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528
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PID
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co
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ar
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till
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s
[
1
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an
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PID
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[
2
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wer
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[
3
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[
4
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.
Oth
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wh
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ac
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p
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f
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m
an
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d
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tab
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[
5
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–
[
7
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.
Fu
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[
8
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,
[
9
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I
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Evaluation Warning : The document was created with Spire.PDF for Python.
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Sep
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6
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8
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co
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Fu
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r
esear
ch
e
r
s
h
av
e
b
ee
n
in
cr
ea
s
in
g
ly
i
n
ter
ested
in
th
e
h
y
b
r
id
i
n
tellig
en
t
an
d
r
o
b
u
s
t
co
n
t
r
o
l
m
eth
o
d
s
o
f
s
elf
-
b
alan
cin
g
r
o
b
o
ts
.
Ad
ap
tiv
e
n
eu
r
al
s
lid
in
g
m
o
d
e
co
n
tr
o
l
an
d
h
ier
ar
ch
ical
s
l
id
in
g
m
o
d
e
co
n
tr
o
l
with
n
o
n
lin
ea
r
d
is
tu
r
b
a
n
ce
o
b
s
er
v
er
s
d
em
o
n
s
tr
ated
th
e
b
ett
er
p
er
f
o
r
m
a
n
ce
o
f
th
e
d
is
tu
r
b
an
ce
r
ejec
tio
n
an
d
r
o
b
u
s
tn
ess
[
2
1
]
,
[
2
2
]
.
Mo
r
eo
v
er
,
f
o
r
u
n
ce
r
tain
en
v
ir
o
n
m
en
t,
o
p
tim
izatio
n
-
b
ased
a
n
d
f
u
zz
y
in
tellig
en
t
co
n
tr
o
l
m
eth
o
d
s
h
av
e
b
ee
n
u
s
ed
to
en
h
an
ce
th
e
ef
f
icien
cy
o
f
co
n
tr
o
ller
tu
n
in
g
an
d
tr
ac
k
i
n
g
p
er
f
o
r
m
an
ce
[
2
3
]
.
Mo
r
e
r
ec
en
tly
,
v
ar
io
u
s
r
ev
iew
p
a
p
er
s
also
p
o
i
n
ted
o
u
t
th
e
in
cr
ea
s
in
g
d
e
m
an
d
f
o
r
h
y
b
r
i
d
n
o
n
lin
ea
r
c
o
n
tr
o
l
alg
o
r
ith
m
s
th
at
co
u
ld
p
r
o
v
id
e
r
o
b
u
s
t
s
tab
ilit
y
,
f
ast
co
n
v
er
g
en
ce
an
d
g
o
o
d
d
is
tu
r
b
an
ce
r
e
jectio
n
in
r
o
b
o
tic
b
alan
cin
g
s
y
s
tem
s
[
2
4
]
.
I
n
s
p
ite
o
f
th
ese
ad
v
an
ce
s
,
th
er
e
ar
e
s
till
s
o
m
e
d
r
awb
ac
k
s
with
th
e
cu
r
r
en
t
m
et
h
o
d
s
.
T
h
e
u
n
ce
r
tain
ties
m
ay
ca
u
s
e
class
ical
co
n
tr
o
ller
s
to
lo
s
e
p
er
f
o
r
m
an
ce
;
s
lid
in
g
m
o
d
e
co
n
t
r
o
ller
s
m
ay
ca
u
s
e
ch
atter
in
g
p
h
en
o
m
en
a;
in
tellig
en
t
co
n
tr
o
l
tech
n
i
q
u
es
m
ay
in
cr
ea
s
e
co
m
p
u
tatio
n
al
co
m
p
l
ex
ity
.
T
h
u
s
,
it
is
a
cr
u
cial
r
esear
ch
p
r
o
b
lem
to
d
ev
elo
p
an
in
te
g
r
ated
r
o
b
u
s
t
n
o
n
lin
ea
r
co
n
tr
o
l
a
r
ch
itec
tu
r
e
with
ac
cu
r
ate
n
o
n
lin
ea
r
c
o
m
p
e
n
s
atio
n
,
d
is
tu
r
b
an
ce
r
ejec
tio
n
an
d
s
y
s
tem
atic
p
ar
am
eter
tu
n
in
g
.
Fo
r
a
two
wh
ee
le
d
s
elf
-
b
alan
cin
g
r
o
b
o
t,
a
s
tr
o
n
g
co
n
tr
o
lle
r
d
esig
n
is
p
r
esen
ted
in
th
is
p
ap
er
u
s
in
g
th
e
f
ee
d
b
ac
k
lin
ea
r
izatio
n
an
d
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l
tech
n
i
q
u
es.
I
n
o
r
d
er
to
en
h
a
n
ce
tr
a
n
s
ien
t
r
esp
o
n
s
e
an
d
r
o
b
u
s
tn
ess
,
th
e
co
n
tr
o
ller
p
ar
am
eter
s
ar
e
o
p
tim
ally
tu
n
e
d
b
y
th
e
u
s
e
o
f
Ato
m
Sear
ch
Op
tim
izatio
n
(
ASO)
alg
o
r
ith
m
.
