I
nte
rna
t
io
na
l J
o
urna
l o
f
Ro
bo
t
ics a
nd
Aut
o
m
a
t
io
n
(
I
J
RA
)
Vo
l.
5
,
No
.
1
,
Ma
r
ch
2
0
1
6
,
p
p
.
1
7
~
28
I
SS
N:
2089
-
4856
17
J
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ur
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ep
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:
h
ttp
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/I
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RA
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nidi
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Des
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J
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us
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Ch
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y:
R
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No
v
15
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0
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R
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J
an
2
5
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1
6
A
cc
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1
0
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In
th
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d
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d
if
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p
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g
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a
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.
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K
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:
Dr
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M
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n
id
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S
p
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ical
M
o
b
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R
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Co
p
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rig
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t
©
201
6
In
s
t
it
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te o
f
A
d
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.
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l
rig
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C
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p
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:
A
j
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R
.
J
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s
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Dep
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aj
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in
1.
I
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D
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I
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N
A
r
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b
o
t c
an
b
e
d
e
f
i
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an
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to
m
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m
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w
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wh
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s
in
a
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u
m
a
n
li
k
e
m
a
n
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er
[
1
]
.
R
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b
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ts
o
r
au
to
m
at
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m
ac
h
in
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s
h
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g
f
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m
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m
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s
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f
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tec
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th
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A
.
Hal
m
e
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[
2
]
.
An
o
th
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d
esig
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s
d
ev
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p
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b
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J
D
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eq
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tio
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[
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
5
,
No
.
1
,
Ma
r
ch
2
0
1
6
:
17
–
28
18
An
o
th
er
d
esi
g
n
d
r
iv
e
s
a
b
all
w
h
ic
h
is
m
ad
e
to
i
m
p
ar
t
m
o
ti
o
n
to
th
e
ex
ter
n
al
s
h
ell
[
4
]
.
No
n
s
p
h
er
ical
m
o
b
ile
ar
e
also
d
ev
elo
p
ed
lik
e
th
e
Ur
an
u
s
r
o
b
o
t
w
h
ic
h
m
a
k
es
u
s
e
o
f
Me
ca
n
u
m
w
h
ee
ls
to
ac
h
iev
e
o
m
n
id
ir
ec
tio
n
a
l
m
o
b
il
it
y
[
5
]
.
Ma
n
y
s
u
ch
r
o
b
o
ts
w
er
e
d
esi
g
n
ed
,
w
h
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h
ar
e
d
is
cu
s
s
ed
in
t
h
e
co
m
i
n
g
s
ec
tio
n
s
.
2.
SO
M
E
DIS
T
I
NC
T
I
VE
M
O
B
I
L
E
RO
B
O
T
S
An
y
r
o
b
o
t
ca
p
ab
le
o
f
lo
co
m
o
tio
n
ca
n
b
e
d
escr
ib
ed
as
a
m
o
b
ile
r
o
b
o
t.
Un
d
er
m
o
b
ile
r
o
b
o
ts
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o
n
l
y
th
o
s
e
r
o
b
o
ts
w
h
ic
h
ar
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ca
p
ab
le
o
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x
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ib
itin
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m
n
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tio
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m
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ied
.
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n
d
er
th
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,
m
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t
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o
m
n
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ir
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n
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o
r
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p
h
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ta
g
e
s
o
v
er
o
th
er
k
i
n
d
s
o
f
r
o
b
o
ts
lik
e
f
a
s
t
co
llis
io
n
r
ec
o
v
er
y
,
s
y
m
m
etr
ic
g
eo
m
etr
y
,
w
h
ic
h
h
elp
s
i
n
ac
h
ie
v
in
g
o
m
n
id
ir
ec
tio
n
al
m
o
t
io
n
w
it
h
o
u
t
r
eo
r
ien
tin
g
its
el
f
.
So
its
m
o
ti
o
n
is
h
o
lo
n
o
m
ic
in
n
atu
r
e.
T
h
e
d
r
iv
in
g
m
ec
h
a
n
i
s
m
f
o
r
th
e
s
e
r
o
b
o
ts
is
t
y
p
icall
y
e
n
clo
s
ed
w
it
h
i
n
t
h
e
s
p
h
er
ic
al
s
h
ell.
A
r
o
b
o
tic
d
r
iv
e
is
s
aid
to
b
e
Ho
lo
n
o
m
ic
if
th
e
to
tal
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
ar
e
eq
u
al
to
th
e
co
n
tr
o
llab
le
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
o
f
th
e
r
o
b
o
t.
I
f
th
e
to
tal
d
eg
r
e
es
o
f
f
r
ee
d
o
m
i
s
m
o
r
e
th
a
n
t
h
e
co
n
tr
o
llab
le
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
,
it
is
k
n
o
w
n
as
a
No
n
Ho
lo
n
o
m
ic
d
r
iv
e.
I
f
th
e
to
tal
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
o
f
a
r
o
b
o
t
a
r
e
less
th
an
t
h
e
co
n
t
r
o
llab
le
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
,
it is
k
n
o
w
n
as a
R
ed
u
n
d
a
n
t d
r
iv
e
[
6
]
.
Sev
er
al
m
o
b
ile
r
o
b
o
ts
h
a
v
e
b
ee
n
d
ev
elo
p
ed
b
ased
o
n
v
ar
io
u
s
d
r
iv
i
n
g
m
ec
h
a
n
i
s
m
s
.
Dr
iv
i
n
g
p
r
in
cip
les b
ased
o
n
w
h
ic
h
al
m
o
s
t a
ll
m
o
b
ile
r
o
b
o
ts
ar
e
d
ev
elo
p
ed
is
g
iv
en
b
elo
w
:
[1
]
Dir
ec
t
d
r
iv
in
g
m
et
h
o
d
:
T
h
e
to
r
q
u
e
p
r
o
d
u
ce
d
b
y
th
e
m
o
to
r
is
d
ir
ec
tl
y
tr
an
s
m
itted
to
th
e
o
u
t
er
s
h
ell
a
s
th
e
p
r
o
p
ellin
g
p
o
w
er
f
o
r
th
e
r
o
b
o
t.
