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w
o
r
k
s
p
ac
e
b
ei
n
g
s
u
s
p
en
d
ed
,
in
d
ee
d
th
e
y
ca
n
b
e
co
n
s
id
er
ed
as
cr
a
n
e
-
t
y
p
e
m
an
ip
u
lato
r
s
[
2
4
,
2
5
]
.
Or
ien
tatio
n
ca
p
ab
i
liti
es
o
f
C
DP
R
s
ca
n
b
e
al
s
o
i
m
p
r
o
v
ed
b
y
co
u
p
lin
g
it
w
it
h
a
p
ar
allel
s
p
h
er
ical
w
r
i
s
t
ac
tu
ated
b
y
ca
b
le
-
d
r
iv
en
o
m
n
i
-
w
h
ee
l
s
,
as d
escr
ib
ed
in
[
2
6
]
.
C
SP
R
s
h
a
v
e
g
r
ea
t
p
o
te
n
tialit
i
es
f
o
r
m
an
y
ap
p
licatio
n
s
,
i
n
f
ac
t,
if
all
th
e
fi
x
ed
attac
h
m
e
n
t
p
o
in
ts
ar
e
lo
ca
ted
ab
o
v
e
th
e
w
o
r
k
s
p
ac
e,
th
en
ca
b
les
d
o
n
o
t
cl
u
tter
t
h
e
p
ar
t
o
f
th
e
r
o
b
o
t
w
o
r
k
s
p
ac
e
lo
ca
ted
b
elo
w
t
h
e
p
latf
o
r
m
.
T
h
is
o
cc
u
r
r
en
ce
d
r
asti
ca
ll
y
r
ed
u
ce
s
th
e
p
o
s
s
ib
l
e
in
ter
f
er
en
ce
a
m
o
n
g
ca
b
les,
en
d
-
e
ec
to
r
,
an
d
en
v
ir
o
n
m
e
n
t,
b
u
t
t
h
e
p
o
s
itio
n
in
g
ca
p
ab
ilit
y
is
s
tr
ictl
y
r
elat
ed
to
th
e
g
r
av
it
y
a
n
d
th
en
to
th
e
s
o
lu
tio
n
o
f
th
e
s
tatic
p
r
o
b
lem
.
Mo
r
eo
v
er
,
ex
t
er
n
al
d
is
tu
r
b
an
ce
s
o
n
t
h
e
en
d
-
e
ec
to
r
d
eter
m
i
n
e
co
m
p
le
x
d
y
n
a
m
ic
s
in
v
o
lv
in
g
ca
b
le
v
ib
r
atio
n
s
.
Ma
in
p
r
o
b
lem
o
f
C
SP
R
is
r
el
ated
to
th
e
n
atu
r
e
o
f
t
h
e
r
o
b
o
t,
th
e
s
u
s
p
en
d
ed
en
d
-
e
ec
to
r
is
p
r
o
n
e
to
v
ib
r
atio
n
s
an
d
s
en
s
iti
v
e
to
e
x
ter
n
al
d
is
t
u
r
b
an
ce
s
.
T
h
ese
f
ac
to
r
s
,
to
g
eth
er
w
it
h
co
m
p
le
x
Ki
n
eto
s
ta
tics
a
n
d
D
y
n
a
m
ic
s
,
m
y
g
r
ea
tl
y
li
m
i
t th
eir
u
s
ab
ilit
y
.
W
o
r
k
s
o
n
s
tatic
s
a
n
d
d
y
n
a
m
ics
o
f
ca
b
le
-
s
u
s
p
en
d
ed
r
o
b
o
ts
ar
e
r
ep
o
r
ted
in
[
2
7
,
2
8
]
.
Vib
r
atio
n
oc
cu
r
r
en
ce
s
w
as
s
tu
d
ied
in
f
u
ll
y
-
co
n
s
tr
ai
n
ed
m
a
n
ip
u
lato
r
s
b
y
co
n
s
id
er
in
g
ca
b
les
as
l
in
ea
r
o
r
n
o
n
lin
ea
r
s
p
r
in
g
s
s
u
ch
a
s
in
[
2
9
,
3
0
]
o
r
C
SP
R
s
[
3
1
]
.
P
ick
an
d
p
lace
o
p
er
atio
n
is
q
u
ite
co
m
m
o
n
in
d
u
s
tr
ial
r
ep
eti
tiv
e
tas
k
i
n
v
o
l
v
i
n
g
a
m
o
tio
n
t
o
w
ar
d
s
an
o
b
j
ec
t
,
p
ick
in
g
a
n
d
m
o
v
i
n
g
to
an
o
th
er
p
lace
to
r
elea
s
e
it.
T
h
er
ef
o
r
e,
th
e
r
o
b
o
tic
ar
m
w
ill
m
o
v
e
w
i
th
a
v
ar
iab
le
m
as
s
(
w
i
th
a
n
d
w
it
h
o
u
t
an
o
b
j
ec
t)
d
u
r
in
g
t
h
e
o
p
er
atio
n
in
v
o
lv
i
n
g
i
m
p
o
r
tan
t
d
y
n
a
m
ic
e
ec
ts
.
T
h
ese
is
s
u
es a
r
e
m
u
c
h
m
o
r
e
r
elev
a
n
t
w
h
en
C
SP
R
s
ar
e
i
n
v
o
l
v
ed
.
T
h
is
p
ap
er
d
etails
i
s
s
u
es
o
f
a
4
DOF
s
p
atial
ca
b
le
-
s
u
s
p
en
d
ed
r
o
b
o
t
to
b
e
u
s
ed
f
o
r
p
ick
an
d
p
lace
o
p
er
atio
n
s
.
