I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
201
7
,
p
p
.
2
0
0
8
~
2
0
1
7
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v7
i
4
.
p
p
2
0
0
8
-
2017
2008
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
JE
C
E
M
o
deling
,
Si
m
ula
tion, and
O
p
ti
m
a
l
Contro
l
for Tw
o
-
Wheeled
Self
-
Ba
la
ncing
R
o
bo
t
M
o
des
t
us
O
liv
er
Asa
li,
F
er
ry
H
a
da
ry
,
B
o
m
o
Wibo
w
o
Sa
nja
y
a
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
T
a
n
ju
n
g
p
u
ra
Un
iv
e
rsity
,
In
d
o
n
e
sia
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Feb
12
,
2
0
1
7
R
ev
i
s
ed
Ma
y
2
0
,
2
0
1
7
A
cc
ep
ted
J
u
n
2
6
,
2
0
1
7
Tw
o
-
w
h
e
e
led
se
lf
-
b
a
lan
c
in
g
ro
b
o
t
is
a
p
o
p
u
lar
m
o
d
e
l
i
n
c
o
n
tr
o
l
sy
ste
m
e
x
p
e
ri
m
e
n
ts
w
h
ich
is
m
o
re
w
id
e
l
y
k
n
o
w
n
a
s
in
v
e
rted
p
e
n
d
u
lu
m
a
n
d
c
a
rt
m
o
d
e
l.
T
h
is
is
a
m
u
lt
i
-
in
p
u
t
a
n
d
m
u
lt
i
-
o
u
tp
u
t
sy
ste
m
w
h
ich
is
th
e
o
re
ti
c
a
l
a
n
d
h
a
s
b
e
e
n
a
p
p
li
e
d
i
n
m
a
n
y
s
y
st
e
m
s
in
d
a
il
y
u
se
.
A
n
y
wa
y
,
m
o
st
r
e
s
e
a
rc
h
ju
st
f
o
c
u
s
o
n
b
a
lan
c
in
g
th
is
m
o
d
e
l
th
ro
u
g
h
try
-
o
n
e
x
p
e
ri
m
e
n
ts
o
r
b
y
u
s
in
g
si
m
p
le
f
o
r
m
o
f
m
a
th
e
m
a
ti
c
a
l
m
o
d
e
l.
T
h
e
re
w
e
re
stil
l
f
e
w
r
e
se
a
r
c
h
e
s
th
a
t
f
o
c
u
s
o
n
c
o
m
p
lete
m
a
th
e
m
a
ti
c
m
o
d
e
li
n
g
a
n
d
d
e
sig
n
in
g
a
m
a
th
e
m
a
ti
c
a
l
m
o
d
e
l
b
a
se
d
c
o
n
tro
ll
e
r
f
o
r
su
c
h
sy
ste
m
.
T
h
is
p
a
p
e
r
a
n
a
ly
z
e
d
m
a
th
e
m
a
ti
c
a
l
m
o
d
e
l
o
f
th
e
s
y
ste
m
.
T
h
e
n
,
th
e
a
u
t
h
o
rs
su
c
c
e
ss
f
u
ll
y
a
p
p
li
e
d
a
L
in
e
a
r
Qu
a
d
ra
ti
c
Re
g
u
lato
r
(L
QR)
c
o
n
tro
ll
e
r
f
o
r
th
is
sy
ste
m
.
T
h
is
c
o
n
tro
ll
e
r
w
a
s
tes
ted
w
it
h
d
if
fe
re
n
t
c
a
se
o
f
s
y
st
e
m
c
o
n
d
it
i
o
n
.
Co
n
tr
o
ll
in
g
re
su
lt
s
w
a
s
p
ro
v
e
d
to
w
o
rk
w
e
ll
a
n
d
tes
ted
o
n
d
if
f
e
re
n
t
c
a
se
o
f
s
y
ste
m
c
o
n
d
it
i
o
n
t
h
ro
u
g
h
sim
u
latio
n
o
n
m
a
tl
a
b
/S
im
u
li
n
k
p
ro
g
ra
m
.
K
ey
w
o
r
d
:
I
n
v
er
ted
p
en
d
u
l
u
m
Ma
tlab
/s
i
m
u
l
in
k
Mo
d
elin
g
a
n
d
s
i
m
u
lat
io
n
Op
ti
m
al
co
n
tr
o
l
Self
-
b
alan
c
in
g
r
o
b
o
t
Co
p
y
rig
h
t
©
201
7
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mo
d
estu
s
Oli
v
er
A
s
al
i,
Dep
ar
t
m
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
T
an
j
u
n
g
p
u
r
a
U
n
iv
er
s
it
y
,
J
alan
J
en
d
r
al
A
h
m
ad
Ya
n
i,
P
o
n
tia
n
ak
7
8
1
2
4
,
I
n
d
o
n
esia.
E
m
ail:
m
o
d
estu
s
_
o
liv
er
@
y
a
h
o
o
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
r
esear
ch
o
n
t
w
o
-
w
h
ee
led
Self
-
b
ala
n
ci
n
g
r
o
b
o
t
h
a
s
g
ain
m
o
m
en
t
u
m
o
v
er
th
e
last
d
ec
ad
e
d
u
e
to
its
n
o
n
li
n
ea
r
it
y
a
n
d
u
n
s
tab
le
n
atu
r
e
d
y
n
a
m
ic
s
y
s
te
m
.
Mo
tio
n
o
f
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
ci
n
g
r
o
b
o
t is
g
o
v
er
n
ed
b
y
u
n
d
er
-
ac
t
u
ated
co
n
f
ig
u
r
ati
o
n
,
i.e
.
,
t
h
e
n
u
m
b
er
o
f
co
n
tr
o
l
in
p
u
t
i
s
less
t
h
an
t
h
e
n
u
m
b
er
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
to
b
e
s
tab
ilized
w
h
ic
h
m
a
k
es
i
t
d
if
f
ic
u
lt
to
ap
p
l
y
th
e
co
n
v
e
n
t
io
n
al
r
o
b
o
tic
ap
p
r
o
ac
h
f
o
r
co
n
tr
o
llin
g
t
h
e
s
y
s
te
m
th
er
ef
o
r
e,
t
h
e
t
w
o
-
w
h
ee
led
s
elf
-
b
ala
n
cin
g
r
o
b
o
t
is
a
g
o
o
d
p
latf
o
r
m
f
o
r
r
esear
ch
er
s
to
i
n
v
est
ig
ate
th
e
ef
f
icien
c
y
o
f
v
ar
io
u
s
co
n
tr
o
ll
er
s
in
co
n
tr
o
l
s
y
s
te
m
.
T
h
e
r
esear
ch
o
n
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
cin
g
r
o
b
o
t
is
o
r
ig
in
all
y
b
ased
o
n
i
n
v
er
ted
p
en
d
u
lu
m
a
n
d
ca
r
t
m
o
d
el.
Ho
w
e
v
er
,
th
e
t
w
o
-
w
h
ee
led
s
elf
b
alan
ci
n
g
r
o
b
o
t
s
y
s
te
m
is
n
o
lo
n
g
er
co
n
s
tr
ain
e
d
to
t
h
e
g
u
id
e
r
ail
b
u
t
m
o
v
e
s
i
n
its
ter
r
ai
n
w
h
ile
b
alan
ci
n
g
th
e
p
en
d
u
lu
m
.
T
h
u
s
,
it
n
ee
d
s
a
g
o
o
d
co
n
tr
o
ller
to
co
n
tr
o
l
its
elf
i
n
u
p
r
i
g
h
t
p
o
s
iti
o
n
an
d
d
esire
d
h
ea
d
in
g
a
n
g
le
w
it
h
o
u
t
t
h
e
n
ee
d
s
f
r
o
m
o
u
t
s
id
e
[
1
]
.
Var
io
u
s
d
esi
g
n
o
f
co
n
tr
o
ller
s
an
d
an
al
y
s
i
s
tec
h
n
iq
u
e
h
ad
b
e
en
p
r
o
p
o
s
ed
b
y
n
u
m
er
o
u
s
r
es
ea
r
ch
er
s
to
co
n
tr
o
l
th
e
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
cin
g
r
o
b
o
t
s
u
ch
t
h
at
th
e
r
o
b
o
t
a
b
le
to
b
a
lan
ce
its
elf
.
I
n
[
2
-
4
]
a
f
u
zz
y
lo
g
i
c
b
ased
co
n
tr
o
ller
w
as
d
esi
g
n
ed
an
d
p
r
o
v
en
s
u
cc
es
s
f
u
l
to
co
n
tr
o
l
an
in
v
er
ted
p
en
d
u
l
u
m
m
o
d
el.
I
n
[
5
]
,
m
o
tio
n
co
n
tr
o
l
o
f
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
ci
n
g
r
o
b
o
t
w
a
s
p
r
o
p
o
s
ed
u
s
i
n
g
lin
ea
r
s
tate
-
s
p
ac
e
m
o
d
e
l.
I
n
[
6
]
,
d
y
n
a
m
ics
w
a
s
d
er
iv
ed
u
s
i
n
g
a
Ne
w
to
n
i
an
ap
p
r
o
ac
h
an
d
th
e
co
n
tr
o
l
w
a
s
d
esig
n
b
y
t
h
e
eq
u
atio
n
s
l
in
ea
r
i
ze
d
ar
o
u
n
d
a
n
o
p
er
atin
g
p
o
in
t.
I
n
[
7
-
9
]
,
an
d
[
1
0
]
a
li
n
ea
r
s
tab
ilizin
g
P
r
o
p
o
r
tio
n
al
I
n
teg
r
al
Der
iv
at
iv
e
(
P
I
D)
an
d
L
i
n
ea
r
Qu
ad
r
atic
R
eg
u
lato
r
(
L
Q
R
)
co
n
tr
o
ller
w
as
d
er
iv
ed
b
y
a
p
lan
ar
m
o
d
el
w
i
th
o
u
t
co
n
s
id
er
i
n
g
r
o
b
o
t’
s
h
ea
d
i
n
g
an
g
le.
T
h
e
ab
o
v
e
co
n
tr
o
l
la
w
w
as
d
esi
g
n
ed
b
y
a
p
lan
ar
m
o
d
el
w
i
th
o
u
t
co
n
s
id
er
i
n
g
r
o
b
o
t’
s
h
ea
d
i
n
g
a
n
g
le
th
er
ef
o
r
e
s
ti
ll
ca
n
n
o
t
b
e
i
m
p
l
e
m
en
ted
in
to
a
r
ea
l
s
y
s
te
m
.
