T
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Laborat
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obile,
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k
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rajec
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U
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A
l
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r
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eser
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.
1
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In
t
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o
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u
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In
th
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ye
a
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ical,
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[1
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u
se
d
in
a
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o
f
a
p
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3
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M
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s
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ticles
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ve
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5
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.
In
o
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[9
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◼
IS
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6
9
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6
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T
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KOM
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V
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m
o
to
r
s
r
o
b
o
t
a
r
e
stu
d
ied
a
n
d
te
ste
d
wi
th
r
e
a
l
im
p
le
m
e
n
ta
tio
n
,
th
e
a
ctu
a
l
a
n
d
r
e
fe
r
e
n
ce
li
n
e
a
r
a
n
d
a
n
g
u
lar
ve
l
o
cities
a
r
e
ca
lcula
te
d
b
y
th
e
ki
n
e
m
a
tics
str
u
ct
u
r
e
c
o
n
tr
o
l,
a
n
d
f
o
r
t
h
e
sta
b
i
li
ty
sta
d
y,
lyap
u
n
o
v
th
e
o
r
y
is
u
se
d
t
o
g
u
a
r
a
n
te
e
t
h
e
st
a
b
il
ity o
f
th
e
syst
e
m
.
S
o
m
e
o
f
p
a
r
a
m
e
te
r
s
syste
m
s
a
r
e
n
o
t
m
o
d
e
le
d
o
r
a
r
e
p
r
o
n
e
to
c
h
a
n
g
e
i
n
tim
e
,
wi
th
is
o
ft
e
n
im
p
o
ssible
fo
r
th
e
a
p
p
li
ca
tio
n
.
I
n
th
is
st
u
d
y,
r
o
b
u
st
P
I/
B
a
ckste
p
p
i
n
g
co
n
t
r
o
is
a
p
p
li
e
d
to
co
m
p
e
n
sa
t
e
fo
r
th
e
d
yn
a
m
ic
d
istu
r
b
a
n
ce
s,
a
n
d
its
sta
b
il
ity
is
a
n
a
lyz
e
d
u
sing
th
e
L
ya
p
u
n
o
v
th
e
o
r
y,
th
e
o
b
jec
tive
is
to
a
m
e
li
o
r
a
te
th
e
B
a
cksto
p
p
ing
a
p
p
r
o
a
ch
b
y
a
d
d
in
g
n
o
n
li
n
e
a
r
P
I
a
ct
ion
to
co
n
tr
o
l
law
e
q
u
a
tio
n
.
P
r
o
p
o
r
tio
n
a
l
i
n
te
g
r
a
l
a
ctio
n
co
n
t
r
o
l
is
a
d
d
e
d
to
r
e
d
u
ce
th
e
e
r
r
o
r
o
f
th
e
tr
a
ject
o
r
y
t
r
a
cking
.
A
co
m
p
a
r
a
tive
stu
d
y
be
tw
e
e
n
th
e
p
r
o
p
o
se
d
a
p
p
r
o
a
ch
a
n
d
th
e
b
a
ckste
p
p
ing
co
n
tr
o
l is p
r
e
se
n
te
d
b
y sim
u
l
a
tio
n
s t
o
s
h
o
w th
e
p
e
r
fo
r
m
a
n
c
e
o
f
th
e
co
n
t
r
o
l str
u
c
tu
r
e
f
o
r
st
a
b
il
ity.
T
h
e
r
e
m
a
inin
p
a
r
t
o
f
th
e
p
a
p
e
r
i
s
p
r
e
se
n
te
d
a
s
fo
ll
o
ws,
fi
r
st
we
g
ives
th
e
d
yn
a
m
ic
m
o
d
e
l
o
f
u
n
icycl
e
typ
e
r
o
b
o
t.
S
e
ctio
n
2
g
ives
th
e
d
y
n
a
m
ic
u
n
icycl
e
-
li
ke
r
o
b
o
t
m
o
d
e
l.
S
e
ctio
n
3
,
p
r
e
se
n
ts
a
n
d
e
xp
lain
s
th
e
p
r
o
p
o
se
d
P
I
o
r
ba
ckste
p
p
in
g
co
n
tr
o
ll
e
r
d
e
sign
.