Sin
ce
t
h
is
tas
k
r
e
q
u
ir
es
t
h
at
t
h
e
r
o
b
o
t
p
a
y
lo
ad
ch
a
n
g
e
s
,
a
r
o
b
u
s
t
co
n
tr
o
l
m
u
s
t
b
e
d
ev
elo
p
ed
in
o
r
d
er
t
o
p
r
o
v
id
e
a
h
ig
h
p
er
f
o
r
m
an
ce
tr
aj
ec
to
r
y
tr
ac
k
i
n
g
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
ll
o
w
s
:
Sectio
n
2
d
etails
t
h
e
ca
b
le
-
s
u
s
p
e
n
d
ed
Kin
e
m
atic
s
a
n
d
D
y
n
a
m
ic
s
f
o
r
th
e
p
r
o
p
o
s
ed
s
p
atial
C
S
P
R
.
Sectio
n
3
i
n
tr
o
d
u
ce
s
t
h
e
tr
aj
ec
to
r
ies
i
m
p
l
e
m
e
n
ted
f
o
r
p
ick
an
d
p
lace
o
p
er
atio
n
s
.
Sectio
n
4
r
ep
o
r
ts
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
ch
e
m
e.
Sectio
n
5
p
r
esen
t
s
s
i
m
u
la
tio
n
r
esu
lt
s
,
a
n
d
fi
n
al
l
y
,
Sectio
n
6
s
u
m
m
ar
izes t
h
e
m
ai
n
co
n
cl
u
s
io
n
s
.
2.
M
O
DE
L
I
N
G
2
.
1
8
-
4
Ca
ble Sus
pend
e
d Ro
bo
t
Descript
io
n
As
it
w
as
s
h
o
w
n
in
t
h
e
d
e
s
ig
n
s
o
lu
t
io
n
p
r
o
p
o
s
ed
in
[
2
1
]
,
an
d
s
u
cc
es
s
f
u
ll
y
ap
p
lied
in
[
1
7
]
,
if
th
e
en
d
-
e
f
f
ec
to
r
is
s
u
s
p
en
d
ed
b
y
m
ea
n
s
o
f
p
air
s
o
f
p
a
r
allel
ca
b
les,
th
e
o
r
ien
tatio
n
o
f
th
e
en
d
-
e
ec
to
r
r
e
m
ain
s
u
n
c
h
an
g
ed
.
I
n
t
h
is
p
a
p
er
,
a
C
ab
le
Su
s
p
en
d
ed
P
ar
allel
R
o
b
o
t,
h
er
ea
f
ter
C
SP
R
,
i
s
co
n
s
id
er
ed
h
av
i
n
g
8
ca
b
les ar
r
an
g
ed
i
n
p
ar
allel
b
y
p
air
s
,
ea
ch
p
air
h
a
v
i
n
g
th
e
s
a
m
e
le
n
g
th
a
n
d
b
ein
g
co
m
m
a
n
d
ed
b
y
4
m
o
to
r
s
,
o
n
e
f
o
r
ea
ch
p
air
o
f
ca
b
les
[
3
2
]
.
I
n
p
ar
ticu
lar
,
ea
c
h
p
air
o
f
ca
b
l
es,
to
g
et
h
er
w
it
h
t
h
e
f
r
a
m
e
a
n
d
th
e
en
d
-
ef
f
ec
to
r
,
co
n
s
tit
u
tes a
p
ar
allelo
g
r
a
m
,
as
it is
s
h
o
w
n
i
n
th
e
s
ch
e
m
e
o
f
F
ig
u
r
e
1
.
A
cc
o
r
d
in
g
to
1
a
W
is
t
h
e
w
id
t
h
o
f
t
h
e
f
r
a
m
e
(
alo
n
g
X
a
x
is
)
,
L
it
s
le
n
g
th
(
alo
n
g
Y
ax
is
)
an
d
H
is
t
h
e
h
eig
h
t
(
alo
n
g
Z
a
x
is
)
,
th
e
s
a
m
e
h
o
ld
s
f
o
r
th
e
e
n
d
-
e
f
f
ec
t
o
r
,
b
ein
g
w
,
l
an
d
h
,
w
id
e,
len
g
th
a
n
d
h
eig
h
t,
r
esp
ec
tiv
el
y
.
T
iu
an
d
T
il
ar
e
th
e
ten
s
io
n
s
o
f
th
e
u
p
p
er
an
d
lo
w
er
c
ab
les
o
f
th
e
i
-
t
h
p
air
,
r
esp
ec
tiv
el
y
.
T
h
e
co
lo
r
ed
r
eg
io
n
s
s
h
o
w
ea
ch
p
ar
allelo
g
r
a
m
co
n
s
ti
tu
ted
b
y
t
wo
fi
x
ed
p
o
i
n
ts
p
lace
d
at
th
e
f
r
a
m
e
a
n
d
t
w
o
p
o
in
t
s
p
lace
d
at
th
e
e
n
d
-
ef
f
ec
to
r
,
as
it
is
s
h
o
w
n
i
n
Fi
g
u
r
e
1
.
T
h
e
ar
ch
itect
u
r
e
b
ased
o
n
th
e
g
eo
m
etr
y
o
f
p
ar
allelo
g
r
a
m
s
r
estra
i
n
s
t
h
e
o
r
ien
tatio
n
o
f
th
e
en
d
-
e
f
f
ec
to
r
,
leav
in
g
o
n
l
y
o
n
e
r
o
tatio
n
ab
o
u
t
Z
-
a
x
i
s
.