I
n
[
1
1
]
,
a
co
m
p
ar
is
o
n
b
et
w
ee
n
P
I
D
an
d
L
QR
h
a
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mo
d
elin
g
,
S
imu
la
tio
n
,
a
n
d
Op
tima
l Co
n
tr
o
l fo
r
Tw
o
-
W
h
ee
le
d
S
elf
-
B
a
la
n
cin
g
….
(
Mo
d
estu
s
Oliver
A
s
a
li
)
2009
b
ee
n
p
r
esen
ted
w
h
ile
t
h
e
h
ea
d
in
g
a
n
g
le
o
f
t
h
e
r
o
b
o
t
w
as
also
s
tu
d
ied
in
t
h
e
d
y
n
a
m
ic
eq
u
atio
n
t
h
at
w
as
d
er
iv
ed
u
s
i
n
g
L
a
g
r
an
g
ia
n
m
et
h
o
d
.
T
h
is
p
ap
er
co
n
ce
r
n
s
t
h
e
t
w
o
-
w
h
ee
led
s
elf
-
b
ala
n
cin
g
r
o
b
o
t
s
y
s
te
m
as
t
h
e
r
esear
c
h
o
b
j
ec
t,
w
h
ic
h
u
s
e
s
th
e
Ne
w
to
n
ian
m
ec
h
a
n
ic
s
eq
u
atio
n
m
et
h
o
d
to
d
er
iv
e
th
e
d
y
n
a
m
ic
eq
u
atio
n
.
T
h
e
lin
ea
r
s
ta
te
-
s
p
ac
e
m
o
d
el
t
h
at
ap
p
r
o
x
im
a
tes
t
h
e
n
o
n
li
n
ea
r
s
y
s
te
m
in
th
e
r
e
g
io
n
o
f
o
p
er
atio
n
t
h
an
o
b
tai
n
ed
b
y
as
s
u
m
i
n
g
t
h
e
s
y
s
te
m
o
p
er
ates
o
n
l
y
ar
o
u
n
d
an
o
p
er
atin
g
p
o
in
t
an
d
th
e
s
ig
n
al
s
in
v
o
lv
ed
ar
e
s
m
al
l
s
ig
n
al.
B
ased
f
r
o
m
th
e
m
at
h
e
m
a
tical
m
o
d
el
o
f
th
e
s
y
s
te
m
,
L
Q
R
C
o
n
tr
o
ller
is
d
esig
n
ed
to
co
n
tr
o
l
th
e
s
y
s
te
m
ti
lt
an
g
le
an
d
h
ea
d
in
g
an
g
le
s
o
th
at
t
h
e
s
y
s
te
m
ca
n
b
e
co
n
tr
o
lled
to
m
o
v
e
to
a
d
esire
d
p
o
s
itio
n
.
Per
f
o
r
m
an
ce
o
f
co
n
tr
o
l
s
tr
ateg
y
w
it
h
r
esp
ec
t
to
th
e
o
u
tp
u
t tilt a
n
g
le
(
)
an
d
h
ea
d
in
g
an
g
le
(
)
ar
e
ex
a
m
i
n
ed
an
d
p
r
ese
n
ted
b
y
u
s
in
g
m
atlab
/ Si
m
u
li
n
k
p
r
o
g
r
a
m
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
M
a
t
he
m
a
t
ica
l M
o
delin
g
o
f
t
he
Ro
bo
t
T
h
e
r
o
b
o
t
c
o
n
s
is
t
s
o
f
3
m
aj
o
r
p
ar
ts
,
n
a
m
e
l
y
th
e
w
h
ee
l
s
,
p
latf
o
r
m
,
a
n
d
t
h
e
p
en
d
u
lu
m
a
s
th
e
m
as
s
.
T
h
e
r
o
b
o
t
w
it
h
its
t
h
r
ee
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
is
ab
le
to
lin
ea
r
ly
m
o
v
e
w
h
ic
h
is
ch
ar
ac
ter
ized
b
y
p
o
s
itio
n
x
,
ab
le
to
r
o
tate
ar
o
u
n
d
th
e
z
-
a
x
is
(
y
a
w
)
w
i
th
a
s
s
o
ciate
d
a
n
g
le
(
)
,
an
d
ab
le
to
r
o
tate
ar
o
u
n
d
th
e
y
-
a
x
i
s
(
p
itch
)
w
h
er
e
th
e
m
o
v
e
m
e
n
t i
s
d
escr
ib
ed
b
y
an
g
le
(
)
as s
h
o
w
n
in
Fi
g
u
r
e
1
.
T
h
e
i
n
p
u
t
s
o
f
th
e
s
y
s
te
m
ar
e
th
e
to
r
q
u
es
an
d
w
h
ic
h
b
o
th
ar
e
ap
p
lied
to
th
e
t
w
o
w
h
ee
ls
w
h
ic
h
lo
c
ated
o
n
th
e
le
f
t
s
id
e
a
n
d
r
ig
h
t
s
id
e
o
f
th
e
r
o
b
o
t.
L
i
s
t
o
f
p
ar
am
eter
s
f
o
r
th
e
t
w
o
-
w
h
ee
le
d
s
elf
-
b
ala
n
cin
g
r
o
b
o
t a
r
e
s
h
o
w
n
i
n
T
ab
le
1
.
T
h
ese
p
ar
a
m
et
er
s
ar
e
b
ased
o
n
th
e
p
r
o
j
ec
t
co
n
d
u
cted
b
y
L
i
as
s
t
ated
b
y
[
1
2
]
.
T
h
e
o
b
j
ec
tiv
es
o
f
t
h
e
co
n
tr
o
l
s
ch
e
m
es
ar
e
to
c
o
n
tr
o
l
th
e
s
y
s
te
m
’
s
m
o
d
el
s
h
o
w
n
in
Fi
g
u
r
e
1
to
m
o
v
e
to
a
d
esire
d
p
o
s
itio
n
w
h
ile
k
ee
p
i
n
g
t
h
e
r
o
b
o
t’
s
tilt
a
n
g
le
i
n
t
h
e
u
p
r
ig
h
t
p
o
s
itio
n
.
T
h
e
co
n
tr
o
ller
m
u
s
t b
e
ab
le
to
s
tab
ilize
th
e
s
y
s
te
m
w
it
h
ac
ce
p
tab
le
o
v
er
s
h
o
o
t a
n
d
s
ettli
n
g
ti
m
e.
Fig
u
r
e
1
.
A
m
o
d
el
o
f
t
w
o
-
w
h
e
eled
s
elf
-
b
alan
ci
n
g
r
o
b
o
t
T
ab
le
1
.
L
is
t o
f
p
ar
a
m
eter
s
o
f
t
w
o
-
w
h
ee
led
s
el
f
-
b
ala
n
ci
n
g
r
o
b
o
t
S
y
mb
o
l
P
a
r
a
me
t
e
r
U
n
i
t
F
l
,
F
r
I
n
t
e
r
a
c
t
i
n
g
f
o
r
c
e
s b
e
t
w
e
e
n
t
h
e
l
e
f
t
a
n
d
r
i
g
h
t
w
h
e
e
l
s a
n
d
t
h
e
p
l
a
t
f
o
r
m
N
H
l
, H
r
F
r
i
c
t
i
o
n
f
o
r
c
e
s a
c
t
i
n
g
o
n
t
h
e
l
e
f
t
a
n
d
r
i
g
h
t
w
h
e
e
l
s
N
T
o
r
q
u
e
s p
r
o
v
i
d
e
d
b
y
w
h
e
e
l
a
c
t
u
a
t
o
r
s
a
c
t
i
n
g
o
n
t
h
e
l
e
f
t
a
n
d
r
i
g
h
t
w
h
e
e
l
s
N/m
R
o
t
a
t
i
o
n
a
l
a
n
g
l
e
s o
f
t
h
e
l
e
f
t
a
n
d
t
h
e
r
i
g
h
t
w
h
e
e
l
s
ra
d
x
l
,
x
r
D
i
sp
l
a
c
e
me
n
t
s
o
f
t
h
e
l
e
f
t
a
n
d
r
i
g
h
t
w
h
e
e
l
s a
l
o
n
g
t
h
e
x
-
a
x
i
s
m
T
i
l
t
a
n
g
l
e
o
f
t
h
e
r
o
b
o
t
ra
d
H
e
a
d
i
n
g
a
n
g
l
e
o
f
t
h
e
r
o
b
o
t
w
i
t
h
r
e
sp
e
c
t
t
o
t
h
e
z
-
a
x
i
s
ra
d
M
W
M
a
ss
o
f
t
h
e
e
a
c
h
w
h
e
e
l
Kg
I
W
M
o
me
n
t
o
f
i
n
e
r
t
i
a
o
f
t
h
e
w
h
e
e
l
a
b
o
u
t
t
h
e
y
-
a
x
i
s
Kg
.
m
2
r
R
a
d
i
u
s o
f
t
h
e
w
h
e
e
l
m
m
M
a
s
s
o
f
t
h
e
p
e
n
d
u
l
u
m
Kg
g
G
r
a
v
i
t
y
a
c
c
e
l
e
r
a
t
i
o
n
m
/
s
2
D
i
st
a
n
c
e
f
r
o
m t
h
e
p
l
a
t
f
o
r
m t
o
t
h
e
c
e
n
t
e
r
o
f
mass
o
f
t
h
e
p
e
n
d
u
l
u
m
a
l
o
n
g
t
h
e
z
-
a
x
i
s
m
d
D
i
st
a
n
c
e
b
e
t
w
e
e
n
t
h
e
l
e
f
t
a
n
d
r
i
g
h
t
w
h
e
e
l
s a
l
o
n
g
t
h
e
y
-
a
x
i
s
m
M
M
a
ss
o
f
t
h
e
p
l
a
t
f
o
r
m
Kg
I
M
M
o
me
n
t
o
f
i
n
e
r
t
i
a
o
f
t
h
e
p
l
a
t
f
o
r
m a
b
o
u
t
t
h
e
y
-
a
x
i
s
Kg
.
m
2
I
P
M
o
me
n
t
o
f
i
n
e
r
t
i
a
o
f
t
h
e
p
l
a
t
f
o
r
m a
n
d
p
e
n
d
u
l
u
m a
b
o
u
t
t
h
e
z
-
a
x
i
s
Kg
.