Resp
e
ctive
ly,
in
se
ctio
n
4
,
T
h
e
fin
d
i
n
g
s
o
f
th
e
p
a
p
e
r
,
fo
cu
si
n
g
o
n
th
e
d
e
sign
e
d
tr
a
ject
o
r
y
tr
a
cking
co
n
tr
o
l m
e
th
o
d
.
F
ina
ll
y,
in
s
e
ctio
n
5
w
e
co
n
clud
e
t
h
is p
a
p
e
r
.
2
.
Ro
b
o
t
M
o
d
e
l
In
t
h
is se
ctio
n
,
th
e
m
o
d
e
l o
f
th
e
m
o
b
il
e
r
o
b
o
t
typ
e
u
n
icycl
e
p
r
o
p
o
se
d
b
y L
a
Cr
u
z
a
n
d
Car
e
ll
i
in
[
1
4
]
is
co
n
side
r
e
d
,
th
e
fig
u
r
e
1
sh
o
w
th
e
m
o
b
il
e
r
o
b
o
t
,
whe
r
e
G
is
m
a
ss
ce
n
te
r
,
h
is
th
e
ta
r
g
e
te
d
p
o
int
u
se
d
.
ω
is
a
n
g
u
lar
ve
lo
cit
y.
ψ
is
t
h
e
a
n
g
le
o
f
r
o
ta
tio
n
,
a
,
b
,
c
a
n
d
d
a
r
e
d
ista
n
c
e
s.
F
igu
r
e
1
.
M
o
b
il
e
r
o
b
o
t
typ
e
u
n
icycl
e
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NIKA
IS
S
N: 1
6
9
3
-
6930
◼
In
t
e
g
r
a
l B
a
ckste
p
p
ing
A
p
p
r
o
a
ch
f
o
r
M
o
b
il
e
Ro
b
o
t
Con
tr
o
l (
B
o
u
zg
o
u
K
a
m
e
l)
1175
F
o
r
ce
s a
n
d
M
o
m
e
n
ts
e
q
u
a
tio
n
s f
o
r
t
h
e
s
yste
m
a
r
e
w
r
itte
n
a
s
[1
5
]:
∑
′
=
(
˙
−
̅
)
=
′
+
′
+
′
,
∑
′
=
(
¯
˙
+
)
=
′
+
′
+
′
∑
=
˙
(
1
)
a
nd
,
,
′
,
′
,
′
and
a
r
e
th
e
lo
n
g
itu
d
ina
l
a
n
d
lat
e
r
a
l
tir
e
fo
r
ce
s
a
p
p
li
e
d
th
e
whe
e
ls
th
e
r
o
b
o
t.
T
h
e
m
o
m
e
n
t
o
f
ine
r
tia
a
t
m
a
ss
ce
n
te
r
is
Iz
.
T
h
e
fir
s
t
p
a
r
t
o
f
m
o
d
e
l
is
wr
itte
n
in
[1
4
]
a
s :
˙
=
−
¯
−
(
−
)
,
˙
=
−
¯
+
(
+
)
(
2
)
w
h
e
r
e
¯
is
th
e
lat
e
r
a
l
ve
locity
o
f
th
e
m
a
ss
c
e
n
te
r
.
T
h
e
f
ina
l m
o
d
e
l o
f
m
o
b
il
e
ro
b
o
t
typ
e
u
n
icy
cle
is g
iven
in
[1
4
]
b
y De
L
a
C
r
u
z a
n
d
Ca
r
e
ll
i a
s:
(
̇
̇
̇
̇
̇
)
=
(
cos
(
)
−
s
in
(
)
us
in
(
)
+
aw
cos
(
)
3
1
2
−
4
1
−
5
2
−
6
2
)
+
(
0
0
0
0
0
0
1
1
0
1
2
0
)
(
)
(
3
)
a
n
d
t
h
e
p
a
r
a
m
e
te
r
s
o
f
th
e
syst
e
m
a
r
e
d
e
fin
e
d
in
[1
4
]
a
s:
1
=
1
2
2
+
(
2
+
)
(
)
,
2
=
1
2
2
+
(
2
2
+
(
)
+
2
)
(
)
,
3
=
2
4
=
(
+
)
(
)
+
1
,
5
=
2
,
6
=
(
+
)
(
)
+
1
whe
r
e
m
is
th
e
A
r
d
u
ino
r
o
b
o
t
m
a
ss,
Ie
is
th
e
m
o
m
e
n
t
o
f
ine
r
ti
a
,
B
e
is
th
e
viscou
s
f
r
i
ctio
n
co
e
f
ficien
t,
r
is
th
e
r
ig
h
t
a
n
d
l
e
ft
wh
e
e
l
r
a
d
ius,
a
n
d
R
t
is
th
e
tir
e
r
a
d
ius,
k
a
is
th
e
t
o
r
q
u
e
co
e
ff
ici
e
n
t,
k
b
is
e
lec
tr
o
m
o
tive
co
e
f
ficien
t,
R
a
is
th
e
m
o
to
r
s
r
e
sist
a
n
ce
.
