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
.
2
,
J
u
n
e
2
0
1
6
,
p
p
.
1
15
~1
35
I
SS
N:
2089
-
4856
115
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
J
RA
Desig
n and
Coo
r
dina
tion o
f
Co
o
pe
ra
tive Mo
bile Ro
bo
ts
M
.
K
rid,
J
.
C.
F
a
uro
ux
,
B
.
C.
B
o
uzg
a
rr
o
u
In
stit
u
t
P
a
sc
a
l
UMR
6
6
0
2
UB
P
/C
NRS,
Ca
m
p
u
s Un
iv
e
rsitaire
d
e
s C
e
z
e
a
u
x
,
F
ra
n
c
e
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Feb
9
,
2
0
1
6
R
ev
i
s
ed
A
p
r
2
8
,
2
0
1
6
A
cc
ep
ted
Ma
y
1
4
,
2
0
1
6
Ob
jec
t
tran
sp
o
rtatio
n
is
a
n
im
p
o
r
tan
t
tas
k
c
o
n
si
d
e
re
d
i
n
m
o
b
il
e
r
o
b
o
ti
c
s.
F
o
r
m
a
n
y
y
e
a
rs,
it
h
a
s
b
e
e
n
p
e
r
f
o
rm
e
d
b
y
sin
g
le
ro
b
o
ts,
c
a
p
a
b
le
to
tran
sp
o
rt
p
a
y
lo
a
d
o
f
m
o
d
e
ra
te
siz
e
a
n
d
m
a
ss
w
it
h
re
sp
e
c
t
to
th
e
ro
b
o
t
siz
e
a
n
d
m
a
ss
.
Bu
t
if
th
e
p
a
y
lo
a
d
g
e
ts
b
ig
g
e
r,
t
h
e
ro
b
o
t
f
a
il
s
in
th
e
tran
sp
o
rti
n
g
tas
k
.
F
o
r
w
id
e
r
o
r
h
e
a
v
ier
p
a
y
lo
a
d
s,
h
u
m
a
n
o
p
e
ra
to
rs
im
p
ro
v
e
th
e
ir
c
a
p
a
c
it
ies
b
y
w
o
rk
in
g
in
g
ro
u
p
.
A
sim
il
a
r
i
m
p
ro
v
e
m
e
n
t
sh
o
u
l
d
b
e
e
x
p
e
c
ted
w
it
h
a
g
ro
u
p
o
f
m
o
b
il
e
ro
b
o
ts
.
In
t
h
is
p
a
p
e
r,
w
e
p
ro
p
o
se
d
a
n
e
w
c
o
n
c
e
p
t
o
f
c
o
o
p
e
ra
ti
v
e
m
o
b
il
e
ro
b
o
ts
t
o
d
e
a
l
w
it
h
t
h
e
p
ro
b
lem
o
f
lo
n
g
o
b
jec
t
t
ra
n
sp
o
rtatio
n
i
n
u
n
stru
c
t
u
re
d
e
n
v
ir
o
n
m
e
n
t
w
h
a
tev
e
r
th
e
p
a
y
lo
a
d
len
g
th
.
T
h
e
p
ro
p
o
s
e
d
C3
Bo
ts
AT
/V
L
P
ro
b
o
t
is
f
o
rm
e
d
b
y
th
e
a
ss
o
c
iatio
n
o
f
tw
o
o
r
m
o
re
m
o
n
o
-
ro
b
o
ts
w
it
h
sim
p
le
k
in
e
m
a
ti
c
s
f
o
r
m
in
g
a
p
o
ly
ro
b
o
t
s
y
ste
m
.
T
h
e
p
a
p
e
r
p
re
se
n
ts
se
v
e
ra
l
k
in
e
m
a
ti
c
sc
h
e
m
e
s
a
n
d
th
e
c
o
rre
sp
o
n
d
in
g
o
b
sta
c
le
-
c
ro
ss
in
g
p
ro
c
e
ss
e
s.
It
d
e
a
ls
w
it
h
th
e
p
ro
b
lem
o
f
h
o
w
to
m
a
in
tain
st
a
b
le
m
o
ti
o
n
f
o
r
t
h
e
p
o
ly
-
ro
b
o
t
d
u
ri
n
g
o
b
sta
c
le
c
ro
ss
in
g
.
Ch
a
n
g
e
s
in
t
h
e
i
n
tern
a
l
c
o
n
_
g
u
ra
ti
o
n
o
f
th
e
r
o
b
o
t
a
d
ju
st
t
h
e
c
e
n
ter
o
f
g
ra
v
it
y
to
g
u
a
ra
n
tee
sta
b
le
m
o
ti
o
n
.
A
sp
e
c
i_
c
sta
b
il
it
y
c
rit
e
rio
n
f
o
r
c
o
n
tac
t
o
n
t
h
re
e
w
h
e
e
ls
is
p
re
se
n
ted
.
By
a
d
ju
stin
g
t
h
e
re
l
a
ti
v
e
p
o
se
s
o
f
th
e
f
ro
n
t
a
n
d
re
a
r
a
x
les
w
it
h
re
sp
e
c
t
to
t
h
e
p
a
y
lo
a
d
,
it
is
p
o
ss
ib
le
t
o
m
a
x
i
m
iz
e
th
e
sta
b
il
it
y
o
f
th
e
p
o
ly
-
ro
b
o
t
a
n
d
it
s
p
a
y
lo
a
d
d
u
rin
g
o
b
sta
c
le
c
ro
ss
in
g
.
K
ey
w
o
r
d
:
C
o
o
p
er
ativ
e
Mo
b
ile
L
o
n
g
P
a
y
lo
ad
Ven
tr
al
Ob
s
tacle
C
r
o
s
s
i
n
g
R
o
b
o
ts
Stab
ilit
y
A
n
al
y
s
is
Stab
ilit
y
C
r
iter
io
n
T
r
an
s
p
o
r
tatio
n
Mo
d
e
Co
p
y
rig
h
t
©
201
6
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
h
a
m
ed
Kr
id
,
Ass
i
s
tan
ce
P
r
o
f
es
s
o
r
,
I
n
s
tit
u
t P
ascal
UM
R
6
6
0
2
UB
P
/C
NR
S,
C
a
m
p
u
s
U
n
i
v
er
s
itair
e
d
es C
ez
ea
u
x
,
L
es
C
ez
ea
u
x
C
S 2
0
2
6
5
,
6
3
1
7
5
A
UB
I
E
R
E
C
ed
ex
,
Fra
n
ce
.
E
m
ail:
m
ed
.
k
r
id
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
So
m
e
tas
k
s
ar
e
i
m
p
o
s
s
ib
le
w
it
h
N
r
o
b
o
ts
b
u
t
p
o
s
s
ib
le
an
d
ea
s
y
w
it
h
N+
1
r
o
b
o
ts
[1
-
3
]
.
T
h
e
co
o
p
er
atio
n
tr
an
s
p
o
r
t ta
s
k
b
et
w
ee
n
t
w
o
o
r
m
o
r
e
r
o
b
o
ts
ca
n
b
e
class
i
f
ied
i
n
t
w
o
ca
te
g
o
r
ies
.
T
h
e
f
i
r
s
t
o
n
e
w
h
en
th
e
r
o
b
o
ts
h
av
e
n
o
t
a
m
ec
h
a
n
ical
co
n
n
ec
tio
n
.
I
n
g
en
er
al
t
h
i
s
t
y
p
e
o
f
r
o
b
o
ts
ar
e
u
s
ed
in
r
eg
u
lar
en
v
ir
o
n
m
e
n
t
[
4
]
,
[
6
,
7
]
.
T
h
e
s
ec
o
n
d
o
n
e
w
h
en
th
e
r
o
b
o
ts
h
av
e
a
m
ec
h
a
n
ic
al
co
n
n
ec
tio
n
[
1
]
,
[
5
]
,
[
3
]
.
I
n
th
is
ca
s
e
t
h
e
r
o
b
o
ts
ar
e
u
s
ed
in
u
n
s
tr
u
ct
u
r
ed
en
v
i
r
o
n
m
e
n
t.
W
e
ca
n
in
tr
o
d
u
ce
th
e
ter
m
o
f
m
o
n
o
-
r
o
b
o
t
f
o
r
th
e
s
in
g
le
r
o
b
o
t
an
d
p
o
ly
-
r
o
b
o
t
f
o
r
t
h
e
a
s
s
o
ciatio
n
o
f
s
e
v
er
al
m
o
n
o
-
r
o
b
o
ts
tr
a
n
s
p
o
r
tin
g
a
p
a
y
lo
ad
.
Us
in
g
s
ev
er
al
co
o
p
er
ativ
e
m
o
n
o
-
r
o
b
o
ts
i
m
p
r
o
v
es
tr
an
s
p
o
r
t
ca
p
ac
ity
an
d
ca
n
b
e
h
el
f
u
l
in
m
a
n
y
s
it
u
atio
n
s
s
u
c
h
a
s
wo
r
k
in
a
d
an
g
er
o
u
s
en
v
ir
o
n
m
e
n
t
(
r
a
d
io
ac
tiv
eo
r
o
r
co
n
ta
m
i
n
ated
)
o
r
d
elica
te
tr
an
s
p
o
r
t
(
tr
an
s
p
o
r
t
o
f
i
n
j
u
r
ed
p
e
o
p
le
o
n
s
tr
etch
er
s
)
.
I
n
th
i
s
ca
s
e,
r
o
b
o
ts
m
u
s
t
b
e
a
b
le
to
m
a
n
o
eu
v
r
e
o
n
ir
r
eg
u
lar
g
r
o
u
n
d
s
a
n
d
to
c
r
o
s
s
o
b
s
tacl
es.
Ma
n
y
all
-
ter
r
ain
m
o
b
ile
r
o
b
o
ts
w
er
e
d
ev
elo
p
ed
f
o
r
p
lan
etar
y
o
r
d
an
g
er
o
u
s
ar
ea
ex
p
lo
r
atio
n
.
T
h
ey
h
av
e
d
i_
er
en
t a
r
ch
itect
u
r
es
[8
]
[
3
]
an
d
lo
co
m
o
tio
n
m
o
d
e
s
[
9
,
1
0
]
b
u
t
th
e
s
a
m
e
p
u
r
p
o
s
es:
th
e
y
m
u
s
t
b
e
ab
le
to
ev
o
lv
e
o
n
ir
r
eg
u
lar
o
r
u
n
s
tr
u
ct
u
r
ed
e
n
v
i
r
o
n
m
e
n
t
an
d
to
g
u
ar
an
tee
a
m
i
n
i
m
u
m
s
tab
ilit
y
d
u
r
i
n
g
a
m
is
s
io
n
.
C
o
o
p
er
ativ
e
m
o
b
ile
r
o
b
o
ts
f
o
r
tr
an
s
p
o
r
t
ar
e
o
f
te
n
co
m
p
l
ex
.
T
h
e
y
u
s
e
m
a
n
y
ac
t
u
ated
j
o
in
ts
a
n
d
a
s
o
p
h
is
ticated
c
o
n
tr
o
l
s
y
s
te
m
.
T
h
e
s
i
m
p
ler
o
n
e
s
,
s
u
c
h
as
A
r
m
y
An
t
co
o
p
er
ativ
e
liftin
g
r
o
b
o
ts
[
8
]
h
av
e
g
r
ea
ter
f
ac
ilit
y
to
co
m
p
ly
w
it
h
n
u
m
er
o
u
s
co
n
s
tr
ain
ts
o
n
t
h
e
p
a
y
lo
ad
an
d
th
e
en
v
ir
o
n
m
e
n
t.