T
h
er
ef
o
r
e,
en
d
-
e
f
f
ec
to
r
p
o
s
e
is
g
iv
e
n
b
y
Q
=
[
x
,
y
,
z
,
δ
]
T
,
b
ein
g
t
h
e
o
r
ien
tatio
n
an
g
le
w
ith
r
esp
ec
t
to
Z
a
x
is
.
T
h
er
ef
o
r
e,
th
is
C
SP
R
co
n
f
i
g
u
r
atio
n
h
as
4
ac
tu
ato
r
s
to
p
r
o
v
id
e
4
DO
Fs
.
I
t
is
w
o
r
th
n
o
tin
g
th
a
t
th
is
h
o
ld
s
if
,
o
th
er
w
is
e
r
o
tatio
n
ab
o
u
t
Z
a
x
i
s
is
also
n
o
t a
llo
w
ed
,
as it i
s
r
ep
o
r
ted
in
[
2
1
]
.
T
h
e
f
r
a
m
e
an
d
t
h
e
e
n
d
-
ef
f
ec
t
o
r
ar
e
th
er
ef
o
r
e
co
n
n
ec
ted
b
y
m
ea
n
s
o
f
4
p
air
s
o
f
ca
b
les
g
o
in
g
f
r
o
m
fi
x
ed
p
o
in
ts
at
th
e
f
r
a
m
e,
Q
i
f
=
[
x
i
f
,
y
i
f
,
z
i
f
]
T
,
t
o
ea
ch
r
esp
ec
tiv
e
en
d
-
e
ff
ec
to
r
an
ch
o
r
p
o
in
t
s
,
Q
i
e
=
[
x
i
e
,
y
i
e
,
z
i
e
]
T
,
as
s
h
o
w
n
F
ig
u
r
e
1
b
ein
g
Q
fi
fi
x
ed
p
o
in
ts
,
w
h
ile
Q
ei
d
ep
en
d
b
y
th
e
e
n
d
-
e
f
f
ec
to
r
p
o
s
e,
Q
.
T
ab
le
1
s
u
m
m
ar
ize
s
x
i
f
,
y
i
f
an
d
z
i
f
co
o
r
d
in
ates o
f
all
f
r
a
m
e
n
o
d
e
co
n
n
ec
tio
n
s
.
Fin
all
y
,
th
e
d
ir
ec
tio
n
o
f
th
e
i
-
t
h
ca
b
le
ca
n
b
e
r
e
p
r
esen
ted
b
y
m
ea
n
s
o
f
an
g
les
θ
i
,
w
i
th
r
eg
ar
d
s
to
Y
-
a
x
is
,
an
d
ϕ
i
,
w
it
h
r
e
s
p
ec
t
to
Z
-
a
x
i
s
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
1
b
.
T
h
e
ac
tiv
e
a
n
g
le
o
f
t
h
e
s
et
g
ea
r
b
o
x
-
m
o
to
r
i
i
s
g
iv
e
n
b
y
α
i
as s
h
o
w
n
in
F
ig
u
r
e
1
c,
ac
co
r
d
in
g
to
th
e
d
esi
g
n
p
r
o
p
o
s
ed
in
[
3
2
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
J
R
A
,
Vo
l.
6
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
2
8
6
–
3
0
2
288
Fig
u
r
e
1
.
Sch
e
m
e
o
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le
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s
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K
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T
h
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Fo
r
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atic
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,
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[
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.
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atics,
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elate
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t
h
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ti
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t
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g
le
s
,
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t Q
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i c
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p
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t
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th
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at
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o
m
e
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itio
n
α
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=
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r
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ce
n
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o
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d
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o
r
ien
ta
tio
n
,
Q
0
=
[x
0
,
y
0
,
z
0
,
δ
0
]
T
=
[
W
/2
,
L/
2,
H
/
2,
0]
T
,
th
e
in
itial le
n
g
t
h
o
f
all
ca
b
les,
L
0
,
ca
n
b
e
o
b
tain
ed
as
(
3
)
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
A
I
SS
N:
2089
-
4856
On
th
e
Desig
n
o
f a
4
Deg
r
ee
s
-
of
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F
r
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ick
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P
a
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llel…
(
C
a
s
till
o
-
Ga
r
cia
)
289
Den
o
tin
g
L
i
=
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iu
= L
id
a
n
d
g
i
v
en
a
n
en
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les len
g
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y
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t
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k
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to
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/
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m
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il
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h
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ess
ed
a
s
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=
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r
,
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h
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e
r
i
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t
h
e
last
p
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lle
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r
u
m
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ad
iu
s
.
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n
t
h
i
s
w
a
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,
ac
t
u
ato
r
s
ets an
g
le
s
ca
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b
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o
b
tain
ed
as
(
5
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(
5
)
w
h
er
e
.
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o
m
b
in
i
n
g
(
3
)
,
(
4
)
an
d
(
5
)
,
th
e
I
n
v
er
s
e
Ki
n
e
m
atic
s
,
ᴧ
I
ca
n
b
e
ex
p
r
ess
ed
as
(
6
)
(
6
)
f
o
r
i =
1
,
2
,
3
,
4.
T
h
e
co
n
tr
o
l
s
tr
ateg
y
f
o
r
en
d
-
e
f
f
ec
to
r
tr
aj
ec
to
r
y
tr
ac
k
in
g
,
p
r
o
p
o
s
ed
in
Sectio
n
3
,
r
eq
u
ir
es
th
e
u
s
e
o
f
th
e
in
v
er
s
e
k
i
n
e
m
a
tics
,
ᴧ
I
,
b
u
t
d
o
es n
o
t th
e
u
s
e
o
f
th
e
f
o
r
w
ar
d
o
n
e
ᴧ
F
.
2
.