P
D
co
n
tr
o
ll
e
r
s
a
r
e
im
p
lem
e
n
t
e
d
wi
th
P
I
k
PT
a
n
d
k
PR
,
a
n
d
d
e
r
ivat
ive
g
a
ins
k
DT
and
k
DR
to
c
o
n
t
r
o
l
th
e
ve
lociti
e
s
o
f
th
e
r
igh
t
a
n
d
lef
t
m
o
to
r
.
3
.
Ar
c
h
it
e
c
t
u
r
e
C
o
n
t
r
o
l
F
o
r
t
h
e
a
r
ch
ite
ctu
r
e
co
n
tr
o
l,
w
e
a
r
e
u
se
d
th
e
kine
m
a
tics
c
o
n
tr
o
ll
e
r
fo
r
e
xte
r
n
a
l
lo
o
p
a
n
d
a
P
I/
b
a
ckst
e
p
p
ing
f
o
r
t
h
e
d
yn
a
m
ics m
o
d
e
l a
s se
e
in
F
i
g
u
r
e
2
.
F
igu
r
e
2
.
S
tr
u
ctu
r
e
co
n
tr
o
l o
f
P
I/
b
a
ckste
p
p
i
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 1
6
9
3
-
6
9
3
0
T
E
L
KOM
NIKA
V
o
l.
15
,
No.
3
,
S
e
p
t
e
m
b
e
r
2
0
1
7
:
1
1
7
3
-
1
1
8
0
1176
3
.1
.
Kin
e
m
a
t
ic
C
o
n
t
r
o
l
T
h
is d
e
sign
c
o
n
tr
o
ll
e
r
is d
e
ve
lo
p
e
d
with
t
h
e
in
ve
r
s
e
kin
e
m
a
tics e
q
u
a
tio
n
s o
f
t
h
e
r
o
b
o
t
m
o
b
il
e
.
T
h
e
o
b
ject
ive
o
f
t
h
is
co
n
tr
o
ll
e
r
is
to
g
e
n
e
r
a
t
e
th
e
r
e
f
e
r
e
n
c
e
va
lue
s
fo
r
th
e
P
I/
B
a
ckste
p
p
ing
co
n
t
r
o
ll
e
r
is
d
e
sign
e
d
in
o
r
d
e
r
th
e
d
e
sir
e
d
va
lu
e
s
o
f
th
e
li
n
e
a
r
a
n
d
a
n
g
u
lar
ve
locitie
s.
F
r
o
m
(
3
)
,
th
e
kin
e
m
a
tic
m
o
d
e
l is g
i
ve
n
a
s:
(
̇
̇
)
=
(
(
)
−
(
)
(
)
(
)
)
(
)
(
4
)
w
h
e
r
e
u
r
e
f
th
e
r
e
fe
r
e
n
c
e
is
va
lue
o
f
th
e
li
n
e
a
r
ve
l
o
city,
a
n
d
ω
r
e
f
is
a
n
g
u
lar
ve
locity
.
T
h
e
m
a
t
r
ix
inve
r
se
is
(
5
)
.