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
.
2
,
J
u
n
e
2
0
1
6
:
1
15
–
1
35
116
1
.
1
.
O
bs
t
a
cle
-
Cro
s
s
ing
Ma
n
y
s
o
l
u
tio
n
s
f
o
r
o
b
s
tacle
cr
o
s
s
in
g
ca
n
b
e
f
o
u
n
d
in
th
e
lit
er
atu
r
e.
W
e
ca
n
class
if
y
t
h
ese
s
o
lu
tio
n
s
ac
co
r
d
in
g
to
s
ev
er
al
cr
iter
ia:
l
o
co
m
o
tio
n
m
o
d
e,
n
u
m
b
er
o
f
a
ctu
ated
j
o
in
ts
o
r
co
n
tr
o
ller
co
m
p
lex
i
t
y
to
ac
h
iev
e
th
e
d
esire
d
m
o
b
ilit
y
.
Var
i
o
u
s
lo
co
m
o
tio
n
m
o
d
es
ca
n
b
e
c
o
n
s
id
er
ed
:
leg
,
tr
ac
k
a
n
d
w
h
e
el
m
o
d
es.
W
h
er
ea
s
leg
g
ed
m
o
b
ile
r
o
b
o
ts
en
s
u
r
e
a
s
u
p
er
io
r
ad
ap
tab
ilit
y
to
m
a
n
y
k
in
d
s
o
f
o
b
s
tac
le,
th
e
ir
m
ec
h
an
ical
ar
ch
itect
u
r
e
is
co
m
p
licated
b
ec
au
s
e
ac
ti
v
e
co
n
tr
o
l
alg
o
r
ith
m
s
ar
e
u
s
ed
[
1
1
]
[
1
2
]
.
T
r
ac
k
ed
m
o
b
ile
r
o
b
o
ts
p
r
o
v
id
e
ac
ce
p
ta
b
le
m
o
b
il
it
y
in
o
f
f
-
r
o
ad
en
v
ir
o
n
m
en
ts
b
y
v
ir
tu
e
o
f
t
h
eir
w
id
e
co
n
tact
s
u
r
f
ac
e
w
it
h
t
h
e
g
r
o
u
n
d
,
b
u
t
e
x
ce
s
s
i
v
e
f
r
ictio
n
lo
s
s
d
u
r
i
n
g
d
ir
ec
tio
n
ch
a
n
g
in
g
al
s
o
r
esu
lt
s
i
n
p
o
o
r
en
er
g
y
e
fi
cie
n
c
y
[
1
3
]
.
C
o
m
p
ar
ed
to
o
th
er
ca
teg
o
r
ies,
w
h
ee
led
m
o
b
ile
r
o
b
o
ts
ca
n
b
e
co
n
s
tr
u
cted
w
it
h
a
s
i
m
p
ler
s
tr
u
ctu
r
e
s
o
t
h
at
f
a
s
t
m
o
v
e
m
en
t
as
w
ell
as
g
o
o
d
en
er
g
y
ef
i
cien
c
y
ar
e
g
u
ar
a
n
teed
w
it
h
o
u
t
a
n
y
co
m
p
licated
co
n
tr
o
l
s
tr
ateg
y
[
1
4
]
[
1
5
]
,
b
u
t
th
e
y
ar
e
li
m
ited
f
o
r
o
b
s
tacle
cli
m
b
i
n
g
.
So
m
e
s
tu
d
ie
s
co
m
b
i
n
e
tr
ac
k
s
a
n
d
le
g
s
o
r
w
h
ee
ls
a
n
d
le
g
s
to
p
r
o
v
id
e
n
e
w
lo
co
m
o
tio
n
m
o
d
es.
I
n
[
9
]
,
l
eg
s
a
n
d
tr
ac
k
s
ar
e
co
m
b
i
n
ed
an
d
allo
w
t
h
e
A
Z
I
M
UT
r
o
b
o
t
to
cli
m
b
o
v
er
ob
s
tacle
s
.
Fo
r
t
h
e
s
a
m
e
g
o
al
Op
en
WH
E
E
L
i3
R
[
1
0
]
an
d
R
o
ck
er
[
1
7
]
m
o
b
iles
r
o
b
o
ts
co
m
b
i
n
e
le
g
s
a
n
d
w
h
ee
ls
to
p
r
o
v
id
e
n
e
w
h
y
b
r
id
lo
co
m
o
tio
n
m
o
d
es.
1
.
2
.
Co
o
pera
t
iv
e
Ro
bo
t
s
C
o
o
p
er
ativ
e
m
o
b
ile
r
o
b
o
ts
ca
n
b
e
class
i
fi
ed
i
n
t
w
o
ca
te
g
o
r
ies
ac
co
r
d
in
g
to
t
h
eir
co
o
p
er
atio
n
s
tr
ateg
y
.
I
n
th
e
f
i
r
s
t
t
y
p
e,
w
e
h
av
e
o
n
e
m
aster
r
o
b
o
t
an
d
th
e
r
est
o
f
t
h
e
r
o
b
o
ts
f
o
llo
w
i
t.
I
t
is
th
e
lead
er
-
f
o
llo
w
er
co
o
p
er
atio
n
t
y
p
e
[
1
8
]
[
1
9
]
.
I
n
th
e
s
ec
o
n
d
ca
te
g
o
r
y
,
a
ll t
h
e
r
o
b
o
ts
ar
e
eq
u
i
v
ale
n
t.
I
f
th
e
i
n
it
ial
s
tates
o
f
th
e
r
o
b
o
ts
ar
e
ex
c
h
an
g
ed
w
e
h
av
e
t
w
o
p
o
s
s
ib
ilit
ies
:
A
l
l
th
e
r
o
b
o
ts
s
h
ar
e
th
eir
in
f
o
r
m
a
tio
n
an
d
p
lan
th
eir
m
o
tio
n
a
f
ter
co
n
s
u
ltatio
n
[
2
0
]
.
E
ac
h
r
o
b
o
t
u
s
es
o
n
l
y
it
s
s
tat
e
to
co
m
p
u
te
it
s
m
o
tio
n
au
to
n
o
m
o
u
s
l
y
[
1
1
]
.
T
h
e
co
o
p
er
atio
n
s
ty
le
d
ep
en
d
s
o
n
th
e
t
y
p
e
o
f
th
e
tas
k
.
Fo
r
ex
a
m
p
le,
w
h
e
n
t
w
o
h
u
m
a
n
s
tr
an
s
p
o
r
t
a
p
ay
lo
ad
,
if
th
e
y
d
o
n
o
t
h
av
e
th
e
s
a
m
e
f
i
eld
o
f
v
is
io
n
t
h
e
y
n
ee
d
to
ad
o
p
t
a
lead
er
-
f
o
llo
w
er
co
o
p
er
at
io
n
.
B
u
t
if
t
h
e
y
h
a
v
e
th
e
s
a
m
e
f
i
eld
o
f
v
is
io
n
,
it is
s
i
m
p
ler
to
u
s
e
au
to
n
o
m
o
u
s
co
o
p
er
a
tio
n
.
1
.
3
.
P
a
y
lo
a
d T
ra
ns
po
rt
Ma
n
y
v
eh
icles
u
s
ed
to
tr
an
s
p
o
r
t
o
b
j
ec
ts
ca
n
b
e
f
o
u
n
d
i
n
th
e
liter
at
u
r
e.
W
e
ca
n
class
i
f
y
t
h
ese
tr
an
s
p
o
r
ter
s
ac
co
r
d
in
g
to
th
eir
s
ize
co
m
p
ar
ed
to
th
e
s
ize
o
f
th
e
p
a
y
lo
ad
.
T
h
e
tr
an
s
p
o
r
ter
c
an
b
e
s
m
aller
t
h
a
n
th
e
p
a
y
lo
ad
[
3
]
[
8
]
o
r
b
ig
g
er
[
2
1
]
.
T
h
e
p
a
y
lo
ad
ca
n
h
av
e
d
i_
er
en
t
p
o
s
itio
n
s
o
n
t
h
e
v
e
h
icle.
I
t
ca
n
b
e
p
lace
d
o
n
th
e
to
p
s
u
r
f
ac
e[
8
]
o
r
o
n
th
e
b
o
tto
m
s
u
r
f
ac
e
[
2
1
]
o
r
ev
en
b
ec
o
m
e
a
p
ar
t
o
f
t
h
e
s
tr
u
ct
u
r
e
[
2
2
]
.
T
h
e
s
o
lu
tio
n
p
r
esen
ted
in
[
2
2
]
is
an
in
ter
esti
n
g
tr
an
s
p
o
r
t
s
y
s
te
m
,
co
m
p
r
is
in
g
a
tr
ac
tiv
e
en
g
i
n
e
an
d
a
tr
ailer
,
w
h
ic
h
ar
e
in
ter
co
n
n
ec
ted
b
y
th
e
p
a
y
lo
ad
its
elf
d
u
r
i
n
g
its
tr
a
n
s
p
o
r
t.
T
h
is
k
i
n
d
o
f
s
o
lu
t
io
n
r
e
m
ai
n
s
a
p
ar
ticu
lar
o
n
e
w
h
ic
h
is
s
u
itab
le
f
o
r
s
p
ec
ial
n
ee
d
s
,
s
u
c
h
as
t
h
e
tr
an
s
p
o
r
t
o
f
lar
g
e
p
ar
ts
(
th
e
g
ia
n
t
b
lad
es
o
f
a
w
i
n
d
-
tu
r
b
i
n
e,
in
t
h
is
ca
s
e)
.
I
n
th
e
liter
atu
r
e,
co
o
p
e
r
ativ
e
m
o
b
ile
r
o
b
o
ts
f
o
r
tr
an
s
p
o
r
t
ar
e
o
f
ten
co
m
p
lex
.
T
h
e
y
u
s
e
m
a
n
y
ac
t
u
ated
j
o
in
ts
an
d
a
s
o
p
h
is
ticated
co
n
tr
o
l
s
y
s
te
m
.
T
h
e
s
i
m
p
ler
o
n
es
m
u
s
t
co
m
p
l
y
w
it
h
m
an
y
co
n
s
tr
ai
n
ts
o
n
t
h
e
p
ay
lo
ad
a
n
d
th
e
en
v
i
r
o
n
m
e
n
t
,
s
u
c
h
as
A
r
m
y
An
t
co
o
p
er
ativ
e
li
f
t
in
g
r
o
b
o
ts
[
8
]
.
I
n
th
i
s
p
ap
er
,
w
e
d
e
s
i
g
n
co
o
p
er
ativ
e
tr
an
s
p
o
r
ter
m
o
b
ile
r
o
b
o
ts
w
it
h
a
m
i
n
i
m
u
m
n
u
m
b
er
o
f
ac
t
u
ato
r
s
an
d
a
s
i
m
p
le
co
n
tr
o
ller
.
Ou
r
r
o
b
o
t,
w
h
ic
h
is
co
m
p
o
s
ed
o
f
s
ev
er
al
m
o
n
o
-
r
o
b
o
ts
,
m
u
s
t
b
e
ab
le
to
f
etch
a
lo
n
g
p
a
y
lo
ad
,
to
tr
an
s
p
o
r
t
it
o
v
er
ir
r
eg
u
lar
g
r
o
u
n
d
a
n
d
to
cr
o
s
s
o
b
s
tacle
s
w
it
h
it.
