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201
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SS
N:
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4856
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1.
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[
1
]
.
W
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m
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2
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ices
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9
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d
p
lan
etar
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&
s
p
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ex
p
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[
10
,
11
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.
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h
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m
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v
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tag
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
K
in
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S
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197
R
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p
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h
ah
[
12
]
h
as
s
h
o
w
n
k
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m
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M.
Go
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[
13
]
h
as
d
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D
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Q
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m
p
u
te
th
e
co
n
f
i
g
u
r
atio
n
o
f
th
e
ch
ain
.
Fo
r
s
er
ia
l
m
an
ip
u
lato
r
s
,
t
h
i
s
i
s
ac
co
m
p
li
s
h
ed
b
y
d
ir
ec
t
s
u
b
s
tit
u
tio
n
o
f
th
e
j
o
in
t
p
ar
a
m
eter
s
in
to
th
e
f
o
r
w
ar
d
k
i
n
e
m
a
ti
c
eq
u
atio
n
s
f
o
r
th
e
s
er
ial
s
tr
i
n
g
.
T
h
e
f
o
r
w
ar
d
k
i
n
e
m
atic
s
d
et
er
m
in
e
t
h
e
p
o
s
itio
n
a
n
d
o
r
ien
tatio
n
,
ac
h
ie
v
ed
b
y
u
s
i
n
g
J
ac
o
b
ian
Ma
tr
ices
f
o
r
ea
ch
w
h
ee
l o
f
t
h
e
r
o
b
o
t.
Sin
ce
th
er
e
is
n
o
s
teer
in
g
,
i
n
o
r
d
er
to
n
u
lli
f
y
th
e
e
f
f
ec
t o
f
r
o
tatio
n
al
s
lip
o
n
th
e
t
u
n
i
n
g
s
,
i
n
v
er
s
e
k
i
n
e
m
atics
m
o
d
el
w
as
d
er
iv
ed
f
o
r
th
e
w
h
ee
l r
o
tatio
n
al
v
elo
cit
y
.
2.
T
H
E
P
I
N
E
N
E
E
D
L
E
CO
L
L
E
CT
O
R
RO
B
O
T
–
AN
O
UT
L
I
N
E
T
h
is
s
ec
tio
n
d
escr
ib
es
th
e
r
o
b
o
t
ch
ar
ac
ter
is
tics
f
o
r
its
k
i
n
e
m
atic
m
o
d
ellin
g
.
T
h
e
r
o
b
o
t
h
as si
x
w
h
ee
l
s
u
s
i
n
g
a
r
o
ck
er
b
o
g
ie
s
u
s
p
e
n
s
i
o
n
m
ec
h
a
n
is
m
as
s
h
o
w
n
i
n
t
h
e
Fig
u
r
e
1
.
T
h
e
P
iNC
o
R
is
5
6
.
5
cm
s
lo
n
g
,
3
1
.
5
c
m
s
w
id
e
a
n
d
2
5
.
5
c
m
s
h
i
g
h
.
T
h
e
P
iNC
o
R
is
eq
u
ip
p
ed
w
it
h
a
s
u
c
tio
n
m
ec
h
a
n
is
m
w
h
ic
h
e
n
ab
les
th
e
co
llectio
n
o
f
p
in
e
n
ee
d
les
f
r
o
m
t
h
e
g
r
o
u
n
d
.
An
ad
j
u
s
tab
le
g
r
o
u
n
d
clea
r
an
ce
o
f
2
0
c
m
is
p
r
o
v
id
ed
w
h
ic
h
en
ab
les
it
to
m
an
e
u
v
er
f
r
ee
l
y
th
r
o
u
g
h
p
its
an
d
h
o
les
o
n
t
h
e
h
ills
.
A
ll
t
h
e
w
h
ee
l
s
in
P
in
C
o
R
ar
e
1
7
cm
in
d
ia
m
et
er
an
d
h
a
v
e
a
n
o
m
in
a
l s
p
ee
d
o
f
0
.