[2
]
B
ar
y
ce
n
ter
o
f
f
s
e
t
o
r
Gr
av
it
y
m
et
h
o
d
:
T
h
e
b
ar
y
ce
n
ter
i
s
t
h
e
ce
n
ter
o
f
m
ass
o
f
t
w
o
r
ev
o
l
v
i
n
g
b
o
d
ies.
B
y
ch
an
g
i
n
g
t
h
e
m
ass
d
is
tr
ib
u
tio
n
,
w
e
ca
n
ch
a
n
g
e
th
e
b
ar
y
ce
n
ter
o
f
th
e
r
o
b
o
t
th
er
eb
y
m
a
k
i
n
g
it
m
o
v
e
to
attain
a
n
e
w
s
tate
o
f
eq
u
ilib
r
iu
m
.
[3
]
Sh
ell
tr
an
s
f
o
r
m
atio
n
m
et
h
o
d
:
T
h
e
tr
an
s
f
o
r
m
atio
n
o
f
t
h
e
o
u
t
er
s
h
ell
o
f
t
h
e
r
o
b
o
t
is
b
ei
n
g
r
elied
u
p
o
n
f
o
r
its
m
o
v
e
m
en
t.
[4
]
An
g
u
lar
m
o
m
e
n
t
u
m
m
eth
o
d
:
I
n
th
is
m
et
h
o
d
,
C
o
n
tr
o
l
Mo
m
en
t
G
y
r
o
s
co
p
es
ar
e
ad
d
ed
to
th
e
s
p
h
er
ica
l
r
o
b
o
t.
T
h
e
la
w
s
o
f
co
n
s
er
v
at
i
o
n
o
f
a
n
g
u
lar
m
o
m
e
n
t
u
m
ar
e
u
s
ed
to
co
n
tr
o
l
t
h
e
m
o
v
e
m
e
n
t
o
f
t
h
e
r
o
b
o
t
.
T
h
e
o
u
tp
u
t to
q
u
e
is
p
r
o
p
o
r
t
io
n
all
y
r
elate
d
to
th
e
an
g
u
lar
m
o
m
en
tu
m
o
f
co
n
tr
o
l
m
o
m
e
n
t
g
y
r
o
s
co
p
es.
Un
d
er
m
o
b
ile
r
o
b
o
ts
,
w
e
h
a
v
e
co
n
s
id
er
ed
ab
o
u
t
ele
v
e
n
d
i
f
f
er
en
t
r
o
b
o
ts
to
s
u
m
m
ar
ize
th
eir
d
r
iv
in
g
p
r
in
cip
les,
p
er
f
o
r
m
an
ce
a
n
d
wh
eth
er
t
h
e
y
ar
e
ab
le
to
ac
h
ie
v
e
o
m
n
id
ir
ec
tio
n
a
l
m
o
tio
n
.
2
.
1
.
B
a
ll Ro
bo
t
T
h
is
is
p
r
o
b
a
b
ly
t
h
e
f
ir
s
t
s
p
h
er
ical
m
o
b
ile
to
b
e
d
ev
elo
p
ed
.
T
h
e
d
r
iv
in
g
m
ec
h
a
n
i
s
m
f
o
r
th
is
r
o
b
o
t
f
alls
u
n
d
er
t
h
e
ca
te
g
o
r
y
o
f
g
r
av
it
y
m
et
h
o
d
[
2
]
.
I
ts
w
o
r
k
in
g
is
s
i
m
p
le.
I
t
co
n
s
is
t
s
o
f
a
d
r
i
v
e
u
n
i
t
(
w
h
ee
l
a
n
d
o
th
er
in
s
id
e
co
m
p
o
n
en
ts
)
p
la
ce
d
in
s
id
e
t
h
e
s
p
h
er
e
w
h
ic
h
is
m
o
v
ed
to
m
a
k
e
th
e
o
u
ter
s
h
ell
m
o
v
e
in
t
h
e
r
eq
u
ir
ed
d
ir
ec
tio
n
.
T
h
er
e
ar
e
t
w
o
m
o
to
r
s
,
w
h
ic
h
ar
e
u
s
ed
to
d
r
iv
e
an
d
s
teer
t
h
e
d
r
iv
i
n
g
w
h
ee
l
in
s
id
e
t
h
e
s
h
e
ll
in
d
ep
en
d
en
tl
y
.
T
h
is
r
o
b
o
t
r
eq
u
ir
es
t
w
o
i
n
p
u
t
s
f
o
r
it
s
lo
co
m
o
tio
n
.
T
h
is
r
o
b
o
t
d
o
es
n
o
t
h
a
v
e
an
y
k
in
d
o
f
f
ee
d
b
ac
k
m
ec
h
a
n
is
m
to
co
r
r
ec
t its
m
o
tio
n
.
T
h
er
ef
o
r
e
it c
an
b
e
d
ef
in
ed
as a
n
o
p
en
-
lo
o
p
s
y
s
t
e
m
[
2
]
.
I
t
is
d
if
f
icu
lt
to
b
alan
ce
t
h
e
r
o
b
o
t
as
its
s
tab
ilit
y
d
ep
en
d
s
o
n
th
e
p
o
s
itio
n
o
f
it
s
I
n
s
id
e
Dr
iv
e
U
n
it
(
I
DU)
w
h
ic
h
i
s
h
ar
d
to
ass
es
s
.
P
er
f
o
r
m
a
n
ce
o
f
th
is
r
o
b
o
t is n
o
t a
v
ailab
le
in
t
h
e
liter
at
u
r
e.
Fig
u
r
e
1.
B
asic
Stru
ctu
r
e
O
f
T
h
e
R
o
b
o
t
[
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Deg
r
ee
o
f A
ch
ieva
b
ilit
y
o
f O
m
n
id
ir
ec
tio
n
a
l
Mo
tio
n
in
V
a
r
io
u
s
Mo
b
ile
R
o
b
o
t D
esig
n
s
.
.
.
(
A
jju
R
.