−
1
=
(
cos
(
ψ
)
s
i
n
(
ψ
)
−
1
a
s
i
n
(
ψ
)
1
a
cos
(
ψ
)
)
(
5
)
T
h
e
co
n
t
r
o
l law ca
n
b
e
ch
o
s
e
n
a
s:
(
)
=
(
(
)
(
)
−
1
(
)
1
(
)
)
(
˙
+
˙
+
)
(
6
)
w
h
e
r
e
ε
x
=
x
d
−
x
a
n
d
=
−
th
e
cu
r
r
e
n
t
a
r
e
p
o
sition
e
r
r
o
r
s,
ℎ
(
,
)
and
h
d
(
x
d
,
y
d
)
a
r
e
th
e
a
ctu
a
l
a
n
d
r
e
fe
r
e
n
ce
p
o
int
s.
T
h
e
stu
d
y
o
f
th
e
sta
b
il
ity
fo
r
th
e
kine
m
a
tic
co
n
t
r
o
ll
e
r
is
d
e
t
a
il
e
d
in
[1
3
].
3
.2
.
No
n
li
n
e
a
r
P
I
-
b
a
s
e
d
Ba
c
k
s
t
e
p
p
i
n
g
C
o
n
t
r
o
ll
e
r
De
s
ig
n
T
h
e
c
o
m
b
ina
tio
n
o
f
int
e
g
r
a
l
a
c
tio
n
a
n
d
b
a
ckst
e
p
p
ing
e
q
u
a
tio
n
s
is
p
r
o
p
o
se
d
to
d
e
sign
th
e
str
u
ctu
r
e
co
n
tr
o
l
th
a
t
im
p
r
o
ve
s
th
e
r
o
b
u
st
n
e
ss
whe
n
th
e
d
yn
a
m
ics
p
a
r
a
m
e
te
r
s
o
f
th
e
r
o
b
o
t
a
r
e
n
o
t
w
e
ll
-
kn
o
wn.
T
h
e
d
y
n
a
m
ic
p
a
r
t
o
f
(
3
)
i
s:
˙
=
3
1
2
−
4
1
+
1
,
˙
=
5
2
−
6
2
+
2
(
7
)
f
ir
st,
we
co
n
sid
e
r
t
h
e
e
r
r
o
r
s co
n
tr
o
l
laws
:
1
=
−
⇒
˙
1
=
˙
−
˙
,
1
=
−
⇒
˙
1
=
˙
−
˙
(
8
)
t
h
e
lya
p
u
n
o
v
f
u
n
ctio
n
s
is d
e
r
ive
d
a
s
(
1
)
=
1
2
1
2
,
(
1
)
=
1
2
1
2
(
9
)
t
he
tim
e
d
e
r
ivat
ive
o
f
th
e
L
ya
p
u
n
o
v ca
n
d
ida
te
fu
n
ctio
n
s is ca
lcula
t
e
d
a
s
˙
(
1
)
=
1
˙
1
,
˙
(
1
)
=
1
˙
1
(
1
0
)
t
h
e
sta
b
il
izat
io
n
o
f
th
e
d
yn
a
m
ics
e
r
r
o
r
s
sy
ste
m
ca
n
b
e
o
b
ta
ine
d
b
y
i
n
tr
o
d
u
cing
a
vi
r
tu
a
l
co
n
tr
o
ls inp
u
t:
=
˙
+
1
1
+
,
=
˙
+
1
1
+
(
1
1
)
W
h
e
r
e
t
h
e
i
n
te
g
r
a
l a
ctio
n
s a
r
e
:
=
∫
1
(
)
∂
,
=
∫
1
(
)
∂
(
1
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NIKA
IS
S
N: 1
6
9
3
-
6930
◼
In
t
e
g
r
a
l B
a
ckste
p
p
ing
A
p
p
r
o
a
ch
f
o
r
M
o
b
il
e
Ro
b
o
t
Con
tr
o
l (
B
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u
zg
o
u
K
a
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1177
w
ith
1
,
1
,
and
a
r
e
d
e
sign
p
a
r
a
m
e
te
r
s
.