2
m
/
s
ec
.
T
h
e
s
m
o
o
th
o
p
er
atio
n
o
f
th
e
P
iNC
o
R
is
d
u
e
to
t
h
e
in
d
ep
en
d
en
tl
y
ac
t
u
ated
w
h
ee
l
s
w
h
ic
h
ar
e
attac
h
ed
to
a
r
o
ck
er
b
o
g
ie
s
u
s
p
en
s
io
n
m
ec
h
a
n
is
m
w
h
ic
h
e
n
ab
les
it
s
m
o
v
e
m
en
t
in
lo
w
v
elo
cit
y
an
d
u
n
ev
e
n
ter
r
ain
.
R
o
ck
er
b
o
g
ie
s
u
s
p
e
n
s
i
o
n
co
n
s
i
s
t
s
o
f
t
w
o
m
a
in
r
o
c
k
e
r
s
w
h
ic
h
ar
e
j
o
in
ed
at
a
ce
n
tr
al
d
if
f
er
en
tia
l
u
n
it,
w
it
h
t
h
e
m
ai
n
b
o
d
y
ca
lled
as
Av
er
ag
i
n
g
Me
ch
a
n
i
s
m
.
T
h
is
s
tab
ilizes
th
e
b
o
d
y
u
n
it
an
d
h
el
p
s
in
p
r
ev
e
n
ti
n
g
t
h
e
to
p
p
lin
g
e
f
f
ec
t
o
f
t
h
e
r
o
v
er
at
in
cli
n
atio
n
s
.
E
ac
h
r
o
ck
er
h
a
s
t
h
r
ee
n
o
n
-
s
teer
ab
le
i
n
d
ep
en
d
en
tl
y
ac
t
u
ated
w
h
ee
ls
;
o
n
e
at
th
e
f
r
o
n
t
a
n
d
th
e
r
e
m
a
in
i
n
g
t
w
o
at
t
h
e
s
m
all
r
o
ck
er
e
n
d
i
n
t
h
e
b
ac
k
p
o
r
tio
n
.
J
o
in
t
an
g
le
b
et
w
ee
n
t
h
e
s
m
al
l
an
d
m
ai
n
r
o
ck
er
is
d
e
n
o
ted
b
y
ψ
1
&
ψ
2
,
th
e
le
f
t
a
n
d
r
i
g
h
t
b
o
g
ie
a
n
g
les
(
m
ai
n
r
o
ck
er
s
v
ia
d
if
f
er
e
n
tial)
ar
e
d
en
o
ted
b
y
β
1
&
β
2
.
T
h
e
w
h
ee
l r
o
tatio
n
is
d
en
o
ted
b
y
δ
i
w
h
er
e
i =
1
–
6
.
T
h
er
e
ar
e
in
to
tal
s
i
x
ac
tu
ato
r
s
i
n
th
e
f
o
r
m
o
f
en
co
d
ed
m
o
to
r
s
co
n
n
ec
ted
to
th
e
wh
ee
ls
w
h
ic
h
en
ab
le
i
n
d
ep
en
d
e
n
t
m
o
v
e
m
en
t
o
f
t
h
e
P
in
C
o
R
alo
n
g
t
h
e
β
1
, β
2
, ψ
1
, ψ
2
r
o
ck
er
b
o
g
ie
jo
in
ts
f
o
r
f
lex
ib
ilit
y
b
ased
o
n
t
h
e
ter
r
ain
.
Fig
u
r
e
1
.
P
r
o
–
E
M
o
d
el
o
f
P
i
n
C
o
R
T
h
e
en
co
d
ed
m
o
to
r
s
h
elp
in
d
eter
m
i
n
in
g
t
h
e
w
h
ee
l a
n
g
u
lar
r
o
tatio
n
δ
i
.