m
2
F
P
I
n
t
e
r
a
c
t
i
n
g
f
o
r
c
e
s b
e
t
w
e
e
n
t
h
e
p
e
n
d
u
l
u
m
a
n
d
t
h
e
p
l
a
t
f
o
r
m o
n
t
h
e
x
-
a
x
i
s
N
M
P
I
n
t
e
r
a
c
t
i
n
g
mo
me
n
t
b
e
t
w
e
e
n
t
h
e
p
e
n
d
u
l
u
m
a
n
d
t
h
e
p
l
a
t
f
o
r
m a
b
o
u
t
t
h
e
y
-
a
x
i
s
N/m
V
T
h
e
f
o
r
w
a
r
d
v
e
l
o
c
i
t
y
o
f
t
h
e
r
o
b
o
t
m
/
s
T
h
e
r
o
t
a
t
i
o
n
v
e
l
o
c
i
t
y
o
f
t
h
e
r
o
b
o
t
ra
d
/
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2017
:
2
0
0
8
–
2
0
1
7
2010
W
ith
as
s
u
m
p
tio
n
t
h
at
t
h
er
e
is
n
o
s
lip
b
et
w
ee
n
t
h
e
w
h
ee
ls
an
d
th
e
g
r
o
u
n
d
,
b
y
ap
p
l
y
i
n
g
Ne
w
to
n
’
s
la
w
f
o
r
th
e
li
n
ea
r
a
n
d
r
o
tatio
n
al
m
o
tio
n
b
ased
[
1
3
]
an
d
[
1
4
]
,
b
alan
cin
g
f
o
r
ce
s
a
n
d
m
o
m
e
n
t
ac
tin
g
o
n
t
h
e
lef
t
w
h
ee
l r
es
u
lts
i
n
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
s
o
f
m
o
tio
n
:
∑
̈
(
)
(
1
)
∑
̈
(
2
)
Si
m
i
liar
l
y
,
f
o
r
th
e
r
ig
h
t
w
h
ee
l
w
e
h
av
e:
∑
̈
(
)
(
3
)
∑
̈
(
4
)
B
alan
cin
g
f
o
r
ce
s
ac
ti
n
g
o
n
th
e
p
en
d
u
lu
m
o
n
t
h
e
x
-
ax
i
s
d
ir
ec
tio
n
an
d
m
o
m
e
n
ts
b
etw
ee
n
t
h
e
p
en
d
u
lu
m
a
n
d
th
e
p
lat
f
o
r
m
ab
o
u
t th
e
y
-
ax
is
r
es
u
lts
i
n
:
̈
̈
̇
(
5
)
̈
(
6
)
̈
̈
(
7
)
̈
(
8
)
B
alan
cin
g
t
h
e
m
o
m
en
t
s
ac
ti
n
g
o
n
th
e
p
latf
o
r
m
a
n
d
p
en
d
u
l
u
m
ab
o
u
t th
e
z
-
a
x
i
s
g
i
v
es
:
̈
(
)
(
9
)
T
h
e
r
elatio
n
s
h
ip
b
et
w
ee
n
th
e
d
is
p
lace
m
e
n
ts
o
f
t
h
e
w
h
ee
l
al
o
n
g
th
e
x
-
a
x
is
an
d
t
h
e
r
o
tatio
n
al
an
g
le
o
f
th
e
w
h
ee
l a
b
o
u
t th
e
y
-
a
x
is
i
s
:
(
1
0
)
On
t
h
e
o
th
er
h
a
n
d
,
th
e
r
elat
i
o
n
s
h
ip
b
et
w
ee
n
t
h
e
h
ea
d
i
n
g
an
g
le
(
)
o
f
t
h
e
r
o
b
o
t
ab
o
u
t
th
e
z
-
ax
is
a
n
d
th
e
d
is
p
lace
m
e
n
t o
f
t
h
e
w
h
ee
l a
lo
n
g
t
h
e
x
-
ax
i
s
is
:
(
1
1
)
B
y
s
u
b
tr
ac
ti
n
g
(
1
)
an
d
(
2
)
f
r
o
m
(
3
)
an
d
(
4
)
r
esp
ec
tiv
ely
t
h
e
n
s
u
b
s
tit
u
ti
n
g
i
t to
(
1
1
)
r
esu
lt in
:
(
̈
̈
)
(
)
(
12
)
(
̈
̈
)
(
)
(
13
)
(
)
̈
(
)
(
)
(
1
4
)
̈
(
(
)
)
(
)
(
1
5
)
B
y
ad
d
in
g
(
1
)
an
d
(
2
)
w
it
h
(
3
)
an
d
(
4
)
r
esp
ec
tiv
el
y
th
e
n
s
u
b
s
titu
ti
n
g
it to
(
1
0
)
,
w
e
h
av
e:
̈
(
)
(
16
)
̈
(
)
(
17
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mo
d
elin
g
,
S
imu
la
tio
n
,
a
n
d
Op
tima
l Co
n
tr
o
l fo
r
Tw
o
-
W
h
ee
le
d
S
elf
-
B
a
la
n
cin
g
….
(
Mo
d
estu
s
Oliver
A
s
a
li
)
2011
A
d
d
in
g
(
1
6
)
an
d
(
1
7
)
w
e
h
a
v
e
:
(
)
̈
(
)
(
18
)
B
y
s
u
b
s
t
itu
tin
g
(
1
8
)
to
(
5
)
an
d
(
6
)
w
e
o
b
tain
:
̈
(
(
)
)
̈
̇
(
1
9
)
B
y
s
u
b
s
t
itu
tin
g
(
7
)
to
(
8
)
r
esu
l
t in
:
(
)
̈
̈
(
20
)
Fro
m
t
h
e
ab
o
v
e
d
er
iv
atio
n
,
we
ca
n
o
b
tain
th
e
d
y
n
a
m
ics
eq
u
atio
n
o
f
m
o
tio
n
o
f
th
e
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
cin
g
r
o
b
o
t
as
(
1
5
)
,
(
1
9
)
,
an
d
(
2
0
)
.
A
s
s
u
m
i
n
g
t
h
at
t
h
e
r
o
b
o
t
o
n
ly
ar
o
u
n
d
a
s
m
all
o
p
er
atin
g
p
o
in
t,
th
e
d
y
n
a
m
ic
m
o
d
el
o
f
th
e
r
o
b
o
t
is
t
h
en
lin
ea
r
ized
ar
o
u
n
d
t
h
e
p
o
in
t
̇
.
E
q
u
atio
n
(
1
9
)
,
an
d
(
2
0
)
th
en
b
ec
a
m
e:
̈
(
(
)
)
̈
(
21
)
(
)
̈
̈
(
22
)
B
y
d
e
f
in
i
n
g
th
e
f
o
llo
w
i
n
g
5
-
d
im
en
s
io
n
a
l v
ec
to
r
o
f
s
tate
v
ar
ia
b
le:
[
]
[
̇
̇
]
(
2
3
)
Usi
n
g
(
1
5
)
,
(
2
1
)
,
an
d
(
2
2
)
th
e
lin
ea
r
ized
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
cin
g
r
o
b
o
t
m
o
d
el
ca
n
b
e
ex
p
r
ess
e
d
in
th
e
f
o
llo
w
i
n
g
s
tate
-
s
p
ac
e
f
o
r
m
:
[
̇
̈
̇
̇
̈
]
[
]
[
̇
̇
]
[
]
*
+
(
2
4
)
w
h
er
e:
(
(
)
)
(
(
(
)
)
(
)
)
(
25)
(
(
(
)
)
(
)
)
(
2
6
)
(
(
(
(
)
)
(
)
)
)
(
2
7
)
(
(
(
(
)
)
(
)
)
)
(
2
8
)
(
(
(
(
)
)
(
)
)
)
(
2
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2017
:
2
0
0
8
–
2
0
1
7
2012
(
(
(
(
)
)
(
)
)
)
(
3
0
)
(
(
)
)
(
31)
(
(
)
)
(
32)
Fro
m
th
e
s
tate
-
s
p
ac
e
m
o
d
el
d
escr
ib
ed
ab
o
v
e,
th
er
e
ar
e
a
n
u
m
b
er
o
f
d
y
n
a
m
ic
p
ar
a
m
e
ter
s
in
t
h
e
s
y
s
te
m
w
h
ich
w
i
ll
r
es
u
lt
i
n
v
a
r
iatio
n
o
f
t
h
e
s
tate
m
atr
ice
s
.
I
n
o
r
d
er
to
s
i
m
p
lify
t
h
e
p
r
o
b
lem
an
d
g
i
v
e
a
clea
r
p
h
y
s
ical
m
ea
n
i
n
g
to
th
e
s
tate
m
a
tr
i
x
an
d
in
p
u
t
m
atr
i
x
to
d
esig
n
a
co
n
tr
o
ller
,
th
e
v
al
u
e
o
f
p
ar
am
eter
s
o
f
t
h
e
s
y
s
te
m
w
as s
h
o
w
n
i
n
T
ab
le
2
.
T
ab
le
2
.
Sp
ec
if
icatio
n
s
o
f
t
h
e
t
w
o
-
w
h
ee
led
s
elf
-
b
ala
n
cin
g
r
o
b
o
t
S
y
mb
o
l
V
a
l
u
e
U
n
i
t
M
W
1
Kg
I
W
0
.
0
3
1
3
Kg
.
m
2
r
0
.
2
5
m
m
70
Kg
g
9
.
8
m
/
s
2
1
m
d
0
.
5
m
M
5
Kg
I
M
0
.
0
3
8
5
Kg
.
m
2
I
P
1
.
8
5
6
9
Kg
.
m
2
B
ased
o
n
th
e
v
al
u
e
in
T
ab
le
2
,
it is
ea
s
y
to
h
av
e
a
li
n
ea
r
s
tate
-
s
p
ac
e
eq
u
atio
n
as:
[
̇
̈
̇
̇
̈
]
[
]
[
̇
̇
]
[
]
*
+
(
3
3
)
2
.
2
.
L
Q
R
Co
ntr
o
ller
Desig
n a
nd
Si
m
ula
t
io
n
L
Q
R
i
s
a
m
et
h
o
d
in
m
o
d
er
n
c
o
n
tr
o
l
th
eo
r
y
th
at
u
s
es
s
tate
-
s
p
ac
e
ap
p
r
o
ac
h
to
an
al
y
ze
s
u
c
h
a
s
y
s
te
m
.
Usi
n
g
s
tate
-
s
p
ac
e
m
et
h
o
d
s
,
it
is
r
elati
v
el
y
s
i
m
p
le
to
w
o
r
k
with
a
m
u
lti
-
i
n
p
u
t
m
u
lti
-
o
u
tp
u
t
s
y
s
te
m
.
