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3
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4
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[
5
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[
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[
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[
4
,
8
-
1
1
]
.
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tu
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in
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in
p
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[
1
2
,
1
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u
m
v
alu
es
f
o
r
elem
e
n
ts
o
f
L
QR
m
atr
ices,
s
u
c
h
as
a
p
ar
ticle
s
war
m
in
s
p
ir
e
d
ev
o
l
u
tio
n
ar
y
alg
o
r
ith
m
(
PS
-
E
A)
,
p
ar
ticle
s
war
m
o
p
t
im
izatio
n
(
PS
O)
,
g
e
n
etic
al
g
o
r
ith
m
(
GA)
[
1
4
]
,
c
o
m
b
in
atio
n
o
f
s
im
u
lated
an
n
ea
lin
g
(
SA)
an
d
GA
[
15
]
,
d
if
f
er
en
tial
ev
alu
atio
n
(
DE
)
[
16
]
an
d
an
t
co
lo
n
y
o
p
tim
iz
atio
n
(
AC
O)
[
17
]
.
T
h
ese
in
tellig
en
t
o
p
tim
izatio
n
to
o
ls
m
ak
e
th
e
L
QR
co
n
tr
o
ller
s
y
s
tem
v
er
y
r
o
b
u
s
t,
an
d
in
s
en
s
itiv
e
to
n
o
is
y
an
d
/o
r
m
is
s
in
g
d
ata.
B
ac
ter
ia
f
o
r
ag
in
g
o
p
tim
izatio
n
alg
o
r
ith
m
(
B
FOA)
is
a
n
ew
tu
n
in
g
alg
o
r
ith
m
th
at
ca
n
b
e
ap
p
lied
to
o
p
tim
ize
th
e
co
s
t
f
u
n
ctio
n
o
f
s
ev
er
al
p
r
o
b
lem
s
in
d
if
f
er
e
n
t
ap
p
licatio
n
f
ie
ld
s
.
T
h
e
B
FOA
is
a
co
m
b
in
ato
r
ial
o
p
tim
i
za
tio
n
alg
o
r
ith
m
wh
ich
ap
p
lied
to
a
ch
iev
e
th
e
b
est
g
l
o
b
al
s
o
lu
tio
n
f
o
r
th
e
p
r
o
p
o
s
ed
L
QR
co
n
tr
o
ller
.
I
t
is
wo
r
th
c
o
n
s
id
er
in
g
th
at
th
e
r
e
is
a
s
ig
n
if
ican
t
im
p
r
o
v
em
e
n
t
in
t
h
e
c
o
n
tr
o
l
r
esp
o
n
s
e
o
f
th
e
L
QR
co
n
tr
o
ller
is
ac
h
iev
ed
b
y
u
s
in
g
th
ese
tu
n
in
g
alg
o
r
ith
m
s
,
h
o
wev
er
,
th
e
r
esear
ch
wo
r
k
is
s
till
o
p
en
to
ex
p
lo
r
e
f
o
r
f
u
r
t
h
er
c
o
n
tr
o
ller
im
p
r
o
v
em
e
n
ts
an
d
d
ev
elo
p
m
e
n
ts
.
I
n
th
is
r
ese
ar
c
h
,
two
t
u
n
i
n
g
alg
o
r
ith
m
s
,
GA
an
d
B
FOA
ar
e
u
tili
ze
d
to
im
p
r
o
v
e
th
e
b
eh
av
i
o
r
o
f
th
e
L
QR
co
n
tr
o
ller
.
T
h
e
r
em
ain
d
er
o
f
th
e
p
a
p
er
is
o
r
g
an
is
ed
as
f
o
llo
ws:
s
ec
tio
n
2
p
r
esen
ts
m
o
d
ellin
g
an
d
d
y
n
am
ics
o
f
th
e
p
r
o
p
o
s
ed
two
-
wh
ee
led
s
elf
-
b
alan
cin
g
h
u
m
an
r
o
b
o
t.
I
n
s
ec
tio
n
3
,
th
e
tech
n
iq
u
e
o
f
th
e
co
n
tr
o
ller
s
y
s
tem
is
in
tr
o
d
u
ce
d
.
Sectio
n
4
,
p
r
esen
t
s
o
p
tim
izatio
n
m
eth
o
d
s
o
f
L
QR
co
n
tr
o
ller
.
Sectio
n
5
an
d
s
ec
tio
n
6
in
tr
o
d
u
ce
co
n
tr
o
ller
d
esig
n
a
n
d
s
im
u
lat
io
n
r
esu
lts
o
f
GA
-
L
QR
an
d
s
ec
tio
n
7
in
tr
o
d
u
ce
B
FOA
-
L
QR
co
n
tr
o
ller
s
f
o
r
th
e
r
o
b
o
t sy
s
tem
r
esp
ec
tiv
ely
.
C
o
n
clu
s
io
n
s
an
d
f
u
t
u
r
e
wo
r
k
a
r
e
p
r
esen
ted
in
s
ec
tio
n
8
.
2.
SYST
E
M
M
O
D
E
L
I
NG
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
a
walk
in
g
r
o
b
o
t
d
e
p
en
d
s
o
n
th
e
r
eli
a
b
ilit
y
o
f
th
e
s
y
s
tem
m
o
d
elin
g
an
d
r
o
b
u
s
tn
ess
o
f
t
h
e
co
n
tr
o
ller
d
esig
n
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
two
-
wh
ee
led
Seg
way
p
er
s
o
n
al
r
o
b
o
t
co
m
p
o
s
es
m
ain
ly
o
f
an
elec
tr
ical
s
u
b
s
y
s
tem
an
d
m
ec
h
an
ical
s
u
b
s
y
s
tem
.
Fig
u
r
e
1
d
em
o
n
s
tr
at
e
s
g
r
ap
h
ic
m
o
d
el
o
f
th
e
Seg
way
r
o
b
o
t.
I
n
th
is
s
ec
tio
n
,
th
e
m
o
tio
n
eq
u
atio
n
o
f
th
e
in
v
er
ted
p
en
d
u
lu
m
is
d
er
iv
e
d
an
d
th
e
d
y
n
am
ic
m
o
d
el
o
f
th
e
m
o
to
r
s
is
f
o
r
m
u
lated
.
T
h
e
m
o
to
r
m
o
d
el
is
th
en
u
tili
ze
d
in
f
o
r
m
u
latio
n
th
e
d
y
n
am
ic
m
o
d
el
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
2
6
4
2
-
2653
2644
th
e
p
er
s
o
n
al
r
o
b
o
t
s
ch
em
e
to
g
iv
e
a
f
u
n
ctio
n
al
r
elatio
n
s
h
i
p
b
etwe
en
a
p
p
lied
v
o
ltag
e
to
t
h
e
DC
m
o
to
r
s
a
n
d
ad
ju
s
tin
g
m
ag
n
etic
to
r
q
u
e
r
eq
u
ir
ed
to
s
tab
ilize
th
e
h
u
m
an
m
o
b
ile
r
o
b
o
t.