Ju
s
tu
s
)
19
T
h
e
d
r
iv
in
g
to
r
q
u
e
o
f
t
h
e
r
o
b
o
t is g
i
v
e
n
b
y
:
l
*
m
=
r
*
m
Si
n
θ
w
h
er
e
r
-
Dis
tan
ce
b
et
w
ee
n
t
h
e
ce
n
ter
o
f
th
e
b
all
lo
t
h
e
m
a
s
s
c
en
ter
o
f
th
e
I
n
ter
n
al
Dr
i
v
e
U
n
i
t,
m
-
Ma
s
s
o
f
I
DU,
1
-
Dis
tan
ce
b
et
w
ee
n
t
h
e
m
ass
ce
n
ter
o
f
I
DU,
a
n
d
th
e
s
u
p
p
o
r
tin
g
p
o
in
t o
f
t
h
e
b
all,
θ
-
in
clin
a
tio
n
a
n
g
le
o
f
I
DU
B
ein
g
t
h
e
f
ir
s
t
o
f
it
s
k
i
n
d
,
it
h
as
v
ar
io
u
s
s
h
o
r
tco
m
i
n
g
s
lik
e
n
o
p
r
o
p
er
c
o
n
tr
o
llin
g
m
ec
h
a
n
is
m
,
n
o
t
b
ein
g
ab
le
to
ac
h
ie
v
e
o
m
n
id
ir
ec
tio
n
al
m
o
b
ilit
y
.
2
2
.
2
.
B
a
ll H
a
m
s
t
er
De
s
ig
n Ro
bo
t
T
h
is
is
a
n
o
th
er
k
i
n
d
o
f
s
p
h
er
i
ca
l
r
o
b
o
t
in
w
h
ich
a
f
o
u
r
-
w
h
e
eled
v
eh
icle
is
k
ep
t
in
s
id
e
t
h
e
s
h
el
l
a
n
d
allo
w
ed
to
m
o
v
e
m
a
k
i
n
g
th
e
o
u
ter
s
h
ell
al
s
o
m
o
v
e.
T
h
e
f
o
u
r
w
h
ee
l
s
ca
n
b
e
co
n
tr
o
lled
in
d
ep
en
d
en
t
l
y
.
T
h
er
ef
o
r
e,
it
is
m
o
r
e
m
an
e
u
v
er
ab
le
an
d
ca
n
g
en
er
ate
d
i
f
f
er
en
t
m
o
tio
n
c
u
r
v
e
s
.
T
h
e
p
o
s
iti
o
n
o
f
t
h
e
ce
n
ter
o
f
g
r
av
it
y
o
f
th
e
i
n
ter
n
al
u
n
i
t
d
eter
m
in
e
s
th
e
m
o
v
e
m
en
t
o
f
t
h
e
r
o
b
o
t.
T
h
e
r
o
b
o
t
is
s
teer
ed
b
y
ch
an
g
i
n
g
t
h
e
later
al
p
o
s
itio
n
o
f
th
e
ce
n
ter
o
f
m
as
s
.
T
h
er
ef
o
r
e,
w
e
ca
n
ca
teg
o
r
iz
e
th
e
w
o
r
k
in
g
o
f
th
is
r
o
b
o
t
u
n
d
er
g
r
av
it
y
m
eth
o
d
[
7
]
.
I
t
h
as
a
clo
s
ed
-
lo
o
p
co
n
tr
o
l.
T
h
e
f
ee
d
b
ac
k
o
f
th
is
r
o
b
o
t
s
y
s
te
m
i
s
ac
h
ie
v
ed
b
y
in
e
r
tial
s
en
s
in
g
.
E
v
e
n
th
o
u
g
h
th
e
w
h
ee
l
s
ac
t
as
a
d
if
f
er
en
tia
l
d
r
iv
e
allo
w
i
n
g
th
e
r
o
b
o
t
to
tu
r
n
in
p
lace
,
it
f
ac
es
m
an
y
p
r
o
b
lem
s
lik
e
s
lip
p
ag
e
o
f
t
h
e
i
n
ter
n
a
l
u
n
i
t,
L
o
w
ac
c
u
r
ac
y
i
n
ac
h
ie
v
in
g
th
e
r
eq
u
ir
ed
m
o
tio
n
p
ath
etc.
T
h
e
r
o
b
o
t
is
v
er
y
ef
f
ec
tiv
e
o
n
s
tr
ai
g
h
t p
ath
s
o
r
o
n
p
at
h
s
w
it
h
s
m
all
c
u
r
v
at
u
r
e
[
3
]
.
Ho
w
ev
er
,
i
t b
ec
o
m
e
s
u
n
s
ta
b
le
o
n
p
ath
s
w
i
th
a
b
ig
g
er
cu
r
v
atu
r
e.
E
v
e
n
th
o
u
g
h
th
i
s
r
o
b
o
t
ca
n
tu
r
n
in
p
lace
,
it
r
eq
u
ir
es
ti
m
e
to
m
o
v
e
t
h
e
r
o
b
o
t
in
th
e
r
eq
u
ir
ed
d
ir
ec
tio
n
.
T
h
er
ef
o
r
e,
th
is
r
o
b
o
t
ca
n
n
o
t
clai
m
to
ac
h
iev
e
o
m
n
id
ir
ec
tio
n
a
l
m
o
b
ilit
y
.
No
d
etails
o
f
its
p
er
f
o
r
m
a
n
ce
ar
e
g
i
v
e
n
in
t
h
e
l
iter
atu
r
e.
Fig
u
r
e
2.
B
all
Ham
s
ter
P
r
o
to
t
y
p
e
De
s
i
g
n
[
3
]
2
.
3
.
Ura
nu
s
Me
ca
n
u
m
w
h
ee
ls
ar
e
al
m
o
s
t s
i
m
ilar
i
n
co
n
s
tr
u
ctio
n
to
th
at
o
f
u
n
i
v
er
s
al
w
h
ee
ls
.
Me
ca
n
u
m
h
as a
ce
n
tr
al
h
u
b
w
h
ic
h
co
n
s
is
t
s
o
f
f
r
ee
m
o
v
i
n
g
r
o
ller
s
.