As
s
u
m
i
n
g
all
s
tate
v
ar
iab
les
ar
e
av
a
ilab
l
e
f
o
r
f
ee
d
b
ac
k
,
t
h
e
s
y
s
te
m
d
es
cr
ib
ed
in
p
r
ev
io
u
s
s
ec
tio
n
ca
n
b
e
s
tab
ilized
u
s
i
n
g
f
u
ll
s
tate
f
ee
d
b
ac
k
[
1
5
]
.
T
h
e
s
ch
e
m
a
tic
o
f
t
h
is
t
y
p
e
o
f
co
n
tr
o
l
s
y
s
te
m
f
o
r
a
t
w
o
-
w
h
ee
led
s
elf
b
ala
n
ci
n
g
r
o
b
o
t
is
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
R
ef
er
r
i
n
g
to
[
1
6
]
Fo
r
th
e
L
i
n
ea
r
T
i
m
e
I
n
v
ar
ia
n
t
(
L
T
I
)
s
y
s
te
m
,
th
e
L
QR
co
n
tr
o
l
t
h
eo
r
y
i
n
v
o
l
v
e
s
ch
o
o
s
in
g
a
co
n
tr
o
l la
w
:
(
)
(
)
(
3
4
)
w
h
ic
h
s
tab
ilize
s
th
e
o
r
ig
in
w
h
i
le
m
i
n
i
m
izi
n
g
t
h
e
q
u
ad
r
atic
co
s
t f
u
n
ctio
n
w
h
ic
h
ca
n
b
e
p
r
esen
ted
:
∫
(
(
)
(
)
(
)
(
)
)
(
3
5
)
w
h
er
e
is
a
s
y
m
m
etr
ic
p
o
s
itiv
e
d
ef
in
ite
o
r
p
o
s
itiv
e
s
e
m
i
-
d
ef
in
ite
m
a
tr
ix
,
R
is
a
s
y
m
m
etr
ic
p
o
s
itiv
e
d
ef
in
ite
m
atr
i
x
an
d
is
u
n
co
n
s
tr
ai
n
ed
.
T
h
e
f
in
al
co
n
tr
o
l la
w
ca
n
b
e
d
er
iv
ed
as:
(
)
(
)
(
3
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mo
d
elin
g
,
S
imu
la
tio
n
,
a
n
d
Op
tima
l Co
n
tr
o
l fo
r
Tw
o
-
W
h
ee
le
d
S
elf
-
B
a
la
n
cin
g
….
(
Mo
d
estu
s
Oliver
A
s
a
li
)
2013
Fig
u
r
e
2
.
T
h
e
L
QR
co
n
tr
o
l sc
h
e
m
e
f
o
r
t
w
o
-
wh
ee
led
s
el
f
-
b
alan
cin
g
r
o
b
o
t
w
h
er
e
a
s
y
m
m
etr
ic
p
o
s
iti
v
e
d
ef
i
n
ite
m
atr
ix
is
a
s
o
lu
tio
n
to
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
:
(
3
7
)
I
n
d
esig
n
in
g
L
QR
co
n
tr
o
ller
,
L
Q
R
f
u
n
ct
io
n
in
m
atlab
m
-
f
il
e
ca
n
b
e
u
s
ed
to
d
eter
m
i
n
e
th
e
v
alu
e
o
f
th
e
v
ec
to
r
K
w
h
ic
h
d
eter
m
i
n
es
th
e
f
ee
d
b
ac
k
co
n
tr
o
l
la
w
.
T
h
is
is
d
o
n
e
b
y
ch
o
o
s
i
n
g
t
wo
p
ar
am
eter
v
alu
e
s
,
m
atr
i
x
an
d
.
T
h
e
o
b
j
ec
tiv
e
o
f
co
n
tr
o
llin
g
th
e
t
w
o
-
w
h
ee
le
d
s
elf
-
b
ala
n
ci
n
g
r
o
b
o
t
s
y
s
te
m
is
to
m
in
i
m
ize
r
o
b
o
t’
s
p
itch
an
g
le
(
)
w
h
i
le
co
n
tr
o
l
th
e
h
ea
d
in
g
an
g
le
(
)
to
w
ar
d
th
e
r
ef
er
en
ce
a
n
g
le,
s
o
d
esig
n
ate
an
d
as
t
w
o
m
ai
n
co
n
tr
o
l
v
ar
iab
les
an
d
an
d
is
g
i
v
e
n
lar
g
er
w
ei
g
h
ts
.
Af
ter
t
u
n
i
n
g
th
e
v
al
u
e
o
f
m
atr
i
x
an
d
m
atr
ix
u
s
in
g
th
e
tr
ial
an
d
er
r
o
r
m
et
h
o
d
,
w
e
f
o
u
n
d
th
e
f
o
llo
w
i
n
g
s
tate
w
ei
g
h
ti
n
g
m
atr
i
x
an
d
in
p
u
t
w
ei
g
h
ti
n
g
m
atr
i
x
to
b
e
ap
p
r
o
p
r
iate:
[
]
*
+
(
3
8
)
Usi
n
g
(
3
8
)
an
d
(
3
7
)
,
th
e
co
n
tr
o
l g
ain
s
in
(
3
6
)
ar
e
f
o
u
n
d
to
b
e:
[
]
(
3
9
)
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
I
n
t
h
is
s
ec
tio
n
,
t
h
e
s
i
m
u
lat
io
n
r
esu
lt
s
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
,
w
h
ic
h
i
s
p
er
f
o
r
m
ed
o
n
t
h
e
m
o
d
el
o
f
a
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
ci
n
g
r
o
b
o
t
ar
e
p
r
esen
ted
.
I
n
o
r
d
er
to
d
esig
n
an
d
s
ti
m
u
late
t
h
e
L
Q
R
C
o
n
tr
o
ller
f
o
r
s
y
s
te
m
,
m
atlab
/s
i
m
u
li
n
k
s
i
m
u
latio
n
to
o
l
is
u
s
ed
.
P
er
f
o
r
m
an
ce
c
h
ar
ac
ter
is
tic
s
o
f
th
e
co
n
tr
o
ller
ar
e
also
d
is
cu
s
s
ed
in
d
etails i
n
t
h
is
s
ec
t
io
n
.
Tw
o
w
h
ee
led
s
el
f
b
alan
ci
n
g
r
o
b
o
t
s
y
s
te
m
w
i
th
L
Q
R
co
n
tr
o
ller
m
e
th
o
d
p
r
o
d
u
ce
d
t
w
o
o
u
tp
u
t
r
esp
o
n
s
es,
r
o
b
o
t’
s
p
itch
a
n
g
le
(
)
an
d
th
e
h
ea
d
i
n
g
an
g
le
(
)
.
I
n
th
i
s
r
esear
ch
,
th
e
in
i
tial
v
a
lu
e
o
f
p
itch
an
g
le
(
)
o
f
th
e
b
alan
ci
n
g
r
o
b
o
t
w
as
s
e
t
to
–
1
r
a
d
to
s
i
m
u
late
t
h
e
p
e
r
f
o
r
m
an
ce
o
f
t
h
e
co
n
tr
o
ller
.
I
t
m
ea
n
s
t
h
at
t
h
e
in
itial
co
n
d
itio
n
o
f
t
h
e
r
o
b
o
t
is
v
er
y
u
n
s
tab
le.
On
t
h
e
o
th
er
h
an
d
,
th
e
in
itial
s
ta
te
o
f
th
e
h
ea
d
in
g
a
n
g
le
(
)
w
a
s
s
et
to
0
r
a
d
an
d
g
iv
e
n
a
u
n
it st
ep
as th
e
r
ef
er
en
ce
s
ig
n
al.
Fig
u
r
e
3
s
h
o
w
s
t
h
e
r
e
s
p
o
n
s
e
o
f
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
cin
g
r
o
b
o
t
p
itch
an
g
le
(
)
in
n
o
r
m
al
co
n
d
itio
n
w
h
ile
Fi
g
u
r
e
4
s
h
o
w
s
t
h
e
r
esp
o
n
s
e
s
o
f
t
w
o
-
w
h
e
eled
s
elf
-
b
ala
n
cin
g
r
o
b
o
t
h
ea
d
in
g
a
n
g
le
(
)
i
n
n
o
r
m
al
co
n
d
itio
n
.
I
n
t
h
e
Fi
g
u
r
e,
th
e
r
esp
o
n
s
e
f
o
r
th
e
p
itc
h
a
n
g
le
(
)
an
d
h
ea
d
i
n
g
an
g
le
(
)
is
r
ep
r
esen
ted
b
y
s
tr
aig
h
t li
n
e
o
r
r
ed
co
lo
r
lin
e
an
d
th
e
r
ef
er
e
n
ce
f
o
r
th
e
s
y
s
te
m
r
esp
o
n
s
e
i
s
r
ep
r
esen
ted
b
y
d
o
tted
lin
e
o
r
b
lu
e
E
r
r
o
r
r
x1
x2
x3
x5
x4
l
e
f
t
t
o
r
q
u
e
r
i
g
h
t
t
o
r
q
u
e
x'
=
A
x+
B
u
y
=
C
x+
D
u
T
w
o
-
w
h
e
e
l
e
d
s
e
l
f
b
a
l
a
n
ci
n
g
r
o
b
o
t
Err
or
U1
U2
K4
x1
x2
x3
x5
U1
U2
K
x1
x2
x3
x4
x5
y
f
cn
C
1
x4
r
e
f
e
r
e
n
ce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2017
:
2
0
0
8
–
2
0
1
7
2014
co
lo
r
lin
e.
Fro
m
th
e
f
i
g
u
r
e,
it
ca
n
b
e
s
ee
n
th
at
th
e
L
QR
co
n
tr
o
ller
ar
e
ca
p
ab
le
to
c
o
n
tr
o
l
t
h
e
p
itch
an
g
le
an
d
h
ea
d
in
g
an
g
le
o
f
t
h
e
r
o
b
o
t
to
t
h
e
d
esire
d
v
alu
e.
T
h
e
s
ettli
n
g
ti
m
e
f
o
r
th
e
p
itch
a
n
g
le
to
r
ea
ch
b
alan
ce
s
tate
i
n
2
.
2
3
s
ec
w
h
ile
t
h
e
s
tead
y
-
s
ta
te
er
r
o
r
is
0
.
0
0
8
6
r
a
d
.
Me
an
w
h
ile,
t
h
e
s
ettli
n
g
ti
m
e
f
o
r
th
e
h
ea
d
i
n
g
an
g
le
to
r
ea
ch
t
h
e
s
tead
y
-
s
ta
te
v
al
u
e
i
s
2
.