T
h
e
b
o
d
y
r
o
ll,
p
itch
an
d
y
a
w
w
a
s
ca
lcu
la
ted
w
i
th
t
h
e
h
elp
o
f
ac
ce
ler
o
m
eter
.
T
h
e
lo
ca
tio
n
o
f
th
e
r
o
v
er
in
t
h
e
f
o
r
est
w
as t
r
ac
k
ed
u
s
i
n
g
a
r
ea
l
ti
m
e
GP
S
m
ap
at
t
h
e
b
ase
s
tati
o
n
an
d
th
e
P
iNC
o
R
eq
u
ip
p
ed
w
it
h
b
atter
y
le
v
el
e
n
co
d
er
s
o
th
at
it c
an
r
et
u
r
n
to
b
ase
w
h
en
t
h
e
p
o
w
er
r
ed
u
ce
s
d
u
r
in
g
its
o
p
er
atio
n
.
I
n
th
e
co
m
i
n
g
s
ec
tio
n
s
,
th
e
f
o
r
w
ar
d
k
i
n
e
m
atic
s
o
f
th
e
P
iNC
o
R
u
s
in
g
w
h
ee
l J
ac
o
b
ian
m
atr
ices
h
as b
ee
n
d
is
c
u
s
s
ed
f
o
llo
w
ed
b
y
th
e
i
n
v
er
s
e
k
i
n
e
m
a
tics
d
er
iv
atio
n
.
3.
F
O
RWARD
K
I
N
E
M
AT
I
CS
Fo
r
th
e
f
o
r
w
ar
d
k
in
e
m
at
ic
an
al
y
s
i
s
o
f
th
e
P
i
N
C
o
R
,
t
h
e
co
o
r
d
in
ate
f
r
a
m
e
s
y
s
te
m
f
o
r
b
o
th
le
f
t
a
n
d
r
ig
h
t
b
o
g
ie
s
w
a
s
d
ef
in
ed
as
s
h
o
w
n
i
n
th
e
Fi
g
u
r
e
(
2
)
&
(
3
)
.
Fo
r
th
e
P
i
N
C
o
R
,
a
lo
c
al
co
o
r
d
in
ate
s
y
s
te
m
w
a
s
d
ef
in
ed
an
d
th
e
o
r
ig
i
n
o
f
th
ese
co
o
r
d
in
ate
s
y
s
te
m
wa
s
ca
lled
as
‘
R
e
f
er
en
ce
p
o
in
t
’
o
n
th
e
r
o
b
o
t
f
r
am
e
d
esig
n
ated
as
‘
O
’
,
th
e
d
if
f
er
e
n
tial
j
o
in
t
as
‘
D
’
,
th
e
l
e
f
t
a
n
d
r
ig
h
t
b
o
g
ie
’
s
as
‘
β
i
(
i
=
1
,
2
)
’
an
d
a
x
es
o
f
all
w
h
ee
ls
as
‘
A
i
(
i =
1
,
2
,
3
,
4
,
5
,
6
)
’
.
Var
io
u
s
d
esig
n
an
g
le
s
a
re
s
h
o
w
n
in
t
h
e
Fi
g
u
r
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(
2
)
&
(
3
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
0
8
9
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4
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No
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3
,
Sep
tem
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er
201
5
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19
6
–
20
1
198
Fig
u
r
e
2
.
L
ef
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ate
Fra
m
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Fig
u
r
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3
.
R
ig
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d
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ate
Fr
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x
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ca
n
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e
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1
.
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h
e
co
o
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d
in
ate
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r
a
m
es
w
a
s
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eter
m
i
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b
y
t
h
e
De
n
av
it
–
Her
ten
b
er
g
n
o
tat
io
n
s
[
14
]
r
elate
d
to
th
e
v
ar
io
u
s
co
o
r
d
in
ate
s
g
i
v
e
n
i
n
t
h
e
T
ab
le
1
.