A
n
d
n
o
w,
we
ca
lcula
te
t
h
e
n
e
w e
r
r
o
r
s
a
s:
2
=
˙
−
˙
+
1
1
+
,
2
=
˙
−
˙
+
1
1
+
(
1
3
)
a
nd
˙
2
=
¨
−
¨
+
1
˙
1
+
1
,
˙
2
=
¨
−
¨
+
1
˙
1
+
1
(
1
4
)
f
r
o
m
(
1
1
)
a
n
d
(
1
4
)
,
it
fo
ll
o
ws th
a
t:
˙
1
=
−
1
1
−
+
2
,
˙
1
=
−
1
1
−
+
2
(
1
5
)
a
nd
˙
2
=
−
2
2
−
1
,
˙
2
=
−
2
2
−
1
(
1
6
)
w
h
e
r
e
2
,
2
a
r
e
p
o
sitive
co
n
sta
n
t
o
f
sta
b
il
ity.
So
,
th
a
t
is
r
e
su
lt,
th
e
int
e
g
r
a
l
b
a
ckste
p
p
in
g
co
n
tr
o
l laws o
f
e
leva
tio
n
,
line
a
r
a
n
d
a
n
g
u
lar
v
e
locitie
s a
r
e
:
=
[
1
(
¨
+
(
1
+
2
)
2
+
(
1
−
1
2
+
)
1
−
)
+
2
3
˙
−
4
˙
]
(
17
)
a
nd
=
[
2
(
¨
+
(
1
+
2
)
2
+
(
1
−
1
2
+
)
1
−
)
−
5
(
˙
+
˙
)
−
6
˙
]
(
1
8
)
t
h
e
sta
b
il
ity
o
f
th
e
c
o
n
tr
o
ll
e
r
ca
n
b
e
stu
d
i
e
d
wi
th
th
e
L
ya
p
u
n
o
v
th
e
o
r
y.
T
h
e
lyap
u
n
o
v
c
a
n
d
ida
te
fu
n
ctio
n
s is g
iven
a
s:
(
1
,
2
)
=
2
+
1
2
+
2
2
2
,
(
1
,
2
)
=
2
+
1
2
+
2
2
2
(
1
9
)
w
h
o
se
f
ir
st
tim
e
d
e
r
ivat
ive
˙
(
1
,
2
)
=
−
1
1
2
−
2
2
2
≤
0
,
˙
(
1
,
2
)
=
−
1
1
2
−
2
2
2
≤
0
(
2
0
)
a
r
e
n
e
g
a
tive
d
e
fin
e
d
,
which
m
e
a
n
s
th
a
t,
t
h
e
t
r
a
cking
e
r
r
o
r
is st
a
b
le.
4
.
E
x
p
e
r
im
e
n
t
r
e
s
u
lt
s
T
h
e
fo
u
r
th
se
ctio
n
p
r
e
se
n
t
th
e
im
p
lem
e
n
ta
t
ion
o
f
th
e
p
r
o
p
o
se
d
co
n
t
r
o
l
law
o
n
a
A
r
d
u
ino
Ro
b
o
t
M
o
b
il
e
,
wi
th
R
a
d
ius:
1
8
5
m
m
,
h
e
igh
t
:
8
5
a
n
d
w
e
ig
h
t:
1
.5
0
kil
o
g
r
a
m
,
it
h
a
s
a
lso
two
p
r
o
ce
sso
r
s
b
a
se
d
o
n
th
e
A
T
m
e
g
a
3
2
u
4
,
se
e
F
igu
r
e
3
,
t
h
e
whe
e
ls
a
r
e
d
r
iv
e
n
b
y
DC
m
o
to
r
s
h
a
ving
r
a
te
d
to
r
q
u
e
3
0
m
Nm
a
t
1
5
0
0
0
r
p
m
,
e
n
c
o
d
e
r
s
o
u
t
p
u
t
o
f
5
0
0
ticks/r
e
vo
lu
tio
n
a
r
e
int
e
g
r
a
te
d
fo
r
th
is
m
o
to
r
s
,
th
e
sa
m
p
le
tim
e
o
f
th
e
r
o
b
o
t
is
0
.1
s
.
A
r
d
u
in
o
Y
u
n
is
co
n
n
e
ct
e
d
to
th
e
r
o
b
o
t
to
s
e
n
d
th
e
co
n
t
r
o
l
law
f
r
o
m
M
A
T
L
A
B
to
th
e
r
o
b
o
t
u
sing
t
h
e
wi
r
e
less
n
e
t
wor
k
co
n
n
e
ctio
n
.