2
.
1
.
E
lect
rica
l su
bs
y
s
t
em
mo
delin
g
T
h
e
m
ain
p
ar
t
o
f
th
e
elec
tr
ic
s
u
b
s
y
s
tem
is
th
e
D
C
m
o
to
r
s
,
wh
ich
ar
e
u
s
ed
to
r
o
tate
th
e
lef
t
an
d
r
ig
h
t
wh
ee
l
o
f
th
e
r
o
b
o
t.
T
h
e
elec
t
r
ic
cir
cu
it
o
f
th
e
DC
m
o
to
r
is
s
h
o
wn
in
Fig
u
r
e
2
.
A
p
p
ly
in
g
v
o
ltag
e
(
)
to
th
e
m
o
to
r
te
r
m
in
als
g
en
er
ates
a
cu
r
r
en
t
(
)
(
)
in
th
e
m
o
to
r
ar
m
at
u
r
e.
T
h
e
ex
cited
m
o
to
r
p
r
o
d
u
c
es
a
to
r
q
u
e
(
)
g
o
v
er
n
ed
b
y
th
e
f
o
llo
win
g
r
el
atio
n
s
h
ip
.
=
(
1
)
wh
er
e
is
to
r
q
u
e
c
o
n
s
tan
t
(
/
)
.
T
h
e
b
ac
k
elec
tr
o
m
o
tiv
e
(
em
f
)
v
o
ltag
e
(
)
p
r
o
d
u
ce
d
in
th
e
m
o
to
r
c
o
il
can
be
ap
p
r
o
x
i
m
ated
as a
lin
ea
r
f
u
n
ctio
n
o
f
m
o
to
r
an
g
u
lar
v
elo
city
̇
(
/
)
,
as f
o
llo
ws:
=
̇
(
2
)
wh
er
e
is
to
r
q
u
e
co
n
s
tan
t
(
/
)
.
Ap
p
ly
in
g
Kir
ch
o
f
f
’
s
v
o
ltag
e
law
to
th
e
m
o
to
r
cir
cu
it
s
h
o
wn
in
Fig
u
r
e
2
y
ield
s
th
e
f
o
llo
win
g
ex
p
r
ess
io
n
:
V
a
=
Ri
+
L
di
dt
+
V
e
(
3
)
I
t
is
wo
r
th
co
n
s
id
er
in
g
th
at
th
e
d
y
n
am
ic
o
f
th
e
m
ec
h
an
ica
l
s
y
s
tem
i
s
co
n
s
id
er
ed
s
lo
w
c
o
m
p
ar
ed
to
th
at
o
f
elec
tr
ical
s
y
s
tem
,
th
er
ef
o
r
e
,
t
h
e
cu
r
r
en
t
tr
a
n
s
ien
ts
o
f
th
e
s
y
s
tem
ca
n
b
e
o
m
itted
.
Hen
ce
,
s
o
lv
in
g
(
3
)
f
o
r
th
e
cu
r
r
e
n
t y
ield
s
:
=
−
(
4
)
b
as
ed
o
n
(
2
)
,
(
4
)
ca
n
b
e
wr
itte
n
as f
o
llo
ws:
i
=
V
a
R
−
K
e
R
θ
̇
(
5
)
s
u
b
s
titu
tin
g
(
5
)
in
(
1
)
g
iv
es a
n
ex
p
r
ess
io
n
f
o
r
th
e
to
r
q
u
e
p
r
o
d
u
ce
d
b
y
DC
m
o
to
r
:
C
=
K
m
R
V
a
−
K
m
K
e
R
θ
̇
(
6
)
Fig
u
r
e
1
.
Mo
d
el
o
f
th
e
two
-
w
h
ee
led
r
o
b
o
t
[
1
8
]
Fig
u
r
e
2
.
E
lectr
ic
m
o
d
el
cir
c
u
it o
f
DC
m
o
to
r
2
.
2
.
M
ec
ha
nica
l su
bs
y
s
t
em
m
o
delin
g
I
t
co
n
s
is
ts
o
f
ch
ass
is
,
wh
ic
h
b
eh
av
io
r
s
as
in
v
er
ted
p
en
d
u
lu
m
,
an
d
th
e
lef
t
an
d
r
ig
h
t
wh
ee
ls
.
I
n
th
is
s
tu
d
y
,
th
e
p
a
r
am
eter
o
f
m
ass
,
r
ad
iu
s
an
d
m
o
m
e
n
t
o
f
in
er
tia
o
f
t
h
e
two
wh
ee
ls
ar
e
ass
u
m
ed
th
e
s
am
e.
B
ased
o
n
th
is
ass
u
m
p
tio
n
th
e
d
y
n
a
m
ic
m
o
d
elin
g
o
f
th
e
r
i
g
h
t
wh
ee
l
is
th
e
s
am
e
as
th
a
t
o
f
th
e
lef
t
wh
ee
l.
I
n
th
is
r
esear
ch
,
f
o
r
m
u
latio
n
o
f
th
e
r
ig
h
t
wh
ee
l
m
o
d
el
is
co
n
s
id
er
ed
in
d
et
ail.
I
t
is
wo
r
th
co
n
s
id
er
in
g
th
at
th
e
m
o
d
elin
g
s
tr
ateg
y
o
f
th
e
m
ec
h
an
ical
r
o
b
o
t
s
u
b
s
y
s
tem
is
b
ased
o
n
an
id
ea
th
at
th
e
d
y
n
am
ics
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
B
a
la
n
cin
g
a
S
e
g
w
a
y
r
o
b
o
t
u
s
in
g
LQR
co
n
tr
o
ller
b
a
s
ed
o
n
g
en
etic
a
n
d
…
(
I
b
r
a
h
im
K
.
Mo
h
a
mme
d
)
2645
th
e
in
v
e
r
ted
p
en
d
u
lu
m
an
d
w
h
ee
ls
ar
e
m
o
d
eled
s
ep
ar
ately
at
th
e
b
eg
in
n
i
n
g
,
an
d
th
e
n
e
q
u
atio
n
s
o
f
m
o
tio
n
wh
ich
co
m
p
letely
d
es
cr
ib
e
th
e
d
y
n
am
ic
b
eh
av
i
o
r
o
f
th
e
s
y
s
tem
ar
e
d
er
i
v
ed
[
19
].
2
.
2
.
1
.
Wheel
m
o
del
Fig
u
r
e
3
p
r
esen
ts
th
e
f
r
ee
b
o
d
y
d
iag
r
am
o
f
th
e
lef
t
an
d
r
ig
h
t
wh
ee
ls
f
o
r
th
e
m
o
b
ile
Seg
way
tr
an
s
p
o
r
t
s
y
s
tem
.