T
h
e
DH
p
ar
a
m
eter
s
d
e
f
i
n
e
t
h
e
tr
a
n
s
f
o
r
m
atio
n
s
f
r
o
m
o
n
e
j
o
in
t
to
t
h
e
n
ex
t
j
o
in
t
in
th
e
k
in
e
m
atic
c
h
ain
,
‘
θ’
d
ef
i
n
es
r
o
tatio
n
b
et
w
ee
n
th
e
z
-
a
x
is
,
‘
d
’
d
ef
i
n
es
th
e
d
is
ta
n
ce
alo
n
g
t
h
e
z
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a
x
i
s
b
et
w
ee
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o
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ts
,
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a
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in
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a
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s
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etw
ee
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o
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d
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in
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th
e
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le
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et
w
ee
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z
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e
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o
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j
o
in
t
s
.
T
h
e
g
en
er
al
tr
an
s
f
o
r
m
atio
n
m
atr
i
x
is
r
ep
r
es
en
ted
b
elo
w
b
ased
o
n
t
h
e
co
o
r
d
in
ate
f
r
a
m
e
i
to
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ate
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r
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u
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a
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o
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o
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e
n
o
u
s
tr
an
s
f
o
r
m
a
tio
n
m
at
r
ix
:
[
]
(
1
)
W
h
er
e
ϑ
j
,
α
j
,
a
j
,
d
j
ar
e
th
e
D
–
H
p
ar
am
eter
s
f
o
r
co
o
r
d
in
ate
f
r
a
m
e
j
.
T
h
e
ab
o
v
e
m
atr
i
x
s
h
o
w
s
t
h
e
tr
an
s
f
o
r
m
atio
n
o
f
co
o
r
d
in
ate
f
r
a
m
e
j
in
ter
m
s
o
f
co
o
r
d
in
ate
f
r
a
m
e
i.
T
h
e
tr
an
s
f
o
r
m
atio
n
s
f
r
o
m
t
h
e
r
o
b
o
t
r
ef
er
en
ce
f
r
a
m
e
‘
0
’
to
th
e
w
h
e
el
ax
le
‘A
1
’
w
a
s
o
b
tain
ed
b
y
ca
s
ca
d
in
g
ea
ch
tr
an
s
f
o
r
m
atio
n
.
T
O,
A1
=
T
O,
D
T
D,
B1
T
B1,
A1
T
ab
le
1
: D
–
H
P
ar
am
eter
s
Jo
i
n
t
A
x
i
s
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Evaluation Warning : The document was created with Spire.PDF for Python.
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1
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Wheel
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f
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an
d
5
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as
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s
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g
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in
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d
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σ
1
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̇
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1
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̇
i
=
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,
5
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q
u
atio
n
(
1
6
)
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ill p
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v
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e
th
e
r
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g
v
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f
w
h
ee
l 3
a
n
d
5
;
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=
̇
̇
(
)
̇
̇
i
=
3
,
5
(
1
7
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Fin
all
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h
e
r
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g
v
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lo
cit
y
o
f
w
h
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l 4
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d
6
f
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m
eq
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atio
n
n
u
m
b
er
(
1
3
)
ca
n
b
e
w
r
itten
a
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
K
in
ema
tic
Mo
d
ellin
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f
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(
1
8
)
T
h
ese
w
h
ee
l
r
o
llin
g
v
elo
citi
es
eq
u
atio
n
s
ar
e
r
elati
v
el
y
s
i
m
p
le
a
n
d
d
o
n
o
t
r
eq
u
ir
e
a
n
y
co
m
p
le
x
m
atr
i
x
o
p
er
atio
n
s
as
i
n
f
o
r
w
ar
d
k
in
e
m
atic
s
.
F
u
r
th
er
t
h
e
s
o
l
u
tio
n
o
f
t
h
e
eq
.