3
E
nd
-
ef
f
e
ct
o
r
dy
na
m
ic
mo
del
Th
e
s
tatic
eq
u
ilib
r
iu
m
o
f
t
h
e
e
n
d
-
e
ff
ec
to
r
ca
n
b
e
ex
p
r
ess
ed
as
(
7
)
(
7
)
W
h
er
e
(
8
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(
8
)
B
ein
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m
t
h
e
en
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f
ec
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r
m
as
s
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m
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is
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x
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th
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tesi
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f
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ay
ap
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les ten
s
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r
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9
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9
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n
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,
T
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ay
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T
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,
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3
,
T
4
]
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g
T
i
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+
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=
1
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2
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4
,
an
d
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s
is
th
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ac
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ield
s
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(
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0
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B
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g
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1
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(
1
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
J
R
A
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Vo
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6
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4
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290
w
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d
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2
.
4
M
o
t
o
r
D
y
na
m
ics M
o
del
A
cc
o
r
d
in
g
to
t
h
e
s
c
h
e
m
e
in
Fig
u
r
e
1
c
th
e
d
y
n
a
m
ic
s
o
f
th
e
s
e
ts
m
o
to
r
/g
ea
r
b
o
x
/d
r
u
m
ca
n
b
e
d
escr
ib
ed
b
y
(
1
2
)
(
1
2
)
w
h
er
e
J
is
th
e
r
o
tatio
n
al
i
n
er
ti
a
m
atr
ix
(
1
3
)
(
1
3
)
ν
is
th
e
v
is
co
u
s
f
r
ictio
n
co
e
f
f
i
cien
ts
m
atr
i
x
(
1
4
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(
1
4
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r
th
e
d
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u
m
/p
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l
le
y
s
r
ad
iu
s
a
n
d
is
th
e
m
o
to
r
s
to
r
q
u
e
ar
r
ay
(
i
n
p
u
t si
g
n
al)
.
2
.
5
Sy
s
t
e
m
dy
na
m
ic
s
R
ea
r
r
an
g
in
g
(
1
2
)
,
ca
b
les ten
s
i
o
n
s
ca
n
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e
ex
p
r
es
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ed
as
(
1
5
)
(
1
5
)
th
at
ca
n
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e
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u
b
s
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ted
i
n
(
9
)
a
n
d
in
tr
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d
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ce
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in
(
7
)
y
ield
i
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g
(
1
6
)
(
1
6
)
S
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te
m
d
y
n
a
m
ic
s
b
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av
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r
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b
y
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1
6
)
th
at
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b
e
ex
p
r
ess
ed
in
C
r
atesia
n
co
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r
d
in
at
es,
Q,
as
(
1
7
)
(
1
7
)
o
r
in
j
o
in
t c
o
o
r
d
in
ates
,
α,
as
(
1
8
)
(
1
8
)
No
te
th
at
(
1
5
)
is
o
n
ly
v
alid
if
all
ca
b
les
ten
s
io
n
s
r
e
m
ai
n
p
o
s
itiv
e
an
d
th
er
e
f
o
r
e,
th
e
v
alid
it
y
o
f
m
o
d
el
s
(
1
6
)
,
(
1
7
)
o
r
(
1
8
)
,
d
ep
en
d
s
o
n
t
h
is
as
s
u
m
p
tio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
A
I
SS
N:
2089
-
4856
On
th
e
Desig
n
o
f a
4
Deg
r
ee
s
-
of
-
F
r
ee
d
o
m
P
ick
a
n
d
P
la
ce
C
a
b
le
S
u
s
p
e
n
d
ed
P
a
r
a
llel…
(
C
a
s
till
o
-
Ga
r
cia
)
291
3.
CO
NT
RO
L
ST
R
AT
E
G
Y
3
.
1
Co
ntr
o
l
o
bje
ct
iv
es
T
h
e
co
n
tr
o
l
o
b
j
ec
tiv
es
f
o
r
th
e
p
r
o
p
o
s
ed
8
-
4
C
SR
o
n
p
ick
an
d
p
lace
o
p
er
atio
n
s
ar
e:
E
n
d
-
ef
f
ec
to
r
ac
cu
r
ate
tr
aj
ec
to
r
y
tr
ac
k
i
n
g
,
i.
e.
.
R
o
b
u
s
t
n
e
s
s
t
o
p
a
y
lo
ad
ch
an
g
e
s
o
w
i
n
g
to
t
h
e
n
ee
d
ed
o
p
er
atio
n
w
it
h
a
n
d
w
it
h
o
u
t
p
a
y
lo
ad
,
i.e
.
.
,
w
h
er
e
m
e
is
th
e
e
n
d
-
e
f
f
ec
to
r
m
a
s
s
an
d
is
th
e
ad
d
o
f
th
e
en
d
-
e
f
f
ec
to
r
m
as
s
an
d
th
e
o
n
e
o
f
th
e
w
ei
g
h
ter
o
b
j
ec
t to
b
e
m
an
ip
u
lated
.
3
.
2
Co
ntr
o
l sche
m
e
T
h
e
m
o
s
t
o
f
th
e
w
o
r
k
s
w
h
ic
h
d
ea
ls
w
it
h
t
h
e
co
n
tr
o
l
o
f
ca
b
le
-
d
r
iv
e
n
r
o
b
o
t
p
r
o
b
lem
u
s
e
(
1
7
)
,
o
r
s
lig
h
t
m
o
d
i
f
i
ca
t
io
n
s
,
a
s
a
d
y
n
a
m
ic
m
o
d
el
o
f
th
e
m
a
n
ip
u
lato
r
,
w
h
er
e
is
t
h
e
i
n
p
u
t
to
r
q
u
e
ar
r
ay
an
d
Q
t
h
e
en
d
-
e
ff
ec
to
r
p
o
s
e,
i.e
.