Usi
n
g
s
ec
o
n
d
New
to
n
’
s
law
o
f
m
o
tio
n
,
th
e
s
u
m
o
f
th
e
ex
ter
n
al
f
o
r
ce
s
(
)
ex
er
ted
o
n
th
e
w
h
ee
l,
wh
ich
g
o
v
e
r
n
s
its
tr
an
s
latio
n
m
o
tio
n
in
t
h
e
h
o
r
izo
n
tal
x
-
d
ir
e
ctio
n
is
g
iv
en
b
y
[
2
0
]
.
∑
F
x
=
M
w
a
(
7
)
M
w
x
̈
=
H
f
−
H
(
8
)
Fig
u
r
e
3
.
Fre
e
b
o
d
y
d
iag
r
am
o
f
th
e
r
o
b
o
t w
h
ee
ls
wh
er
e
(
)
is
th
e
w
h
ee
l
m
ass
o
f
th
e
r
o
b
o
t,
a
is
th
e
g
r
av
ity
ac
ce
ler
atio
n
(
/
2
)
an
d
is
th
e
f
r
ictio
n
f
o
r
ce
b
etwe
en
g
r
o
u
n
d
an
d
w
h
ee
ls
(
)
.
W
h
ile
th
e
r
o
tatio
n
al
m
o
ti
o
n
o
f
th
e
wh
ee
l is g
iv
e
n
b
y
: g
o
∑
M
o
=
I
w
θ
̈
w
(
9
)
I
w
θ
̈
w
=
C
−
H
f
r
(
1
0
)
wh
er
e
(
2
)
an
d
̈
(
/
2
)
ar
e
m
o
m
e
n
t
o
f
i
n
er
tia
an
d
ac
ce
ler
atio
n
o
f
th
e
wh
ee
ls
r
esp
ec
tiv
ely
,
an
d
r
is
th
e
r
ad
iu
s
o
f
wh
ee
l
(
)
.
B
ased
o
n
(
6
)
,
th
e
a
b
o
v
e
eq
u
atio
n
b
ec
o
m
es:
I
w
θ
̈
w
=
K
m
R
V
a
−
K
m
K
e
R
θ
̇
w
−
H
f
r
(
1
1
)
H
f
=
K
m
Rr
V
a
−
K
m
K
e
Rr
θ
̇
w
−
I
w
r
θ
̈
(
1
2
)
wh
er
e
̇
is
th
e
an
g
u
lar
v
elo
city
o
f
wh
ee
l
(
/
)
.
Su
b
s
titu
tin
g
(
1
2
)
i
n
to
(
8
)
y
ield
s
(
1
3
)
an
d
(
1
4
)
f
o
r
th
e
lef
t
an
d
r
ig
h
t w
h
ee
ls
r
esp
ec
tiv
ely
.
M
w
x
̈
=
K
m
Rr
V
a
−
K
m
K
e
Rr
θ
̇
w
−
I
w
r
θ
̈
w
−
H
L
(
1
3
)
M
w
x
̈
=
K
m
Rr
V
a
−
K
m
K
e
Rr
θ
̇
w
−
I
w
r
θ
̈
w
−
H
R
(
1
4
)
B
ec
au
s
e
th
e
ce
n
ter
o
f
th
e
r
o
b
o
t
wh
ee
l
is
ac
ted
b
y
th
e
lin
ea
r
m
o
tio
n
,
th
e
an
g
u
lar
r
o
tatio
n
o
f
th
e
wh
ee
l
ca
n
b
e
tr
an
s
f
o
r
m
ed
in
to
lin
ea
r
m
o
tio
n
b
y
th
e
f
o
llo
win
g
s
im
p
le
tr
an
s
f
o
r
m
atio
n
,
̈
=
̈
→
̈
=
̈
/
,
̇
=
̇
→
̇
=
̇
/
.
B
y
th
e
lin
ea
r
tr
an
s
f
o
r
m
atio
n
,
(
1
3
)
a
n
d
(
1
4
)
b
ec
o
m
e
as f
o
llo
ws:
M
w
x
̈
=
K
m
Rr
V
a
−
K
m
K
e
R
r
2
x
̇
w
−
I
w
r
2
x
̈
−
H
L
(
1
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
2
6
4
2
-
2653
2646
M
w
x
̈
=
K
m
Rr
V
a
−
K
m
K
e
R
r
2
x
̇
w
−
I
w
r
2
x
̈
−
H
R
(
1
6
)
Ad
d
in
g
(
1
5
)
a
n
d
(
1
6
)
to
g
eth
e
r
y
ield
s
th
e
f
o
llo
win
g
ex
p
r
ess
io
n
,
2
(
+
2
)
̈
=
2
−
2
2
̇
−
(
+
)
(
1
7
)
2
.
2
.
2
.
Cha
s
s
is
m
o
del
T
h
e
ch
ass
is
o
f
th
e
m
o
b
ile
r
o
b
o
t
ca
n
b
e
m
o
d
eled
as
an
in
v
er
ted
p
en
d
u
lu
m
,
Fig
u
r
e
4
p
r
esen
ts
th
e
f
r
ee
b
o
d
y
d
iag
r
a
m
o
f
th
e
c
h
ass
is
.
Ag
ain
,
b
ased
o
n
New
to
n
’
s
law
o
f
m
o
tio
n
,
th
e
s
u
m
o
f
f
o
r
ce
s
ac
tin
g
o
n
th
e
ch
ass
is
in
th
e
h
o
r
izo
n
tal
x
-
d
ir
ec
tio
n
is
g
iv
en
b
y
[
2
0
]
:
∑
F
x
=
M
p
x
̈
(
1
8
)
M
p
x
̈
=
H
L
+
H
R
−
M
p
l
θ
p
̈
c
os
θ
p
+
M
p
l
θ
̇
2
p
s
in
θ
p
(
1
9
)
wh
er
e
is
th
e
wh
ee
l
m
ass
o
f
th
e
r
o
b
o
t
(
)
an
d
is
th
e
r
o
tatio
n
al
an
g
le
o
f
th
e
ch
ass
is
(
)
.