7
6
s
ec
w
h
ile
t
h
e
s
tead
y
-
s
ta
te
er
r
o
r
is
0
r
a
d
.
T
h
e
co
n
tr
o
l e
f
f
o
r
t o
f
t
h
e
s
y
s
te
m
’
s
r
esp
o
n
s
e
i
s
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
5
.
T
h
e
to
r
q
u
es
ap
p
lied
to
th
e
lef
t
a
n
d
t
h
e
r
i
g
h
t
w
h
ee
l
s
h
o
w
a
s
li
g
h
t
d
i
f
f
er
en
ce
.
T
h
is
is
d
u
e
to
th
e
d
esire
d
v
alu
e
o
f
th
e
s
y
s
te
m
’
s
h
ea
d
i
n
g
an
g
le
=
1
r
a
d
an
d
th
e
s
y
s
te
m
tr
y
to
f
o
llo
w
th
e
r
ef
er
en
ce
s
i
g
n
al.
Fig
u
r
e
3
.
T
w
o
-
w
h
ee
led
s
el
f
-
b
alan
ci
n
g
r
o
b
o
t p
itch
an
g
le
r
esp
o
n
s
e
i
n
n
o
r
m
al
co
n
d
itio
n
Fig
u
r
e
4
.
T
w
o
-
w
h
ee
led
s
el
f
-
b
alan
ci
n
g
r
o
b
o
t
h
ea
d
in
g
an
g
le
r
esp
o
n
s
e
in
n
o
r
m
al
co
n
d
itio
n
Fig
u
r
e
6
s
h
o
w
s
t
h
e
r
esp
o
n
s
e
o
f
t
w
o
-
w
h
ee
led
s
el
f
-
b
ala
n
cin
g
r
o
b
o
t
p
itch
an
g
le
(
)
w
it
h
t
h
e
p
en
d
u
lu
m
’
s
m
a
s
s
b
ein
g
d
ec
r
ea
s
ed
to
4
0
Kg
.
Fro
m
t
h
e
f
i
g
u
r
e
it
ca
n
b
e
s
ee
n
t
h
at
t
h
e
L
Q
R
co
n
tr
o
ller
ar
e
ca
p
ab
le
to
co
n
tr
o
l
an
d
b
alan
c
e
th
e
p
itc
h
a
n
g
le
d
esp
ite
t
h
e
ch
an
g
e
i
n
t
h
e
p
e
n
d
u
l
u
m
’
s
m
a
s
s
.
I
t
s
h
o
w
t
h
at
th
e
r
esu
lt
h
as
g
o
t
s
i
m
ilar
p
atter
n
a
n
d
n
o
t
m
u
c
h
d
if
f
er
en
t
f
r
o
m
t
h
e
n
o
r
m
al
co
n
d
itio
n
s
y
s
te
m
.
A
l
m
o
s
t
n
o
s
ig
n
i
f
ica
n
t
d
if
f
er
e
n
ce
s
w
er
e
ap
p
ar
en
t
f
r
o
m
co
n
tr
o
l
ler
’
s
p
er
f
o
r
m
an
ce
in
n
o
r
m
al
co
n
d
itio
n
w
it
h
d
ec
r
ea
s
ed
m
a
s
s
co
n
d
it
io
n
as sh
o
w
n
b
y
Fi
g
u
r
es 3
an
d
Fi
g
u
r
e
6
.
Fig
u
r
e
5
.
C
o
n
tr
o
l e
f
f
o
r
t o
f
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
cin
g
r
o
b
o
t in
n
o
r
m
al
co
n
d
itio
n
Fig
u
r
e
6
.
T
w
o
-
w
h
ee
led
s
el
f
-
b
alan
ci
n
g
r
o
b
o
t p
itch
an
g
le
r
esp
o
n
s
e
w
it
h
d
ec
r
ea
s
ed
m
as
s
o
f
th
e
p
en
d
u
lu
m
=
4
0
Kg
Me
an
w
h
ile,
Fi
g
u
r
e
7
.
s
h
o
w
s
t
h
e
r
esp
o
n
s
e
o
f
t
w
o
-
w
h
ee
led
s
elf
-
b
alan
ci
n
g
r
o
b
o
t
p
itch
an
g
l
e
(
)
w
it
h
th
e
p
en
d
u
l
u
m
’
s
m
ass
b
ei
n
g
i
n
cr
ea
s
ed
to
1
1
0
Kg
.
Fro
m
th
e
f
i
g
u
r
e
it
ca
n
b
e
s
ee
n
th
at
th
e
s
y
s
te
m
’
s
r
esp
o
n
s
e
b
ec
am
e
a
litt
le
b
it
q
u
ic
k
er
wh
ile
c
h
an
g
e
s
in
th
e
s
tead
y
-
s
t
ate
er
r
o
r
is
r
elativ
el
y
s
m
all
a
n
d
ca
n
b
e
i
g
n
o
r
ed
.
W
h
en
t
h
e
p
en
d
u
lu
m
’
s
m
as
s
w
er
e
b
ein
g
i
n
cr
ea
s
ed
,
th
er
e
i
s
a
s
i
g
n
i
f
ica
n
ce
i
n
cr
ea
s
e
i
n
s
y
s
te
m
’
s
m
a
x
i
m
u
m
0
1
2
3
4
5
6
7
8
9
10
-1
-
0
.
8
-
0
.
6
-
0
.
4
-
0
.
2
0
0
.
2
0
.
4
t
i
m
e
(
s
e
c
)
p
i
t
c
h
a
n
g
l
e
(
r
a
d
)
T
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
p
i
t
c
h
a
n
g
l
e
r
e
s
p
o
n
s
e
p
i
t
c
h
a
n
g
l
e
r
e
s
p
o
n
s
e
r
e
f
e
r
e
n
c
e
0
1
2
3
4
5
6
7
8
9
10
-
0
.
5
0
0
.
5
1
1
.
5
T
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
h
e
a
d
i
n
g
a
n
g
l
e
r
e
s
p
o
n
s
e
H
e
a
d
i
n
g
a
g
l
e
(
r
a
d
)
t
i
m
e
(
s
e
c
)
0
1
2
3
4
5
6
7
8
9
10
-1
-
0
.
8
-
0
.
6
-
0
.
4
-
0
.
2
0
0
.
2
0
.
4
t
i
m
e
(
s
e
c
)
p
i
t
c
h
a
n
g
l
e
(
r
a
d
)
T
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
p
i
t
c
h
a
n
g
l
e
r
e
s
p
o
n
s
e
p
i
t
c
h
a
n
g
l
e
r
e
s
p
o
n
s
e
r
e
f
e
r
e
n
c
e
0
1
2
3
4
5
6
7
8
9
10
-
0
.
5
0
0
.
5
1
1
.
5
t
i
m
e
(
s
e
c
)
H
e
a
d
i
n
g
a
n
g
l
e
(
r
a
d
)
T
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
h
e
a
d
i
n
g
a
n
g
l
e
r
e
s
p
o
n
s
e
h
e
a
d
i
n
g
a
n
g
l
e
r
e
s
p
o
n
s
e
r
e
f
e
r
e
n
c
e
0
1
2
3
4
5
6
7
8
9
10
-
1
6
0
-
1
4
0
-
1
2
0
-
1
0
0
-
8
0
-
6
0
-
4
0
-
2
0
0
20
t
i
m
e
(
s
e
c
)
T
o
r
q
u
e
(
N
/
m
)
C
o
n
t
r
o
l
e
f
f
o
r
t
o
f
t
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
L
e
f
t
T
o
r
q
u
e
(
u
1
)
R
i
g
h
t
T
o
r
q
u
e
(
u
2
)
0
1
2
3
4
5
6
7
8
9
10
-1
-
0
.
8
-
0
.
6
-
0
.
4
-
0
.
2
0
0
.
2
0
.
4
t
i
m
e
(
s
e
c
)
p
i
t
c
h
a
n
g
l
e
(
r
a
d
)
T
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
p
i
t
c
h
a
n
g
l
e
r
e
s
p
o
n
s
e
p
i
t
c
h
a
n
g
l
e
r
e
s
p
o
n
s
e
r
e
f
e
r
e
n
c
e
0
1
2
3
4
5
6
7
8
9
10
-
0
.
5
0
0
.
5
1
1
.
5
t
i
m
e
(
s
e
c
)
H
e
a
d
i
n
g
a
n
g
l
e
(
r
a
d
)
T
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
h
e
a
d
i
n
g
a
n
g
l
e
r
e
s
p
o
n
s
e
h
e
a
d
i
n
g
a
n
g
l
e
r
e
s
p
o
n
s
e
r
e
f
e
r
e
n
c
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mo
d
elin
g
,
S
imu
la
tio
n
,
a
n
d
Op
tima
l Co
n
tr
o
l fo
r
Tw
o
-
W
h
ee
le
d
S
elf
-
B
a
la
n
cin
g
….
(
Mo
d
estu
s
Oliver
A
s
a
li
)
2015
o
v
er
s
h
o
o
t
a
n
d
s
tead
y
-
s
tate
er
r
o
r
b
u
t
o
v
er
all,
t
h
e
p
er
f
o
r
m
an
c
e
o
f
t
h
e
co
n
tr
o
ller
w
as
s
till
ac
ce
p
tab
le
b
ec
au
s
e
it
ca
n
s
t
ill
m
ai
n
tai
n
it
’
s
u
p
r
ig
h
t
p
o
s
itio
n
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
co
n
tr
o
ller
i
n
F
ig
u
r
e
7
g
i
v
es
th
e
co
n
c
lu
s
io
n
t
h
a
t
th
e
p
er
f
o
r
m
a
n
ce
o
f
L
Q
R
co
n
tr
o
ller
s
i
s
li
m
ited
to
a
ce
r
t
ain
r
an
g
e
o
f
p
en
d
u
l
u
m
’
s
m
a
s
s
f
r
o
m
t
h
e
n
o
r
m
al
co
n
d
itio
n
s
.
I
f
t
h
e
p
en
d
u
l
u
m
m
as
s
is
in
cr
ea
s
ed
to
a
ce
r
tai
n
p
o
in
t,
it
is
p
o
s
s
ib
le
th
a
t
th
e
c
o
n
tr
o
ller
w
i
ll
f
ail
to
co
n
tr
o
l
th
e
s
y
s
te
m
s
o
th
at
th
e
r
o
b
o
t
w
ill
f
all.