B
u
t t
h
e
d
if
f
er
en
ce
f
r
o
m
t
h
e
u
n
i
v
er
s
al
w
h
ee
l is in
t
h
e
f
ac
t
th
at
t
h
e
r
o
ller
s
ar
e
o
r
ien
ted
at
4
5
º
to
th
e
cir
cu
m
f
er
e
n
ce
o
f
t
h
e
h
u
b
[
5
]
.
Fig
u
r
e
3.
Ur
an
u
s
[
8
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
5
,
No
.
1
,
Ma
r
ch
2
0
1
6
:
17
–
28
20
A
t
y
p
ica
l
r
o
b
o
t
u
tili
zin
g
Me
ca
n
u
m
w
h
ee
l
is
th
e
Ur
a
n
u
s
r
o
b
o
t.
I
t
w
a
s
b
u
ilt
b
y
t
h
e
Mo
b
ile
R
o
b
o
t
L
ab
o
f
t
h
e
C
ar
n
e
g
ie
-
Me
llo
n
Un
iv
e
r
s
it
y
.
T
h
e
e
x
ter
n
a
l
m
o
r
p
h
o
lo
g
y
o
f
t
h
e
r
o
b
o
t is r
ec
ta
n
g
u
lar
with
7
5
c
m
le
n
g
t
h
,
6
0
c
m
b
r
ea
d
th
an
d
4
0
c
m
h
ei
g
h
t.
I
ts
w
eig
h
t
i
s
ab
o
u
t
5
0
k
g
[
9
]
.
T
h
e
Ur
an
u
s
u
tili
ze
s
d
ir
e
ct
d
r
iv
in
g
m
eth
o
d
.
I
t
co
n
s
is
ts
o
f
f
o
u
r
Me
ca
n
u
m
wh
ee
ls
.
T
h
e
w
h
ee
ls
ar
e
p
lace
d
in
s
u
c
h
a
w
a
y
t
h
at
t
h
e
r
o
ller
s
o
n
ea
ch
w
h
ee
l
ar
e
o
p
p
o
s
ite
in
d
ir
ec
tio
n
to
its
ad
jace
n
t
w
h
ee
l
s
.
W
h
en
all
th
e
wh
ee
ls
ar
e
d
r
iv
en
in
t
h
e
s
a
m
e
d
ir
ec
tio
n
,
th
e
r
o
ller
m
o
tio
n
o
f
th
e
o
p
p
o
s
itel
y
o
r
ien
ted
w
h
ee
l
s
ca
n
ce
ls
ea
c
h
o
th
er
an
d
th
e
r
o
b
o
t
m
o
v
es
in
f
o
r
w
ar
d
o
r
b
ac
k
w
ar
d
d
ir
ec
tio
n
.
W
h
en
th
e
w
h
ee
ls
with
o
p
p
o
s
ite
r
o
ller
o
r
ien
tatio
n
s
ar
e
d
r
iv
en
in
o
p
p
o
s
ite
d
ir
ec
tio
n
s
,
th
e
r
o
ller
s
ac
t
as a
s
cr
e
w
a
n
d
t
h
er
ef
o
r
e,
t
h
e
w
h
ee
ls
m
o
v
e
s
id
e
w
a
y
s
.
I
t
m
u
s
t
b
e
n
o
ted
th
at
it
h
a
s
f
o
u
r
m
o
t
o
r
s
to
in
d
ep
en
d
e
n
tl
y
tr
an
s
m
it
t
h
e
d
r
iv
i
n
g
f
o
r
ce
to
ea
ch
w
h
ee
l.
T
h
e
n
u
m
b
er
o
f
ac
tu
ato
r
s
is
m
o
r
e
t
h
a
n
th
e
r
eq
u
ir
ed
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
f
o
r
ac
h
iev
in
g
o
m
n
id
ir
ec
tio
n
al
m
o
tio
n
.
T
h
er
ef
o
r
e,
it
ca
n
lead
to
r
ed
u
n
d
an
t
ac
tu
a
tio
n
.
B
u
t
it
ca
n
b
e
co
n
tr
o
lled
w
it
h
o
u
t
m
u
ch
d
i
f
f
ic
u
lt
y
.
Ur
an
u
s
u
s
es
a
s
u
s
p
en
s
io
n
s
y
s
te
m
w
h
ic
h
h
as
t
h
e
ad
v
a
n
t
ag
es
o
f
m
ak
i
n
g
t
h
e
r
id
e
s
m
o
o
th
er
an
d
Help
in
g
all
t
h
e
w
h
ee
ls
to
co
n
ti
n
u
o
u
s
l
y
h
a
v
e
g
r
o
u
n
d
co
n
t
ac
t.
T
h
e
v
o
ltag
e
in
p
u
t
to
Ur
an
u
s
is
2
4
V
DC
.
I
t
u
tili
ze
s
a
s
er
v
o
co
n
tr
o
ller
to
p
r
o
p
er
ly
r
ec
eiv
e
th
e
m
o
tio
n
co
m
m
a
n
d
s
a
n
d
ac
t
u
ate
t
h
e
m
o
to
r
s
.
A
m
a
x
i
m
u
m
to
r
q
u
e
o
f
4
.
7
n
m
an
d
t
h
r
u
s
t
o
f
1
5
0
lb
s
ca
n
b
e
g
e
n
er
ated
.
I
t
h
a
s
h
o
lo
n
o
m
ic
ca
p
ab
ilit
y
.
T
h
e
m
ax
i
m
u
m
s
p
ee
d
th
at
ca
n
b
e
ac
h
ie
v
ed
b
y
Ur
an
u
s
is
al
m
o
s
t e
q
u
al
to
1
m
/s
o
r
3
k
m
/
h
r
.
I
t
w
as b
u
ilt a
s
a
g
en
er
al
p
u
r
p
o
s
e
r
o
b
o
t f
o
r
h
elp
r
esear
ch
in
r
o
b
o
t n
av
i
g
atio
n
in
d
o
o
r
s
[
1
0
]
.
2
.
4
.
T
hree
-
Di
m
e
ns
io
na
l F
ly
w
heel
Ro
bo
t
ic
Sy
s
t
e
m
T
h
is
r
o
b
o
t
b
elo
n
g
s
to
a
n
e
w
b
r
ee
d
o
f
s
p
h
er
ical
r
o
b
o
ts
.