T
h
is
co
n
c
ep
t
o
f
co
llab
o
r
ativ
e
tr
an
s
p
o
r
t
allo
w
s
t
h
e
r
o
b
o
ts
co
m
p
le
x
it
y
to
b
e
ad
ap
ted
to
th
e
s
h
ap
e
a
n
d
m
a
s
s
o
f
t
h
e
p
a
y
-
l
o
ad
.
A
p
o
l
y
-
r
o
b
o
t
w
it
h
N
u
n
it
s
w
ill
b
e
ca
p
ab
le
o
f
ca
r
r
y
i
n
g
N
t
i
m
e
s
t
h
e
m
a
x
i
m
u
m
p
a
y
lo
ad
o
f
a
s
i
n
g
le
m
o
n
o
-
ro
b
o
t.
I
n
o
r
d
er
to
d
ec
r
ea
s
e
th
e
m
a
s
s
o
f
t
h
e
co
n
n
ec
ti
n
g
p
ar
ts
,
it
w
a
s
d
ec
id
ed
to
u
s
e
th
e
p
ay
lo
ad
as
a
s
tr
u
ctu
r
al
f
r
a
m
e
b
et
w
ee
n
th
e
m
o
n
o
-
r
o
b
o
ts
.
I
n
th
is
p
ap
er
,
w
e
p
r
ese
n
t
t
h
e
s
y
n
t
h
e
s
is
o
f
t
h
e
co
o
p
er
ativ
e
C
3
B
o
ts
A
T
/VL
P
(
A
l
l
-
T
er
r
ain
/Ve
n
t
r
al
L
o
n
g
P
a
y
lo
ad
)
m
o
b
ile
ro
b
o
t.
Sectio
n
2
d
escr
ib
es th
e
r
e
s
u
lti
n
g
p
o
l
y
-
r
o
b
o
t,
ass
o
ciati
n
g
t
w
o
o
r
m
o
r
e
id
en
tic
al
m
o
n
o
-
r
o
b
o
ts
th
at
co
n
n
ec
t
d
ir
ec
tl
y
to
th
e
p
a
y
l
o
ad
f
o
r
tr
an
s
p
o
r
tin
g
it.
Secti
o
n
3
d
escr
ib
e
a
k
in
e
m
a
tics
o
f
th
e
m
o
n
o
-
r
o
b
o
t,
illu
s
tr
atin
g
th
e
r
eq
u
ir
ed
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
f
o
r
t
h
e
v
en
tr
al
m
a
n
ip
u
lato
r
.
Sectio
n
4
p
r
esen
t
s
a
m
et
h
o
d
o
f
s
y
s
te
m
a
tic
s
y
n
t
h
esi
s
o
f
p
o
s
s
i
b
le
eq
u
iv
ale
n
t
k
i
n
e
m
atics.
I
n
s
ec
tio
n
5
,
t
h
e
m
o
b
ili
ties
ar
e
c
o
m
b
i
n
ed
to
p
r
esen
t
t
w
o
o
b
s
tacle
-
cr
o
s
s
in
g
m
o
d
es,
w
h
er
e
s
tab
ilit
y
i
s
ac
h
iev
ed
b
y
m
o
tio
n
s
o
f
t
h
e
m
o
n
o
-
r
o
b
o
ts
w
i
t
h
r
esp
ec
t
to
t
h
e
p
ay
lo
ad
.
T
h
e
_
r
s
t
m
o
d
e
u
s
es
o
n
l
y
t
w
o
m
o
n
o
-
r
o
b
o
ts
b
u
t
r
eq
u
ir
es
co
m
p
le
x
co
n
tr
o
l
a
n
d
3
D
m
o
tio
n
s
.
T
h
e
s
ec
o
n
d
m
o
d
e
u
s
es
o
n
l
y
2
D
m
o
tio
n
s
b
u
t
r
eq
u
ir
es
3
m
o
n
o
-
r
o
b
o
ts
o
r
m
o
r
e.
Sectio
n
6
p
r
esen
t
a
r
ed
u
ce
d
m
u
lt
i
-
b
o
d
y
m
o
d
el
o
f
t
h
e
p
lo
y
-
r
o
b
o
t
th
at
h
as
b
ee
n
b
u
ilt
to
s
i
m
u
late
t
h
e
cr
o
s
s
i
n
g
o
p
er
atio
n
o
n
MSC
-
AD
A
MS
s
o
f
t
w
ar
e.
Sectio
n
3
p
r
esen
ts
an
o
b
s
tacle
-
cr
o
s
s
in
g
p
r
o
ce
s
s
in
eig
h
tee
n
s
ta
g
es
w
it
h
o
n
l
y
t
w
o
m
o
n
o
-
r
o
b
o
ts
,
w
h
er
e
s
tab
il
it
y
is
ac
h
ie
v
ed
b
y
p
o
s
itio
n
i
n
g
t
h
e
m
o
n
o
-
r
o
b
o
ts
w
it
h
r
esp
ec
t
to
t
h
e
p
a
y
l
o
ad
.
I
n
s
ec
tio
n
4
,
g
eo
m
etr
ic
an
d
k
in
e
m
atic
m
o
d
els
ar
e
p
r
esen
ted
.
T
h
ese
t
w
o
m
o
d
el
s
w
ill
b
e
u
s
ed
in
s
ec
tio
n
5
in
o
r
d
er
to
s
tu
d
y
th
e
s
tab
ili
t
y
o
f
t
h
e
p
o
l
y
-
r
o
b
o
t a
n
d
its
p
a
y
lo
ad
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Desig
n
a
n
d
C
o
o
r
d
in
a
tio
n
o
f Co
o
p
era
tive
Mo
b
ile
R
o
b
o
ts
(
M.K
r
id
)
117
2.
DE
S
I
G
N
AP
P
RO
ACH
T
h
e
co
n
ce
p
t
p
r
esen
ted
i
n
th
is
w
o
r
k
i
s
i
n
s
p
ir
ed
f
r
o
m
th
e
O
p
en
W
HE
E
L
i3
R
p
lat
f
o
r
m
[
1
0
]
.
I
t
u
s
e
s
a
s
i
m
ilar
an
d
e
x
ten
d
ed
p
r
o
ce
s
s
f
o
r
o
b
s
tacle
cr
o
s
s
i
n
g
a
s
t
h
e
o
r
ig
in
al
Op
en
W
HE
E
L
i3
R
p
latf
o
r
m
b
u
t
w
it
h
an
o
th
er
k
i
n
e
m
atics
s
c
h
e
m
e
s
u
it
ab
le
f
o
r
tr
a
n
s
p
o
r
tin
g
lo
n
g
p
ay
lo
ad
s
.
T
h
e
r
o
b
o
t
co
n
ce
p
t
w
a
s
also
in
tr
o
d
u
ce
d
to
b
r
in
g
m
o
d
u
lar
it
y
a
n
d
s
i
m
p
l
if
y
r
o
b
o
t
m
a
n
u
f
ac
t
u
r
i
n
g
a
n
d
m
ai
n
ten
a
n
ce
,
as
a
d
ef
ec
ti
v
e
m
o
n
o
-
r
o
b
o
t
ca
n
ea
s
il
y
b
e
r
ep
lace
d
.
2
.
1
.
O
penWH
E
E
L
i3
R
Arc
hite
ct
ure
T
h
e
m
ai
n
p
u
r
p
o
s
e
o
f
t
h
is
p
ap
er
is
to
d
esig
n
a
g
r
o
u
n
d
-
b
ase
d
r
o
b
o
t
ab
le
to
tr
an
s
p
o
r
t
a
l
o
n
g
p
a
y
lo
ad
an
d
to
cli
m
b
o
b
s
tacle
s
i
n
co
o
p
er
ativ
e
m
o
d
e.
A
lo
n
g
er
r
o
b
o
t
v
er
s
io
n
w
a
s
d
er
iv
ed
f
r
o
m
t
h
e
o
r
ig
i
n
al
Op
en
W
HE
E
L
i3
R
(
F
ig
.
1
)
an
d
ad
ap
ted
t
o
th
e
co
n
s
id
er
ed
task
s
(
Fig
.
?
?
)
.
Desig
n
in
g
m
o
b
i
le
r
o
b
o
ts
w
it
h
t
h
e
ab
ilit
y
to
cli
m
b
o
b
s
tacle
s
r
ep
r
esen
t
s
a
n
i
m
p
o
r
tan
t
tas
k
f
o
r
r
o
b
o
t
d
esig
n
er
s
.
On
e
o
f
t
h
ese
a
r
ch
i
-
tect
u
r
es
i
s
t
h
e
Op
en
W
HE
E
L
i3
R
p
lat
f
o
r
m
[
1
0
]
w
ith
its
o
r
ig
i
n
al
cli
m
b
i
n
g
p
r
o
ce
s
s
as
s
h
o
w
n
i
n
Fi
g
.
1
.
I
t
co
n
tain
s
t
w
o
a
x
le
s
,
lin
k
ed
w
it
h
a
s
er
ial
i
n
ter
-
ax
i
al
m
ec
h
a
n
is
m
u
s
i
n
g
th
r
ee
s
i
m
p
le
r
ev
o
l
u
te
j
o
in
ts
(
a
n
ac
ti
v
e
ce
n
tr
al
j
o
in
t
f
o
r
w
ar
p
in
g
a
n
d
t
w
o
p
ass
i
v
e
j
o
i
n
ts
f
o
r
s
teer
i
n
g
)
.
E
ac
h
a
x
le
co
n
tai
n
s
t
w
o
ac
t
u
ated
w
h
ee
ls
(
F
ig
.
2
)
.
T
h
e
cli
m
b
i
n
g
p
r
o
ce
s
s
o
f
t
h
e
Op
e
n
W
HE
E
L
i
3
R
p
latf
o
r
m
i
s
a
s
er
p
en
ti
n
e
m
o
v
e
m
e
n
t
d
i
v
id
ed
in
to
n
i
n
etee
n
s
ta
g
es.
E
ac
h
s
tag
e
co
r
r
esp
o
n
d
s
to
a
j
o
in
t m
o
tio
n
(
a
m
o
v
e
m
en
t o
f
a
j
o
in
t o
r
a
w
h
ee
l c
o
n
tact
b
ein
g
r
e
m
o
v
ed
o
r
r
eg
ain
ed
)
(
Fi
g
.
1
)
.
Fig
u
r
e
1
.
T
h
e
C
li
m
b
in
g
P
r
o
ce
s
s
o
f
t
h
e
Op
en
w
h
ee
l I
3
r
Mo
b
ile
R
o
b
o
t
T
h
e
s
tab
ilit
y
o
f
th
e
p
latf
o
r
m
is
a
n
ec
e
s
s
ar
y
co
n
d
itio
n
to
p
er
f
o
r
m
t
h
e
cli
m
b
i
n
g
p
r
o
ce
s
s
.
P
r
ev
io
u
s
w
o
r
k
s
[
2
3
]
s
h
o
w
ed
t
h
at
Op
e
n
W
HE
E
L
i3
R
s
tab
ilit
y
d
u
r
i
n
g
s
ta
g
es
4
-
8
-
13
-
1
7
o
f
t
h
e
cli
m
b
in
g
p
r
o
ce
s
s
(
Fig
.
1
)
ca
n
b
e
m
a
x
i
m
ized
if
t
h
e
W
h
ee
lb
ase
/T
r
ac
k
r
atio
=
1
.