T
h
e
a
b
o
v
e
eq
u
atio
n
is
r
ea
r
r
an
g
e
d
as f
o
llo
ws:
H
L
+
H
R
=
M
p
x
̈
+
M
p
l
θ
̈
p
c
os
θ
p
−
M
p
l
θ
̇
2
p
s
in
θ
p
(
2
0
)
T
h
e
s
u
m
o
f
p
er
p
en
d
icu
lar
f
o
r
c
es a
ctin
g
o
n
th
e
p
en
d
u
lu
m
is
:
∑
F
p
=
M
p
x
̈
c
os
θ
p
(
2
1
)
(
+
)
+
(
+
)
−
−
̈
̈
=
̈
(
2
2
)
wh
er
e
an
d
ar
e
th
e
r
ea
ctio
n
f
o
r
ce
s
b
etwe
en
lef
t
a
n
d
r
i
g
h
t
wh
ee
l
an
d
c
h
ass
is
(
)
r
esp
ec
tiv
el
y
an
d
̈
is
ch
ass
is
an
g
u
lar
ac
ce
ler
atio
n
(
/
2
)
,
s
u
m
o
f
m
o
m
en
ts
ar
o
u
n
d
th
e
ce
n
ter
o
f
p
en
d
u
lu
m
m
ass
is
g
iv
e
n
b
y
:
∑
M
o
=
I
p
θ
̈
p
(
2
3
)
I
p
θ
̈
p
=
−
(
H
L
+
H
R
)
l
c
os
θ
p
−
(
P
L
+
P
R
)
l
s
in
θ
p
−
(
C
L
+
C
R
)
(
2
4
)
w
h
e
r
e
a
n
d
ar
e
th
e
m
o
to
r
to
r
q
u
e
ap
p
lied
to
lef
t
an
d
r
ig
h
t
wh
ee
ls
r
esp
ec
tiv
ely
(
)
t
h
e
m
o
to
r
t
o
r
q
u
e
e
x
e
r
t
ed
o
n
t
h
e
p
en
d
u
l
u
m
ap
p
li
e
d
a
s
d
e
f
in
ed
i
n
(
6
)
a
n
d
a
f
te
r
l
i
n
e
ar
t
r
a
n
s
f
o
r
m
a
t
i
o
n
,
C
L
+
C
R
=
2
K
m
R
V
a
−
2
K
m
K
e
R
x
̇
r
(
2
5
)
s
u
b
s
titu
tin
g
(
2
5
)
i
n
to
(
2
4
)
y
ield
s
,
I
p
θ
̈
p
−
2
K
m
K
e
R
x
̇
r
+
2
K
m
R
V
a
=
−
(
H
L
+
H
R
)
l
c
os
θ
p
(
P
L
+
P
R
)
l
s
in
θ
p
(
2
6
)
s
u
b
s
titu
te
(
2
6
)
in
(
2
2
)
af
ter
m
u
ltip
ly
(
2
2
)
b
y
(
−
)
y
ield
s
:
I
p
θ
̈
p
−
2
K
m
K
e
R
x
̇
r
+
2
K
m
R
V
a
+
M
p
gl
s
in
θ
p
+
M
p
l
2
θ
̈
p
̈
=
−
M
p
l
x
̈
c
os
θ
p
(
2
7
)
Su
m
o
f
m
o
m
en
ts
ar
o
u
n
d
t
h
e
c
en
ter
o
f
p
en
d
u
lu
m
m
ass
is
g
iv
en
:
−
M
p
l
x
̈
c
os
θ
p
=
(
I
p
+
M
p
l
2
)
θ
̈
p
−
2
K
m
K
e
R
r
2
x
̇
+
2
K
m
Rr
V
a
+
M
p
gl
s
in
θ
p
(
2
8
)
to
elim
in
ate
th
e
ter
m
(
+
)
f
r
o
m
th
e
m
o
to
r
d
y
n
am
ic
(
2
0
)
is
s
u
b
s
titu
ted
in
(
1
7
)
.
2
K
m
Rr
V
a
=
(
2
M
w
+
I
w
r
2
+
M
p
)
x
̈
+
2
K
m
K
e
R
r
2
x
̇
+
M
p
l
θ
̈
p
c
os
θ
p
−
M
p
l
θ
̇
2
p
̈
s
in
θ
p
(
2
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
B
a
la
n
cin
g
a
S
e
g
w
a
y
r
o
b
o
t
u
s
in
g
LQR
co
n
tr
o
ller
b
a
s
ed
o
n
g
en
etic
a
n
d
…
(
I
b
r
a
h
im
K
.
Mo
h
a
mme
d
)
2647
f
o
r
p
u
r
p
o
s
e
o
f
d
esig
n
a
lin
e
ar
co
n
tr
o
l
s
y
s
tem
,
th
e
s
y
s
tem
d
y
n
am
ic
(
2
8
)
an
d
(
2
9
)
a
r
e
lin
ea
r
ized
a
b
o
u
t
an
o
p
er
atin
g
p
o
in
t
b
ased
o
n
th
e
ass
u
m
p
tio
n
=
+
wh
er
e
d
en
o
tes
an
an
g
le
m
ea
s
u
r
ed
f
r
o
m
th
e
v
er
tical
u
p
war
d
d
ir
ec
tio
n
.
T
h
er
ef
o
r
e,
=
−
,
=
−
1
an
d
(
/
)
2
=
0
f
o
r
p
u
r
p
o
s
e
o
f
s
tate
s
p
ac
e
r
ep
r
esen
tatio
n
,
t
h
e
d
y
n
a
m
ic
(
2
8
)
an
d
(
2
9
)
ar
e
r
ewr
itte
n
as f
o
llo
ws:
ϕ
̈
=
M
p
I
(
I
p
+
M
p
I
2
)
x
̈
+
2
K
m
K
e
Rr
(
I
p
+
M
p
I
2
)
x
̇
+
M
p
gI
Rr
(
I
p
+
M
p
I
2
)
ϕ
−
2
K
m
(
I
p
+
M
p
I
2
)
V
a
(
3
0
)
x
̈
=
2
K
m
Rr
K
w
V
a
−
2
K
m
K
e
R
r
2
K
w
x
̇
+
M
p
I
R
r
2
K
w
ϕ
̈
(
3
1
)
wh
er
e
=
2
+
2
/
2
.
Af
ter
a
s
er
ies o
f
alg
eb
r
aic
m
an
ip
u
latio
n
,
th
e
s
tate
eq
u
atio
n
b
ec
o
m
es:
[
̇
̈
̇
̈
]
=
[
0
1
0
0
1
(
−
−
2
)
2
2
2
0
0
0
0
1
(
−
)
2
0
0
1
0
]
[
̇
̇
]
+
[
0
2
(
+
2
−
)
0
2
(
−
)
]
(
3
2
)
wh
er
e,
1
=
2
,
=
2
+
2
2
+
an
d
=
[
+
2
2
(
+
2
)
]
.
I
t
is
wo
r
th
co
n
s
id
er
in
g
th
at
th
e
s
y
s
tem
m
o
d
elin
g
is
b
ased
o
n
th
e
s
u
p
p
o
s
itio
n
th
at
b
o
t
h
wh
ee
ls
o
f
th
e
walk
in
g
r
o
b
o
t a
r
e
ass
u
m
ed
in
s
tate
o
f
co
n
tact
with
th
e
g
r
o
u
n
d
an
d
with
o
u
t
s
lid
in
g
.
C
o
r
n
er
in
g
f
o
r
ce
s
p
r
o
d
u
ce
d
b
y
v
eh
icle
wh
ee
ls
d
u
r
in
g
co
r
n
er
i
n
g
ar
e
also
co
n
s
id
er
ed
n
eg
lig
ib
le
[
1
9
]
.
Fig
u
r
e
4
.