T
h
e
k
e
y
ac
h
iev
em
e
n
ts
o
f
th
is
wo
r
k
a
r
e
b
r
ief
l
y
s
u
m
m
ar
ized
b
elo
w:
−
A
r
o
b
u
s
t
co
n
tr
o
l
s
tr
ateg
y
b
ased
o
n
f
ee
d
b
ac
k
lin
ea
r
izatio
n
is
p
r
o
p
o
s
ed
to
co
m
p
en
s
ate
f
o
r
th
e
n
o
n
lin
ea
r
d
y
n
am
ics o
f
th
e
s
y
s
tem
.
−
T
h
e
ASO
alg
o
r
ith
m
is
u
s
ed
f
o
r
o
p
tim
al
co
n
tr
o
ller
p
ar
am
eter
tu
n
in
g
.
−
T
h
e
co
n
tr
o
ller
p
r
o
p
o
s
ed
in
th
is
wo
r
k
e
n
h
an
ce
s
th
e
r
o
b
u
s
tn
ess
o
f
th
e
s
y
s
tem
to
d
i
s
tu
r
b
an
ce
s
an
d
u
n
ce
r
tain
ties
.
−
T
h
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
is
test
ed
with
s
im
u
latio
n
s
an
d
c
o
m
p
a
r
ed
to
o
t
h
er
co
n
tr
o
l so
lu
tio
n
s
.
2.
SE
L
F
-
B
A
L
ANC
I
NG
RO
B
O
T
DYNA
M
I
C
S
T
h
is
s
ec
tio
n
d
is
cu
s
s
es
th
e
d
y
n
am
ic
m
o
d
el
o
f
th
e
wh
ee
le
d
s
e
lf
-
b
alan
cin
g
m
o
b
ile
r
o
b
o
t.
I
n
t
h
is
p
ap
er
,
th
e
n
o
is
e,
r
o
ad
r
esis
tan
ce
,
v
ib
r
atio
n
,
an
d
f
r
ictio
n
b
etwe
en
th
e
wh
ee
ls
an
d
th
e
s
u
r
f
ac
e
ar
e
co
n
s
id
er
ed
as
d
is
tu
r
b
an
ce
s
.
T
h
e
m
o
d
el
is
d
er
iv
ed
b
ased
o
n
m
eth
o
d
s
p
r
esen
ted
b
y
[
2
5
]
as
s
h
o
wn
Fig
u
r
e
1
.
T
h
e
f
o
llo
win
g
d
if
f
er
en
tial e
q
u
atio
n
s
d
escr
ib
e
th
e
d
y
n
am
ic
m
o
d
el
o
f
th
e
r
o
b
o
tic
s
y
s
tem
b
ased
o
n
New
to
n
’
s
s
ec
o
n
d
law.
(
̈
−
s
in
̇
+
c
os
̈
)
=
(
1
)
(
−
c
os
̇
+
s
in
̈
)
=
−
(
2
)
̈
=
s
in
−
c
os
(
3
)
̈
=
−
(
4
)
W
h
er
e,
d
en
o
tes
t
h
e
d
is
p
lace
m
en
t,
r
ep
r
esen
ts
th
e
a
n
g
le
o
f
th
e
b
ar
,
r
ef
er
s
t
o
th
e
m
ass
o
f
th
e
b
ar
,
d
en
o
tes
th
e
m
ass
o
f
th
e
m
o
b
il
e
p
latf
o
r
m
,
r
e
p
r
esen
ts
th
e
h
o
r
izo
n
tal
f
o
r
ce
,
r
e
p
r
esen
ts
th
e
v
er
tical
f
o
r
ce
,
is
th
e
f
o
r
ce
ap
p
lied
b
y
DC
m
o
to
r
,
is
th
e
len
g
th
o
f
t
h
e
b
a
r
,
d
en
o
tes
th
e
in
e
r
tia
o
f
th
e
r
o
b
o
t,
an
d
r
ep
r
esen
ts
th
e
g
r
av
itatio
n
al
ac
ce
ler
ati
o
n
.
T
h
e
m
o
m
e
n
t o
f
i
n
er
tia
ca
n
b
e
ex
p
r
ess
ed
as
(
5
)
.
=
1
3
2
(
5
)
W
ith
s
im
p
le
s
u
b
s
titu
tio
n
s
,
we
o
b
tain
(
6
)
.
(
+
)
̈
=
−
(
c
os
̈
−
s
in
̇
2
)
(
6
)
4
3
2
̈
=
s
in
−
c
os
̈
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Op
tima
l ro
b
u
s
t c
o
n
tr
o
l fo
r
s
elf
-
b
a
la
n
ci
n
g
r
o
b
o
t
-
b
a
s
ed
fee
d
b
a
ck
lin
ea
r
iz
a
tio
n
…
(
A
la
a
Ju
m
a
a
h
A
L
-
Ma
ia
h
y
)
521
T
h
is
p
ap
er
aim
s
to
d
esig
n
a
c
o
n
tr
o
l
s
y
s
tem
t
h
at
tr
ac
k
s
th
e
(
)
in
th
e
p
r
esen
ce
o
f
s
y
s
tem
u
n
ce
r
tain
ty
an
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
.