I
ts
s
tr
u
ct
u
r
e
is
s
i
m
ilar
to
t
h
at
o
f
a
g
i
m
b
a
l.
T
h
is
r
o
b
o
t c
o
n
s
is
t
s
o
f
t
h
r
ee
s
p
h
er
ical
s
h
ells
,
t
h
e
o
u
ter
s
h
ell,
m
id
d
le
s
h
e
ll,
in
n
er
s
h
ell
an
d
a
p
latf
o
r
m
co
n
n
ec
ted
to
th
e
in
n
er
s
h
ell.
T
h
e
r
o
tatio
n
a
x
es
o
f
t
h
e
th
r
ee
s
h
e
lls
ar
e
d
ef
i
n
ed
as
α
-
ax
is
,
β
-
ax
is
a
n
d
γ
-
a
x
is
.
T
h
e
y
ar
e
o
r
th
o
g
o
n
al
to
ea
ch
o
th
er
.
I
n
a
ll,
th
er
e
ar
e
th
r
ee
ac
tu
at
o
r
s
to
d
r
iv
e
th
e
r
o
b
o
t.
Α
-
a
x
is
ac
t
u
at
o
r
,
β
-
ax
is
ac
t
u
ato
r
an
d
γ
-
ax
i
s
ac
tu
ato
r
.
Α
-
a
x
is
ac
tu
ato
r
is
co
n
n
ec
ted
to
th
e
o
u
te
r
s
h
ell.
I
t
p
r
o
d
u
ce
s
tr
an
s
lato
r
m
o
tio
n
to
th
e
r
o
b
o
t
(
f
o
r
w
ar
d
/
b
ac
k
w
ar
d
)
.
T
h
e
β
-
ax
is
ac
t
u
ato
r
ca
u
s
es
r
o
tatio
n
o
f
t
h
e
m
id
d
le
s
h
el
l,
w
h
ich
i
n
t
u
r
n
m
a
k
es
th
e
o
u
ter
s
h
ell
to
t
u
r
n
a
n
d
r
o
ll
ab
o
u
t
a
p
o
in
t
b
y
v
ir
tu
e
o
f
co
n
s
er
v
a
tio
n
o
f
an
g
u
lar
m
o
m
e
n
t
u
m
.
I
n
s
h
o
r
t,
w
e
ca
n
s
a
y
t
h
a
t
th
e
s
teer
i
n
g
m
o
t
io
n
o
f
th
e
r
o
b
o
t is p
r
o
v
id
ed
b
y
β
-
ax
i
s
ac
t
u
a
to
r
.
Γ
-
ax
i
s
ac
t
u
ato
r
p
r
o
v
id
es b
alan
ce
to
th
e
r
o
b
o
t.
T
h
is
r
o
b
o
t
p
r
o
v
id
es
i
m
p
r
o
v
ed
tr
aj
ec
to
r
y
co
n
tr
o
l
as
a
r
es
u
lt
o
f
it
s
clo
s
ed
lo
o
p
f
ee
d
b
ac
k
m
ec
h
an
i
s
m
.
T
h
e
r
o
b
o
t
is
co
n
tr
o
lled
b
ased
o
n
th
e
k
i
n
e
m
atic
s
an
d
d
y
n
a
m
ic
s
o
f
th
e
s
y
s
te
m
.
T
h
e
to
tal
m
as
s
o
f
t
h
e
r
o
b
o
t
is
a
litt
le
o
v
er
3
2
5
k
g
[
1
1
]
.
I
t h
as a
n
o
u
ter
d
i
a
m
eter
o
f
ab
o
u
t 2
m
.
Fig
u
r
e
4
.
Stru
ct
u
r
e
o
f
th
e
r
o
b
o
t [
1
1
]
T
h
e
d
r
iv
in
g
m
et
h
o
d
o
f
th
i
s
r
o
b
o
t
is
a
co
m
b
i
n
atio
n
o
f
d
ir
ec
t
d
r
iv
i
n
g
an
d
co
n
s
er
v
atio
n
o
f
a
n
g
u
la
r
m
o
m
e
n
t
u
m
.
I
t
u
s
es
d
ir
ec
t
d
r
iv
in
g
m
et
h
o
d
f
o
r
ac
h
iev
i
n
g
li
n
e
ar
m
o
tio
n
w
h
er
ea
s
f
o
r
s
teer
in
g
m
o
tio
n
,
it
g
o
es
f
o
r
co
n
s
er
v
atio
n
o
f
a
n
g
u
lar
m
o
m
en
tu
m
m
eth
o
d
.
T
h
e
t
h
r
ee
s
h
e
lls
o
f
t
h
e
r
o
b
o
t
ac
t
li
k
e
t
h
r
ee
f
l
y
w
h
ee
ls
t
h
er
eb
y
h
elp
in
g
to
s
to
r
e
r
o
tatio
n
al
en
e
r
g
y
.
I
t
h
elp
s
i
n
s
a
v
i
n
g
ac
t
u
ati
o
n
en
er
g
y
as
th
e
s
to
r
ed
e
n
er
g
y
i
n
t
h
e
m
id
d
le
a
n
d
in
n
er
s
h
ells
ca
n
b
e
u
tili
ze
d
to
tu
r
n
th
e
r
o
b
o
t.
I
n
s
p
ite
o
f
i
ts
s
h
o
r
tco
m
i
n
g
s
l
ik
e
e
x
ce
s
s
i
v
e
v
ib
r
atio
n
s
,
th
is
r
o
b
o
t
h
as
g
r
ea
t sco
p
e
f
o
r
f
u
t
u
r
e
ap
p
licatio
n
s
.
2
.
5
.
G
ro
un
d
bo
t
Gr
o
u
n
d
B
o
t
is
a
m
o
b
ile
r
o
b
o
t
d
ev
elo
p
ed
b
y
R
o
tu
n
d
u
s
.
I
t
is
a
n
ea
r
s
p
h
er
ical
m
o
b
ile
r
o
b
o
t
w
it
h
a
h
i
g
h
d
eg
r
ee
o
f
m
an
e
u
v
er
ab
il
it
y
.