Fre
e
b
o
d
y
d
iag
r
am
o
f
th
e
ch
ass
is
3.
CO
NT
RO
L
L
E
R
T
E
CH
NIQ
UE
I
n
th
is
r
esear
ch
,
L
QR
tech
n
iq
u
e
is
u
tili
ze
d
to
im
p
lem
en
t
th
e
p
r
o
p
o
s
ed
r
o
b
o
t
co
n
tr
o
l
s
y
s
tem
.
L
QR
is
a
co
m
m
o
n
c
o
n
tr
o
ller
ap
p
r
o
ac
h
u
s
ed
ef
f
ec
tiv
ely
i
n
th
e
co
n
tr
o
l
ap
p
licatio
n
s
o
f
t
h
e
m
o
v
em
en
t
s
y
s
tem
s
.
Fig
u
r
e
5
s
h
o
ws
b
lo
ck
d
iag
r
am
o
f
th
e
Seg
way
r
o
b
o
t
co
n
tr
o
l
s
y
s
tem
b
ased
o
n
L
QR
co
n
tr
o
ller
.
T
h
e
s
tate
an
d
o
u
tp
u
t
m
atr
ix
eq
u
atio
n
s
d
escr
ib
in
g
t
h
e
Seg
way
r
o
b
o
t e
q
u
atio
n
s
o
f
m
o
tio
n
ar
e
g
iv
en
b
y
:
̇
(
)
=
(
)
+
(
)
(
3
3
)
(
)
=
(
)
+
(
)
(
3
4
)
w
h
e
r
e
(
)
,
(
)
,
(
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,
(
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a
r
e
t
h
e
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y
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t
e
m
,
i
n
p
u
t
,
o
u
t
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t
a
n
d
f
e
e
d
f
o
r
w
a
r
d
m
a
t
r
i
x
r
e
s
p
e
c
t
i
v
e
l
y
.
I
n
t
h
i
s
a
p
p
r
o
a
c
h
,
t
h
e
i
n
p
u
t
v
e
c
to
r
:
(
)
=
−
(
)
(
3
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
2
6
4
2
-
2653
2648
wh
er
e
=
[
1
2
3
4
]
is
an
o
p
tim
al
f
ee
d
b
ac
k
g
ain
m
atr
ix
o
f
th
e
co
n
tr
o
ller
u
s
ed
to
tr
ac
k
th
e
in
p
u
t
co
m
m
an
d
wh
ile
th
e
f
o
llo
win
g
p
er
f
o
r
m
an
ce
in
d
ex
:
=
∫
(
(
)
(
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(
)
+
(
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(
)
(
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∞
0
(
3
6
)
wh
er
e
(
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an
d
(
)
ar
e
weig
h
tin
g
s
tate
an
d
in
p
u
t
m
atr
ices
r
esp
ec
ti
v
ely
.
T
h
e
f
ee
d
b
ac
k
g
ain
m
atr
ix
K
c
an
b
e
d
eter
m
in
ed
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y
u
s
in
g
th
e
f
o
llo
win
g
:
=
−
1
(
3
7
)
wh
er
e
P
d
en
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tes th
e
s
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lu
tio
n
o
f
th
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llo
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icca
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=
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3
8
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T
h
e
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n
tr
o
ller
weig
h
tin
g
m
atr
ices
s
h
o
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ld
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e
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n
e
d
p
r
o
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er
ly
in
o
r
d
er
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m
in
im
ize
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e
f
o
ll
o
win
g
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e
r
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o
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m
an
ce
in
d
ex
)
(
J
:
=
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(
11
1
2
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22
2
2
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33
3
2
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44
4
2
+
2
)
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0
(
3
9
)
wh
er
e
11
,
22
,
33
an
d
44
q
r
ep
r
esen
t
th
e
weig
h
tin
g
elem
en
ts
o
f
p
o
s
itio
n
,
s
p
ee
d
,
an
g
le
a
n
d
an
g
u
lar
v
elo
city
o
f
th
e
p
r
o
p
o
s
ed
r
o
b
o
t
s
y
s
tem
r
e
s
p
ec
tiv
ely
.
I
t
is
wo
r
th
co
n
s
id
er
in
g
th
at
b
y
u
s
in
g
co
n
tr
o
ller
weig
h
tin
g
m
atr
ices
(
)
an
d
(
)
wh
ich
g
o
v
e
r
n
th
e
b
e
h
av
io
r
o
f
th
e
r
o
b
o
t
s
y
s
tem
s
tates
an
d
co
n
tr
o
l
ef
f
o
r
t
r
es
p
ec
tiv
ely
,
th
e
o
p
tim
al
L
QR
g
ain
m
atr
i
x
is
co
m
p
u
ted
b
ased
o
n
t
h
e
Ma
tlab
co
m
m
a
n
d
”
l
q
r
”.
Fig
u
r
e
5
.
Seg
way
r
o
b
o
t c
o
n
t
r
o
l sy
s
tem
u
s
in
g
L
QR
co
n
tr
o
ller
4.
L
Q
R
O
P
T
I
M
I
Z
A
T
I
O
N
M
E
T
H
O
DS
I
n
th
is
r
esear
ch
,
two
o
p
tim
izatio
n
alg
o
r
ith
m
s
,
GA
an
d
B
FOA,
ar
e
u
s
ed
to
tu
n
e
th
e
(
)
an
d
(
)
m
atr
ices
o
f
th
e
L
QR
co
n
tr
o
ller
,
wh
ich
ar
e
ad
o
p
ted
t
o
ca
lcu
late
th
e
g
ain
m
atr
ix
r
e
q
u
ir
ed
to
b
ala
n
ce
th
e
Seg
way
s
y
s
tem
.
B
a
s
ed
o
n
o
p
tim
ized
g
ain
m
atr
ix
a
g
o
o
d
o
u
tp
u
t tim
e
r
esp
o
n
s
e
with
m
in
im
al
o
f
r
is
e
tim
e
(
)
,
s
ettlin
g
tim
e
(
)
,
m
ax
im
u
m
o
v
er
s
h
o
o
t
(
)
an
d
s
tead
y
s
tate
er
r
o
r
(
)
c
an
b
e
in
v
esti
g
ated
.
4
.
1
.
G
enet
ic
a
lg
o
rit
h
m
GA
is
an
o
p
tim
izatio
n
tech
n
i
q
u
e
u
s
ed
to
f
in
d
g
lo
b
al
s
o
lu
tio
n
f
o
r
m
o
r
e
co
n
t
r
o
l
p
r
o
b
lem
s
.
B
ased
o
n
th
e
m
ec
h
an
is
m
s
o
f
n
atu
r
al
s
elec
tio
n
.
I
n
th
is
o
p
tim
izatio
n
ap
p
r
o
ac
h
,
th
e
s
o
lu
tio
n
s
p
ac
e
is
s
elec
ted
b
y
g
en
er
atin
g
a
p
o
p
u
latio
n
o
f
ca
n
d
id
ate
in
d
iv
id
u
als
to
f
in
d
o
p
tim
u
m
v
alu
es
f
o
r
th
e
p
r
o
b
lem
.