T
h
u
s
,
t
o
f
o
c
u
s
o
n
attitu
d
e
co
n
tr
o
l,
th
e
d
y
n
am
ics
o
f
th
e
r
o
b
o
tic
s
y
s
tem
ar
e
d
ec
o
u
p
led
as
(
8
)
an
d
(
9
)
.
̈
=
2
2
s
in
2
2
−
(
+
2
)
(
)
̇
2
−
(
+
2
)
co
s
2
−
4
/
3
(
8
)
̈
=
−
(
+
)
(
)
+
2
2
̇
2
s
in
2
2
+
(
)
co
s
2
−
4
/
3
(
9
)
Fig
u
r
e
1
.
T
wo
-
wh
ee
led
s
elf
-
b
alan
cin
g
[
2
5
]
3.
AT
O
M
S
E
AR
CH
O
P
T
I
M
I
Z
AT
I
O
N
Ato
m
Sear
ch
Op
tim
izatio
n
(
A
SO)
is
o
n
e
o
f
th
e
p
r
o
m
is
in
g
m
etah
eu
r
is
tic
o
p
tim
izatio
n
alg
o
r
ith
m
s
th
at
h
as
b
ee
n
wid
ely
u
s
ed
in
en
g
in
ee
r
in
g
p
r
o
b
le
m
s
[
2
6
]
.
I
n
th
is
p
ap
er
,
ASO
is
u
s
ed
to
d
e
s
ig
n
th
e
co
n
tr
o
ller
b
ec
au
s
e
o
f
its
ab
ilit
y
to
p
r
o
v
id
e
a
g
o
o
d
b
alan
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
e
x
p
lo
itatio
n
wh
ich
lead
s
t
o
a
n
en
h
an
ce
d
s
ea
r
ch
p
er
f
o
r
m
a
n
ce
an
d
f
aster
co
n
v
er
g
en
ce
to
t
h
e
o
p
tim
u
m
.
ASO
b
alan
ce
s
th
e
in
ter
ac
tio
n
b
etwe
en
p
ar
ticles
ac
co
r
d
in
g
t
o
th
eir
m
ass
an
d
d
is
tan
ce
,
an
d
d
o
es
n
o
t
s
u
f
f
er
f
r
o
m
p
r
em
atu
r
e
c
o
n
v
e
r
g
en
ce
to
lo
ca
l
o
p
tim
a,
as
is
th
e
ca
s
e
with
o
th
er
m
etah
e
u
r
is
tic
alg
o
r
ith
m
s
in
m
u
ltimo
d
al
s
ea
r
ch
s
p
ac
e.
T
h
e
p
r
esen
ted
co
n
t
r
o
l
s
y
s
tem
is
h
ig
h
ly
n
o
n
lin
ea
r
a
n
d
h
a
s
s
tr
o
n
g
p
ar
am
eter
in
ter
d
ep
en
d
en
ce
,
a
n
d
ASO
o
f
f
er
s
an
ef
f
ec
tiv
e
a
n
d
r
eliab
le
w
ay
to
o
b
tain
o
p
tim
al
c
o
n
tr
o
ller
g
ain
s
.
C
o
m
p
ar
ed
to
o
th
e
r
p
o
p
u
lar
co
m
p
u
tatio
n
al
in
tellig
en
ce
(
C
I
)
tech
n
iq
u
es
s
u
ch
as
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
an
d
g
en
eti
c
alg
o
r
ith
m
(
GA)
,
ASO
p
r
o
v
i
d
es
m
o
r
e
s
tab
le
s
ea
r
c
h
in
g
an
d
b
etter
co
n
v
er
g
en
ce
in
n
o
n
lin
ea
r
o
p
tim
izatio
n
p
r
o
b
lem
s
.
Mo
r
eo
v
e
r
,
ASO
h
as
f
ewe
r
p
ar
am
eter
s
to
b
e
tu
n
e
d
an
d
ca
n
also
wo
r
k
r
o
b
u
s
tly
in
m
u
ltim
o
d
al
o
p
tim
i
za
tio
n
p
r
o
b
lem
s
,
wh
ich
m
ak
es
it h
ig
h
ly
ap
p
licab
le
f
o
r
co
n
tr
o
ller
g
ain
s
tu
n
in
g
in
th
e
n
o
n
lin
ea
r
s
y
s
tem
s
o
f
th
e
r
o
b
o
t.
T
h
e
ASO
alg
o
r
ith
m
o
f
f
er
s
a
m
o
r
e
ef
f
ec
tiv
e
e
x
p
l
o
r
atio
n
–
e
x
p
lo
itatio
n
b
alan
ce
an
d
a
m
o
r
e
s
tab
le
co
n
v
er
g
e
n
ce
f
o
r
n
o
n
lin
ea
r
o
p
ti
m
izatio
n
p
r
o
b
lem
s
th
an
PS
O
an
d
GA.
Ho
wev
er
,
p
er
f
o
r
m
in
g
a
d
etailed
s
en
s
itiv
ity
an
aly
s
is
is
b
ey
o
n
d
th
e
s
co
p
e
o
f
th
is
s
tu
d
y
b
u
t
th
e
s
im
u
latio
n
r
esu
lts
co
n
f
ir
m
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
s
elec
ted
ASO
p
ar
am
eter
s
.
