tr
aj
ec
t
o
r
y
an
d
s
h
ar
es
its
p
r
ed
icted
s
tate
s
eq
u
en
ce
[
0
:
]
w
it
h
d
ir
ec
tl
y
co
n
n
ec
ted
f
o
ll
o
w
er
s
.
First
-
la
y
er
f
o
llo
w
er
s
r
ec
eiv
e
th
i
s
tr
aj
ec
to
r
y
an
d
s
o
lv
e
lo
ca
l
DM
P
C
p
r
o
b
lem
s
in
co
r
p
o
r
atin
g
f
o
r
m
a
tio
n
-
k
ee
p
i
n
g
,
o
b
s
tacle
av
o
id
a
n
ce
v
ia
b
ar
r
ier
f
u
n
ctio
n
s
,
a
n
d
a
L
y
ap
u
n
o
v
-
b
ased
ter
m
i
n
al
co
s
t.
Seco
n
d
-
la
y
er
f
o
llo
w
er
s
,
d
is
co
n
n
ec
ted
f
r
o
m
t
h
e
lead
er
,
o
p
tim
ize
b
ased
o
n
n
eig
h
b
o
r
co
n
s
e
n
s
u
s
,
o
b
s
tacle
av
o
id
an
ce
,
an
d
ter
m
i
n
al
s
tab
ili
t
y
.
Af
ter
o
b
tain
i
n
g
t
h
e
m
o
tio
n
tr
aj
ec
to
r
y
,
to
v
er
if
y
th
e
p
r
o
p
o
s
ed
m
o
d
el
’
s
ca
p
ab
ilit
y
o
f
av
o
i
d
in
g
s
tatic
o
b
s
tacle
s
,
f
o
u
r
ad
d
itio
n
al
o
b
s
tacle
s
o
f
d
if
f
er
e
n
t
s
izes
a
n
d
s
h
ap
es
w
er
e
in
tr
o
d
u
ce
d
in
th
e
s
i
m
u
latio
n
.
T
h
ese
o
b
s
tacle
s
w
er
e
p
lace
d
ad
j
ac
en
t
to
o
r
o
v
er
lap
p
in
g
th
e
p
r
ev
io
u
s
l
y
g
e
n
er
ated
tr
aj
ec
to
r
y
(
Fig
u
r
e
2
)
.
I
n
th
is
w
a
y
,
th
e
ex
p
er
i
m
en
t
e
v
al
u
ates
b
o
th
th
e
ab
ilit
y
o
f
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
to
av
o
id
s
tatic
o
b
s
tacle
s
en
co
u
n
ter
ed
d
u
r
in
g
m
o
tio
n
a
n
d
its
ca
p
ab
ilit
y
to
m
ain
tai
n
th
e
f
o
r
m
at
io
n
o
f
t
h
e
r
o
b
o
t te
am
.
Fig
u
r
e
2
.
E
n
v
ir
o
n
m
e
n
tal
m
ap
co
n
tain
i
n
g
th
e
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