(
1
5
,
1
7
an
d
1
8
)
ca
n
b
e
d
ef
in
ed
b
y
th
e
o
p
er
atin
g
r
an
g
e
o
f
k
in
e
m
atic
p
ar
a
m
eter
s
s
u
ch
a
s
β,
σ
1
an
d
σ
2
.
5.
CO
NCLU
SI
O
NS
A
h
i
g
h
m
o
b
ilit
y
Kin
e
m
atic
m
o
d
elin
g
o
f
P
iNC
o
R
is
d
is
c
u
s
s
ed
in
th
i
s
p
ap
er
.
T
h
e
ap
p
r
o
ac
h
u
s
ed
is
d
if
f
er
e
n
t
f
r
o
m
th
e
co
n
v
e
n
tio
n
all
y
u
s
ed
m
et
h
o
d
s
w
h
ich
ar
e
o
n
l
y
a
p
p
licab
le
to
th
e
m
o
b
ile
r
o
b
o
ts
w
o
r
k
i
n
g
o
n
f
lat
a
n
d
s
m
o
o
t
h
s
u
r
f
ac
es.
T
h
e
p
ap
er
also
s
h
ar
es
t
h
e
De
n
av
it
–
Har
ten
b
er
g
n
o
tatio
n
b
ein
g
t
h
e
s
er
ial
li
n
k
m
an
ip
u
lato
r
f
o
r
th
e
r
o
ck
er
b
o
g
ie
s
u
s
p
en
s
io
n
s
y
s
te
m
f
o
r
t
h
e
lo
co
m
o
tio
n
o
f
t
h
e
r
o
b
o
t.
Fo
r
th
e
k
in
e
m
atic
ca
lcu
lat
io
n
s
,
t
h
e
m
e
th
o
d
u
s
e
d
is
s
i
m
p
le
a
n
d
m
o
d
i
f
ied
ac
co
r
d
in
g
to
th
e
co
n
f
i
g
u
r
atio
n
o
f
th
e
P
in
e
Nee
d
le
C
o
llecto
r
R
o
b
o
t
(
P
iNC
o
R
)
.
T
h
e
D
–
H
P
ar
am
eter
s
w
er
e
ap
p
lied
an
d
th
e
r
esu
l
ts
o
b
t
ain
ed
w
as
u
s
ed
to
o
p
tim
ize
th
e
k
i
n
e
m
a
tics
a
n
d
f
o
r
ef
f
icie
n
t d
r
iv
i
n
g
o
f
th
e
w
h
e
els
.
ACK
NO
WL
E
D
G
E
M
E
NT
T
h
is
w
o
r
k
i
s
ca
r
r
ied
o
u
t
a
n
d
s
u
p
p
o
r
ted
b
y
t
h
e
R
esear
c
h
an
d
Dev
elo
p
m
e
n
t
Dep
ar
t
m
en
t
o
f
Un
i
v
er
s
it
y
o
f
P
etr
o
leu
m
a
n
d
E
n
er
g
y
St
u
d
ies,
De
h
r
ad
u
n
.
I
w
o
u
ld
li
k
e
to
th
a
n
k
Mr
.
Ven
k
ate
s
w
a
r
an
P
S
–
R
esear
ch
Scien
ti
s
t
UP
E
S,
f
o
r
h
is
k
i
n
d
h
elp
in
r
e
v
ie
w
i
n
g
a
n
d
a
m
e
n
d
i
n
g
t
h
is
ar
ticle.
I
al
s
o
ac
k
n
o
w
le
d
g
e
t
h
e
w
o
r
k
d
o
n
e
b
y
Mr
.
P
r
ash
a
n
t S
h
u
k
la
–
A
s
s
i
s
tan
t P
r
o
f
es
s
o
r
,
UP
E
S in
d
ev
elo
p
in
g
t
h
e
s
o
f
t
w
ar
e
m
o
d
el
o
f
t
h
e
p
r
o
to
ty
p
e.