ASO,
o
r
i
g
in
ally
p
r
o
p
o
s
ed
in
[
2
6
]
is
in
s
p
ir
ed
b
y
m
o
lec
u
lar
d
y
n
am
ics
wh
er
e
th
er
e
ar
e
two
ty
p
es
o
f
f
o
r
ce
s
ac
tin
g
o
n
t
h
e
ato
m
s
:
in
ter
ac
tio
n
an
d
co
n
s
tr
ain
t
f
o
r
ce
s
.
I
n
th
e
ASO
alg
o
r
ith
m
,
th
e
ato
m
'
s
p
o
s
itio
n
is
ca
lcu
lated
as
(
1
0
)
,
(
+
1
)
=
(
)
+
(
+
1
)
(
1
0
)
w
h
er
e
(
+
1
)
an
d
(
)
ar
e
th
e
p
o
s
itio
n
s
o
f
th
e
i
th
ato
m
in
th
e
n
th
a
n
d
(
n+
1)
th
iter
atio
n
s
r
esp
ec
tiv
ely
an
d
(
+
1
)
is
th
e
v
elo
city
o
f
i
th
ato
m
in
t
h
e
(
n+
1)
th
iter
atio
n
.
T
h
is
is
d
eter
m
in
ed
as
(
1
1
)
,
(
+
1
)
=
∗
(
)
+
(
)
(
1
1
)
w
h
er
e
is
a
p
o
s
itiv
e
r
a
n
d
o
m
n
u
m
b
er
less
th
an
o
n
e
,
a
n
d
(
)
is
ac
ce
ler
atio
n
o
f
th
e
i
th
at
o
m
a
t
th
e
n
th
iter
atio
n
,
an
d
is
ca
lcu
lated
as
(
1
2
)
to
(
1
5
)
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
5
1
9
-
5
2
8
522
(
)
=
(
1
2
)
=
∑
∈
(
1
3
)
=
(
)
∗
−
+
‖
−
‖
(
1
4
)
=
∑
=
1
(
1
5
)
w
h
er
e
r
ef
er
s
to
th
e
f
o
r
ce
ac
tin
g
o
n
th
e
ato
m
,
(
)
d
en
o
tes
th
e
v
ar
iab
le
th
at
b
alan
ce
s
b
etwe
en
ex
p
lo
r
atio
n
an
d
ex
p
l
o
itatio
n
,
an
d
d
en
o
tes
a
co
n
s
tan
t
th
at
p
r
e
v
en
ts
d
iv
is
io
n
b
y
ze
r
o
.
wh
er
e
is
a
s
u
b
s
et
o
f
th
e
b
est
ato
m
s
.
4.
P
RO
P
O
SE
D
CO
NT
RO
L
SY
ST
E
M
Sli
d
in
g
m
o
d
e
c
o
n
tr
o
l
-
b
ased
F
ee
d
b
ac
k
lin
ea
r
izatio
n
is
u
s
ed
to
co
n
tr
o
l
t
h
e
a
n
g
le
o
f
th
e
r
o
b
o
t
b
o
d
y
to
tr
ac
k
th
e
d
esire
d
an
g
le
with
an
g
u
lar
v
elo
city
ap
p
r
o
ac
h
in
g
ze
r
o
as
tim
e
ten
d
s
to
in
f
in
ity
.
Feed
b
ac
k
lin
ea
r
izatio
n
h
as
b
ee
n
u
s
ed
to
ca
n
ce
l
th
e
n
o
n
lin
ea
r
ities
in
th
e
d
y
n
am
ics
o
f
th
e
r
o
b
o
tic
s
y
s
tem
an
d
tr
an
s
f
o
r
m
it
in
to
a
lin
ea
r
s
y
s
tem
h
o
wev
e
r
,
g
o
o
d
ca
n
ce
llatio
n
n
ee
d
s
ac
cu
r
ate
d
y
n
am
ic
m
o
d
el
o
f
th
e
co
n
tr
o
lled
s
y
s
tem
an
d
th
is
m
ay
n
o
t
b
e
ac
h
iev
ed
in
p
r
ac
tical
im
p
lem
en
tatio
n
s
.
T
o
e
n
s
u
r
e
r
o
b
u
s
tn
ess
,
SMC
is
u
s
ed
to
c
o
m
p
en
s
ate
t
h
e
s
y
s
tem
u
n
ce
r
tain
ty
an
d
m
o
d
e
llin
g
er
r
o
r
s
.
T
h
e
co
m
b
in
atio
n
o
f
f
ee
d
b
ac
k
lin
ea
r
izatio
n
an
d
SMC
ca
n
b
en
ef
it
f
r
o
m
tr
ajec
to
r
y
tr
ac
k
i
n
g
in
f
ee
d
b
ac
k
lin
ea
r
izatio
n
an
d
r
o
b
u
s
tn
ess
in
SMC
.
T
h
e
d
y
n
a
m
ic
m
o
d
el
ca
n
b
e
ex
p
r
ess
ed
as a
g
en
er
al
n
o
n
lin
e
ar
s
ec
o
n
d
-
o
r
d
er
s
y
s
tem
as
(
1
6
)
to
(
1
8
)
,
̈
=
(
,
)
+
(
,
)
+
(
1
6
)
(
,
)
=
−
(
+
)
(
)
+
2
2
̇
2
s
in
2
2
co
s
2
−
4
/
3
(
1
7
)
(
,
)
=
(
1
8
)
w
h
er
e
is
ex
ter
n
al
d
is
tu
r
b
an
ce
.