A
t
t
h
e
s
a
m
e
ti
m
e,
i
n
cr
ea
s
in
g
t
h
e
W
h
ee
lb
ase/T
r
ac
k
r
atio
im
p
r
o
v
es th
e
p
itc
h
s
tab
ilit
y
o
f
t
h
e
r
o
b
o
t
w
h
en
r
o
lli
n
g
o
n
ir
r
e
g
u
lar
g
r
o
u
n
d
.
2
.
2
.
P
a
y
lo
a
d
P
o
s
it
io
n
T
h
e
s
tu
d
y
o
f
t
h
e
r
o
b
o
t
s
tab
i
lit
y
d
u
r
in
g
t
h
e
ta
s
k
is
i
m
p
o
r
tan
t.
B
ef
o
r
e
t
h
at,
t
h
e
r
o
b
o
t
k
in
e
m
at
ic
s
tr
u
ct
u
r
e
s
h
o
u
ld
b
e
s
y
n
th
e
s
ize
d
,
u
s
i
n
g
s
u
itab
le
m
o
b
ilit
ies
s
p
th
at
s
tab
ilizatio
n
co
u
ld
b
e
p
o
s
s
ib
le
[
2
4
]
.
R
o
b
o
t
s
tab
ilit
y
i
s
ev
al
u
ated
ac
co
r
d
in
g
to
d
ev
elo
p
ed
m
etr
ics
in
lite
r
atu
r
e.
Stab
ilit
y
m
ar
g
i
n
ca
n
b
e
class
i_
ed
in
t
w
o
cat
eg
o
r
ies
s
tatic
[
2
5
]
an
d
d
y
n
a
m
ic
[
2
6
]
s
tab
ilit
y
m
ar
g
in
s
.
T
h
is
p
ap
er
o
n
l
y
co
n
s
id
er
s
lo
w
s
p
p
ed
m
o
b
ile
r
o
b
o
ts
an
u
s
es
th
e
s
tatic
s
tab
ili
t
y
m
a
r
g
in
to
co
m
p
ar
e
d
if
e
er
e
n
te
s
tr
u
ctu
r
e
s
.
Sta
tic
s
tab
i
li
t
y
in
d
ica
to
r
s
,
s
u
c
h
as
Stati
c
R
o
llo
v
er
T
h
r
esh
o
ld
(
SR
T
)
o
r
Static
Stab
ilit
y
Facto
r
(
SS
F)
[
2
7
]
r
ely
o
n
l
y
o
n
t
h
e
r
o
b
o
t
g
eo
m
e
tr
ic
ch
ar
ac
ter
-
is
tics
.
I
n
t
h
i
s
s
ec
tio
n
,
th
e
c
h
o
ice
o
f
th
e
p
o
s
itio
n
o
f
th
e
g
r
ip
p
er
m
ec
h
a
n
is
m
a
n
d
th
e
p
a
y
lo
ad
w
il
l b
e
d
is
cu
s
s
e
d.
T
o
in
cr
ea
s
e
th
e
w
o
r
k
s
p
ac
e
o
f
th
e
r
o
b
o
tic
s
y
s
te
m
,
th
e
r
o
b
o
tic
m
a
n
ip
u
lato
r
is
o
f
te
n
p
u
t
o
n
to
p
o
f
th
e
m
o
b
ile
p
lat
f
o
r
m
[
2
8
]
[
2
9
]
[
3
0
]
[
3
1
]
.
T
h
is
lo
ca
tio
n
o
ff
er
s
h
i
g
h
ex
ib
ilit
y
to
m
an
ip
u
late
th
e
o
b
ject.
B
u
t
in
th
e
ca
s
e
o
f
tr
an
s
p
o
r
t
in
u
n
s
tr
u
ctu
r
ed
e
n
v
ir
o
n
m
e
n
t
an
d
o
b
s
tacle
cr
o
s
s
in
g
[
3
]
[
3
2
]
[
1
1
]
it
w
il
l
b
e
s
o
u
r
ce
o
f
in
s
tab
ilit
y
,
b
ec
au
s
e
it
in
cr
ea
s
es
t
h
e
h
ei
g
h
t
o
f
th
e
ce
n
ter
o
f
m
as
s
[
3
3
]
[
3
4
]
o
r
m
o
v
es
it
i
n
an
u
n
d
e
s
ir
ab
le
ar
ea
[
2
8
]
[
3
5
]
.
T
o
i
m
p
r
o
v
e
s
tatic
s
tab
ilit
y
as s
h
o
w
n
i
n
fi
g
u
r
es 3
an
d
4
,
th
e
g
r
ip
p
er
w
ill b
e
i
n
te
g
r
ated
in
t
h
e
b
o
tto
m
o
f
t
h
e
r
o
b
o
t
b
et
w
ee
n
th
e
t
w
o
w
h
ee
l
s
(
lef
t
an
d
r
ig
h
t)
.
I
n
th
is
ca
s
e,
t
h
e
g
r
asp
in
g
tas
k
o
f
t
h
e
p
a
y
lo
ad
w
il
l
b
e
ea
s
ier
as
s
h
o
wn
in
fi
g
u
r
e
3
.
T
h
e
r
o
b
o
t
s
h
o
u
ld
ju
s
t
p
o
s
itio
n
it
s
el
f
ab
o
v
e
th
e
p
a
y
lo
ad
.
T
h
en
,
in
th
e
ca
s
e
o
f
at
g
r
o
u
n
d
,
th
e
w
e
i
g
h
t
o
f
th
e
p
a
y
lo
ad
w
ill
b
e
s
h
ar
ed
b
et
w
ee
n
lef
t
a
n
d
r
ig
h
t
s
id
e
d
u
r
in
g
a
n
d
af
ter
t
h
e
g
r
asp
i
n
g
ta
s
k
as
s
h
o
w
n
in
f
i
g
u
r
e
4
.
T
h
e
v
er
tical
m
o
tio
n
o
f
t
h
e
g
r
ip
p
er
r
e
q
u
ir
es
a
s
u
itab
le
m
o
b
i
lit
y
i
n
t
h
e
s
y
s
te
m
to
elev
ate
t
h
e
p
ay
lo
ad
(
ch
an
g
e
th
e
h
eig
h
t
o
f
t
h
e
to
tal
ce
n
tr
e
o
f
m
a
s
s
o
f
th
e
r
o
b
o
t)
.
A
s
a
co
n
clu
s
io
n
,
t
h
e
i
n
te
g
r
atio
n
o
f
t
h
e
th
e
g
r
ip
p
er
at
th
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
.
2
,
J
u
n
e
2
0
1
6
:
1
15
–
1
35
118
b
o
tto
m
o
f
ea
c
h
a
x
le
s
i
m
p
li
f
i
e
s
th
e
p
a
y
lo
ad
g
r
ip
p
in
g
tas
k
a
n
d
i
m
p
r
o
v
e
s
s
tab
ilit
y
b
y
d
ec
r
ea
s
in
g
t
h
e
h
ei
g
h
t
o
f
th
e
to
tal
ce
n
tr
e
o
f
m
as
s
.
Fig
u
r
e
2
.
Op
en
W
HE
E
L
i3
R
Fig
u
r
e
3
.
I
n
u
e
n
ce
o
f
th
e
p
a
y
lo
ad
p
o
s
itio
n
: a
lo
w
er
p
a
y
lo
ad
lead
s
to
s
m
aller
m
o
tio
n
s
o
f
th
e
p
r
o
j
ec
ted
to
tal
ce
n
tr
e
o
f
m
a
s
s
G
’
T
o
n
in
cli
n
e
d
g
r
o
u
n
d
s
.
Fig
u
r
e
4
.
I
n
u
e
n
ce
o
f
th
e
g
r
ip
p
er
m
ec
h
a
n
is
m
p
o
s
itio
n
: v
e
n
tr
a
l tr
an
s
p
o
r
t d
e
cr
ea
s
es r
o
ll
-
o
v
er
r
is
k
.
2
.
3
.
F
un
ct
io
na
l
Require
m
ent
s
f
o
r
t
he
New
P
o
l
y
-
Ro
bo
t
T
h
e
fi
r
s
t
id
ea
is
th
at
w
h
ee
lb
ase
=
tr
ac
k
is
r
eq
u
ir
ed
f
o
r
t
h
e
cli
m
b
i
n
g
p
h
a
s
es
a
n
d
a
lo
n
g
w
h
ee
lb
ase
(
w
h
ee
lb
ase
>>
tr
ac
k
)
f
o
r
th
e
r
o
llin
g
p
h
ases
,
w
h
ich
m
ea
n
s
an
ad
j
u
s
tab
le
w
h
ee
lb
a
s
e
is
n
ee
d
ed
(
f
u
n
ctio
n
a
l
r
eq
u
ir
e
m
en
t
FR
)
.
A
s
ec
o
n
d
i
d
ea
led
u
s
to
s
ep
ar
ate
th
e
in
itial
Op
en
W
HE
E
L
i3
R
r
o
b
o
t
in
to
t
w
o
id
en
tical
s
in
g
le
a
x
le
m
o
n
o
-
r
o
b
o
ts
to
i
m
p
r
o
v
e
m
o
d
u
lar
it
y
(
r
eq
u
ir
e
m
e
n
t
R
2
)
.
C
o
m
b
i
n
i
n
g
th
e
s
e
r
eq
u
ir
e
m
en
ts
g
a
v
e
r
is
e
to
th
e
C
3
B
o
ts
A
T
/V
L
P
(
A
ll
-
T
er
r
ain
/
L
o
n
g
P
a
y
lo
ad
s
)
ro
b
o
t c
o
n
ce
p
t u
s
i
n
g
t
w
o
s
i
n
g
le
-
a
x
le
m
o
n
o
-
r
o
b
o
ts
th
at
w
ill
h
av
e
to
li
f
t
t
h
e
p
a
y
lo
ad
,
tr
an
s
late
alo
n
g
its
a
x
is
to
c
h
an
g
e
t
h
e
w
h
ee
lb
ase
len
g
t
h
a
n
d
r
o
tate
ar
o
u
n
d
th
e
s
a
m
e
ax
is
to
w
ar
p
th
e
p
o
l
y
-
r
o
b
o
t a
n
d
elev
ate
o
n
e
w
h
ee
l
w
i
th
r
esp
ec
t to
th
e
th
r
ee
o
th
er
s
.
1.
FR
1
C
h
o
o
s
in
g
t
h
e
ap
p
r
o
p
r
iate
n
u
m
b
er
o
f
ax
le
s
f
o
r
r
o
llin
g
.
2.
FR
2
L
if
t
in
g
t
h
e
p
a
y
lo
ad
f
r
o
m
th
e
g
r
o
u
n
d
.
3.
FR
3
Han
d
li
n
g
v
ar
io
u
s
t
y
p
e
o
f
p
ay
lo
ad
s
(
u
n
s
tr
u
ct
u
r
ed
/lo
w
s
ti
_
n
ess
)
.
4.
FR
4
C
h
an
g
i
n
g
d
ir
ec
tio
n
.
5.
FR
5
C
li
m
b
i
n
g
o
b
s
tacle
s
.
6.
FR
6
E
n
s
u
r
i
n
g
s
tab
ilit
y
.
7.
FR
7
Kee
p
in
g
all
t
h
e
w
h
ee
l
s
in
co
n
tact
o
n
ir
r
eg
u
lar
g
r
o
u
n
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Desig
n
a
n
d
C
o
o
r
d
in
a
tio
n
o
f Co
o
p
era
tive
Mo
b
ile
R
o
b
o
ts
(
M.K
r
id
)
119
2
.
4
.