,
th
e
o
u
tp
u
t o
f
th
e
m
o
d
el
(
s
ee
e.
g
.
[
3
3
]
)
.
On
t
h
e
o
th
er
h
a
n
d
,
s
en
s
o
r
s
w
h
ich
p
r
o
v
id
e
a
r
ea
l
ti
m
e
m
ea
s
u
r
e
m
en
t
o
f
t
h
e
e
n
d
-
e
f
f
ec
to
r
p
o
s
e,
in
o
r
d
er
to
f
ee
d
b
ac
k
i
t
i
n
t
h
e
co
n
tr
o
l
s
ch
e
m
e,
ar
e
ex
p
e
n
s
i
v
e
a
n
d
th
er
ef
o
r
e
t
h
e
m
o
s
t
ex
ten
d
ed
an
d
u
s
ed
s
o
l
u
tio
n
co
n
s
is
ts
o
f
m
ea
s
u
r
i
n
g
t
h
e
m
o
t
o
r
s
an
g
u
lar
co
n
f
i
g
u
r
ati
o
n
,
α
,
an
d
to
e
s
ti
m
a
te
th
e
e
n
d
-
e
f
f
ec
to
r
p
o
s
e,
Q
,
b
y
m
ea
n
s
o
f
th
e
f
o
r
w
ar
d
k
in
e
m
atic
s
tr
an
s
f
o
r
m
a
tio
n
,
Q
=
ᴧ
F
(
α
)
.
I
n
th
is
w
a
y
,
i
n
p
u
t
s
i
g
n
al
to
th
e
co
n
tr
o
ller
is
th
e
tr
ac
k
in
g
er
r
o
r
,
E
=
Q
*
-
Q
,
s
in
ce
it
s
o
u
tp
u
t is t
h
e
m
o
to
r
s
i
n
p
u
t to
r
q
u
e
s
,
.
I
t
is
u
s
u
al
to
n
d
m
ec
h
a
n
ical
s
o
lu
tio
n
s
w
h
ich
s
y
n
th
e
s
is
ar
e
d
esig
n
ed
to
m
ak
e
th
e
s
y
s
te
m
q
u
asil
in
ea
r
,
i.e
,
lin
ea
r
r
elat
io
n
b
et
w
ee
n
ac
t
u
atio
n
an
d
tip
p
o
s
itio
n
[
3
4
]
.
T
h
is
s
o
l
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tio
n
is
n
o
t
f
ea
s
ib
le
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n
c
ab
le
r
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o
ts
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d
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n
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er
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o
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tain
an
ac
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r
at
e
en
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-
e
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to
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aj
ec
to
r
y
tr
ac
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g
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o
m
e
au
th
o
r
s
li
n
ea
r
ize
th
e
d
y
n
a
m
ics
eq
u
atio
n
(
1
7
)
f
ee
d
f
o
r
w
a
r
d
in
g
th
e
n
o
n
li
n
ea
r
ter
m
N(
Q
,
Q
)
[
3
5
]
o
r
ass
u
m
i
n
g
i
t n
e
g
li
g
ib
le
[
3
3
]
.
I
n
th
is
p
ap
er
,
w
e
p
r
o
p
o
s
e
a
ca
s
ca
d
e
P
D
co
n
tr
o
ller
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it
h
a
f
ee
d
f
o
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d
ter
m
.
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t
ten
d
i
n
g
to
(
1
6
)
,
a
n
e
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i
n
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u
t si
g
n
al
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n
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e
d
esig
n
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9
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(
1
9
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b
ein
g
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er
e
A
G
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[
0
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0
,
-
g
;
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T
.
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n
t
h
is
w
a
y
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d
y
n
a
m
i
cs
eq
u
atio
n
(
1
6
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ca
n
be
th
er
ef
o
r
e
r
e
w
r
itte
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(
2
0
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(
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o
r
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…
,
4
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a
d
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o
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p
led
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o
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o
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et,
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n
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u
t
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ig
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al
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w
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ic
h
co
m
m
a
n
d
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e
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t
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ato
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i
.
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p
p
l
y
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n
g
L
ap
lace
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s
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o
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m
to
(
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e
tr
an
s
f
er
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u
n
ctio
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h
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elate
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e
in
p
u
t t
o
r
q
u
e
to
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e
m
o
to
r
,
y
ield
s
(
2
1
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(
2
1
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W
h
er
e
(
2
2
)
(
2
2
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w
h
er
e
an
d
.
No
te
th
at
th
e
n
e
w
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p
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t
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ig
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al
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u
s
ed
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ec
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le
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o
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el,
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ee
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s
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n
d
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s
it
w
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s
p
r
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o
r
is
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ailab
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o
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tai
n
a
d
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t
m
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s
u
r
e
o
f
th
e
e
n
d
-
ef
f
ec
to
r
p
o
s
e.
T
h
en
,
w
e
fi
n
d
t
w
o
p
o
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s
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ili
ties
to
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o
m
p
u
te
:
a)
esti
m
ate
it
b
y
m
ea
n
s
o
f
α
,
t
h
at
is
d
ir
ec
tl
y
m
ea
s
u
r
ed
b
y
m
ea
n
s
o
f
th
e
m
o
to
r
s
e
n
co
d
er
s
,
an
d
t
h
e
f
o
r
w
ar
d
k
i
n
e
m
atics,
ᴧ
F
(
α
)
,
o
r
b
)
u
s
e
d
ir
ec
tl
y
Q
*
in
s
tead
o
f
Q
.