T
h
e
p
r
o
ce
d
u
r
e
o
f
GA
o
p
tim
izatio
n
m
eth
o
d
i
n
cl
u
d
es
th
r
ee
b
asic
s
tep
s
,
n
am
el
y
s
elec
tio
n
,
cr
o
s
s
o
v
er
an
d
m
u
tatio
n
.
B
y
ap
p
ly
in
g
th
ese
s
tag
es
n
ew
in
d
iv
id
u
als
ca
n
b
e
cr
ea
ted
,
wh
ich
,
co
u
ld
b
e
b
etter
th
an
th
eir
p
ar
en
ts
.
B
ased
o
n
th
e
f
itn
ess
f
u
n
ctio
n
o
f
th
e
s
y
s
tem
,
th
e
GA
s
tep
s
ar
e
r
e
p
ea
ted
f
o
r
m
an
y
g
e
n
er
at
io
n
s
a
n
d
ev
en
tu
ally
s
to
p
at
g
e
n
er
atin
g
ca
n
d
id
ate
in
d
iv
id
u
al
elem
en
ts
th
at
ca
n
r
ep
r
esen
t
th
e
b
est
s
o
lu
tio
n
f
o
r
th
e
ap
p
licatio
n
p
r
o
b
lem
[
1
4
]
.
Fig
u
r
e
6
s
h
o
ws th
e
g
r
ap
h
ical
illu
s
tr
atio
n
o
f
th
e
GA
lo
o
p
.
T
h
e
d
ef
i
n
itio
n
o
f
th
e
GA
s
tep
s
is
as
f
o
llo
ws
Ab
d
u
lla
[
14
]:
R
an
d
o
m
in
itial
p
o
p
u
latio
n
-
C
h
o
o
s
e
in
d
iv
id
u
als
f
o
r
m
atin
g
-
Ma
t
e
th
e
p
o
p
u
latio
n
to
g
en
e
r
ate
p
r
o
g
en
y
-
Mu
tate
p
r
o
g
e
n
y
-
New
in
d
iv
i
d
u
als
in
s
er
ted
in
to
p
o
p
u
latio
n
-
Ar
e
cr
iter
ia
s
atis
f
ied
?
-
E
n
d
o
f
s
o
lu
tio
n
s
ea
r
ch
i
n
g
.
E
ac
h
ch
r
o
m
o
s
o
m
e
r
ep
r
esen
ted
b
y
f
iv
e
r
ea
l
v
alu
e
ce
lls
th
at
co
r
r
esp
o
n
d
to
th
e
L
QR
co
n
tr
o
lle
r
weig
h
tin
g
m
atr
ices
(
)
an
d
(
)
as
s
h
o
wn
in
Fig
u
r
e
7.
T
h
e
ch
r
o
m
o
s
o
m
e
elem
en
ts
11
,
22
,
33
,
44
an
d
R
s
h
o
u
ld
b
e
ad
ju
s
ted
p
r
o
p
er
ly
b
y
o
p
tim
u
m
p
o
s
itiv
e
n
u
m
b
e
r
s
in
o
r
d
er
to
a
ch
iev
e
b
est co
n
tr
o
l p
er
f
o
r
m
a
n
ce
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
B
a
la
n
cin
g
a
S
e
g
w
a
y
r
o
b
o
t
u
s
in
g
LQR
co
n
tr
o
ller
b
a
s
ed
o
n
g
en
etic
a
n
d
…
(
I
b
r
a
h
im
K
.
Mo
h
a
mme
d
)
2649
Fig
u
r
e
6
.
Gen
etic
alg
o
r
ith
m
l
o
o
p
Fig
u
r
e
7
.
C
h
r
o
m
o
s
o
m
e
d
ef
in
it
io
n
4
.
2
.
B
F
O
a
l
g
o
rit
hm
T
h
e
b
ac
ter
ia
f
o
r
a
g
in
g
b
eh
av
i
o
r
is
a
co
m
p
u
tatio
n
al
m
o
d
el,
wh
ich
,
h
as
attr
ac
ted
m
o
r
e
atten
t
io
n
as
it
is
a
r
ich
s
o
u
r
ce
o
f
p
o
ten
tial e
n
g
i
n
ee
r
in
g
ap
p
licatio
n
s
.
B
FO is a
s
im
p
le
an
d
p
o
wer
f
u
l p
o
p
u
latio
n
-
b
ased
n
u
m
er
ical
o
p
tim
izatio
n
alg
o
r
ith
m
th
at
h
as
b
ee
n
in
tr
o
d
u
ce
d
b
y
Pas
s
in
o
in
2
0
0
2
[
2
1
]
.
T
h
e
B
FO
alg
o
r
ith
m
h
as
b
ee
n
g
ain
in
g
a
co
n
s
id
er
ab
le
in
ter
est in
r
esear
ch
er
s
d
u
e
to
its
ef
f
icien
cy
in
s
o
lv
in
g
a
n
d
o
p
tim
izin
g
m
o
r
e
en
g
in
ee
r
in
g
p
r
o
b
lem
s
in
s
ev
er
al
a
p
p
licat
io
n
d
o
m
ai
n
s
,
s
u
ch
as
o
p
tim
al
co
n
tr
o
l
[
2
2
]
,
h
ar
m
o
n
ic
esti
m
atio
n
[
2
3
]
an
d
tr
an
s
m
is
s
io
n
lo
s
s
r
ed
u
ctio
n
[
2
4
]
.
T
h
e
s
tr
ateg
y
o
f
b
ac
te
r
ia
s
elec
tio
n
f
o
r
th
e
B
FO
alg
o
r
ith
m
b
ases
o
n
an
id
ea
th
at
th
e
b
ac
ter
ia
with
p
o
o
r
f
o
r
ag
in
g
is
elim
in
ated
an
d
f
o
l
lo
win
g
u
p
th
o
s
e
b
ac
ter
ia
wh
i
ch
h
av
e
s
u
cc
ess
f
u
l
f
o
r
ag
in
g
to
m
ax
im
ize
en
e
r
g
y
o
b
tain
ed
p
er
u
n
it
tim
e
[
2
1
]
.
I
t
is
wo
r
th
co
n
s
id
er
in
g
th
at,
in
th
is
n
ew
o
p
tim
izatio
n
alg
o
r
ith
m
a
s
o
ci
al
f
o
r
ag
in
g
ap
p
r
o
ac
h
o
f
th
e
E
-
co
li
b
ac
ter
ia
ca
n
b
e
ap
p
lied
s
u
cc
ess
f
u
lly
to
s
o
lv
e
m
u
lti
-
o
p
tim
al
f
u
n
ctio
n
o
p
tim
i
za
tio
n
p
r
o
b
lem
.