M
o
no
-
Ro
bo
t
Arc
hite
ct
ure
T
h
e
tr
an
s
p
o
r
t
p
latf
o
r
m
d
ep
en
d
s
o
n
th
e
m
o
n
o
-
r
o
b
o
t
ar
ch
itectu
r
e.
Mo
r
e
s
p
ec
if
i
ca
ll
y
,
p
o
ly
-
r
o
b
o
t
m
o
b
il
it
y
d
ep
en
d
s
o
n
th
e
i
n
ter
c
o
n
n
ec
tio
n
b
et
w
ee
n
all
t
h
e
m
o
n
o
-
r
o
b
o
ts
,
s
o
m
e
o
f
th
e
m
b
ein
g
r
ed
u
n
d
an
t.
T
h
e
m
o
n
o
-
r
o
b
o
t
m
u
s
t
b
e
ab
le
to
r
o
ll
o
n
th
e
g
r
o
u
n
d
(
R
y
m
o
b
ilit
y
)
an
d
li
f
t
t
h
e
p
a
y
lo
ad
.
I
t
n
ee
d
s
a
g
r
ip
p
i
n
g
m
ec
h
a
n
i
s
m
(
g
r
ip
p
er
)
th
at
en
s
u
r
es
th
e
co
n
n
ec
tio
n
b
et
w
ee
n
t
h
e
ax
le
f
r
a
m
e
an
d
t
h
e
p
a
y
lo
ad
.
T
h
e
m
o
n
o
-
r
o
b
o
t
m
u
s
t
b
e
ab
le
to
c
h
a
n
g
e
its
m
o
tio
n
d
ir
ec
tio
n
(
u
s
in
g
R
z
s
teer
in
g
m
o
b
ilit
y
)
w
it
h
o
u
t
m
o
d
if
y
i
n
g
t
h
e
p
a
y
lo
ad
o
r
ien
tatio
n
d
u
r
in
g
tr
an
s
p
o
r
t
in
o
r
d
er
to
p
er
f
o
r
m
ap
p
r
o
p
r
iate
g
r
a
s
p
in
g
o
p
er
atio
n
s
.
Du
r
in
g
th
e
tr
an
s
p
o
r
t
m
is
s
io
n
,
ea
c
h
m
o
n
o
-
r
o
b
o
t
m
u
s
t
b
e
ab
leto
tr
an
s
late
alo
n
g
t
h
e
p
ay
lo
ad
ax
i
s
(
T
x
m
o
b
ilit
y
)
a
n
d
r
o
tate
ar
o
u
n
d
th
e
s
a
m
e
a
x
i
s
(
R
x
m
o
b
il
it
y
)
.
R
x
m
o
b
ilit
y
w
ill
a
ls
o
h
elp
to
k
ee
p
all
th
e
w
h
ee
l
s
i
n
co
n
tact
w
i
th
th
e
ir
r
eg
u
lar
ter
r
ain
.
T
h
e
m
o
n
o
-
r
o
b
o
t
ca
n
tr
an
s
p
o
r
t
s
m
al
l
p
a
y
lo
ad
s
o
v
e
r
at
g
r
o
u
n
d
b
y
its
el
f
.
Du
r
i
n
g
s
o
lo
lo
co
m
o
tio
n
,
s
tab
ilit
y
ca
n
b
e
o
b
tain
ed
u
s
i
n
g
v
ar
io
u
s
s
o
l
u
tio
n
s
:
1.
A
cti
v
e
p
itc
h
co
n
tr
o
l in
t
h
e
s
a
m
e
w
a
y
a
s
[
1
6
]
.
2.
A
d
d
in
g
a
r
etr
ac
tab
le
ar
m
w
it
h
a
p
ass
iv
e
ca
s
ter
w
h
ee
l.
Fig
u
r
e
5
.
DOF
b
et
w
ee
n
d
if
f
er
en
t b
o
d
ies o
f
th
e
m
o
n
o
-
r
o
b
o
t.
3.
RE
Q
UIR
E
D
M
O
B
I
L
I
T
I
E
S
AND
E
XAM
P
L
E
O
F
K
I
N
E
M
AT
I
CS
T
h
e
m
o
n
o
-
r
o
b
o
t
in
clu
d
es
an
a
x
le,
a
p
o
s
itio
n
in
g
m
ec
h
an
is
m
an
d
a
g
r
ip
p
in
g
m
ec
h
a
n
is
m
.
On
e
f
ea
s
ib
le
k
in
e
m
at
ics
o
f
t
h
e
p
o
s
itio
n
n
in
g
m
ec
h
a
n
is
m
is
p
r
esen
ted
in
Fig
.
6
an
d
7
.
T
h
e
m
o
n
o
-
r
o
b
o
t,
d
en
o
ted
MRa,
in
cl
u
d
es
t
w
o
w
h
ee
ls
W
a1
an
d
W
a2
m
o
to
r
ized
in
d
ep
en
d
en
tl
y
w
i
th
t
w
o
m
o
to
r
s
(
w
ith
i
n
d
ex
"
a
"
e
q
u
als
t
o
"1
"
f
o
r
f
r
o
n
ta
x
le
an
d
"
2
"
f
o
r
r
ea
r
ax
le,
"
1
"
f
o
r
r
ig
h
t
w
h
ee
l
a
n
d
"
2
"
f
o
r
lef
t
w
h
ee
l)
.
T
o
b
e
ab
l
e
to
m
a
n
ip
u
la
te
t
h
e
o
b
j
ec
t,
th
e
r
o
b
o
t
is
eq
u
ip
p
ed
w
it
h
a
g
r
ip
p
er
m
o
u
n
ted
at
th
e
b
o
tto
m
o
f
th
e
c
h
ass
is
.
T
h
e
o
r
ig
in
alit
y
o
f
t
h
e
co
n
ce
p
t
la
y
s
o
n
t
h
e
k
in
e
m
ati
c
ch
a
in
o
f
t
h
e
p
o
s
itio
n
in
g
m
ec
h
an
i
s
m
.
T
h
e
ax
le
f
r
a
m
e
(
Aa)
ca
n
f
r
ee
l
y
s
tee
r
ar
o
u
n
d
t
h
e
c
y
li
n
d
r
ical
j
o
in
t
C
a
w
it
h
r
esp
ec
t
to
s
l
id
er
(
S1
a)
.
T
h
e
r
e
m
ai
n
i
n
g
v
er
tical
m
o
-
to
r
ized
tr
an
s
la
tio
n
T
za
o
f
C
a
allo
w
s
co
n
tr
o
lli
n
g
t
h
e
altit
u
d
e
o
f
t
h
e
g
r
ip
p
er
an
d
co
n
s
eq
u
e
n
tl
y
o
f
t
h
e
p
a
y
lo
ad
.
T
h
e
r
o
ll
m
o
tio
n
R
x
a
b
et
w
ee
n
t
h
e
s
lid
er
b
o
d
y
(
S1
a)
an
d
th
e
s
u
p
p
o
r
t
b
o
d
y
(
S2
a)
is
en
s
u
r
ed
b
y
t
h
e
r
e
v
o
lu
te
m
o
to
r
ized
jo
in
t
(
R
a3
)
w
h
ic
h
is
co
m
p
u
l
s
o
r
y
to
r
ep
r
o
d
u
ce
w
ar
p
in
g
m
o
tio
n
o
f
o
n
e
ax
le
r
o
u
g
h
l
y
ar
o
u
n
d
th
e
lo
n
g
i
tu
d
in
al
a
x
is
o
f
t
h
e
p
ay
lo
ad
,
as t
h
e
o
r
ig
in
a
l O
p
en
W
HE
E
L
i3
R
d
id
.
T
h
e
co
n
n
ec
tio
n
b
et
w
ee
n
th
e
m
o
n
o
-
r
o
b
o
ts
is
en
s
u
r
ed
b
y
th
e
tr
an
s
p
o
r
ted
p
ay
lo
ad
as
s
h
o
w
n
in
Fi
g
.
1
1
.
T
h
e
co
-
m
an
ip
u
latio
n
o
f
t
h
e
p
ay
lo
ad
b
y
t
h
e
t
w
o
m
o
n
o
-
r
o
b
o
ts
allo
w
s
o
b
s
tacle
cr
o
s
s
i
n
g
.
T
h
e
p
o
l
y
-
r
o
b
o
t
co
m
b
i
n
es
t
h
e
m
o
b
ilit
ies
o
f
th
e
m
o
n
o
-
r
o
b
o
ts
.
I
t
ca
n
co
n
tr
o
l
th
e
p
ass
i
v
e
r
o
tatio
n
R
za
o
f
t
h
e
c
y
li
n
d
r
ical
j
o
in
t
(
C
a)
o
n
ea
ch
m
o
n
o
-
r
o
b
o
t
b
y
t
h
e
d
i_
er
en
ce
o
f
a
n
g
u
lar
v
elo
cities
o
f
t
h
e
t
w
o
w
h
ee
ls
o
f
ea
ch
a
x
le.
T
h
e
r
ed
u
n
d
an
t
r
ev
o
l
u
te
j
o
in
ts
R
1
3
(
f
r
o
n
t)
an
d
R
2
3
(
r
ea
r
)
g
iv
e
a
w
ar
p
in
g
d
eg
r
ee
o
f
f
r
ee
d
o
m
to
th
e
p
o
l
y
-
r
o
b
o
t.
W
h
en
j
o
in
ts
R
a3
ar
e
ac
t
u
ated
(
eith
er
R
1
3
o
r
R
2
3
)
,
a
w
ar
p
in
g
m
o
t
io
n
i
s
g
e
n
er
ated
o
f
o
n
e
m
o
n
o
-
r
o
b
o
t
ar
o
u
n
d
th
e
j
o
in
t
R
a3
a
x
is
w
i
th
r
e
s
p
ec
t
to
th
e
o
th
er
m
o
n
o
-
r
o
b
o
t.
T
h
is
m
o
v
e
m
e
n
t
al
lo
w
s
to
li
f
t
t
h
e
ex
p
lo
r
atio
n
w
h
ee
l
o
f
f
t
h
e
g
r
o
u
n
d
.
W
e
h
a
v
e
t
h
e
r
ef
o
r
e
a
n
e
w
co
n
fi
g
u
r
atio
n
o
f
th
e
s
y
s
te
m
w
ith
o
n
l
y
3
w
h
e
el
-
g
r
o
u
n
d
co
n
tac
ts
.
Fin
all
y
,
p
r
is
m
atic
j
o
in
t
P
a
b
et
w
ee
n
g
r
ip
p
er
GW
a
an
d
s
u
p
p
o
r
t
S2
a
in
ea
ch
m
o
n
o
-
r
o
b
o
t
allo
w
s
tr
a
n
s
lat
in
g
t
h
e
m
o
n
o
-
r
o
b
o
t
alo
n
g
t
h
e
p
a
y
lo
a
d
ax
is
.
As
a
co
n
cl
u
s
io
n
,
t
h
e
i
m
p
le
m
e
n
tat
io
n
s
h
o
w
n
i
n
Fi
g
.
??
p
r
o
v
id
es
th
e
f
o
u
r
m
o
b
il
ities
r
eq
u
ir
ed
o
n
ea
ch
m
o
n
o
-
r
o
b
o
t f
o
r
s
tab
le
p
ay
lo
ad
tr
an
s
p
o
r
t a
n
d
o
b
s
tacle
o
f
th
e
p
o
l
y
-
r
o
b
o
t:
1.
a
r
o
tatio
n
R
x
a
f
o
r
w
h
ee
l e
le
v
a
tio
n
o
n
o
b
s
tacle
s
.