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e
h
av
e
c
h
o
s
e
n
o
p
tio
n
b
)
o
w
in
g
to
t
h
e
d
i
f
f
i
cu
lt
y
o
f
a
r
ea
l
ti
m
e
co
m
p
u
ti
n
g
o
f
t
h
e
f
o
r
w
ar
d
k
i
n
e
m
atic
s
,
ᴧ
F
(
α
)
.
Fi
g
u
r
e
2
r
ep
r
esen
ts
t
h
e
b
lo
ck
d
iag
r
a
m
o
f
th
e
p
r
o
p
o
s
ed
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n
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l
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ateg
y
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o
r
o
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tain
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n
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n
eq
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i
v
ale
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ea
r
-
d
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p
led
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el.
Usi
n
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li
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r
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d
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p
led
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el
s
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i
n
Fig
u
r
e
2
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a
co
n
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e
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tio
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n
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o
ller
ca
n
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e
d
esig
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o
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te
t
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a
n
s
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2
2
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is
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a
DC
-
m
o
to
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e
(
s
ee
e.
g
.
[
3
6
]
)
an
d
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tr
ateg
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f
o
r
DC
-
m
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to
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o
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
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u
r
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u
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3
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3
.
3
Co
ntr
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ller
t
uning
I
n
Fig
u
r
e
3
K
p
an
d
K
d
ar
e
d
iag
o
n
al
4
x
4
m
atr
i
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w
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ch
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al
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e
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ts
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pi
a
n
d
K
di
,
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e
r
esp
ec
tiv
el
y
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e
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ig
n
ed
f
o
r
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n
t
r
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llin
g
G
i
(
s
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.
T
h
e
clo
s
ed
lo
o
p
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an
s
f
er
f
u
n
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tio
n
o
f
a
x
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i
ca
n
b
e
w
r
itte
n
as
(
2
3
)
(
2
3
)
an
d
th
er
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o
r
e,
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e
eq
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iv
a
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t o
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o
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s
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er
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u
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y
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d
s
(
2
4
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2
4
)
No
te
th
at
ap
p
l
y
i
n
g
th
e
F
in
a
l
V
a
lu
e
Th
eo
r
em
(
s
ee
e.
g
.
[
3
7
]
)
,
th
e
s
tead
y
s
tate
er
r
o
r
o
f
th
e
clo
s
ed
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o
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s
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er
f
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n
t
h
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h
e
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co
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e
s
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m
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r
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c
o
n
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(
s
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g
.
[
3
7
]
)
.
T
h
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co
m
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t
u
n
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n
g
eq
u
at
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n
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f
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lls
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en
c
y
r
eq
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ir
e
m
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ts
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an
d
ϕ
m
is
(
2
5
)
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On
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Desig
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(
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2
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2
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T
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s
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o
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all
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o
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(
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3
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So
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e
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k
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e
d
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e
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tag
e
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s
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o
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r
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o
l
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ch
e
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e
(
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ee
e.
g
.
[
3
6
]
)
.
4.
T
RAJ
E
C
T
O
RI
E
S
F
O
R
P
I
C
K
AND
P
L
AC
E
O
P
E
RA
T
I
O
N
T
h
is
Sectio
n
d
escr
ib
es
th
e
d
esig
n
ed
tr
aj
ec
to
r
ies
f
o
r
p
ick
an
d
p
lace
o
p
er
atio
n
w
ith
t
h
e
p
r
o
p
o
s
ed
8
-
4
C
S
R
.
Den
o
ti
n
g
t
h
e
r
e
f
er
en
ce
tr
aj
ec
to
r
y
as
Q
*
,
Fi
g
u
r
e
4
r
ep
r
esen
ts
a
s
c
h
e
m
e
o
f
a
s
p
atia
l
tr
aj
ec
to
r
y
f
o
r
p
ick
an
d
p
lace
o
p
er
atio
n
f
r
o
m
Q
*
a
=
[x
*
a
,
y
*
a
,
z
*
a
,
δ
*
a
]
T
to
Q
*
b
=
[
x
*
b
,
y
*
b
,
z
*
b
,
δ
*
b
]
T
.
Fi
g
u
r
e
4
r
ep
r
esen
ts
t
h
e
p
r
o
p
o
s
ed
tr
a
j
ec
to
r
y
th
at
is
u
s
u
all
y
ap
p
lied
to
p
ick
an
d
p
l
ac
e
o
p
er
atio
n
(
e.
g
.
s
ee
[
3
8
]
)
.
T
h
is
tr
aj
e
cto
r
y
is
ch
ar
ac
ter
ized
b
y
p
r
o
v
id
in
g
a
v
er
tical
o
r
ien
ta
tio
n
f
o
r
b
o
th
,
p
ick
i
n
g
a
n
d
p
lacin
g
an
d
it
m
u
s
t
b
e
a
C
2
co
n
tin
u
o
u
s
l
y
d
i
f
f
er
en
tiab
le
f
u
n
ctio
n
.
I
n
Fig
u
r
e
4
,
p
lan
e
*
i
s
th
e
o
n
e
th
at
co
n
tai
n
s
p
o
i
n
ts
a
an
d
b
an
d
Z
ax
i
s
.
P
o
in
ts
1
to
4
ca
n
b
e
ea
s
il
y
o
b
tain
ed
b
y
p
o
i
n
t
s
a
a
n
d
b
a
n
d
h
i
an
d
b
i
p
ar
a
m
eter
s
.
L
et
's
d
ef
i
n
e
t
h
e
p
at
h
v
ar
iab
le
s
a
lo
n
g
p
lan
e
*
.