T
h
e
E
-
co
li
b
a
cter
ia
ca
n
m
o
v
e
in
two
way
s
n
am
ely
,
s
wim
m
in
g
an
d
tu
m
b
lin
g
.
Fig
u
r
e
8
s
h
o
ws
th
e
s
wim
an
d
tu
m
b
le
m
o
v
em
e
n
t o
f
a
b
ac
ter
iu
m
.
Fig
u
r
e
8
.
m
o
v
em
e
n
t m
o
d
es
o
f
a
b
ac
ter
iu
m
4
.
3
.
B
F
O
f
o
ra
g
ing
s
t
r
a
t
eg
y
[
2
5
]
−
C
h
em
o
tax
is
:
T
h
is
p
r
o
ce
s
s
is
r
elate
d
to
m
o
v
em
en
t
o
f
b
ac
ter
i
u
m
d
u
r
in
g
s
ea
r
ch
f
o
r
f
o
o
d
.
T
h
e
E
-
co
li
b
ac
te
r
ia
ca
n
m
o
v
e
in
two
way
s
n
am
el
y
,
s
wim
m
in
g
an
d
tu
m
b
li
n
g
,
an
d
th
ey
ar
e
ab
le
to
alter
n
ate
b
et
wee
n
th
ese
two
m
o
v
em
en
t
s
ty
les
f
o
r
th
e
wh
o
le
o
f
th
eir
life
tim
e.
I
n
th
e
s
wim
m
in
g
m
o
d
e
,
th
e
b
ac
ter
ia
w
alk
in
a
ce
r
tain
d
ir
ec
tio
n
f
o
r
g
ath
e
r
in
g
f
o
o
d
,
wh
ile
in
th
e
tu
m
b
lin
g
m
o
d
e,
t
h
ey
m
o
v
e
with
r
an
d
o
m
d
ir
ec
ti
o
n
s
.
−
Swa
r
m
in
g
:
T
h
e
s
war
m
in
g
ac
tio
n
m
ea
n
s
th
e
b
ac
ter
ia
with
a
g
o
o
d
f
itn
ess
v
alu
e,
tr
y
to
attr
ac
t
o
th
er
s
to
f
o
r
m
g
r
o
u
p
s
,
s
o
th
at
th
ey
all
ca
n
ar
r
iv
e
at
th
e
d
esire
d
lo
ca
tio
n
.
T
h
ese
g
r
o
u
p
s
o
f
E
-
c
o
li
ce
lls
ar
r
an
g
e
th
em
s
elv
es,
in
wh
ich
,
th
e
y
ca
n
m
o
v
e
as c
o
n
ce
n
tr
ic
p
atte
r
n
s
f
o
r
f
o
o
d
s
ea
r
ch
in
g
.
−
R
ep
r
o
d
u
ctio
n
:
I
n
t
h
is
s
tag
e,
all
th
e
b
ac
ter
ia
p
o
p
u
latio
n
ar
e
class
if
ied
b
ased
o
n
h
ea
lth
s
tatu
s
.
T
h
e
h
ea
lth
ier
b
ac
ter
ia,
wh
ich
,
h
av
e
h
a
d
s
u
f
f
icien
t
n
u
tr
ien
t
s
will
b
e
r
e
p
r
o
d
u
ce
d
,
wh
ile
t
h
e
less
h
ea
lth
y
b
ac
ter
ia
will
d
ie.
T
h
e
s
u
r
v
iv
i
n
g
b
ac
ter
ia
will
s
p
lit
i
n
to
a
n
id
en
tical
r
ep
lica
o
f
its
elf
p
lac
ed
in
th
e
s
am
e
lo
ca
tio
n
s
with
a
th
at
n
u
m
b
er
e
q
u
als to
th
e
n
u
m
b
er
o
f
th
e
d
ea
d
o
n
es.
−
E
lim
in
atio
n
an
d
Dis
p
er
s
al:
Du
r
in
g
th
is
ev
o
lu
tio
n
ar
y
s
tep
,
g
r
ad
u
al
o
r
s
u
d
d
e
n
ev
en
ts
o
r
attac
k
s
in
th
e
lo
ca
l
l
iv
in
g
en
v
ir
o
n
m
e
n
t
o
f
th
e
b
ac
ter
ia,
m
ay
o
cc
u
r
d
u
e
t
o
s
ig
n
if
ican
t
r
is
in
g
o
f
th
e
tem
p
er
atu
r
e
ca
u
s
ed
b
y
o
cc
u
p
an
cy
o
f
a
h
ig
h
d
en
s
ity
o
f
b
ac
te
r
ia
f
o
r
a
s
p
ec
if
ic
ar
e
a.
T
h
is
h
ig
h
tem
p
er
atu
r
e
m
ay
k
ill
a
g
r
o
u
p
o
f
b
ac
ter
ia
an
d
d
is
p
er
s
al
o
f
o
th
e
r
s
in
to
s
o
m
e
n
ew
lo
ca
ti
o
n
s
.
5.
RO
B
O
T
CO
N
T
RO
L
S
YS
T
E
M
D
E
S
I
G
N
I
n
th
is
r
esear
ch
,
an
o
p
tim
al
c
o
n
tr
o
l
s
y
s
tem
f
o
r
th
e
Seg
way
r
o
b
o
t
is
d
esig
n
e
d
u
s
in
g
th
e
s
tat
e
f
ee
d
b
ac
k
L
QR
co
n
tr
o
ller
.
T
h
e
g
ain
p
ar
am
eter
s
o
f
th
e
c
o
n
tr
o
ller
ar
e
t
u
n
ed
e
f
f
ec
tiv
ely
,
u
s
in
g
o
p
tim
izatio
n
alg
o
r
ith
m
s
,
GA
an
d
B
FO
A.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
d
esig
n
is
v
alid
ated
u
s
in
g
Ma
tlab
p
r
o
g
r
am
m
i
n
g
.
B
ased
o
n
s
tep
in
p
u
t
,
th
e
co
n
tr
o
l
s
y
s
tem
is
d
esig
n
e
d
f
o
r
th
e
f
o
llo
win
g
r
e
q
u
ir
em
e
n
ts
:
r
is
e
t
im
e
les
s
th
an
1
0
(
m
s
)
,
s
ettlin
g
tim
e
le
s
s
th
an
3
0
(
m
s
)
,
m
ax
im
u
m
o
v
er
s
h
o
o
t
p
er
ce
n
tag
e
less
th
a
n
5
%.
T
h
e
f
itn
ess
f
u
n
ctio
n
o
f
th
e
r
o
b
o
t
co
n
tr
o
l
s
y
s
tem
is
as f
o
llo
ws
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
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NI
KA
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elec
o
m
m
u
n
C
o
m
p
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t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
2
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2653
2650
=
.