T
h
e
d
esire
d
a
n
g
le
is
(
)
an
d
th
e
er
r
o
r
ca
n
b
e
e
x
p
r
ess
ed
as
(
1
9
)
an
d
(
2
0
)
.
=
(
)
−
(
)
(
1
9
)
=
[
̇
]
(
2
0
)
T
h
e
s
lid
in
g
s
u
r
f
ac
e
is
ch
o
s
en
to
g
u
ar
an
tee
s
tab
ilit
y
o
f
th
e
er
r
o
r
d
y
n
a
m
ics
an
d
r
a
p
id
co
n
v
er
g
en
ce
to
th
e
d
esire
d
eq
u
ilib
r
iu
m
.
T
h
e
c
h
o
ice
o
f
th
e
s
lid
in
g
v
a
r
iab
le
d
ef
in
es
th
e
tr
an
s
ien
t
b
eh
av
i
o
r
o
f
th
e
clo
s
ed
-
l
o
o
p
s
y
s
tem
,
s
u
ch
as
co
n
v
er
g
e
n
ce
r
ate
an
d
d
is
tu
r
b
an
ce
r
ejec
tio
n
.
Ap
p
r
o
p
r
iate
d
esig
n
o
f
th
e
s
lid
in
g
s
u
r
f
ac
e
en
s
u
r
es
th
at
th
e
s
y
s
tem
tr
ajec
to
r
ies
co
n
v
er
g
e
to
th
e
s
lid
in
g
m
a
n
if
o
ld
an
d
s
tay
o
n
it
d
esp
ite
u
n
ce
r
tain
ties
a
n
d
d
is
tu
r
b
an
ce
s
.
T
h
e
s
lid
in
g
v
ar
ia
b
le
is
d
ef
in
ed
as:
=
(
2
1
)
=
[
1
]
(
2
2
)
w
h
er
e
is
a
p
o
s
itiv
e
s
ca
lar
.
B
y
f
ee
d
b
ac
k
lin
ea
r
izatio
n
,
th
e
p
r
o
p
o
s
ed
r
o
b
u
s
t
co
n
tr
o
ller
ca
n
b
e
d
ef
in
ed
as
(
2
3
)
an
d
(
2
4
)
.
=
−
(
,
)
(
,
)
(
2
3
)
=
̈
−
−
(
)
̇
(
2
4
)
W
e
d
ef
in
e
as a
L
y
ap
u
n
o
v
f
u
n
ctio
n
:
=
1
2
2
(
2
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Op
tima
l ro
b
u
s
t c
o
n
tr
o
l fo
r
s
elf
-
b
a
la
n
ci
n
g
r
o
b
o
t
-
b
a
s
ed
fee
d
b
a
ck
lin
ea
r
iz
a
tio
n
…
(
A
la
a
Ju
m
a
a
h
A
L
-
Ma
ia
h
y
)
523
T
h
en
,
̇
=
̇
=
(
̈
+
̇
)
=
(
̈
−
̈
+
̇
)
(
2
6
)
=
(
(
,
)
+
(
,
)
+
−
̈
+
̇
)
(
2
7
)
B
y
u
s
in
g
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l la
w
in
(
2
3
)
.
̇
=
(
+
−
̈
+
̇
)
(
2
8
)
=
(
−
(
)
+
)
≤
−
|
|
+
(
)
≤
0
(
2
9
)
T
h
e
o
p
tim
al
v
alu
e
f
o
r
th
e
p
r
o
p
o
s
ed
co
n
t
r
o
ller
p
ar
am
ete
r
s
ca
n
b
e
o
b
tain
ed
b
y
u
s
in
g
th
e
ASO
alg
o
r
ith
m
b
y
s
elec
tin
g
a
g
o
o
d
o
b
jectiv
e
f
u
n
ctio
n
.
I
n
t
h
is
p
ap
er
,
i
n
teg
r
al
ab
s
o
lu
te
er
r
o
r
(
I
AE
)
is
u
s
ed
to
t
u
n
e
th
e
co
n
tr
o
ller
:
=
∫
|
(
)
|
0
dt
(
3
0
)
w
h
er
e
r
ef
er
s
to
th
e
d
u
r
atio
n
o
f
th
e
s
im
u
latio
n
.
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
th
is
s
ec
tio
n
,
th
e
p
r
o
p
o
s
ed
r
o
b
u
s
t
co
n
tr
o
l
s
y
s
tem
f
o
r
c
o
n
tr
o
llin
g
th
e
wh
ee
led
m
o
b
ile
s
elf
-
b
alan
cin
g
r
o
b
o
t
is
ev
alu
ated
b
y
s
im
u
lat
in
g
th
e
clo
s
ed
lo
o
p
co
n
tr
o
l
s
y
s
tem
u
s
in
g
MA
T
L
AB
/Si
m
u
l
in
k
2
0
2
4
with
t
h
e
f
o
llo
win
g
s
o
lv
er
p
a
r
am
eter
s
:
So
lv
er
ty
p
e:
Var
iab
le
-
s
tep
,
So
lv
er
:
o
d
e4
5
a
n
d
s
im
u
latio
n
tim
e
1
0
s
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
is
co
m
p
ar
ed
with
th
e
PID
co
n
tr
o
ller
,
wh
o
s
e
p
ar
a
m
eter
s
ar
e
tu
n
ed
b
y
PS
O
o
p
tim
izatio
n
alg
o
r
ith
m
a
n
d
PD
-
SMC
co
n
tr
o
l
m
eth
o
d
.