R
e
g
ar
d
in
g
to
th
is
p
ath
v
ar
iab
le,
tr
aj
ec
to
r
y
s
h
o
w
n
i
n
Fi
g
u
r
e
4
ca
n
b
e
ex
p
r
ess
ed
as
(
2
7
)
(
2
7
)
w
h
er
e
an
d
co
e
f
f
i
cie
n
ts
ca
n
b
e
attain
ed
g
i
v
i
n
g
t
h
e
f
o
llo
w
in
g
co
n
s
tr
ain
ts
(
2
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
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I
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4
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Dec
em
b
er
2
0
1
7
:
2
8
6
–
3
0
2
294
Fig
u
r
e
4
.
8
-
4
C
SR
T
r
aj
ec
to
r
ies d
escr
ip
tio
n
f
o
r
p
ick
an
d
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lac
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o
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er
atio
n
s
(
2
8
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On
ce
th
a
t tr
aj
ec
to
r
y
is
d
ef
i
n
ed
in
p
lan
e
*
,
i
n
XY
Z
it
y
ield
s
(
2
9
)
(
29)
w
h
er
e
.
No
te
th
at
a
lin
ea
r
p
r
o
le
h
as
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ee
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ad
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ed
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o
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ex
p
r
ess
in
g
δ
*
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s
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.
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n
o
r
d
er
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en
s
u
r
e
th
at
x
*
(
t
)
,
y*
(
t
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t
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a
n
d
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t)
ar
e
C
2
co
n
t
in
u
o
u
s
l
y
d
i
f
f
er
en
tiab
le
f
u
n
ctio
n
s
,
p
ath
v
ar
iab
le
s
h
as
b
ee
n
p
ar
am
eter
ized
b
y
a
3
th
o
r
d
e
r
B
ezier
f
u
n
ctio
n
.
I
n
o
r
d
er
to
av
o
id
a
p
o
s
s
ib
le
lo
s
s
o
f
c
ab
les
ten
s
io
n
,
t
h
e
m
ax
i
m
u
m
Z
a
x
is
d
ec
eler
atio
n
h
a
s
b
ee
n
li
m
ited
to
b
y
i
n
cr
ea
s
in
g
th
e
tr
aj
ec
to
r
y
ti
m
e.
F
ig
u
r
e
5
s
h
o
w
s
a
n
t
h
e
illu
s
tr
ati
v
e
ex
a
m
p
le
o
f
a
t
r
aj
ec
to
r
y
f
r
o
m
Q
a
=
[
0
.
2m
,
0
.
23m
,
0
.
3m
,
-
7
o
]
to
Q
b
=
[
0
.
7m
,
0
.
72m
,
0
.
4
2
m
,
10
o
]
w
i
th
h
0
= h
1
= b
0
= b
1
= b
2
=
0
.
1
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
A
I
SS
N:
2089
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4856
On
th
e
Desig
n
o
f a
4
Deg
r
ee
s
-
of
-
F
r
ee
d
o
m
P
ick
a
n
d
P
la
ce
C
a
b
le
S
u
s
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e
n
d
ed
P
a
r
a
llel…
(
C
a
s
till
o
-
Ga
r
cia
)
295
Fig
u
r
e
5
.
E
x
a
m
p
le
o
f
p
ic
k
an
d
p
lace
tr
aj
e
cto
r
y
: Sp
atial
p
at
h
,
x
*
(
t)
,
y
*
(
t)
,
z
*
(
t
)
an
d
δ
*
(
t)
5.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
5
.
1
M
o
del pa
ra
m
et
er
s
a
nd
d
y
na
m
ic
s
v
a
lid
a
t
io
n
T
h
e
8
-
4
C
S
P
R
m
o
d
el
p
ar
a
m
ete
r
s
u
s
ed
f
o
r
s
i
m
u
latio
n
s
ar
e
s
u
m
m
ar
ized
in
T
ab
le
2
.
T
ab
le
2
.
P
ar
am
eter
s
o
f
t
h
e
P
r
o
p
o
s
ed
8
-
4
C
SR
Mo
d
el
Usi
n
g
i
n
Si
m
u
latio
n
s
F
r
a
me
W
(
m
)
L
(
m
)
H
(
m
)
1
.
2
1
.
2
1
.
2
En
d
-
e
ff
e
c
t
o
r
w
(m)
l
(m)
W
(
m
)
m
e
(
K
g
)
0
.
1
0
.
2
0
.
2
1
M
o
t
o
r
/
g
e
r
a
b
o
x
/
d
r
u
m se
t
J
i
(
K
g
/
m
2
)
v
i
(
N
m
s)
r(
m
)
2
.
6
1
0
-
4
2
.
1
1
0
-
2
0
.
0
7
5
A
d
y
n
a
m
ic
m
o
d
el
h
as
b
ee
n
s
i
m
u
lated
u
s
i
n
g
Ma
t
lab
/Si
m
u
li
n
k
.
I
n
o
r
d
er
to
v
alid
ate
it
f
o
r
th
e
8
-
4
C
SP
R
an
an
alo
g
o
u
s
m
o
d
el
o
f
t
h
e
r
o
b
o
t
h
as
b
ee
n
b
u
ilt
u
s
i
n
g
th
e
m
u
lt
ib
o
d
y
d
y
n
a
m
ics
s
i
m
u
latio
n
s
o
f
t
w
ar
e
MS
C
-
A
DA
Ms
.
Mu
ltip
le
s
ce
n
ar
io
s
h
av
e
b
ee
n
s
i
m
u
lated
in
o
r
d
er
to
ch
ec
k
t
h
e
v
alid
it
y
o
f
t
h
e
Ma
tla
b
/S
imu
lin
k
m
o
d
el.