T
h
er
ef
o
r
e,
w
h
en
d
esig
n
i
n
g
L
Q
R
co
n
tr
o
ller
s
it
s
h
o
u
ld
also
tak
e
in
to
ac
co
u
n
t th
e
r
a
n
g
e
o
f
p
e
n
d
u
lu
m
’
s
m
a
s
s
i
n
w
h
ich
t
h
e
s
y
s
t
e
m
w
ill
o
p
er
ate
m
o
s
t
.
T
h
e
d
is
tu
r
b
an
ce
r
ej
ec
tio
n
p
er
f
o
r
m
an
ce
o
f
th
e
co
n
tr
o
ller
is
s
h
o
w
n
in
Fig
u
r
e
8
.
An
i
m
p
u
l
s
e
d
is
tu
r
b
an
ce
is
ap
p
lied
at
ar
o
u
n
d
5
s
ec
to
t
h
e
r
o
b
o
t
w
h
ile
it
is
s
tab
ilizi
n
g
.
I
t
ca
n
b
e
o
b
s
er
v
ed
th
at
th
e
r
o
b
o
t
i
s
ab
le
to
r
e
j
ec
t
th
is
d
is
t
u
r
b
an
ce
an
d
r
eg
ai
n
s
it
s
b
alan
ce
p
o
s
it
io
n
in
a
s
h
o
r
t
a
m
o
u
n
t
o
f
t
i
m
e
.
A
g
r
ea
ter
co
n
tr
o
l
ef
f
o
r
t is
u
s
ed
b
y
t
h
e
r
o
b
o
t to
o
v
er
co
m
e
t
h
e
d
is
tu
r
b
a
n
ce
f
o
r
ce
as sh
o
w
n
in
Fig
u
r
e
9
.
Fig
u
r
e
7
.
T
w
o
-
w
h
ee
led
s
el
f
-
b
alan
ci
n
g
r
o
b
o
t p
itch
an
g
le
r
esp
o
n
s
e
w
it
h
i
n
cr
ea
s
ed
m
as
s
o
f
t
h
e
p
en
d
u
lu
m
=
1
1
0
Kg
Fig
u
r
e
8
.
T
w
o
-
w
h
ee
led
s
el
f
-
b
alan
ci
n
g
r
o
b
o
t p
itch
an
g
le
r
esp
o
n
s
e
w
it
h
d
is
t
u
r
b
an
ce
ap
p
lied
to
th
e
b
o
d
y
p
itch
a
n
g
le
Fig
u
r
e
9
.
C
o
n
tr
o
l e
f
f
o
r
t o
f
t
w
o
-
w
h
ee
led
s
el
f
-
b
ala
n
ci
n
g
r
o
b
o
t d
u
r
in
g
d
is
t
u
r
b
an
ce
r
ej
ec
tio
n
T
ab
le
3
s
h
o
w
s
t
h
e
s
u
m
m
ar
y
o
f
th
e
p
er
f
o
r
m
an
ce
c
h
ar
ac
ter
i
s
tics
o
f
th
e
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
cin
g
r
o
b
o
t
in
v
ar
io
u
s
co
n
d
it
io
n
s
.
B
ased
o
n
t
h
e
d
ata
tab
u
lated
i
n
T
ab
le
3
,
it
ca
n
b
e
s
ee
n
t
h
at
t
h
e
r
esp
o
n
s
es
o
f
th
e
s
elf
-
b
ala
n
cin
g
r
o
b
o
t p
itch
an
g
l
e
an
d
h
ea
d
in
g
an
g
le
h
av
e
ac
ce
p
tab
le
o
v
er
s
h
o
o
t a
n
d
u
n
d
er
s
h
o
o
t.
Fro
m
t
h
is
r
esear
c
h
it
ca
n
b
e
s
ee
n
t
h
at
L
Q
R
co
n
tr
o
ller
s
c
an
b
e
i
m
p
le
m
e
n
ted
to
co
n
tr
o
l
th
e
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
c
in
g
r
o
b
o
t
s
y
s
te
m
an
d
p
r
o
v
id
e
q
u
ite
g
o
o
d
r
esu
lts
.
I
n
t
h
i
s
r
esear
ch
,
w
e
a
ls
o
tes
ted
th
e
co
n
tr
o
ller
o
n
v
ar
io
u
s
s
tate
o
f
t
h
e
s
y
s
te
m
w
h
ic
h
h
a
s
n
o
t
b
ee
n
s
h
o
w
n
s
o
clea
r
l
y
i
n
p
r
ev
io
u
s
r
esear
ch
.
Fro
m
th
e
s
i
m
u
lat
io
n
,
it
ca
n
b
e
s
ee
n
t
h
at
alth
o
u
g
h
th
e
co
n
tr
o
ller
is
ca
p
ab
le
o
f
co
n
tr
o
llin
g
t
h
e
s
y
s
te
m
d
esp
ite
b
ei
n
g
s
u
b
j
ec
ted
to
a
ch
an
g
e
i
n
m
as
s
o
r
d
is
tu
r
b
an
ce
to
t
h
e
b
o
d
y
p
itc
h
an
g
le
,
t
h
er
e
i
s
a
t
o
ler
ab
le
li
m
it
o
f
m
as
s
ch
a
n
g
e
0
1
2
3
4
5
6
7
8
9
10
-1
-
0
.
8
-
0
.
6
-
0
.
4
-
0
.
2
0
0
.
2
0
.
4
t
i
m
e
(
s
e
c
)
p
i
t
c
h
a
n
g
l
e
(
r
a
d
)
T
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
p
i
t
c
h
a
n
g
l
e
r
e
s
p
o
n
s
e
p
i
t
c
h
a
n
g
l
e
r
e
s
p
o
n
s
e
r
e
f
e
r
e
n
c
e
0
1
2
3
4
5
6
7
8
9
10
-
0
.
5
0
0
.
5
1
1
.
5
t
i
m
e
(
s
e
c
)
H
e
a
d
i
n
g
a
n
g
l
e
(
r
a
d
)
T
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
h
e
a
d
i
n
g
a
n
g
l
e
r
e
s
p
o
n
s
e
h
e
a
d
i
n
g
a
n
g
l
e
r
e
s
p
o
n
s
e
r
e
f
e
r
e
n
c
e
0
1
2
3
4
5
6
7
8
9
10
-3
-2
-1
0
1
2
3
t
i
m
e
(
s
e
c
)
p
i
t
c
h
a
n
g
l
e
(
r
a
d
)
T
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
p
i
t
c
h
a
n
g
l
e
r
e
s
p
o
n
s
e
p
i
t
c
h
a
n
g
l
e
r
e
s
p
o
n
s
e
r
e
f
e
r
e
n
c
e
0
1
2
3
4
5
6
7
8
9
10
-
0
.
5
0
0
.
5
1
1
.
5
t
i
m
e
(
s
e
c
)
H
e
a
d
i
n
g
a
n
g
l
e
(
r
a
d
)
T
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
h
e
a
d
i
n
g
a
n
g
l
e
r
e
s
p
o
n
s
e
h
e
a
d
i
n
g
a
n
g
l
e
r
e
s
p
o
n
s
e
r
e
f
e
r
e
n
c
e
0
1
2
3
4
5
6
7
8
9
10
-
1
6
0
-
1
4
0
-
1
2
0
-
1
0
0
-
8
0
-
6
0
-
4
0
-
2
0
0
20
40
t
i
m
e
(
s
e
c
)
T
o
r
q
u
e
(
N
/
m
)
C
o
n
t
r
o
l
e
f
f
o
r
t
o
f
t
w
o
-
w
h
e
e
l
e
d
s
e
l
f
-
b
a
l
a
n
c
i
n
g
r
o
b
o
t
L
e
f
t
T
o
r
q
u
e
(
u
1
)
R
i
g
h
t
T
o
r
q
u
e
(
u
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2017
:
2
0
0
8
–
2
0
1
7
2016
o
r
p
itch
an
g
le
ch
an
g
e
.
T
h
er
ef
o
r
e,
w
h
en
d
esi
g
n
in
g
th
e
co
n
tr
o
ller
,
th
e
v
alu
es
o
f
t
h
e
s
y
s
te
m
p
ar
am
eter
s
s
h
o
u
ld
b
e
co
n
s
id
er
ed
so
th
at
th
e
co
n
tr
o
ller
ca
n
w
o
r
k
w
el
l u
n
d
er
id
ea
l o
r
n
o
n
id
ea
l c
o
n
d
itio
n
s
.
T
ab
le
3
.
Sp
ec
if
icatio
n
s
o
f
t
h
e
t
w
o
-
w
h
ee
led
s
elf
-
b
ala
n
cin
g
r
o
b
o
t
S
y
st
e
m
’
s c
o
n
d
i
t
i
o
n
P
i
t
c
h
a
n
g
l
e
(
)
H
e
a
d
i
n
g
a
n
g
l
e
(
)
(
s)
(
ra
d
)
(
s)
(r
ad
)
N
o
r
mal
c
o
n
d
i
t
i
o
n
2
.
2
3
0
.
0
0
8
6
2
.
7
6
0
I
n
c
r
e
a
se
d
p
e
n
d
u
l
u
m’
s
mass
7
.
0
4
0
.
0
1
4
4
-
-
D
e
c
r
e
a
se
d
p
e
n
d
u
l
u
m’
s
mass
0
.
5
2
0
.
0
0
5
7
-
-
4.
CO
NCLU
SI
O
N
I
n
th
i
s
p
ap
er
,
th
e
d
esig
n
an
d
i
m
p
le
m
en
ta
tio
n
o
f
L
Q
R
co
n
tr
o
ller
f
o
r
s
tab
ilizin
g
a
t
w
o
-
w
h
ee
led
s
elf
-
b
alan
cin
g
r
o
b
o
t
is
p
r
esen
ted
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
L
Q
R
i
s
s
i
m
u
lated
an
d
an
a
l
y
ze
d
w
i
th
m
atlab
/s
i
m
u
li
n
k
p
r
o
g
r
am
.
B
ased
o
n
th
e
r
es
u
lt
s
an
d
th
e
a
n
al
y
s
i
s
,
a
co
n
clu
s
io
n
h
as
b
ee
n
m
ad
e
th
a
t
th
e
L
Q
R
co
n
tr
o
ller
ar
e
ca
p
ab
le
o
f
co
n
tr
o
llin
g
th
e
t
w
o
-
w
h
ee
led
s
elf
-
b
alan
ci
n
g
r
o
b
o
t’
s
p
itch
an
g
le
an
d
h
ea
d
in
g
a
n
g
le
a
n
d
y
ield
s
ac
ce
p
tab
le
an
d
g
o
o
d
r
esu
lts
with
o
u
t
f
al
lin
g
.