T
h
e
I
AE
p
er
f
o
r
m
a
n
ce
in
d
ex
is
u
s
ed
to
co
m
p
ar
e
b
etwe
en
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
co
n
tr
o
ller
s
.
T
h
e
p
a
r
am
ete
r
s
o
f
t
h
e
o
p
tim
ized
PID
co
n
t
r
o
ller
u
s
ed
in
th
is
s
im
u
latio
n
ar
e:
=
1
,
=
2
an
d
=
2
.
W
h
ile
th
e
PD
-
SM
C
co
n
tr
o
l
law
u
s
ed
i
n
th
is
s
im
u
latio
n
ex
p
r
ess
ed
as
(
3
1
)
.
−
=
+
̇
+
(
)
(
3
1
)
w
h
er
e
=
10
,
=
5
,
=
15
,
an
d
=
1
.
5
+
̇
.
T
h
e
s
ettin
g
p
ar
am
eter
s
o
f
ASO
u
s
ed
in
th
i
s
s
im
u
latio
n
ar
e
lis
ted
in
T
ab
le
1
.
T
ab
le
1
.
ASO
p
ar
am
eter
s
V
a
l
u
e
N
30
T
1
5
0
0
.
5
T
h
e
p
a
r
am
eter
s
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
a
f
ter
a
p
p
ly
in
g
A
SO
alg
o
r
ith
m
a
r
e:
=
0
.
22
an
d
=
1
.
5
.
T
h
e
p
ar
am
eter
s
o
f
t
h
e
d
y
n
am
i
c
s
y
s
tem
ar
e
lis
ted
in
T
ab
le
2
.
T
h
r
ee
ca
s
es
ar
e
d
is
cu
s
s
ed
in
th
is
s
im
u
latio
n
,
th
e
f
ir
s
t
ca
s
e
d
is
cu
s
s
es
th
e
s
tep
tr
ac
k
in
g
,
t
h
e
s
ec
o
n
d
ca
s
e
p
r
esen
ts
th
e
s
in
u
s
o
id
al
tr
ac
k
in
g
,
w
h
ile
th
e
th
ir
d
ca
s
e
d
is
cu
s
s
es r
o
b
u
s
tn
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
a
g
ain
s
t sy
s
tem
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tu
r
b
an
ce
r
ejec
tio
n
is
a
s
tr
u
ct
u
r
al
p
r
o
p
er
ty
o
f
th
e
co
n
tr
o
ller
.
T
h
e
p
er
f
o
r
m
an
ce
i
n
d
ices
ar
e
s
h
o
wn
in
Fig
u
r
e
8
an
d
th
ese
in
d
ices
s
h
o
w
r
o
b
u
s
tn
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
a
g
ain
s
t e
x
ter
n
al
d
is
t
u
r
b
an
ce
.
Fig
u
r
e
6
.
Dis
tu
r
b
a
n
ce
in
ca
s
e
2
Fig
u
r
e
7
.
R
o
b
u
s
tn
ess
ag
ain
s
t d
is
tu
r
b
an
ce
Fig
u
r
e
8
.
I
AE
v
ar
iatio
n
s
o
f
ca
s
e
2
T
h
e
p
r
o
p
o
s
ed
c
o
n
tr
o
ller
ca
n
b
e
p
r
ac
tically
im
p
lem
en
ted
o
n
a
r
ea
l
s
elf
-
b
alan
cin
g
r
o
b
o
t
with
em
b
ed
d
e
d
co
n
tr
o
ller
,
wh
ee
l
e
n
co
d
er
s
,
an
d
I
MU
s
en
s
o
r
(
w
h
ich
h
as
an
ac
ce
ler
o
m
eter
an
d
g
y
r
o
s
co
p
e
)
.
T
h
e
f
ee
d
b
ac
k
lin
ea
r
izatio
n
p
o
r
tio
n
is
d
esig
n
ed
to
elim
in
ate
th
e
n
o
n
lin
ea
r
ch
ar
ac
ter
is
tics
o
f
th
e
r
o
b
o
t
an
d
th
e
s
lid
in
g
m
o
d
e
p
o
r
tio
n
is
d
esig
n
ed
to
elim
in
ate
th
e
ef
f
ec
t
o
f
d
is
tu
r
b
an
ce
s
s
u
ch
as
th
e
ef
f
ec
t
o
f
ch
an
g
es
in
th
e
wo
r
k
s
p
ac
e,
ch
an
g
es
in
lo
ad
,
an
d
ex
ter
n
al
p
u
s
h
es
d
u
e
to
ir
r
eg
u
lar
f
lo
o
r
s
.