2.
a
r
o
tatio
n
R
za
f
o
r
s
teer
in
g
a
n
d
s
tab
ilizatio
n
o
n
3
w
h
ee
ls
co
n
_
g
u
r
atio
n
.
3.
a
tr
an
s
latio
n
T
x
a
f
o
r
o
n
i
m
p
r
o
v
ed
s
tab
ilizatio
n
w
it
h
a
lo
n
g
p
a
y
lo
ad
.
4.
a
tr
an
s
latio
n
T
za
f
o
r
p
ay
lo
ad
elev
atio
n
.
Sev
er
al
eq
u
i
v
ale
n
t
s
er
ial
k
in
e
m
atic
c
h
ain
s
ar
e
p
r
esen
ted
in
Fig
.
9
an
d
ca
n
b
e
u
s
ed
f
o
r
a
r
ea
l
i
m
p
le
m
en
ta
tio
n
.
T
h
e
k
in
e
m
at
ics
p
r
ese
n
ted
i
n
Fig
.
6
a
n
d
Fi
g
.
1
1
allo
w
s
th
e
p
o
ly
-
r
o
b
o
t
to
tr
an
s
p
o
r
t
lo
n
g
p
a
y
lo
ad
in
a
m
o
d
u
lar
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
.
2
,
J
u
n
e
2
0
1
6
:
1
15
–
1
35
120
w
a
y
an
d
al
s
o
to
cr
o
s
s
o
b
s
tacle
s
.
B
ef
o
r
e
d
etailin
g
th
e
cr
o
s
s
in
g
m
o
d
e
s
,
th
e
n
ex
t
s
ec
ti
o
n
w
ill
p
r
esen
t
a
n
ex
h
a
u
s
tiv
e
m
et
h
o
d
to
s
y
n
th
e
s
i
ze
alter
n
ativ
e
k
i
n
e
m
atics.
Fig
u
r
e
6
.
Kin
e
m
atic
d
iag
r
a
m
o
f
a
m
o
n
o
-
r
o
b
o
t M
R
a
.
Fig
u
r
e
7
.
Kin
e
m
atic
g
r
ap
h
o
f
a
m
o
n
o
-
r
o
b
o
t M
R
a.
4
.
SYST
E
M
AT
I
C
SY
NT
H
E
SI
S O
F
T
H
E
P
O
SI
T
I
O
N
I
N
G
M
E
CH
ANIS
M
T
h
e
p
o
s
itio
n
in
g
m
ec
h
an
i
s
m
is
th
e
k
i
n
e
m
atic
c
h
ai
n
t
h
at
co
n
n
ec
ts
th
e
ax
le
to
th
e
g
r
ip
p
er
m
ec
h
a
n
i
s
m
o
f
t
h
e
co
n
s
id
er
ed
m
o
n
o
-
r
o
b
o
t
(
Fig
.
9
)
.
I
n
t
h
is
w
o
r
k
,
o
n
l
y
s
er
ial
c
h
ai
n
s
w
ill
b
e
co
n
s
id
er
ed
.
T
h
e
r
eq
u
ir
ed
m
o
b
il
ities
o
f
t
h
e
e
n
d
o
f
t
h
e
c
h
ain
(
g
r
ip
p
er
)
w
it
h
r
esp
ec
t
to
its
b
eg
i
n
n
in
g
(
a
x
le)
ar
e
R
x
,
R
z,
T
x
a
n
d
T
z,
as
f
o
u
n
d
in
th
e
p
r
ev
io
u
s
s
ec
tio
n
.
T
h
e
co
n
s
id
er
ed
j
o
in
ts
w
ill
b
e:
th
e
r
ev
o
l
u
te
j
o
in
t
R
,
to
p
r
o
v
id
e
r
o
tatio
n
s
R
x
a
n
d
R
z;
t
h
e
p
r
is
m
atic
j
o
in
t
P
to
p
r
o
v
id
e
tr
an
s
lat
io
n
s
T
x
an
d
T
z;
th
e
c
y
li
n
d
r
ical
j
o
in
t
C
to
p
r
o
v
id
e
in
d
ep
en
d
e
n
t
r
o
tatio
n
al
an
d
tr
an
s
la
tio
n
al
m
o
tio
n
s
alo
n
g
a
g
iv
e
n
ax
is
.
Helic
al
j
o
in
t H
w
ill
n
o
t b
e
c
o
n
s
id
er
ed
h
er
e
b
ec
au
s
e
o
f
t
h
e
co
u
p
led
m
o
tio
n
s
.
T
h
e
s
y
s
te
m
atic
s
y
n
th
e
s
is
i
s
b
ased
o
n
th
e
en
u
m
er
atio
n
o
f
t
h
e
n
o
n
-
r
ed
u
n
d
an
t
co
m
b
i
n
atio
n
s
o
f
R
,
P
an
d
C
j
o
in
ts
ca
p
ab
le
to
p
r
o
v
id
e
th
e
r
eq
u
ir
ed
m
o
b
ilit
ies
R
x
,
R
z,
T
x
an
d
T
z.
Fo
u
r
ca
s
es c
an
b
e
d
is
tin
g
u
is
h
ed
:
1.
P
er
m
u
tatio
n
s
o
f
t
w
o
j
o
in
ts
C
x
an
d
C
z;
2.
P
er
m
u
tatio
n
s
o
f
t
h
r
ee
j
o
in
ts
C
x
,
R
z
an
d
P
z;
3.
P
er
m
u
tatio
n
s
o
f
t
h
r
ee
j
o
in
ts
C
z,
R
x
an
d
P
x
;
4.
P
er
m
u
tatio
n
s
o
f
f
o
u
r
j
o
in
ts
R
x
,
T
x
,
R
z
an
d
P
z.
As
th
e
n
u
m
b
er
o
f
p
er
m
u
tatio
n
s
o
f
n
ele
m
e
n
ts
i
s
eq
u
al
to
n
!
,
th
e
to
tal
n
u
m
b
er
o
f
p
o
ten
tia
l
k
in
e
m
atic
s
is
2
!
+
3
!
+
3
!
+
4
!
,
th
a
t
is
t
o
s
a
y
a
to
tal
o
f
3
8
p
o
s
s
i
b
le
m
ec
h
an
i
s
m
s
,
e
n
u
m
er
ated
in
T
a
b
le
1
.
Ho
w
e
v
er
,
t
h
e
_
n
al
s
o
l
u
tio
n
s
h
a
v
e
to
co
m
p
l
y
to
ad
d
itio
n
al
f
u
n
ct
io
n
al
r
eq
u
i
r
e
m
en
t
s
,
t
h
at
ca
n
b
e
tr
a
n
s
la
te
d
in
to
d
e
s
i
g
n
r
u
les,
an
d
th
at
w
ill
r
estrict
t
h
e
co
m
b
in
ato
r
ial
e
x
p
lo
s
io
n
.
I
n
th
e
f
o
ll
o
w
i
n
g
li
n
es,
t
h
e
k
in
e
m
at
ic
ch
ain
s
ar
e
a
ll
o
r
ien
te
d
f
r
o
m
t
h
e
ax
le
to
th
e
g
r
ip
p
er
.
A
f
i
r
s
t
r
eq
u
ir
e
m
en
t
is
t
h
at
j
o
i
n
ts
R
x
o
r
C
x
s
h
o
u
ld
s
er
v
e
f
o
r
w
ar
p
in
g
th
e
a
x
l
e
ar
o
u
n
d
th
e
p
a
y
lo
ad
ax
is
,
i
n
t
h
e
s
a
m
e
w
a
y
as
th
e
Op
en
W
HE
E
L
i3
R
r
o
b
o
t.
T
h
is
m
ea
n
s
t
h
a
t
th
e
o
r
ie
n
tatio
n
o
f
r
o
tatio
n
ax
is
o
f
j
o
in
ts
R
x
o
r
C
x
s
h
o
u
ld
b
e
k
ep
t
p
ar
allel
to
th
e
p
a
y
lo
ad
ax
is
,
u
n
m
o
d
if
i
e
d
b
y
th
e
k
i
n
e
m
a
tic
ch
ain
t
h
at
f
o
llo
w
s
th
e
s
e
j
o
in
ts
.
T
h
e
co
r
r
esp
o
n
d
in
g
d
esig
n
r
u
le
R
3
is
th
at
R
z
o
r
C
z
j
o
in
ts
ar
e
f
o
r
b
id
d
en
af
ter
Rx
o
r
C
x
j
o
in
ts
.
A
p
p
l
y
i
n
g
R
3
to
th
e
3
8
m
ec
h
a
n
i
s
m
s
allo
w
s
to
ex
tr
ac
t
1
9
s
o
lu
tio
n
s
(
T
ab
le
1
,
co
lu
m
n
R
u
le
R
3
)
.
A
s
ec
o
n
d
r
eq
u
ir
e
m
en
t is t
h
at
j
o
in
ts
R
z
o
r
C
z
s
h
o
u
ld
s
er
v
e
f
o
r
ax
le
s
teer
in
g
.
T
h
is
m
ea
n
s
t
w
o
t
h
in
g
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Desig
n
a
n
d
C
o
o
r
d
in
a
tio
n
o
f Co
o
p
era
tive
Mo
b
ile
R
o
b
o
ts
(
M.K
r
id
)
121
1.
T
h
e
R
z
o
r
C
z
r
o
tatio
n
a
x
i
s
s
h
o
u
ld
b
e
k
ep
t
p
er
p
en
d
icu
l
ar
to
th
e
w
h
ee
l
a
x
is
.
T
h
is
a
s
s
er
tio
n
ca
n
b
e
r
ef
o
r
m
u
lated
in
to
th
e
f
o
llo
w
i
n
g
:
t
h
e
o
r
ien
tatio
n
o
f
t
h
e
ax
i
s
o
f
r
o
tatio
n
o
f
R
z
o
r
C
z
j
o
i
n
t
s
h
o
u
ld
n
o
t
b
e
m
o
d
i
f
ied
b
y
th
e
k
i
n
e
m
atic
c
h
ain
t
h
at
p
r
ec
ed
es
th
e
s
e
j
o
in
ts
.
Fin
all
y
,
t
h
e
d
esi
g
n
r
u
le
R
4
ap
p
ea
r
s
to
b
e
:
R
x
o
r
C
x
ar
e
f
o
r
b
id
d
en
b
ef
o
r
e
R
z
o
r
C
z.
2.
T
h
e
R
z
o
r
C
z
r
o
tatio
n
ax
is
s
h
o
u
ld
p
ass
th
r
o
u
g
h
t
h
e
w
h
ee
l
a
x
is
.
T
h
is
r
eq
u
ir
es
th
at
t
h
e
p
o
s
itio
n
o
f
th
e
ax
i
s
o
f
r
o
tatio
n
o
f
R
z
o
r
C
z
j
o
in
t s
h
o
u
ld
n
o
t b
e
m
o
d
i_
ed
b
y
t
h
e
k
in
e
m
atic
c
h
ai
n
t
h
at
p
r
ec
ed
es t
h
ese
j
o
in
t
s
.
T
h
is
ca
n
b
e
s
u
m
m
ar
ized
in
a
f
if
t
h
d
esig
n
r
u
le
R
5
: P
x
o
r
C
x
ar
e
f
o
r
b
id
d
en
b
ef
o
r
e
R
z
o
r
C
z.
Fig
u
r
e
8
.