Fig
u
r
e
6
co
m
p
ar
es
t
h
e
r
esu
lt
s
th
at
Ma
tlab
/Si
m
u
li
n
k
an
d
MS
C
-
A
DA
Ms
m
o
d
el
s
p
r
o
v
id
e
f
o
r
a
in
itial
p
o
s
e
o
f
th
e
en
d
-
e
f
f
ec
to
r
,
Q
0
=
[
0
.
6m
,
0
.
6m
,
0
.
2m
,
0
o
]
,
an
d
th
e
f
o
llo
w
i
n
g
s
tep
to
r
q
u
es
ap
p
lied
o
n
ea
ch
ac
tu
ato
r
,
an
d
,
b
ein
g
N
m
a
n
d
.
No
te
th
at
th
e
er
r
o
r
b
et
w
ee
n
Ma
tla
b
/S
imu
lin
k
an
d
MS
C
-
A
DA
Ms
m
o
d
el
f
o
r
th
e
s
i
m
u
lati
o
n
s
h
o
w
n
in
F
ig
u
r
e
6
is
less
t
h
a
n
2
.
10
-
4
.
T
h
e
s
am
p
le
ti
m
e
f
o
r
th
e
s
i
m
u
latio
n
s
h
as b
ee
n
s
e
t e
q
u
al
to
T
s
=
0
.
0
0
1
s
.
5
.
2
P
ick
a
nd
pla
ce
s
ce
na
rio
I
n
o
r
d
er
to
ch
ec
k
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
y
f
o
r
o
u
r
8
-
4
C
S
P
R
,
a
r
ea
lis
tic
s
ce
n
ar
io
h
as
b
ee
n
s
i
m
u
lated
.
I
t
co
n
s
i
s
ts
o
n
t
h
e
r
o
b
o
t
in
itiall
y
p
lace
d
o
n
th
e
ce
n
tr
o
id
o
f
th
e
f
r
a
m
e
w
i
t
h
ze
r
o
o
r
ien
tatio
n
,
.
I
t
s
eq
u
e
n
ti
al
l
y
p
ick
-
u
p
o
b
j
ec
ts
1
to
5
f
r
o
m
t
h
eir
i
n
itial
p
o
s
es,
Q
1a
...
Q
5a
,
t
o
th
eir
fi
n
al
o
n
e
s
,
Q
1b
...
Q
5b
an
d
co
m
e
b
ac
k
to
in
itial
p
o
s
e
as
it is
in
d
icate
d
i
n
Fi
g
u
r
e
7.
T
ab
le
3
s
u
m
m
ar
izes
th
e
i
n
it
ia
l
an
d
fi
n
al
p
o
s
es
o
f
t
h
e
fi
v
e
o
b
j
ec
ts
an
d
th
eir
m
a
s
s
.
No
te
t
h
at
d
u
r
in
g
th
e
r
o
b
o
t
m
a
n
o
eu
v
r
es
t
h
e
m
an
ip
u
lato
r
m
as
s
i
s
t
h
e
s
u
m
o
f
e
n
d
-
e
ff
ec
to
r
m
a
s
s
,
m
e,
a
n
d
ea
ch
o
b
j
ec
t
m
as
s
,
m
1
,
...,
m
5
d
u
r
in
g
th
e
ir
s
r
esp
ec
t
iv
e
tr
aj
ec
to
r
ies
.
5
.
3
T
ra
j
ec
t
o
ries
Ass
u
m
in
g
t
h
at
th
e
i
n
it
ial
an
d
fi
n
al
p
o
s
es
o
f
t
h
e
e
n
d
-
e
f
f
e
cto
r
ar
e
Q
0
=
[
W
/
2
,
L
/
2
,
H
/
2
,
0]
T
,
th
e
d
escr
ib
ed
s
ce
n
ar
io
d
em
a
n
d
s
1
1
tr
a
j
ec
to
r
ies
(
f
i
r
s
t
o
n
e:
f
r
o
m
0
to
1
a,
s
ec
o
n
d
o
n
e:
f
r
o
m
1
a
to
1
b
,
th
ir
d
o
n
e:
f
r
o
m
1
b
to
2
a,
.
.
.
,
ten
th
o
n
e
:
f
r
o
m
5
a
to
5
b
,
an
d
th
e
last
o
n
e:
f
r
o
m
5
b
to
h
o
m
e)
.
T
h
e
tr
ajec
to
r
ies
d
etailed
in
Sectio
n
4
h
av
e
b
ee
n
u
s
ed
to
o
b
tain
th
e
d
esire
d
en
d
-
e
f
f
ec
to
r
p
o
s
e
r
ef
er
en
ce
,
Q
*
(
t)
.
Fig
u
r
e
8
r
ep
r
esen
ts
t
h
e
C
ar
tesi
a
n
co
m
p
o
n
e
n
ts
o
f
th
e
r
eq
u
ir
ed
tr
aj
ec
to
r
y
s
h
o
w
n
in
F
ig
u
r
e
7
,
an
d
it
s
Z
a
x
i
s
ac
ce
ler
atio
n
.
No
te
th
at
it
s
n
eg
at
iv
e
v
al
u
e
h
as
b
ee
n
li
m
it
ed
to
8
0
%
o
f
th
e
g
r
a
v
it
y
ac
c
eler
atio
n
(
a
Z
>
0
.
8
g
)
,
in
o
r
d
er
to
en
s
u
r
e
p
o
s
itiv
e
ten
s
io
n
in
al
l c
ab
les.
T
h
is
fi
g
u
r
e
also
s
h
o
w
s
t
h
e
p
a
y
lo
ad
v
ar
i
atio
n
d
u
r
in
g
t
h
e
r
o
b
o
t o
p
e
r
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.