An
au
to
n
o
m
o
u
s
m
o
b
ile
p
latf
o
r
m
,
in
s
p
ec
tio
n
r
o
b
o
ts
,
a
n
d
co
m
p
a
ct
r
o
b
o
tic
ca
r
r
ie
r
s
m
o
v
in
g
in
co
n
f
i
n
ed
m
an
u
f
ac
tu
r
in
g
ar
ea
s
ar
e
ex
am
p
les
o
f
ap
p
licatio
n
s
f
o
r
w
h
ich
s
u
ch
a
co
n
tr
o
ller
ca
n
b
e
u
s
ed
in
in
d
u
s
tr
ial
en
v
ir
o
n
m
en
ts
.
T
h
e
r
o
b
o
t
tilt
an
g
le
an
d
its
an
g
u
lar
v
elo
city
ca
n
b
e
ac
q
u
ir
ed
f
r
o
m
th
e
I
MU
s
en
s
o
r
in
r
ea
l
t
im
e
in
th
e
im
p
lem
en
tatio
n
,
wh
ich
c
o
u
ld
b
e
ac
q
u
ir
ed
b
y
f
u
s
in
g
t
h
e
d
ata
f
r
o
m
th
e
ac
ce
ler
o
m
ete
r
an
d
g
y
r
o
s
co
p
e
o
f
th
e
I
MU
s
en
s
o
r
.
T
h
e
wh
ee
l
p
o
s
itio
n
an
d
v
elo
city
ca
n
b
e
s
u
p
p
lied
b
y
w
h
ee
l
en
co
d
er
s
to
g
iv
e
m
o
tio
n
f
ee
d
b
ac
k
.
Fil
ter
in
g
(
e.
g
.
co
m
p
lem
e
n
tar
y
f
ilter
in
g
,
Kalm
a
n
f
ilter
in
g
)
m
ay
b
e
n
ec
ess
ar
y
p
r
io
r
t
o
th
e
ap
p
licatio
n
o
f
t
h
e
co
n
tr
o
l
s
ig
n
al
d
u
e
t
o
th
e
ef
f
e
cts
o
f
n
o
is
e,
b
ias
an
d
s
am
p
lin
g
d
elay
in
th
e
s
en
s
o
r
m
ea
s
u
r
em
en
ts
.
T
h
u
s
,
th
e
0
1
2
3
p
rop
os
e
d
PID
PD-
s
m
c
I
A
E
IAE
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
5
1
9
-
5
2
8
526
p
r
o
p
o
s
ed
co
n
t
r
o
ller
n
ee
d
s
t
o
b
e
test
ed
in
f
u
t
u
r
e
u
n
d
er
r
ea
lis
tic
s
en
s
o
r
n
o
is
e
an
d
ac
tu
ato
r
s
atu
r
atio
n
en
v
ir
o
n
m
en
ts
.
T
h
e
p
r
esen
t stu
d
y
m
ain
ly
f
o
c
u
s
es o
n
tr
an
s
ien
t r
esp
o
n
s
e
an
d
d
is
tu
r
b
an
ce
r
eje
ctio
n
p
er
f
o
r
m
an
ce
.
Oth
er
ass
es
s
m
en
ts
lik
e
en
er
g
y
co
n
s
u
m
p
tio
n
an
d
co
m
p
u
tat
io
n
al
co
m
p
lex
ity
an
al
y
s
es
as
well
as
lo
n
g
-
ter
m
s
tab
ilit
y
an
aly
s
is
ca
n
g
iv
e
ad
d
itio
n
al
in
s
ig
h
t
in
to
t
h
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
c
o
n
tr
o
ller
an
d
will
b
e
tak
en
in
t
o
ac
co
u
n
t in
f
u
tu
r
e
wo
r
k
.
6.
CO
NCLU
SI
O
N
I
n
th
is
p
ap
er
,
r
o
b
u
s
t
co
n
t
r
o
l
d
esig
n
u
s
in
g
th
e
co
m
b
in
atio
n
o
f
th
e
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
an
d
th
e
f
ee
d
b
ac
k
lin
ea
r
izatio
n
is
p
r
esen
ted
to
co
n
tr
o
l
th
e
m
o
b
ile
s
elf
-
b
alan
cin
g
r
o
b
o
ts
.
T
h
e
f
ir
s
t
s
tep
is
to
estab
li
s
h
th
e
m
ath
em
atica
l
m
o
d
el
o
f
th
e
r
o
b
o
t.
L
y
ap
u
n
o
v
'
s
s
ec
o
n
d
th
eo
r
em
is
u
s
ed
to
d
em
o
n
s
tr
ate
th
e
s
tab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
.
T
h
e
s
im
u
latio
n
was
d
o
n
e
f
o
r
two
s
ce
n
ar
io
s
;
th
e
f
ir
s
t
o
n
e
is
a
b
o
u
t
tr
ac
k
in
g
th
e
d
esire
d
tr
ajec
to
r
y
an
d
th
e
s
ec
o
n
d
o
n
e
is
ab
o
u
t
th
e
r
o
b
u
s
tn
ess
with
an
ex
ter
n
al
d
is
tu
r
b
an
ce
.