E
n
u
m
er
atio
n
o
f
t
h
e
3
8
p
er
m
u
tat
io
n
s
u
s
i
n
g
eit
h
er
tw
o
j
o
in
ts
(
C
x
,
C
z)
o
r
th
r
ee
j
o
i
n
ts
(
C
x
,
R
z,
P
z)
o
r
th
r
ee
j
o
in
ts
(
C
z,
R
x
,
P
x
)
o
r
f
o
u
r
j
o
in
ts
(
R
x
,
P
x
,
R
z,
P
z)
an
d
p
r
o
v
id
in
g
t
h
e
f
o
u
r
in
d
ep
en
d
en
t
m
o
b
ilit
ies
R
x
,
R
z,
T
x
an
d
T
z.
I
t
ap
p
ea
r
s
th
at
r
u
le
R
4
g
i
v
es
ex
ac
tl
y
t
h
e
s
a
m
e
s
o
l
u
tio
n
s
a
s
r
u
le
R
3
.
T
h
is
w
o
u
ld
n
o
t
b
e
t
h
e
ca
s
e
i
f
w
er
e
co
n
s
id
er
ed
also
r
ed
u
n
d
an
t
s
o
lu
tio
n
s
.
T
h
e
last
r
u
le
R
5
r
estricts
th
e
n
u
m
b
e
r
o
f
s
o
lu
tio
n
s
to
2
2
o
u
t
o
f
3
8
(
T
a
b
le
1
,
co
lu
m
n
R
u
le
R
5
)
.
B
y
k
ee
p
i
n
g
o
n
l
y
th
e
s
o
l
u
tio
n
s
co
m
p
l
y
i
n
g
s
i
m
u
lta
n
eo
u
s
l
y
t
o
R
3
,
R
4
a
n
d
R
5
,
a
fi
n
al
g
r
o
u
p
o
f
1
5
s
o
lu
tio
n
s
ca
n
b
e
f
o
u
n
d
.
T
h
e
f
if
tee
n
f
i
n
al
s
o
lu
tio
n
s
ar
e
S0
2
,
S0
5
-
06,
S0
8
-
1
0
,
S2
7
-
3
2
,
S
36
-
3
8
an
d
ar
e
r
ep
r
esen
ted
in
Fig
.
9
,
w
h
er
e
ca
n
b
e
s
ee
n
all
th
e
g
en
er
ated
k
i
n
e
m
atics.
T
h
is
s
y
n
t
h
e
s
is
m
et
h
o
d
is
r
ath
er
g
en
er
al
a
n
d
co
u
ld
b
e
ea
s
il
y
co
m
p
leted
w
it
h
ad
d
itio
n
al
d
esig
n
r
u
le
s
,
p
r
o
v
id
ed
th
at
th
e
y
ca
n
b
e
f
o
r
m
u
lated
i
n
d
ep
en
d
en
tl
y
f
r
o
m
t
h
e
d
i
m
en
s
io
n
s
o
f
th
e
m
ec
h
an
i
s
m
a
n
d
r
ef
er
r
in
g
o
n
l
y
to
its
q
u
alitati
v
e
s
tr
u
ct
u
r
e.
5.
P
RO
CE
SS
F
O
R
O
B
ST
ACL
E
CRO
SS
I
N
G
C
3
B
o
ts
A
T
/VL
P
ca
n
ad
o
p
t
m
o
r
e
th
a
n
o
n
e
p
r
o
ce
s
s
f
o
r
o
b
s
tacle
cr
o
s
s
in
g
[
3
6
]
.
I
t
ca
n
b
e
d
ef
i
n
ed
b
y
th
e
n
u
m
b
er
o
f
a
x
le
t
h
at
f
o
r
m
th
e
p
o
l
y
-
r
o
b
o
t.
T
h
e
cli
m
b
i
n
g
p
r
o
ce
s
s
w
ith
t
h
r
ee
ax
les
a
n
d
m
o
r
e
is
v
er
y
s
i
m
p
le
co
m
p
ar
ed
to
t
h
e
t
w
o
a
x
le
co
n
f
i
g
u
r
at
io
n
,
b
ec
au
s
e
d
u
r
i
n
g
t
h
e
cli
m
b
i
n
g
p
r
o
ce
s
s
t
h
e
p
o
l
y
-
r
o
b
o
t
h
as
al
w
a
y
s
t
w
o
ax
les o
r
m
o
r
e
o
n
th
e
g
r
o
u
n
d
,
an
d
o
n
l
y
o
n
e
ax
le
i
s
liftin
g
o
f
f
t
o
cli
m
b
th
e
o
b
s
tacle
(
m
o
r
e
d
etails in
[
3
6
]
)
.
Fig
.
1
0
r
ep
r
e
s
en
t
s
a
v
ie
w
o
f
al
l
p
h
ase
s
o
f
t
h
e
cli
m
b
i
n
g
p
r
o
ce
s
s
.
E
ac
h
s
u
b
-
fi
g
u
r
e
r
ep
r
esen
t
s
t
h
e
p
o
s
e
o
f
th
e
p
o
l
y
-
r
o
b
o
t
at
th
e
en
d
o
f
th
e
1
8
clim
b
i
n
g
p
h
a
s
es.
E
ac
h
p
h
ase
is
ac
h
ie
v
ed
b
y
t
h
e
m
o
ti
o
n
o
f
a
s
in
g
le
j
o
in
t
o
r
b
y
a
ch
a
n
g
e
i
n
th
e
w
h
ee
l
-
g
r
o
u
n
d
co
n
tact
s
.
B
y
c
o
n
s
id
er
i
n
g
d
if
f
er
en
t
p
o
s
s
ib
le
co
n
f
i
g
u
r
atio
n
s
f
o
r
t
h
e
r
o
b
o
t
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
.
2
,
J
u
n
e
2
0
1
6
:
1
15
–
1
35
122
d
esig
n
,
w
e
ca
n
s
tate
a
s
a
g
e
n
er
al
co
n
clu
s
io
n
t
h
at
t
h
e
th
r
ee
-
ax
le
(
an
d
m
o
r
e)
d
esig
n
en
ab
les
an
ea
s
y
2
D
o
b
s
tacle
cr
o
s
s
in
g
m
o
d
e
at
t
h
e
p
r
ice
o
f
a
h
ig
h
n
u
m
b
er
o
f
ax
le
s
.
Her
ein
a
f
ter
,
w
e
f
o
cu
s
o
n
a
p
o
ly
-
r
o
b
o
t
w
it
h
t
w
o
m
o
n
o
-
r
o
b
o
ts
,
s
in
ce
it
r
ep
r
esen
ts
a
m
o
r
e
attr
ac
tiv
e
d
esi
g
n
.
T
h
e
ass
o
ciate
d
w
ar
p
in
g
m
o
d
e
d
escr
ib
ed
in
(
Fig
.
1
0
)
w
il
l b
e
o
p
tim
ized
to
m
ax
i
m
ize
s
tab
ilit
y
.
Fig
u
r
e
9
.
R
ep
r
esen
tatio
n
o
f
t
h
e
3
8
k
in
e
m
at
ics
co
r
r
esp
o
n
d
in
g
to
th
e
e
n
u
m
er
at
ed
jo
in
t
p
er
m
u
tatio
n
s
Fig
u
r
e
1
0
.
C
li
m
b
i
n
g
s
eq
u
e
n
ce
o
f
th
e
p
o
l
y
-
r
o
b
o
t
w
it
h
o
n
l
y
t
w
o
ax
les.
6.
P
O
L
Y
-
RO
B
O
T
M
O
DE
L
L
I
NG
I
n
th
i
s
s
ec
tio
n
,
g
eo
m
etr
ic
an
d
k
in
e
m
atic
m
o
d
els
ar
e
p
r
esen
t
ed
.
T
h
e
f
o
r
m
u
latio
n
o
f
th
e
s
e
m
o
d
el
s
is
p
er
f
o
r
m
ed
u
s
i
n
g
th
e
as
s
u
m
p
ti
o
n
o
f
r
o
llin
g
w
it
h
o
u
t
s
li
p
p
in
g
at
th
e
w
h
ee
l
-
g
r
o
u
n
d
co
n
tacts.
W
ith
th
e
s
e
m
o
d
els
,
w
e
ca
n
d
e_
n
e
th
e
r
elatio
n
b
etw
ee
n
d
i
ff
er
en
t g
eo
m
etr
ic
v
ar
i
ab
les o
f
th
e
p
o
l
y
-
r
o
b
o
t.
T
h
is
w
il
l b
e
u
s
ed
later
in
s
ec
tio
n
7
.
f
o
r
th
e
s
tab
ilit
y
a
n
al
y
s
i
s
o
f
th
e
p
o
l
y
-
r
o
b
o
t b
ased
o
n
an
o
r
ig
in
al
s
tab
ilit
y
cr
it
er
io
n
.
6
.
1
.
G
eo
m
et
ric
P
a
ra
m
et
er
s
T
h
is
s
ec
tio
n
in
tr
o
d
u
ce
s
th
e
g
eo
m
e
tr
ic
p
ar
am
eter
s
o
f
th
e
r
o
b
o
t
w
h
ich
w
i
ll
b
e
u
s
ed
to
e
v
alu
a
te
th
e
s
tab
ilit
y
cr
iter
io
n
i
n
t
h
e
n
e
x
t
s
ec
tio
n
.
E
ac
h
b
o
d
y
o
f
t
h
e
r
o
b
o
t
h
as
a
lo
ca
l
r
e
f
er
en
ce
f
r
a
m
e.
F
a1
an
d
F
a2
ar
e
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
Desig
n
a
n
d
C
o
o
r
d
in
a
tio
n
o
f Co
o
p
era
tive
Mo
b
ile
R
o
b
o
ts
(
M.K
r
id
)
123
r
esp
ec
tiv
el
y
th
e
lo
ca
l
f
r
a
m
es
fi
x
ed
to
ax
le
f
r
a
m
e
A
a
a
n
d
s
l
id
er
S1
a
.
FW
a
1
an
d
FW
a2
a
r
e
r
esp
ec
tiv
el
y
t
h
e
lo
ca
l
f
r
a
m
es
f
i
x
ed
to
th
e
r
ig
h
t
an
d
lef
t
w
h
ee
ls
o
f
a
x
le
a.
T
h
e
g
r
o
u
n
d
r
ef
er
en
ce
f
r
a
m
e
F0
is
f
i
x
ed
to
th
e
h
al
f
-
w
id
t
h
o
f
t
h
e
r
ea
r
w
h
ee
l
ax
les.
Fp
is
th
e
f
r
a
m
e
f
i
x
ed
to
th
e
p
a
y
lo
ad
.
I
n
o
r
d
er
to
s
i
m
p
li
f
y
t
h
e
ex
p
r
ess
io
n
o
f
th
e
g
eo
m
etr
ic
m
o
d
el,
th
e
ce
n
tr
es
o
f
f
r
a
m
es
F1
2
,
F2
2
an
d
Fp
ar
e
alig
n
ed
.
T
h
e
r
o
tatio
n
s
o
f
t
h
e
f
r
a
m
es
ar
e
g
iv
e
n
b
y
th
r
ee
r
o
tatio
n
v
ar
iab
les:
θ
a,
β
a
an
d
ϕ
a
(
Fig
.
1
1
)
.
I
n
th
is
p
ap
er
w
e
s
tu
d
y
o
n
l
y
th
e
cli
m
b
i
n
g
ta
s
k
.