RE
F
E
R
E
NC
E
S
[1
]
Kala
,
C
.
P
.
,
I
n
d
ig
en
o
u
s
u
s
es
an
d
s
tr
u
ctu
r
e
o
f
ch
ir
p
in
e
f
o
r
est
in
Uttar
an
c
h
al
Hi
m
ala
y
a
,
I
n
d
ia
.
I
n
tern
a
tio
n
a
l J
o
u
r
n
a
l
o
f S
u
s
ta
in
a
b
le
Dev
elo
p
men
t
&
W
o
r
ld
E
co
lo
g
y
,
2
0
0
4
.
1
1
(
2
)
:
p
.
2
0
5
-
210.
[2
]
Mu
r
p
h
y
,
R
.
R
.
,
Hu
m
an
-
r
o
b
o
t
in
ter
ac
tio
n
i
n
r
escu
e
r
o
b
o
tics
.
Sy
s
te
m
s
,
Ma
n
,
an
d
C
y
b
er
n
etics,
P
ar
t
C
:
A
p
p
licatio
n
s
an
d
R
e
v
ie
w
s
,
I
E
E
E
Tr
a
n
s
a
ctio
n
s
,
2
0
0
4
.
3
4
(
2
)
: p
.
1
3
8
-
153.
[3
]
W
ein
er
,
T
.
,
A
n
ew mo
d
el
a
r
my
s
o
ld
ier r
o
lls
clo
s
e
r
to
th
e
b
a
tt
lefield
.
Ne
w
Yo
r
k
T
i
m
e
s
,
2
0
0
5
.
1
6
:
p
.
A
1
.
[4
]
Sh
ar
k
e
y
,
N.
,
Gro
u
n
d
s
fo
r
d
i
s
crimin
a
tio
n
:
A
u
to
n
o
mo
u
s
r
o
b
o
t
w
ea
p
o
n
s
.
R
USI
Def
e
n
ce
S
y
s
te
m
s
,
2
0
0
8
.
1
1
(
2
)
:
p
.
8
6
-
89.
[5
]
P
asto
r
e,
T
.
H.
,
H.
E
v
er
ett,
an
d
K.
B
o
n
n
er
,
Mo
b
ile
r
o
b
o
ts
fo
r
o
u
td
o
o
r
s
ec
u
r
ity
a
p
p
lica
tio
n
s
,
1
9
9
9
,
DT
I
C
Do
cu
m
e
n
t.
[6
]
No
r
eils
,
F.R
.
,
T
o
w
ar
d
a
r
o
b
o
t
ar
ch
itect
u
r
e
i
n
te
g
r
atin
g
co
o
p
er
atio
n
b
et
w
ee
n
m
o
b
ile
r
o
b
o
t
s
:
A
p
p
licatio
n
to
in
d
o
o
r
en
v
ir
o
n
m
e
n
t.
I
n
tern
a
tio
n
a
l J
o
u
r
n
a
l o
f R
o
b
o
tics
R
e
s
ea
r
ch
,
1
9
9
3
.
1
2
(
1
)
:
p
.
7
9
-
98.
[7
]
Gr
o
o
v
er
,
M.
P.,
M.
W
eiss
,
an
d
R
.
N.
Nag
el,
I
n
d
u
s
tr
ia
l
R
o
b
o
tics
:
Tech
n
o
l
o
g
y,
P
r
o
g
r
a
mmin
g
a
n
d
A
p
p
lica
tio
n
1
9
8
6
: M
cGr
aw
-
Hi
ll Hig
h
er
E
d
u
ca
tio
n
.
[8
]
Ma
r
o
h
n
,
C
.
M.
R
.
an
d
C
.
E
.
J
.