T
h
e
tr
an
s
ien
t
s
p
ec
if
icatio
n
s
,
in
teg
r
al
ab
s
o
lu
t
e
er
r
o
r
(
IA
E
)
a
n
d
i
n
teg
r
al
tim
e
ab
s
o
lu
te
er
r
o
r
(
I
T
AE
)
ar
e
ca
lcu
lated
to
ev
alu
ate
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
an
d
th
e
PID
co
n
t
r
o
ller
.
Sin
ce
th
e
o
p
tim
izatio
n
is
o
f
f
lin
e,
th
e
co
m
p
u
tatio
n
al
co
s
t
h
as
n
o
s
ig
n
if
ican
t
e
f
f
ec
t
o
n
th
e
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
.
On
ce
th
e
o
p
tim
al
p
ar
am
eter
s
ar
e
o
b
tain
ed
,
it
will
b
e
im
p
lem
en
ted
o
n
lin
e.
I
n
p
ar
ticu
lar
,
th
e
p
r
o
p
o
s
ed
h
y
b
r
i
d
c
o
n
tr
o
ller
h
a
s
th
e
s
h
o
r
test
s
ettlin
g
tim
e,
s
m
aller
o
v
e
r
s
h
o
o
t
an
d
b
etter
d
is
tu
r
b
an
ce
r
ejec
tio
n
p
er
f
o
r
m
an
ce
.
I
n
p
r
esen
ce
o
f
d
is
tu
r
b
an
ce
s
,
th
e
h
y
b
r
id
co
n
t
r
o
ller
will
k
ee
p
th
e
tr
ac
k
in
g
er
r
o
r
b
o
u
n
d
ed
an
d
r
ap
id
ly
b
r
in
g
s
it
to
th
e
d
esir
ed
d
y
n
am
ics.
T
h
is
h
ig
h
lig
h
ts
th
e
r
o
b
u
s
tn
ess
o
f
th
e
r
o
b
u
s
t
p
ar
t
o
f
th
e
h
y
b
r
id
co
n
tr
o
ller
.
T
h
e
ab
o
v
e
r
esu
lts
ju
s
tify
th
e
u
s
e
o
f
f
ee
d
b
ac
k
lin
ea
r
izatio
n
an
d
SMC
.
A
d
r
awb
ac
k
is
th
at
h
ig
h
-
f
r
eq
u
e
n
cy
r
ef
er
e
n
ce
in
p
u
ts
r
eq
u
ir
e
h
ig
h
s
witch
in
g
g
ai
n
s
,
an
d
th
u
s
h
ig
h
c
o
n
tr
o
l
ef
f
o
r
t.
W
h
ile
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
d
e
m
o
n
s
tr
ates
h
ig
h
r
o
b
u
s
tn
ess
an
d
g
o
o
d
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
in
t
h
e
s
im
u
latio
n
,
it
is
lim
ited
to
s
im
u
latio
n
s
tu
d
ies.
T
h
e
co
n
tr
o
ller
p
er
f
o
r
m
an
ce
m
u
s
t
b
e
test
ed
ex
p
er
im
en
tally
with
h
ar
d
war
e
lim
itatio
n
s
an
d
s
en
s
o
r
/actu
ato
r
n
o
is
e.
I
n
f
u
tu
r
e
wo
r
k
,
it
ca
n
b
e
s
tu
d
ied
t
h
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
co
n
t
r
o
l
ler
o
n
a
r
ea
l
s
elf
-
b
alan
cin
g
r
o
b
o
t
to
v
er
if
y
th
e
r
ea
l
-
tim
e
f
ea
s
ib
ilit
y
an
d
co
m
p
u
tatio
n
al
ef
f
icien
c
y
with
u
s
in
g
m
ac
h
in
e
lear
n
i
n
g
alg
o
r
ith
m
s
f
o
r
tu
n
in
g
th
e
c
o
n
tr
o
ller
p
ar
am
eter
s
.
F
UNDING
I
N
F
O
RM
A
T
I
O
N
No
f
u
n
d
in
g
was
i
n
v
o
l
v
e
d
.
AUTHO
R
CO
N
T
RI
B
U
T
I
O
NS
ST
AT
E
M
E
NT
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
me
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
Alaa
J
u
m
aa
h
Al
-
Ma
iah
y
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Yah
y
a
Gh
u
f
r
an
Kh
id
h
ir
✓
✓
✓
✓
✓
Ad
n
an
J
ab
b
ar
Attiy
a
✓
✓
✓
✓
✓
✓
His
h
am
H.
J
asim
✓
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
i
t
i
n
g
-
O
r
i
g
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n
a
l
D
r
a
f
t
E
:
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r
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t
i
n
g
-
R
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v
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e
w
&
E
d
i
t
i
n
g
Vi
:
Vi
su
a
l
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z
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t
i
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n
Su
:
Su
p
e
r
v
i
s
i
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n
P
:
P
r
o
j
e
c
t
a
d
mi
n
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st
r
a
t
i
o
n
Fu
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Fu
n
d
i
n
g
a
c
q
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i
si
t
i
o
n
CO
NF
L
I
C
T
OF
I
NT
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RE
ST
ST
AT
E
M
E
NT
T
h
e
au
th
o
r
s
s
tate
no
co
n
f
lict
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DATA
AV
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Evaluation Warning : The document was created with Spire.PDF for Python.
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Evaluation Warning : The document was created with Spire.PDF for Python.