W
e
co
n
tr
o
l
th
e
r
ev
o
lu
te
j
o
in
t
s
R
a1
;R
a2
;
R
a3
o
f
ea
c
h
m
o
n
o
-
r
o
b
o
t,
th
e
tr
a
n
s
latio
n
m
o
tio
n
o
f
ea
ch
c
y
lin
d
r
i
-
ca
l
j
o
in
t
C
a
a
n
d
p
r
is
m
atic
j
o
in
t
P
a.
W
e
s
tar
t
b
y
d
e
n
o
tin
g
t
h
e
an
g
u
lar
p
o
s
iti
o
n
o
f
ea
ch
w
h
ee
l,
d
ef
i
n
ed
b
y
th
e
r
o
tatio
n
an
g
le
be
t
w
ee
n
th
e
w
h
ee
l a
n
d
ch
as
s
is
ar
o
u
n
d
W
as
(
Fig
u
r
e1
2
)
(
1
)
W
e
d
en
o
te
I
as
th
e
p
o
in
t
o
f
co
n
tact
b
et
w
ee
n
w
h
ee
l
W
as
an
d
th
e
g
r
o
u
n
d
.
W
e
d
en
o
t
e
th
e
y
a
w
(
p
as
s
i
v
e
c
y
li
n
d
r
ical
j
o
in
t
C
a)
a
n
d
r
o
ll
(
ac
tiv
e
r
e
v
o
lu
te
j
o
in
t
R
a3
)
m
o
t
io
n
s
b
et
w
ee
n
f
r
o
n
t
a
n
d
r
ea
r
m
o
n
o
-
r
o
b
o
ts
an
d
th
e
p
ay
lo
ad
b
y
θ
1
,
θ
2
an
d
ϕ
1
,
ϕ
2
r
esp
ec
tiv
el
y
.
(
2
)
(
3
)
Fin
all
y
,
w
e
d
en
o
te
t
h
e
p
itch
m
o
tio
n
b
et
w
ee
n
th
e
r
ea
r
m
o
n
o
-
r
o
b
o
t a
n
d
th
e
f
i
x
ed
f
r
a
m
e
F
0
b
y
β
a.
(
4
)
Fig
u
r
e
1
1
.
R
elativ
e
p
o
s
itio
n
o
f
ea
ch
f
r
a
m
e
an
d
ass
o
ciate
d
a
n
g
les.
Fig
u
r
e
1
2
.
Geo
m
etr
ic
p
ar
a
m
et
er
s
o
f
th
e
w
h
ee
l:
later
al
a
n
d
lo
n
g
i
tu
d
i
n
al
m
o
t
io
n
Mo
n
o
-
r
o
b
o
ts
ca
n
tr
a
n
s
la
te
al
o
n
g
t
h
e
p
a
y
lo
ad
.
T
h
eir
r
elativ
e
p
o
s
itio
n
is
d
e
f
i
n
ed
b
y
t
h
e
d
is
tan
ce
f
r
o
m
th
e
c.
o
.
m
o
f
t
h
e
m
o
n
o
-
r
o
b
o
t
MR
a
to
th
e
c.
o
.
m
o
f
t
h
e
p
a
y
lo
ad
,
d
en
o
ted
d
a.
T
h
e
cy
li
n
d
r
ical
jo
in
t
in
ea
c
h
m
o
n
o
-
r
o
b
o
t
allo
w
s
th
e
g
r
ip
p
er
to
tr
an
s
late
v
er
ticall
y
i
n
o
r
d
er
to
g
r
asp
an
d
ad
j
u
s
t
th
e
h
ei
g
h
t
o
f
t
h
e
p
ay
lo
ad
.
Fo
r
th
is
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
.
2
,
J
u
n
e
2
0
1
6
:
1
15
–
1
35
124
g
eo
m
etr
ic
co
n
f
ig
u
r
atio
n
,
w
e
d
ef
i
n
e
a
h
o
m
o
g
e
n
eo
u
s
m
at
r
ix
b
et
w
ee
n
t
h
e
f
r
a
m
e
a
n
d
th
e
f
i
x
ed
f
r
a
m
e
o
f
r
ef
er
en
ce
F0
.
T
h
u
s
t
h
e
co
o
r
d
in
ates
o
f
th
e
w
h
ee
l
g
r
o
u
n
d
co
n
t
ac
t
p
o
in
ts
ar
e
e
x
p
r
ess
ed
i
n
F0
an
d
w
e
ca
n
o
b
tain
th
e
p
o
s
itio
n
o
f
t
h
e
c.
o
.
m
o
f
t
h
e
p
o
ly
-
r
o
b
o
t.
6
.
2
.
G
eo
m
et
ric
M
o
del
T
h
e
aim
o
f
t
h
e
g
eo
m
etr
ic
m
o
d
el
is
to
ex
p
r
ess
th
e
r
elatio
n
b
et
w
ee
n
th
e
in
p
u
t
v
ar
iab
les
o
f
th
e
p
o
l
y
-
r
o
b
o
t,
w
h
ich
ar
e
th
e
w
ar
p
i
n
g
an
g
le
s
ϕ
1
;
ϕ
2
,
an
d
th
e
o
u
tp
u
t
v
ar
iab
les
β
a
;
θ
1
;
θ
2.
W
e
s
tar
t
b
y
d
eFI
n
i
n
g
th
e
co
o
r
d
in
ates
o
f
ea
c
h
co
n
tact
p
o
in
t
I
as
in
t
h
e
lo
ca
l
f
r
a
m
e
F
W
as
;
w
e
o
b
tain
t
h
e
d
is
p
lace
m
en
t
o
f
t
h
e
co
n
tact
p
o
in
t
u
n
d
er
th
e
as
s
u
m
p
tio
n
o
f
r
o
llin
g
w
it
h
o
u
t
s
l
ip
p
in
g
a
n
d
th
e
p
o
s
itio
n
o
f
th
e
ce
n
tr
e
o
f
m
ass
ex
p
r
ess
ed
i
n
th
e
r
ef
er
en
ce
f
r
a
m
e
F0
.
6
.
2
.
1
.
Co
o
rdina
t
es
O
f
Whee
l C
o
nta
ct
P
o
ints
E
ac
h
m
o
n
o
-
r
o
b
o
t
is
a
s
s
u
m
ed
to
h
av
e
to
r
u
s
-
s
h
ap
ed
w
h
ee
ls
,
w
h
ic
h
lead
s
u
s
to
co
n
s
id
er
t
wo
r
ad
ii,
R
an
d
r
(
Fig
u
r
e
1
2
)
.
T
h
e
r
o
ll
in
g
w
h
ee
l
r
ad
iu
s
ca
n
b
e
ap
p
r
o
x
i
m
ated
b
y
R
w
=
R
+
r
.
W
e
d
e_
n
e
th
e
'
e
x
p
lo
r
in
g
ax
le
'
as
t
h
e
a
x
le
t
h
at
co
n
tai
n
s
th
e
ex
p
lo
r
i
n
g
w
h
ee
l,
w
h
ile
t
h
e
o
th
er
ax
le
i
s
r
ef
er
r
ed
to
as
t
h
e
'
s
u
p
p
o
r
tin
g
a
x
le
'
.
T
h
e
co
n
tact
p
o
in
t
is
th
e
in
ter
s
ec
tio
n
o
f
t
h
e
e
x
ter
n
a
l
s
u
r
f
ac
e
o
f
th
e
w
h
ee
l
w
it
h
t
h
e
g
r
o
u
n
d
an
d
it
d
ep
en
d
s
o
n
th
e
p
o
s
itio
n
o
f
th
e
v
e
h
icle
s
a
n
d
th
e
v
alu
e
o
f
th
e
r
o
ll
a
n
d
t
h
e
p
itch
a
n
g
les
o
f
a
x
les
(
ϕ
a
an
d
β
a)
.
T
h
e
ex
p
lo
r
in
g
w
h
ee
l
o
n
l
y
h
as
co
n
tact
w
it
h
th
e
g
r
o
u
n
d
in
s
ta
g
es
M0
1
an
d
M0
4
.
T
h
e
o
th
er
w
h
ee
l
o
f
t
h
e
ex
p
lo
r
in
g
ax
le
al
w
a
y
s
r
e
m
ai
n
s
i
n
co
n
tac
t
w
it
h
t
h
e
g
r
o
u
n
d
.
A
s
s
h
o
w
n
i
n
Fi
g
u
r
e
1
2
-
a,
th
e
co
n
tact
p
o
in
t
I
as
is
d
e_
n
ed
in
t
h
e
w
h
ee
l
f
r
a
m
e
b
y
:
(
5
)
Fo
r
th
e
s
u
p
p
o
r
tin
g
ax
le,
t
h
e
wh
ee
ls
ar
e
co
n
n
ec
ted
to
th
e
leg
s
b
y
ac
t
u
-
ated
r
ev
o
lu
te
j
o
in
ts
w
h
ic
h
ar
e
lo
ck
ed
,
s
o
th
e
p
itch
a
n
g
le
w
i
ll
also
h
av
e
a
n
ac
tio
n
o
n
th
e
w
h
e
els b
y
a
r
ea
r
m
o
v
e
m
en
t.
T
h
e
w
h
ee
ls
w
i
ll h
a
v
e
a
r
o
llin
g
m
o
tio
n
o
f
t
h
e
p
itc
h
an
g
le
β
a
co
u
p
led
w
it
h
a
r
ea
r
tr
an
s
latio
n
,
an
d
as s
h
o
w
n
in
F
i
g
u
r
e
1
2
-
b
,
th
e
co
n
tact
p
o
in
t
w
i
ll b
e
ex
p
r
ess
ed
in
t
h
e
w
h
ee
l
f
r
a
m
e
as
:
(
6
)
6
.
2
.
2
.
Ro
llin
g
Wit
ho
ut
Sli
pp
ing
I
n
t
h
e
ca
s
e
f
o
r
r
o
llin
g
w
i
th
o
u
t
s
lip
p
in
g
,
t
h
e
p
o
s
i
tio
n
,
v
elo
cit
y
a
n
d
ac
ce
ler
atio
n
o
f
th
e
ce
n
t
r
e
o
f
m
as
s
ar
e
d
ir
ec
tly
r
elate
d
to
th
e
r
o
ll
in
g
a
n
g
le
o
f
r
o
tatio
n
,
t
h
e
an
g
u
lar
v
elo
cit
y
,
an
d
t
h
e
an
g
u
lar
ac
ce
ler
atio
n
o
f
th
e
w
h
ee
l.
T
w
o
r
i
g
id
b
o
d
ies
i
n
c
o
n
tact,
as
s
u
m
i
n
g
r
o
llin
g
w
it
h
o
u
t
s
l
ip
p
in
g
,
h
a
v
e
a
ze
r
o
r
ela
tiv
e
s
p
ee
d
at
t
h
eir
p
o
in
t o
f
co
n
tact.
T
h
u
s
w
e
ca
n
w
r
ite:
(
7
)
(
8
)
w
it
h
(
9
)
an
d
th
e
f
o
llo
w
in
g
ex
s
p
r
ess
io
n
(
1
0
)
W
e
d
ed
u
ce
b
y
in
te
g
r
atio
n
o
f
t
h
e
k
i
n
e
m
atic
r
elatio
n
s
(
1
0
)
th
e
co
o
r
d
in
ate
v
ar
iatio
n
o
f
t
h
e
co
n
tact
p
o
in
ts
o
f
t
h
e
s
u
p
p
o
r
tin
g
a
n
d
ex
p
lo
r
in
g
a
x
les
:
Evaluation Warning : The document was created with Spire.PDF for Python.