I
t
s
w
ei
g
h
t i
s
ab
o
u
t 2
5
k
g
a
n
d
ca
n
n
av
i
g
ate
th
r
o
u
g
h
an
y
s
u
r
f
ac
e
ea
s
il
y
.
I
t
is
s
li
g
h
tl
y
lar
g
er
th
an
a
co
n
v
en
t
io
n
al
ca
r
tire
w
ith
a
d
ia
m
eter
o
r
h
eig
h
t
o
f
ab
o
u
t
6
0
cm
.
I
t
h
as
a
w
id
th
o
f
ab
o
u
t
8
0
cm
.
T
h
e
d
en
s
it
y
o
f
Gr
o
u
n
d
B
o
t
is
s
o
lo
w
t
h
at
it
ca
n
e
v
en
f
lo
at
.
Gr
o
u
n
d
B
o
t
ca
n
r
u
n
i
n
m
o
s
t
t
er
r
ain
s
at
u
p
to
1
0
k
m
/h
(
6
m
p
h
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Deg
r
ee
o
f A
ch
ieva
b
ilit
y
o
f O
m
n
id
ir
ec
tio
n
a
l
Mo
tio
n
in
V
a
r
io
u
s
Mo
b
ile
R
o
b
o
t D
esig
n
s
.
.
.
(
A
jju
R
.
Ju
s
tu
s
)
21
Fig
u
r
e
5
.
Gr
o
u
n
d
B
o
t [
1
2
]
T
h
e
s
h
ell
is
b
asicall
y
m
ad
e
o
f
p
o
ly
ca
r
b
o
n
ate
o
v
er
w
h
ic
h
a
h
ig
h
f
r
ictio
n
co
atin
g
is
g
i
v
en
to
in
cr
ea
s
e
tr
ac
tio
n
f
o
r
ce
s
.
T
h
e
d
r
iv
i
n
g
m
ec
h
an
i
s
m
o
f
Gr
o
u
n
d
B
o
t c
o
n
s
i
s
ts
o
f
a
p
e
n
d
u
l
u
m
w
h
ich
is
co
n
tr
o
lled
to
m
o
v
e
t
h
e
r
o
b
o
t
in
th
e
d
esire
d
d
ir
ec
tio
n
.
I
t
co
m
es
u
n
d
er
g
r
av
it
y
m
et
h
o
d
.
I
t
u
tili
ze
s
t
w
o
m
o
to
r
s
to
m
o
v
e
th
e
r
o
b
o
t
in
th
e
d
esire
d
d
ir
ec
tio
n
[
1
3
]
.
T
h
e
ce
n
ter
o
f
g
r
a
v
it
y
al
w
a
y
s
lies
i
n
s
id
e
t
h
e
s
p
h
er
ical
s
h
ell.
A
t
r
est,
t
h
e
ce
n
ter
o
f
g
r
av
it
y
is
clo
s
e
to
th
e
g
r
o
u
n
d
.
So
th
e
r
o
b
o
t d
o
es n
o
t te
n
d
to
t
ip
o
v
er
,
an
d
s
tab
ilit
y
i
s
in
cr
ea
s
ed
[
1
4
]
.
I
t
h
as
an
in
–
b
u
ilt
m
o
to
r
,
w
h
ich
m
o
v
e
s
th
e
p
en
d
u
l
u
m
.
As
th
e
p
en
d
u
l
u
m
m
o
v
es,
m
o
m
en
tu
m
i
s
d
ev
elo
p
ed
.
T
h
u
s
,
th
e
ce
n
ter
o
f
g
r
av
it
y
o
f
t
h
e
Gr
o
u
n
d
B
o
t
ch
an
g
es.
A
s
a
r
es
u
lt,
it
m
o
v
e
s
in
th
e
d
ir
ec
tio
n
o
f
m
o
tio
n
o
f
t
h
e
p
en
d
u
lu
m
.
I
t
h
as
a
q
u
ic
k
an
d
e
f
f
icie
n
t
ac
c
eler
atio
n
an
d
d
ec
eler
atio
n
.
G
r
o
u
n
d
B
o
t
tu
r
n
s
b
y
m
o
v
i
n
g
th
e
p
en
d
u
lu
m
to
th
e
s
id
e.
GP
S
an
d
d
ea
d
-
r
ec
k
o
n
i
n
g
ar
e
b
o
th
u
s
ed
to
en
s
u
r
e
h
ig
h
r
o
u
te
ac
c
u
r
ac
y
.
Sin
ce
it
h
as
a
s
m
all
t
u
r
n
i
n
g
r
ad
iu
s
f
o
r
s
teer
i
n
g
m
o
v
e
m
e
n
ts
,
it
ca
n
n
o
t
b
e
co
n
s
id
er
ed
as
an
o
m
n
id
ir
ec
tio
n
al
r
o
b
o
t
[
7
]
.
L
i
-
io
n
b
atter
ies
ar
e
b
ein
g
u
s
ed
in
Gr
o
u
n
d
B
o
t
as
th
e
p
o
w
er
s
o
u
r
ce
.
Gr
o
u
n
d
B
o
t
is
w
id
el
y
u
s
ed
in
A
ir
p
o
r
ts
,
Secu
r
i
t
y
es
tab
lis
h
m
e
n
ts
f
o
r
s
u
r
v
eilla
n
ce
p
u
r
p
o
s
es.
2
.
6
.
G
lo
ry
Glo
r
y
is
a
m
o
b
ile
r
o
b
o
t
w
it
h
a
s
p
h
er
ical
o
u
ter
s
h
ell.
T
h
e
ex
ter
n
al
m
o
r
p
h
o
lo
g
y
o
f
t
h
e
r
o
b
o
t
is
s
p
h
er
ical.
I
t
h
a
s
t
h
e
ab
ili
t
y
to
ex
h
ib
it
o
m
n
id
ir
ec
tio
n
al
m
o
tio
n
w
it
h
h
o
lo
n
o
m
ic
ca
p
a
b
ilit
y
.