Han
l
y
,
Tw
en
ty
-
fir
s
t
ce
n
tu
r
y
s
u
r
g
ery
u
s
in
g
tw
en
ty
-
fir
s
t
ce
n
tu
r
y
tech
n
o
lo
g
y
:
s
u
r
g
ica
l ro
b
o
tics
.
C
u
r
r
en
t
Su
r
g
er
y
,
2
0
0
4
.
6
1
(
5
)
:
p
.
4
6
6
-
473.
[9
]
E
w
i
n
g
,
D.
R
.
,
et
al.
,
R
o
b
o
ts
in
th
e
o
p
era
tin
g
r
o
o
m
—
th
e
h
is
to
r
y.
Su
r
g
ical
I
n
n
o
v
a
tio
n
,
2
0
0
4
.
1
1
(
2
)
:
p
.
6
3
-
71.
[1
0
]
B
o
g
u
e,
R
.
,
R
o
b
o
ts
f
o
r
s
p
ac
e
ex
p
lo
r
atio
n
.
I
n
d
u
s
tr
ial
R
o
b
o
t
.
I
n
tern
a
tio
n
a
l
J
o
u
r
n
a
l
,
2
0
1
2
.
3
9
(
4
)
:
p
.
3
2
3
-
328.
[1
1
]
E
lf
es,
A
.
,
et
al.
S
a
fe
a
n
d
E
fficien
t
R
o
b
o
tic
S
p
a
ce
E
xp
lo
r
a
tio
n
w
ith
Tele
-
S
u
p
ervis
ed
A
u
to
n
o
mo
u
s
R
o
b
o
ts
.
i
n
A
A
A
I
S
p
r
in
g
S
ymp
o
s
iu
m:
To
B
o
ld
ly
Go
W
h
ere
N
o
Hu
ma
n
-
R
o
b
o
t Tea
m
Ha
s
Go
n
e
B
efo
r
e
.
2
0
0
6
.
[1
2
]
Sh
a
h
,
J
.
A
.
,
S.
R
atta
n
,
an
d
B
.
C
.
Nak
r
a,
Ki
n
e
m
atic
An
al
y
s
i
s
o
f
3
-
DOF
P
lan
er
R
o
b
o
t
Us
in
g
A
r
ti
f
icial
Neu
r
al
Net
w
o
r
k
.
I
A
E
S
I
n
tern
a
tio
n
a
l
Jo
u
r
n
a
l
o
f
R
o
b
o
tics
a
n
d
A
u
to
m
a
tio
n
(
I
JR
A
)
,
2
0
1
2
.
1
(
3
)
:
p
.
1
4
5
-
151.
[1
3
]
Go
u
as
m
i,
M.
,
R
o
b
o
t
Kin
e
m
at
ics,
u
s
in
g
D
u
al
Qu
a
ter
n
io
n
s
.
I
A
E
S
I
n
tern
a
tio
n
a
l
Jo
u
r
n
a
l
o
f
R
o
b
o
tics
a
n
d
A
u
to
ma
tio
n
(
I
JR
A
)
,
2
0
1
2
.
1
(
1
)
: p
.
1
3
-
30.
[1
4
]
C
r
aig
,
J
.
J
.
,
I
n
tr
o
d
u
ctio
n
to
r
o
b
o
tics
:
mec
h
a
n
ics
a
n
d
co
n
tr
o
l
.
Vo
l.
3
.
2
0
0
5
:
P
ea
r
s
o
n
P
r
e
n
tice
Hall
Up
p
er
Sad
d
le
R
iv
er
.
[1
5
]
Mu
ir
,
P
.
F.
an
d
C
.
P
.
Neu
m
a
n
,
Ki
n
e
m
atic
m
o
d
eli
n
g
o
f
w
h
ee
led
m
o
b
ile
r
o
b
o
ts
.
Jo
u
r
n
a
l
o
f
r
o
b
o
tic
s
ystem
s
,
1
9
8
7
.
4
(
2
)
: p
.
2
8
1
-
3
4
0
.
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