I
n
n
o
r
m
a
l
co
n
d
itio
n
t
h
e
s
y
s
te
m
ca
n
b
e
en
g
a
g
ed
to
b
alan
ce
its
el
f
an
d
g
i
v
e
tr
a
n
s
ie
n
t
r
esp
o
n
s
e
ch
ar
ac
ter
is
tics
s
e
ttli
n
g
ti
m
e
=
2
.
2
3
s
ec
an
d
s
tead
y
-
s
tate
er
r
o
r
=
0
.
0
0
8
6
r
a
d
f
o
r
tilt
an
g
le
r
esp
o
n
s
e
an
d
s
ettli
n
g
ti
m
e
=
2
.
7
6
s
ec
an
d
s
tead
y
-
s
tat
e
er
r
o
r
=
0
r
a
d
f
o
r
h
ea
d
in
g
a
n
g
le
r
esp
o
n
s
e.
W
h
e
n
th
e
p
en
d
u
l
u
m
’
s
m
ass
is
b
ei
n
g
in
cr
ea
s
ed
b
y
3
0
Kg
,
t
h
e
s
y
s
t
e
m
g
iv
e
tr
an
s
ien
t
r
esp
o
n
s
e
ch
ar
ac
ter
is
tics
s
ettli
n
g
ti
m
e
=
7
.
0
4
s
ec
a
n
d
s
tead
y
-
s
t
ate
er
r
o
r
=
0
.
0
1
4
4
r
a
d
f
o
r
tilt
an
g
le
an
d
w
h
e
n
t
h
e
p
en
d
u
lu
m
’
s
m
as
s
i
s
b
ein
g
d
ec
r
ea
s
ed
b
y
3
0
Kg
t
h
e
s
y
s
te
m
g
iv
e
tr
a
n
s
ie
n
t
r
esp
o
n
s
e
ch
a
r
ac
ter
is
tics
s
et
tli
n
g
t
i
m
e
=
0
.
5
2
s
ec
an
d
s
tead
y
-
s
tate
er
r
o
r
=
0
.
0
0
5
7
r
a
d
f
o
r
tilt
a
n
g
le.
Ho
w
ev
er
,
m
o
r
e
e
x
p
er
im
e
n
t
n
ee
d
s
to
b
e
p
er
f
o
r
m
ed
to
e
v
al
u
ate
t
h
e
r
o
b
u
s
tn
es
s
o
f
th
e
s
y
s
te
m
.
No
n
li
n
ea
r
co
n
tr
o
ller
is
f
u
ll
y
r
ec
o
m
m
e
n
d
ed
f
o
r
b
alan
ci
n
g
th
e
t
w
o
-
w
h
ee
led
s
el
f
-
b
alan
cin
g
r
o
b
o
t a
s
it
w
il
l u
p
g
r
ad
e
th
e
r
o
b
u
s
tn
e
s
s
o
f
t
h
e
s
y
s
te
m
.
RE
F
E
R
E
NC
E
S
[
1
]
A
.
N.K.
N
a
sir,
M
.
A
.
A
h
m
a
d
,
R.
M
.
T
.
Ra
ja
Is
m
a
il
,
“
T
h
e
Co
n
tro
l
o
f
a
Hig
h
l
y
No
n
li
n
e
a
r
Tw
o
-
wh
e
e
ls
Ba
lan
c
in
g
Ro
b
o
t:
A
Co
m
p
a
ra
ti
v
e
A
ss
e
ss
m
e
n
t
b
e
tw
e
e
n
L
Q
R
a
n
d
P
ID
-
P
ID
Co
n
tr
o
l
S
c
h
e
m
e
s
”
,
in
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
M
e
c
h
a
n
ica
l,
Aer
o
sp
a
c
e
,
In
d
u
stri
a
l,
M
e
c
h
a
tro
n
ic,
a
n
d
M
a
n
u
fa
c
t
u
rin
g
En
g
i
n
e
e
rin
g
,
v
o
l.
4
,
n
o
.
1
0
,
p
p
.
9
4
2
-
9
4
7
,
Oc
to
b
e
r
2
0
1
0
.
[2
]
H.
L
iu
,
J.
Xu
,
Y.
S
u
n
,
“
A
d
a
p
t
iv
e
F
u
z
z
y
S
li
d
in
g
M
o
d
e
S
tab
il
i
z
a
ti
o
n
Co
n
tro
ll
e
r
f
o
r
In
v
e
rted
P
e
n
d
u
l
u
m
s
”
,
in
T
e
lec
o
mm
u
n
ica
ti
o
n
,
C
o
mp
u
t
in
g
,
El
e
c
tro
n
ics
,
a
n
d
C
o
n
tr
o
l
(
T
EL
KOM
NIKA)
,
v
o
l.
1
1
,
n
o
.
1
2
,
p
p
.
7
2
4
3
-
7
2
5
0
,
De
c
e
m
b
e
r
2
0
1
3
.
[3
]
T
.
Y.
Ch
u
a
n
,
L
.
F
e
n
g
,
Q.
Qia
n
,
Y.
Ya
n
g
,
“
S
tab
il
izin
g
P
la
n
a
r
In
v
e
rted
P
e
n
d
u
l
u
m
S
y
ste
m
s
Ba
s
e
d
o
n
F
u
z
z
y
Nin
e
-
P
o
in
t
Co
n
tr
o
ll
e
r
”,
in
T
e
lec
o
mm
u
n
ica
ti
o
n
,
Co
mp
u
ti
n
g
,
E
lec
tro
n
ics
,
a
n
d
C
o
n
tr
o
l
(
T
EL
KOM
NIKA)
,
v
o
l.
1
2
,
n
o
.
1
,
p
p
.
422
-
4
3
2
,
Ja
n
u
a
ry
2
0
1
4
.
[4
]
T
.
O.S
Ha
n
a
fy
,
M
.
K.
M
e
tw
a
ll
y
,
“
S
im
p
li
f
ica
ti
o
n
s
th
e
Ru
le
Ba
se
f
o
r
S
tab
il
iza
ti
o
n
o
f
In
v
e
rted
P
e
n
d
u
l
u
m
S
y
ste
m
”
,
in
T
e
lec
o
mm
u
n
ica
ti
o
n
,
Co
m
p
u
ti
n
g
,
El
e
c
tro
n
ics
,
a
n
d
C
o
n
tr
o
l
(
T
EL
K
OM
NIKA)
,
v
o
l.
1
2
,
n
o
.
7
,
p
p
.
5
2
2
5
-
5
2
3
4
,
Ju
ly
2
0
1
4
.
[5
]
M
.
u
l
Ha
sa
n
,
K.
M
.
Ha
sa
m
,
e
t
a
l.
,
“
De
sig
n
a
n
d
Ex
p
e
rime
n
ta
l
Ev
a
l
u
a
ti
o
n
o
f
a
S
t
a
te
Fee
d
b
a
c
k
Co
n
t
ro
ll
e
r
fo
r
T
w
o
W
h
e
e
led
Ba
la
n
c
in
g
R
o
b
o
t
”
,
1
7
th
IEE
E
In
tern
a
ti
o
n
a
l
M
u
lt
i
T
o
p
ic C
o
n
f
e
re
n
c
e
(INM
IC),
Ka
ra
c
h
i,
2
0
1
4
:3
6
6
-
3
7
1
.
[6
]
Jia
n
F
a
n
g
,
“
T
h
e
L
QR
Co
n
tro
ll
e
r
De
sig
n
o
f
Tw
o
-
w
h
e
e
led
S
e
lf
-
b
a
lan
c
in
g
Ro
b
o
t
Ba
se
d
o
n
th
e
P
a
rti
c
le
S
w
a
rm
Op
ti
m
iza
ti
o
n
A
lg
o
rit
h
m
”
,
in
M
a
th
e
ma
ti
c
a
l
Pro
b
lem
s
in
En
g
in
e
e
r
in
g
,
v
o
l.
2
0
1
4
,
a
rti
c
le
id
.
7
2
9
0
9
5
,
p
p
.
1
-
6
,
Ju
n
e
2
0
1
4
.
[7
]
K.
P
ra
k
a
sh
,
K.
T
h
o
m
a
s
,
“
S
tu
d
y
o
f
Co
n
tr
o
ll
e
r
fo
r
a
T
w
o
W
h
e
e
led
S
e
lf
-
b
a
la
n
c
in
g
Ro
b
o
t
”,
I
n
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
Ne
x
t
G
e
n
e
ra
ti
o
n
In
tell
ig
e
n
t
S
y
ste
m
s (ICN
G
IS
),
Ko
tt
a
y
a
m
,
2
0
1
6
.
[8
]
H.S
.
Zad
,
A
.
Ula
s
y
a
r,
A
.
Zo
h
a
ib
,
a
n
d
S
.
S
.
Hu
ss
a
in
,
“
Op
ti
ma
l
Co
n
tro
ll
e
r
De
sig
n
fo
r
S
e
lf
-
b
a
la
n
c
in
g
T
wo
-
w
h
e
e
led
Ro
b
o
t
S
y
ste
m
”,
In
tern
a
ti
o
n
a
l
C
o
n
f
e
r
e
n
c
e
o
n
F
r
o
n
ti
e
rs
o
f
In
f
o
rm
a
ti
o
n
T
e
c
h
n
o
l
o
g
y
(F
IT
)
,
Isla
m
a
b
a
d
.
2
0
1
6
:
1
1
-
16.
[
9
]
C.
S
u
n
,
T
.
L
u
,
K.
Yu
a
n
,
“
Ba
l
a
n
c
e
Co
n
tr
o
l
o
f
T
w
o
-
wh
e
e
led
S
e
l
f
-
b
a
l
a
n
c
i
n
g
Ro
b
o
t
Ba
se
d
o
n
L
i
n
e
a
r
Qu
a
d
ra
ti
c
Reg
u
l
a
to
r
a
n
d
Ne
u
r
a
l
Ne
two
rk
”
,
4
th
In
ter
n
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
In
telli
g
e
n
t
C
o
n
t
ro
l
a
n
d
In
f
o
rm
a
t
io
n
P
ro
c
e
ss
in
g
(ICICIP
)
,
Be
ij
in
g
,
2
0
1
3
:8
6
2
-
8
6
7
.
[1
0
]
M
.
M
a
jcz
a
k
,
P
.