T
h
e
d
r
iv
i
n
g
m
ec
h
a
n
i
s
m
f
o
r
g
lo
r
y
is
a
b
it
d
if
f
er
e
n
t
a
n
d
in
ter
es
tin
g
w
h
e
n
co
m
p
ar
ed
to
m
o
s
t
o
th
er
s
p
h
e
r
ical
m
o
b
ile
r
o
b
o
ts
.
I
t
ca
n
b
e
class
i
f
ied
u
n
d
er
th
e
g
r
av
it
y
m
et
h
o
d
.
T
h
is
r
o
b
o
t
h
a
s
a
to
tal
o
f
f
o
u
r
s
p
o
k
es,
m
o
v
i
n
g
r
ad
iall
y
o
u
t
w
ar
d
s
f
r
o
m
t
h
e
ce
n
ter
to
th
e
i
n
n
er
cir
cu
m
f
er
e
n
ce
o
f
t
h
e
s
p
h
er
e.
T
h
e
s
p
o
k
e
s
ar
e
p
lace
d
at
s
o
m
e
s
p
ec
if
ic
a
n
g
les
to
ea
ch
o
th
er
.
W
ei
g
h
t
s
ar
e
p
lac
ed
at
ea
ch
o
f
t
h
e
f
o
u
r
s
p
o
k
e
s
,
w
h
ic
h
ca
n
b
e
m
o
v
ed
alo
n
g
th
e
s
p
o
k
e
s
u
s
i
n
g
a
s
tep
p
er
m
o
to
r
.
T
h
is
to
tal
m
ec
h
an
is
m
ca
n
b
e
ter
m
ed
as Fi
x
ed
I
n
ter
n
al
P
r
o
p
u
ls
io
n
.
Fig
u
r
e
6
.
Stru
ctu
r
e
o
f
Gl
o
r
y
[
1
5
]
Glo
r
y
is
a
s
s
e
m
b
led
in
s
u
ch
a
w
a
y
t
h
at
it
h
a
s
g
eo
m
etr
ical
s
y
m
m
etr
y
.
As a
r
es
u
lt o
f
t
h
is
s
y
m
m
etr
y
,
t
h
e
ce
n
ter
o
f
m
as
s
o
f
th
e
r
o
b
o
t,
e
v
en
a
f
ter
in
cl
u
d
in
g
t
h
e
w
ei
g
h
t
s
al
w
a
y
s
lie
at
t
h
e
g
eo
m
e
tr
ic
ce
n
ter
o
f
th
e
r
o
b
o
t.
T
h
e
ad
v
an
tag
e
o
f
t
h
is
i
s
th
a
t
th
e
r
o
b
o
t
h
as
in
cr
ea
s
ed
s
tab
il
it
y
.
I
t
d
o
es
n
o
t
ten
d
to
tip
o
v
er
.
So
m
e
tec
h
n
ical
d
etail
o
f
th
i
s
r
o
b
o
t is g
iv
e
n
b
y
[
1
6
]
.
[1
]
T
h
e
an
g
le
b
et
w
ee
n
t
h
e
s
p
o
k
e
s
ar
e
1
0
9
.
4
7
º
[2
]
Ma
s
s
o
f
ea
c
h
w
ei
g
h
t i
s
1
.
1
2
5
k
g
[3
]
Fo
u
r
s
tep
p
er
m
o
to
r
ar
e
r
eq
u
ir
e
d
[4
]
T
h
e
s
tep
p
er
m
o
t
o
r
h
as 2
0
0
s
tep
s
p
er
r
ev
o
lu
tio
n
.
T
h
e
m
o
tio
n
o
f
t
h
e
s
tep
p
er
m
o
t
o
r
cir
cu
it
is
co
n
tr
o
lled
b
y
a
m
i
cr
o
co
n
tr
o
ller
.
T
h
e
f
ee
d
b
ac
k
co
n
tr
o
l
o
f
th
is
r
o
b
o
t
is
b
ased
o
n
o
p
en
lo
o
p
co
n
tr
o
l.
T
h
er
ef
o
r
e,
th
e
s
co
p
e
f
o
r
in
ac
c
u
r
ate
m
o
v
e
m
en
ts
o
f
th
e
r
o
b
o
t
is
q
u
it
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
5
,
No
.
1
,
Ma
r
ch
2
0
1
6
:
17
–
28
22
h
ig
h
.
On
e
th
in
g
to
n
o
te
is
th
at
th
e
m
o
t
io
n
o
f
t
h
is
r
o
b
o
t
is
p
lan
n
ed
a
n
d
co
n
tr
o
lled
b
y
m
ea
n
s
o
f
a
s
i
m
p
le
alg
o
r
ith
m
ic
i
ter
atio
n
a
n
d
ca
n
b
e
ea
s
il
y
i
m
p
le
m
en
ted
.
I
t
m
i
g
h
t
b
e
a
b
it
s
lo
w
w
h
en
w
e
c
o
m
p
ar
e
it
s
r
esp
o
n
s
e
ti
m
e
w
i
th
o
t
h
er
s
p
h
er
ical
r
o
b
o
ts
,
b
u
t
it
ca
n
b
e
n
eg
lecte
d
.
T
h
e
in
ac
cu
r
ac
ie
s
f
o
r
t
h
e
m
o
v
e
m
e
n
t
o
f
t
h
e
r
o
b
o
t
m
a
y
b
e
d
u
e
to
f
ac
to
r
s
li
k
e
s
u
r
f
ac
e
i
m
p
er
f
ec
tio
n
s
,
ce
n
ter
o
f
m
as
s
n
o
t
b
ein
g
at
t
h
e
g
eo
m
etr
ical
c
en
ter
o
f
t
h
e
r
o
b
o
t,
o
p
en
lo
o
p
c
o
n
tr
o
l o
f
th
e
r
o
b
o
t
etc.
2
.
7
.
O
m
ni Cr
a
w
ler
M
ec
ha
nis
m
Wit
h Cir
cula
r
Sect
io
n
T
h
e
O
m
n
i
cr
a
w
ler
lo
o
k
s
s
i
m
ilar
to
a
tan
k
e
x
ce
p
t
th
at
is
ab
le
to
m
o
v
e
o
m
n
i
d
ir
ec
tio
n
all
y
.