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wh
er
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s
f
er
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way
r
o
b
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ch
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e
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e
r
is
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s
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ettlin
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t
r
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th
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m
ax
im
u
m
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er
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o
o
t
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al
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h
is
f
u
n
ctio
n
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co
n
s
id
er
ed
in
o
p
tim
izatio
n
p
r
o
ce
s
s
o
f
th
e
co
n
tr
o
ller
g
ain
m
at
r
ix
u
s
in
g
GA
an
d
B
FO tu
n
in
g
alg
o
r
ith
m
s
.
6.
GA
-
L
Q
R
CO
NT
RO
L
L
E
R
DE
S
I
G
N
AND
R
E
SU
L
T
S
T
h
e
b
lo
ck
d
iag
r
am
o
f
th
e
Se
g
way
co
n
tr
o
l
s
y
s
tem
u
s
in
g
GA
-
L
QR
co
n
tr
o
ller
is
s
h
o
wn
in
Fig
u
r
e
9
.
B
ased
o
n
th
e
s
y
s
tem
p
ar
am
eter
s
(
=
1
.
6
,
=
1
.
2
,
=
0
.
1
6
,
=
0
.
0
2
,
=
0
.
5
2
,
=
0
.
0
0
3
2
2
,
=
0
.
0
0
3
8
2
)
th
e
s
tate
an
d
o
u
tp
u
t
eq
u
atio
n
ar
e
g
i
v
en
in
(
4
1
)
an
d
(
4
2
)
r
esp
ec
tiv
ely
.
T
h
e
g
lo
b
al
o
p
tim
al
s
o
lu
tio
n
f
o
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th
e
L
QR
co
n
tr
o
ller
p
r
o
b
lem
is
ac
h
iev
ed
u
s
in
g
g
en
etic
alg
o
r
ith
m
p
r
o
g
r
a
m
m
in
g
.
T
h
is
s
o
lu
tio
n
in
clu
d
es
d
eter
m
in
e
o
p
tim
u
m
v
alu
es
f
o
r
th
e
weig
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g
m
atr
ic
es
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en
ts
,
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ich
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e
g
iv
en
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elo
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B
ased
o
n
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e
o
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ized
weig
h
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g
m
atr
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ce
s
,
th
e
L
QR
g
ain
m
atr
ix
K
was
co
m
p
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ted
u
s
in
g
th
e
Ma
tlab
co
m
m
an
d
“
”
as
f
o
llo
ws
:
=
(
11
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22
,
33
,
44
)
wh
er
e
11
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8
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9
6
9
.
,
22
=
0
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3
0
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33
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1
2
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44
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8
5
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1
2
3
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5
an
d
=
[
-
6
.
4
9
8
8
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3
.
8
5
9
2
-
5
.
1
9
8
2
-
0
.
7
3
4
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]
.
[
̇
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[
0
1
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0
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0316
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3817
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3927
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[
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05746
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[
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T
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e
r
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e
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t
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ized
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d
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ac
k
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m
atr
ix
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s
h
o
wn
in
Fig
u
r
e
1
0
.
Fig
u
r
e
1
1
p
r
esen
ts
th
e
in
p
u
t
s
ig
n
al
o
f
t
h
e
Seg
way
s
y
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te
m
.
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t
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r
f
r
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m
Fig
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es
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n
d
1
1
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at
th
e
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ller
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n
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g
m
eth
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f
f
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r
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e
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ep
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le
in
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o
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ased
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n
Fig
u
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e
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h
e
o
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tp
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t
s
tates
(
)
an
d
(
)
tr
ac
k
ed
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e
d
em
a
n
d
in
p
u
t
tr
ajec
to
r
ies
with
o
u
t
o
v
er
s
h
o
o
t,
r
is
e
tim
e
an
d
s
ettlin
g
tim
e
o
f
ap
p
r
o
x
im
ately
8
0
m
s
an
d
9
5
m
s
r
esp
ec
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el
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d
ap
p
r
o
x
im
ate
ly
ze
r
o
s
tead
y
s
tate
er
r
o
r
.
Fig
u
r
e
1
2
p
r
esen
ts
co
n
v
er
g
in
g
o
f
t
h
e
L
QR
weig
h
tin
g
m
atr
ices th
r
o
u
g
h
iter
atio
n
s
b
ased
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n
GA
tu
n
in
g
m
eth
o
d
.
Fig
u
re
9
.
B
lo
ck
d
iag
r
am
o
f
S
e
g
way
co
n
tr
o
ller
GA
-
L
QR
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
B
a
la
n
cin
g
a
S
e
g
w
a
y
r
o
b
o
t
u
s
in
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LQR
co
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n
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(
I
b
r
a
h
im
K
.
Mo
h
a
mme
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)
2651
Fig
u
r
e
1
0
.
Sy
s
tem
r
esp
o
n
s
e
u
s
in
g
GA
-
L
QR
co
n
tr
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ller
Fig
u
r
e
1
1
.
Sy
s
tem
in
p
u
t b
ased
o
n
GA
-
L
QR
co
n
tr
o
ller
(
a)
(
b
)
(
c)
(
d
)
(
e)
Fig
u
r
e
1
2
.
Gen
er
atio
n
elem
en
t
s
o
f
(
)
an
d
(
)
m
atr
ices f
o
r
GA
-
L
QR
co
n
tr
o
ller
; (
a)
11
elem
en
t,
(
b
)
22
elem
en
t,
(
c)
q
33
elem
en
t,
(
d
)
44
elem
en
t,
an
d
(
e)
elem
en
t
7.
B
F
O
-
L
Q
R
CO
NT
RO
L
L
E
R
DE
S
I
G
N
AND
R
E
SU
L
T
S
T
h
e
d
esig
n
o
f
L
QR
co
n
tr
o
ller
b
ased
o
n
B
FOA
m
eth
o
d
is
a
n
alo
g
o
u
s
to
th
at
o
f
th
e
GA
-
L
QR
co
n
tr
o
l
s
y
s
tem
as
p
r
ev
io
u
s
ly
p
r
ese
n
ted
in
Fig
u
r
e
9
.
T
h
e
o
p
tim
ized
L
QR
m
atr
ices
(
)
an
d
(
)
an
d
co
n
tr
o
ller
g
ain
m
atr
ix
u
s
in
g
B
FO
alg
o
r
it
h
m
ar
e
as
f
o
llo
ws:
=
(
11
,
22
,
33
,
44
)
wh
er
e
11
=
2
8
9
.
1
0
4
,
22
=
-
5
.
1
5
*
10
−
5
,
33
=
-
5*
10
−
5
,
44
q
=
-
5
.
1
*
10
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5
=
0
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0
0
0
2
8
a
n
d
=
[
-
1
0
2
2
-
2
6
0
.
2
8
8
6
.
7
2
7
7
.
7
]
.
T
he
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e
r
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o
n
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e
o
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e
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o
b
o
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s
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(
)
,
(
)
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s
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g
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L
QR
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ller
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s
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Fig
u
r
e
1
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.
Fig
u
r
e
1
4
s
h
o
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