W
a
w
rz
y
ń
sk
i
,
“
C
o
mp
a
ris
o
n
o
f
T
wo
Ef
fi
c
ien
t
C
o
n
tro
l
S
tr
a
teg
ies
fo
r
T
w
o
-
wh
e
e
l
e
d
Ba
l
a
n
c
in
g
Ro
b
o
t
”
,
2
0
t
h
In
ter
n
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
M
e
th
o
d
s
a
n
d
M
o
d
e
ls
in
A
u
to
m
a
ti
o
n
a
n
d
Ro
b
o
ti
c
s
(M
M
A
R),
M
ied
z
y
z
d
ro
je,
2
0
1
5
:
7
4
4
-
7
4
9
.
[
11
]
Mi
k
a
e
l
A
r
v
id
ss
o
n
,
Jo
n
a
s
Ka
rlsso
n
,
“
De
sig
n
,
Co
n
stru
c
ti
o
n
a
n
d
Ver
if
ica
ti
o
n
o
f
a
S
e
lf
-
b
a
la
n
c
in
g
Ve
h
i
c
le
”
,
Ch
a
lm
e
rs
Un
iv
e
rsit
y
o
f
Tec
h
n
o
lo
g
y
,
De
p
a
rtme
n
t
o
f
S
ig
n
a
ls
a
n
d
S
y
ste
m
s,
Re
p
o
rt
n
u
m
b
e
r:
E
X
0
5
0
,
2
0
1
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mo
d
elin
g
,
S
imu
la
tio
n
,
a
n
d
Op
tima
l Co
n
tr
o
l fo
r
Tw
o
-
W
h
ee
le
d
S
elf
-
B
a
la
n
cin
g
….
(
Mo
d
estu
s
Oliver
A
s
a
li
)
2017
[
12
]
Zh
ij
u
n
L
i,
Ch
e
n
g
u
a
n
g
Ya
n
g
,
L
ip
in
g
F
a
n
,
“
A
d
v
a
n
c
e
d
Co
n
tr
o
l
o
f
W
h
e
e
led
In
v
e
rted
P
e
n
d
u
l
u
m
S
y
s
tem
s”
,
L
o
n
d
o
n
:
S
p
rin
g
e
r,
2
0
1
3
.
[1
3
]
Da
v
id
M
o
rin
,
“
In
tr
o
d
u
c
ti
o
n
t
o
Clas
sic
a
l
M
e
c
h
a
n
in
c
s
w
it
h
P
ro
b
lem
s
a
n
d
S
o
lu
ti
o
n
s”
,
Ne
w
Y
o
rk
:
Ca
m
b
rid
g
e
Un
iv
e
rsit
y
P
re
ss
,
2
0
0
8
.
[1
4
]
H.
D.
Yo
u
n
g
,
R.
A
.
F
re
e
d
m
a
n
,
“
Un
iv
e
rsi
t
y
P
h
y
sic
s
w
it
h
M
o
d
e
rn
P
h
y
sic
s
”
,
Twe
l
f
th
Ed
it
io
n
.
S
a
n
F
r
a
n
sisc
o
:
P
e
a
rso
n
A
d
isso
n
-
W
e
sle
y
,
2
0
0
7
.
[1
5
]
Ka
tsu
h
ik
o
Og
a
ta,
“
M
o
d
e
r
n
Co
n
tr
o
l
E
n
g
in
e
e
rin
g
”
,
T
h
ird
E
d
it
i
o
n
,
N
e
w
J
e
rse
y
:
P
re
n
ti
c
e
Ha
ll
,
1
9
9
7
.
[1
6
]
R.
C.
Do
rf
,
R.
H.
Bis
h
o
p
,
“
M
o
d
e
rn
Co
n
tr
o
l
S
y
ste
m
,
Tw
e
l
f
th
Ed
it
io
n
,
Ne
w
J
e
rse
y
:
P
re
n
ti
c
e
Ha
ll
,
2
0
1
1
.
B
I
O
G
RAP
H
I
E
S O
F
AUTH
O
RS
M
o
d
e
stu
s
O
li
v
e
r
As
a
li
w
a
s
b
o
rn
in
P
o
n
ti
a
n
a
k
,
I
n
d
o
n
e
sia
,
i
n
1
9
9
4
.
He
re
c
e
iv
e
d
h
is
Ba
c
h
e
lo
r’s
d
e
g
re
e
w
it
h
a
c
o
n
c
e
n
tratio
n
in
c
o
n
tro
l
e
n
g
in
e
e
rin
g
f
ro
m
De
p
a
rt
m
e
n
t
o
f
El
e
c
tri
c
a
l,
Tan
ju
n
g
p
u
ra
Un
iv
e
rsi
ty
,
P
o
n
t
ian
a
k
in
2
0
1
7
.
He
is
i
n
tere
ste
d
in
m
o
d
e
rn
c
o
n
tr
o
l
e
n
g
in
e
e
ri
n
g
,
a
n
d
c
o
n
tro
l
o
f
n
o
n
li
n
e
a
r
d
y
n
a
m
ic
a
l
s
y
ste
m
.
He
n
o
w
li
v
e
d
in
P
o
n
ti
a
n
a
k
a
n
d
m
a
y
b
e
re
a
c
h
e
d
a
t
m
o
d
e
stu
s_
o
li
v
e
r@y
a
h
o
o
.
c
o
m
F
e
r
r
y
H
a
d
a
r
y
is
a
n
A
ss
istan
t
P
r
o
f
e
ss
o
r
o
f
Ro
b
o
t
ics
,
C
o
n
tro
l
a
n
d
Co
m
p
u
tati
o
n
a
t
T
a
n
ju
n
g
p
u
ra
Un
iv
e
rsit
y
(UN
TA
N),
P
o
n
t
ian
a
k
,
In
d
o
n
e
sia
.
He
e
a
rn
e
d
h
is
B.
En
g
.
d
e
g
re
e
f
ro
m
T
a
n
ju
n
g
p
u
ra
Un
iv
e
rsit
y
,
M
.
En
g
.
f
ro
m
T
o
k
y
o
In
stit
u
te o
f
T
e
c
h
n
o
lo
g
y
,
J
a
p
a
n
,
a
n
d
Dr.
En
g
.
f
ro
m
K
y
u
sh
u
In
stit
u
te o
f
T
e
c
h
n
o
lo
g
y
,
Ja
p
a
n
.
He
is
c
u
rr
e
n
tl
y
t
e
a
c
h
in
g
a
t
D
e
p
a
rt
m
e
n
t
o
f
E
lec
tri
c
a
l
En
g
in
e
e
rin
g
,
Tan
ju
n
g
p
u
ra
Un
iv
e
rsit
y
.
In
h
is
c
a
re
e
r
a
s
a
re
se
a
rc
h
e
r
h
e
re
c
e
iv
e
d
se
v
e
ra
l
re
se
a
rc
h
g
ra
n
ts
p
re
stig
e
o
f
th
e
M
i
n
istry
o
f
Re
se
a
rc
h
T
e
c
h
n
o
l
o
g
y
a
n
d
Hig
h
e
r
Ed
u
c
a
ti
o
n
o
f
th
e
Re
p
u
b
li
c
o
f
In
d
o
n
e
sia
,
G
ra
n
ts
In
te
rn
a
ti
o
n
a
l
Co
o
p
e
ra
ti
o
n
a
n
d
th
e
Na
ti
o
n
a
l
S
tr
a
teg
ic
(h
ig
h
e
st
r
e
se
a
r
c
h
g
ra
n
ts
in
In
d
o
n
e
sia
).
He
is
a
lso
a
r
e
c
ip
ien
t
o
f
th
e
Na
ti
o
n
a
l
W
o
rk
F
e
a
tu
re
d
T
e
c
h
n
o
lo
g
y
o
f
th
e
M
in
istry
o
f
Re
se
a
rc
h
a
n
d
T
e
c
h
n
o
l
o
g
y
o
f
In
d
o
n
e
sia
i
n
2
0
1
4
.
His
in
tere
sts
a
re
in
c
o
n
tro
l
s
y
ste
m
s,
ro
b
o
ti
c
s,
n
e
w
a
n
d
re
n
e
wa
b
le
e
n
e
rg
y
.
He
m
a
y
b
e
r
e
a
c
h
e
d
a
t
f
e
rr
y
.
h
a
d
a
r
y
@in
v
e
n
t.
u
n
ta
n
.
a
c
.
id
B
o
m
o
W
i
b
o
w
o
S
a
n
ja
y
a
wa
s b
o
rn
in
P
o
n
ti
a
n
a
k
,
In
d
o
n
e
sia
,
in
1
9
7
4
.
He
re
c
e
iv
e
d
h
is
Ba
c
h
e
lo
r’s d
e
g
re
e
in
c
o
n
tro
l
e
n
g
in
e
e
rin
g
f
ro
m
De
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l,
Tan
ju
n
g
p
u
ra
Un
iv
e
rsity
,
P
o
n
t
ian
a
k
in
2
0
0
8
,
h
is
M
a
ste
r’s
De
g
r
e
e
in
c
o
n
tro
l
e
n
g
in
e
e
rin
g
f
ro
m
De
p
a
rt
m
e
n
t
o
f
El
e
c
tri
c
a
l,
Ba
n
d
u
n
g
In
stit
u
te
o
f
T
e
c
h
n
o
lo
g
y
in
2
0
1
3
,
a
n
d
h
is
Do
c
to
r’s
De
g
re
e
in
c
o
n
tro
l
e
n
g
in
e
e
rin
g
f
ro
m
S
c
h
o
o
l
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
a
n
d
In
f
o
rm
a
ti
c
s,
B
a
n
d
u
n
g
In
stit
u
te
o
f
T
e
c
h
n
o
lo
g
y
in
2
0
1
4
.
No
w
,
h
e
is
a
lec
tu
re
r
a
t
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l,
T
a
n
ju
n
g
p
u
ra
Un
iv
e
rsity
.
He
c
u
rre
n
t
re
se
a
rc
h
in
tere
sts
a
r
e
in
f
u
z
z
y
lo
g
ic,
n
e
u
ra
l
n
e
tw
o
rk
s,
c
o
n
tro
l
o
f
n
o
n
li
n
e
a
r
d
y
n
a
m
ic
a
l
s
y
ste
m
s.
He
m
a
y
b
e
re
a
c
h
e
d
a
t
b
o
m
o
.
w
ib
o
w
o
@e
e
.
u
n
tan
.
a
c
.
id
Evaluation Warning : The document was created with Spire.PDF for Python.