I
t
s
lo
co
m
o
tio
n
s
tr
u
ct
u
r
e
is
i
n
t
h
e
f
o
r
m
o
f
a
ca
p
s
u
le.
T
h
e
ca
p
ab
ilit
y
o
f
t
h
e
cr
a
w
ler
to
m
o
v
e
o
m
n
i
d
ir
ec
tio
n
all
y
i
s
d
u
e
to
th
e
d
ev
elo
p
m
e
n
t
o
f
a
n
o
v
el
o
m
n
i
b
all
d
esi
g
n
ed
w
h
i
ch
is
u
s
ed
i
n
th
e
o
m
n
i
cr
a
w
le
r
.
T
h
e
o
m
n
i
b
all
i
s
u
s
ed
to
cr
ea
te
th
e
o
m
n
i c
r
a
w
le
r
.
Om
n
i c
r
a
w
ler
u
tili
ze
s
d
ir
ec
t
d
r
iv
in
g
m
e
th
o
d
.
Fig
u
r
e
7.
W
o
r
k
in
g
p
r
in
cip
le
o
f
O
m
n
i b
all
[
1
7
]
T
h
e
o
m
n
i
b
all
co
n
s
is
t
s
o
f
t
w
o
h
e
m
i
s
p
h
er
es
o
n
eit
h
er
s
i
d
es
o
f
an
a
x
le.
T
h
e
t
w
o
s
tr
u
ctu
r
e
s
ca
n
r
o
tate
in
d
ep
en
d
en
tl
y
o
r
to
g
et
h
er
as a
s
p
h
er
e.
T
h
e
ac
tiv
e
r
o
tatio
n
ax
le
is
r
o
tated
u
s
i
n
g
a
r
o
ller
.
Fig
u
r
e
8.
O
m
n
i
C
r
a
w
ler
P
r
o
to
t
y
p
e
Desi
g
n
[
1
7
]
T
h
e
s
id
e
w
a
y
s
m
o
tio
n
o
f
t
h
e
r
o
b
o
t
ca
n
b
e
ac
h
iev
ed
b
y
th
e
r
o
tatio
n
o
f
t
h
e
ac
ti
v
e
r
o
tatio
n
a
x
is
.
A
to
tal
o
f
th
r
ee
m
o
to
r
s
ar
e
r
eq
u
ir
ed
to
g
iv
e
t
h
e
r
eq
u
ir
ed
in
p
u
ts
.
A
g
e
ar
m
o
to
r
is
u
s
ed
to
r
o
tate
th
e
i
n
n
er
s
h
a
f
t a
n
d
g
ea
r
w
h
ic
h
in
t
u
r
n
r
o
tates
t
h
e
s
p
r
o
ck
ets
s
itu
a
ted
at
th
e
en
d
s
.
T
h
is
r
esu
lt
s
in
t
h
e
m
o
t
io
n
in
f
o
r
w
ar
d
o
r
b
ac
k
w
ar
d
d
ir
ec
tio
n
.
T
h
er
ef
o
r
e,
tw
o
m
o
t
o
r
s
ar
e
u
s
ed
to
r
o
tate
th
e
lef
t a
n
d
r
ig
h
t c
r
a
w
ler
u
n
its
i
n
d
ep
en
d
en
tl
y
f
o
r
ac
h
ie
v
i
n
g
th
e
co
m
p
lete
tr
an
s
latio
n
al
m
o
t
io
n
o
f
th
e
cr
a
w
ler
.
T
h
e
y
h
a
v
e
a
p
o
w
er
r
atin
g
o
f
9
0
W
.
A
s
i
n
g
le
m
o
to
r
is
u
s
ed
to
r
o
tate
b
o
th
th
e
cr
a
w
ler
ab
o
u
t
th
eir
ac
tiv
e
r
o
lli
n
g
a
x
es
to
ac
h
iev
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[
1
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
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Deg
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23
T
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ical
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u
r
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9
.
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m
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I
n
ter
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d
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in
g
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m
[
1
8
]
T
h
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ates
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ir
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m
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r
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[
1
8
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f
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t [
1
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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9
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4856
IJ
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Vo
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5
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1
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Ma
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6
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17
–
28
24
G
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w
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Fig
u
r
e
11.
Gy
r
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p
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ty
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[
2
1
]
G
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[
1
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.
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[
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Deg
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alls
[
2
3
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.
2
.
1
1
.
O
m
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p
h
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o
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.
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h
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cip
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[
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4
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.
Fig
u
r
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13.
Stru
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f
O
m
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Qiu
[
2
4
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T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8
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4856
IJ
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Vo
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26
Fig
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14.
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[
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a
s
tr
ai
g
h
t
-
l
in
e
p
ath
,
t
h
e
later
al
er
r
o
r
is
o
n
l
y
0
.
0
4
1
m
f
o
r
a
1
m
le
n
g
t
h
o
f
tr
a
v
el.
Fro
m
th
ese
r
es
u
lt
s
,
w
e
ca
n
s
a
y
t
h
at
t
h
is
r
o
b
o
t is a
s
p
h
er
ical,
o
m
n
id
ir
ec
tio
n
al
r
o
b
o
t w
ith
h
i
g
h
m
o
ti
o
n
ac
cu
r
ac
y
[
2
4
]
.
3.
R
E
SU
L
T
S
On
t
h
e
b
asis
o
f
d
ata
o
b
tain
ed
f
o
r
th
e
co
n
s
id
er
ed
r
o
b
o
ts
,
r
ele
v
an
t
p
ar
a
m
eter
s
f
o
r
th
e
f
ield
o
f
s
t
u
d
y
i
n
th
e
cu
r
r
e
n
t
to
p
ic
ar
e
s
elec
ted
.
A
ll
t
h
e
m
o
b
ile
r
o
b
o
ts
tak
en
f
o
r
s
tu
d
y
ar
e
co
m
p
ar
ed
w
i
th
e
ac
h
o
th
er
b
ased
o
n
th
ese
p
ar
a
m
eter
s
.
T
ab
le
1
.
C
o
m
p
ar
is
o
n
o
f
v
ar
io
u
s
r
o
b
o
t c
o
n
f
i
g
u
r
atio
n
s
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