T
h
e
o
d
o
m
e
t
r
ic
se
n
s
o
r
s
a
r
e
u
se
d
to
se
n
sing
th
e
p
o
int
h
o
f
r
o
b
o
t
p
o
s
ition
.
T
h
e
a
p
p
r
o
a
ch
is
p
r
o
g
r
a
m
m
e
d
wi
th
t
h
e
M
A
T
L
A
B
u
sing
th
e
wi
n
d
o
ws
syste
m
.
In
o
r
d
e
r
to
te
st
th
e
p
r
o
p
o
se
d
P
I/
B
a
ckste
p
p
i
n
g
co
n
t
r
o
l
la
w
o
f
th
is
p
a
p
e
r
,
se
ve
r
a
l
e
xp
e
r
im
e
n
ts
wer
e
ca
r
r
ied
o
u
t
wi
th
cir
cu
la
r
tr
a
ck
r
e
fe
r
e
n
ce
tr
a
ject
o
r
y
o
f
2
m
.
T
h
e
r
o
b
o
t
sta
r
t
fr
o
m
th
e
p
o
sition
P
0
=
(
x,
y,
ψ
)
= (
0
,
0
,
0
)
.
T
h
e
g
a
ins
o
f
th
e
im
p
l
e
m
e
n
te
d
co
n
t
r
o
ll
e
r
a
r
e
se
lect
e
d
a
s:
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 1
6
9
3
-
6
9
3
0
T
E
L
KOM
NIKA
V
o
l.
15
,
No.
3
,
S
e
p
t
e
m
b
e
r
2
0
1
7
:
1
1
7
3
-
1
1
8
0
1178
[
1
=
120
,
2
=
75
]
[
1
=
14
,
2
=
2
]
[
=
12
.
75
,
=
3
.
5
]
T
h
e
r
o
b
o
t
m
o
b
il
e
tr
a
cks
th
e
cir
cu
lar
way
wi
th
sm
a
ll
e
r
e
r
r
o
r
.
T
h
u
s,
sh
o
w
g
o
o
d
p
e
r
fo
r
m
a
n
ce
a
s
se
e
in
F
igu
r
e
4
(
a
)
,
th
e
e
vo
lu
tio
n
s
o
f
th
e
d
e
sir
e
d
a
n
d
a
c
tu
a
l
li
n
e
a
r
ve
locity
a
n
d
a
n
g
u
lar
ve
l
o
city
a
r
e
p
lot
te
d
i
n
F
igu
r
e
4
(
b
)
,
in
th
e
fig
u
r
e
s
r
e
su
lts
,
we
sh
o
w
th
a
t
th
e
r
o
b
o
t
tr
a
cks
th
e
r
e
fe
r
e
n
ce
tr
a
ject
o
r
y
co
r
r
e
ctl
y
a
n
d
th
e
e
r
r
o
r
s
te
n
d
to
ze
r
o
.
F
igu
r
e
5
(
a
)
il
lust
r
a
te
s
t
h
e
co
n
tr
o
l
th
e
r
o
b
o
t
'
s
whe
e
ls
sp
e
e
d
sign
a
l
g
e
n
e
r
a
te
d
b
y
th
e
M
o
to
r
b
o
a
r
d
p
r
o
ce
sso
r
.
T
h
e
li
n
e
a
r
ve
l
o
city
a
n
d
a
n
g
u
lar
co
n
t
r
o
l
l
a
ws
a
r
e
in
d
icat
e
d
in
F
ig
u
r
e
5
(
b
)
.
T
h
e
Y
u
n
Ar
d
u
ino
ca
r
d
is
u
se
d
to
r
e
ce
ive
th
e
co
n
tr
o
l laws f
r
o
m
M
A
T
L
A
B
to
t
h
e
r
o
b
o
t
th
r
o
u
g
h
wir
e
less
c
a
r
d
.
F
igu
r
e
3
.
A
r
d
u
ino
r
o
b
o
t
m
o
b
il
e
(
a
)
(
b
)
F
igu
r
e
4
.
S
im
u
lat
i
o
n
r
e
su
lts
(
a
)
T
h
e
t
r
a
ject
o
r
y
fo
ll
o
wed
b
y t
h
e
m
o
b
il
e
r
o
b
o
t
,
(b
)
T
h
e
li
n
e
a
r
ve
locity
a
n
d
a
n
g
u
lar
ve
locity
4
.1
.
Co
m
p
a
r
a
t
i
v
e
S
t
u
d
y
T
h
e
se
c
o
n
d
e
x
p
e
r
im
e
n
t
is
d
e
sign
e
d
to
co
m
p
a
r
e
b
e
twe
e
n
t
h
e
B
a
ckste
p
p
ing
a
p
p
r
o
a
c
h
p
r
o
p
o
se
d
in
[1
3
]
a
n
d
P
I/
b
a
ckste
p
p
ing
,
we
c
a
r
r
ied
o
u
t
th
e
e
xp
e
r
im
e
n
t
wi
th
sa
m
e
cir
c
u
la
r
t
r
a
ck
r
e
fe
r
e
n
ce
tr
a
ject
o
r
y
o
f
2
m
e
t
e
r
s
o
f
r
a
d
ius
a
n
d
sa
m
e
initia
l
p
o
stu
r
e
0
=
(
,
,
)
=
(
0
,
0
,
0
)
.
F
igu
r
e
6
p
r
e
s
e
n
ts
th
e
r
e
su
lts
o
f
th
e
st
r
u
ctu
r
e
co
n
tr
o
l
wi
th
th
e
e
vo
lut
io
n
th
e
d
ist
a
n
ce
e
r
r
o
r
u
sing
th
e
a
p
p
r
o
a
c
h
a
n
d
b
a
cks
te
p
p
ing
co
n
t
r
o
ll
e
r
,
it
ca
n
b
e
se
e
th
a
t
t
h
e
P
I/
b
a
cks
te
p
p
ing
is
t
h
e
m
o
st
sta
b
le
a
n
d
a
ccu
r
a
te
m
e
t
h
o
d
co
m
p
a
r
ing
th
e
b
a
ckste
p
p
ing
a
p
p
r
o
a
ch
.
No
w
in
T
a
b
le
1
,
we
h
a
ve
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NIKA
IS
S
N: 1
6
9
3
-
6930
◼
In
t
e
g
r
a
l B
a
ckste
p
p
ing
A
p
p
r
o
a
ch
f
o
r
M
o
b
il
e
Ro
b
o
t
Con
tr
o
l (
B
o
u
zg
o
u
K
a
m
e
l)
1179
th
e
n
u
m
e
r
ical
r
e
su
lts:
th
e
m
e
a
n
e
r
r
o
r
,
va
r
i
a
n
ce
a
n
d
sta
n
d
a
r
d
de
viat
ion
o
f
tr
a
ject
o
r
y
u
sing
b
a
ckste
p
p
ing
a
n
d
P
I/
b
a
ckst
e
p
p
ing
a
p
p
r
o
a
ch
e
s,
we
n
o
tice
th
a
t
th
e
P
I/
b
a
ckst
e
p
p
ing
g
ives
g
o
od
r
e
su
lts
in
a
ccu
r
a
cy,
b
y
t
h
e
n
u
m
e
r
ical
r
e
su
lts
its
ca
n
sh
o
w
th
e
ef
fe
ctive
n
e
ss
o
f
th
is
a
lg
or
i
th
m
.
On
e
o
f
th
e
a
d
va
n
ta
g
e
s
o
f
th
is a
p
p
r
o
a
ch
is
th
a
t
th
e
y
ca
n
u
su
a
ll
y t
o
co
m
p
e
n
s
a
te
f
o
r
th
e
d
yn
a
m
ics
n
o
t
m
o
d
e
led
a
s h
ys
te
r
e
tic
d
a
m
p
in
g
,
whe
e
l ti
r
e
d
iam
e
te
r
s a
n
d
vi
b
r
a
tio
n
s.
(
a
)
(
b
)
F
igu
r
e
5
.
E
xp
e
r
im
e
n
ta
l r
e
su
lts
(
a
)
P
o
wer
lin
e
a
r
ve
locity
,
(
b
)
Con
t
r
o
l law in
p
u
ts
T
a
b
le
1
.
N
u
m
e
r
ic
a
l co
m
p
a
r
ison
r
e
su
lts
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].
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