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g
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o
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m
a
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ip
u
lato
rs
is
u
n
d
e
n
iab
le.
Ho
we
v
e
r,
fa
u
lt
s
in
t
h
e
se
sy
ste
m
s
c
a
n
sig
n
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ica
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tl
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imp
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sp
a
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n
v
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n
m
e
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t
a
n
d
p
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rso
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a
l
sa
fe
ty
.
To
a
d
d
re
ss
th
e
se
c
h
a
ll
e
n
g
e
s,
a
n
e
w
a
d
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p
ti
v
e
a
p
p
ro
a
c
h
h
a
s
b
e
e
n
p
ro
p
o
se
d
t
h
a
t
e
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sily
a
d
a
p
ts
to
a
fa
u
lt
y
a
c
tu
a
to
r
wh
il
e
p
re
c
ise
ly
trac
k
in
g
it
s
d
e
sire
d
p
o
si
ti
o
n
.
T
h
e
v
ir
tu
a
l
d
e
c
o
m
p
o
siti
o
n
c
o
n
tr
o
l
(VD
C)
m
e
th
o
d
d
e
c
o
m
p
o
se
s
th
e
ro
b
o
t
in
t
o
su
b
s
y
ste
m
s,
e
a
c
h
with
it
s
su
b
-
c
o
n
tr
o
ll
e
r,
wh
il
e
e
n
s
u
rin
g
th
e
o
v
e
ra
ll
sy
ste
m
re
m
a
in
s
sta
b
le.
M
e
a
n
wh
il
e
,
ti
m
e
d
e
la
y
e
stim
a
ti
o
n
(TDE
)
is
u
se
d
to
e
sti
m
a
te
u
n
k
n
o
w
n
a
n
d
u
n
c
e
rtain
p
a
r
a
m
e
ters
.
A
co
-
sim
u
latio
n
wa
s c
o
n
d
u
c
ted
t
o
t
e
st t
h
e
TD
-
VD
C
m
e
th
o
d
o
n
a
6
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F
s ro
b
o
t,
wh
ich
b
e
c
o
m
e
s
u
n
d
e
ra
c
tu
a
ted
d
u
rin
g
i
ts
r
u
n
n
in
g
.
Th
e
re
su
lt
s
o
f
th
e
ro
o
t
m
a
in
sq
u
a
re
e
rro
r
o
f
th
e
p
r
o
p
o
se
d
c
o
n
tr
o
ll
e
r
we
re
lo
we
r
o
f
6
%
t
h
a
n
th
o
se
o
f
slid
in
g
m
o
d
e
c
o
n
tro
l
b
a
se
d
o
n
p
a
rti
a
l
fe
e
d
b
a
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in
e
a
riza
ti
o
n
c
o
n
tro
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(S
M
C
-
P
F
LC)
,
wh
ic
h
p
r
o
v
e
s t
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p
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o
sa
l'
s e
ffe
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ti
v
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e
ss
a
n
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fficie
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K
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s
:
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s
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latio
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No
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lin
ea
r
co
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tr
o
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T
im
e
d
elay
esti
m
atio
n
Un
d
er
ac
tu
ated
r
o
b
o
t
m
an
ip
u
lato
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Vir
tu
al
d
ec
o
m
p
o
s
itio
n
co
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tr
o
l
T
h
is i
s
a
n
o
p
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n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
I
m
an
e
C
h
eik
h
L
I
MA
S lab
o
r
ato
r
y
,
Facu
lty
o
f
Scien
ce
s
,
Sid
i M
o
h
am
m
ed
B
en
Ab
d
ellah
Un
i
v
er
s
ity
Fes
,
Mo
r
o
cc
o
E
m
ail: im
an
e.
ch
eik
h
@
u
s
m
b
a.
ac
.
m
a
1.
I
NT
RO
D
UCT
I
O
N
I
n
m
an
y
r
ec
en
t
ap
p
licatio
n
s
,
m
an
ip
u
lato
r
r
o
b
o
ts
h
av
e
b
e
co
m
e
a
k
ey
p
r
o
d
u
ctio
n
to
o
l
in
m
o
d
er
n
in
d
u
s
tr
y
[
1
]
,
[
2
]
.
Ho
wev
e
r
,
th
e
lik
elih
o
o
d
o
f
u
n
in
ten
tio
n
al
ac
tu
ato
r
f
ailu
r
es
r
em
ai
n
s
p
r
esen
t
at
an
y
s
tag
e
o
f
th
e
r
o
b
o
t’
s
life
cy
cle,
c
o
n
tin
u
o
u
s
ly
ex
p
o
s
in
g
th
e
c
o
n
tr
o
ller
t
o
th
e
r
is
k
o
f
lo
s
in
g
its
s
tab
ilit
y
an
d
ef
f
ec
tiv
en
ess
.
T
h
er
ef
o
r
e,
co
n
t
r
o
llin
g
u
n
d
e
r
ac
tu
ated
r
o
b
o
t
m
an
ip
u
lato
r
s
f
o
r
tr
ac
k
i
n
g
tr
ajec
to
r
ies
ef
f
e
ctiv
ely
h
as
g
ain
ed
s
ig
n
if
ican
t
atten
tio
n
an
d
b
ec
o
m
e
m
o
r
e
c
h
allen
g
in
g
[
3
]
.
I
n
s
u
ch
ca
s
es,
we
ar
e
d
ea
lin
g
with
u
n
d
er
ac
tu
ate
d
r
o
b
o
ts
,
wh
ich
h
av
e
a
g
r
ea
ter
n
u
m
b
er
o
f
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
(
Do
Fs
)
th
an
ac
tiv
e
ac
tu
ato
r
s
,
tr
an
s
f
o
r
m
in
g
th
eir
d
y
n
am
ic
s
y
s
tem
in
to
a
n
o
n
li
n
ea
r
co
m
p
lex
p
r
o
b
lem
.
T
o
m
itig
ate
th
is
ch
allen
g
e,
a
r
ed
u
n
d
an
t
c
o
n
tr
o
ller
is
r
eq
u
ir
ed
to
m
ain
tai
n
th
e
s
y
s
t
em
'
s
s
tab
ilit
y
wh
en
ev
er
a
n
a
ctu
ato
r
f
a
u
lt
o
cc
u
r
s
[
4
]
.
T
o
a
ch
iev
e
th
is
,
a
n
ew
co
n
tr
o
ller
f
o
r
th
e
u
n
d
e
r
ac
tu
at
ed
r
o
b
o
t
is
p
r
o
p
o
s
ed
in
th
is
p
ap
er
,
en
ab
lin
g
th
e
r
o
b
o
t
to
p
er
f
o
r
m
its
task
s
an
d
b
ec
o
m
e
r
esil
ien
t to
ac
tu
ato
r
f
a
u
lts
.
T
o
ad
d
r
ess
th
is
is
s
u
e,
th
e
lite
r
atu
r
e
h
as
p
r
o
p
o
s
ed
v
ar
io
u
s
m
eth
o
d
s
to
co
n
tr
o
l
u
n
d
er
ac
tu
ated
r
o
b
o
ts
,
wh
ich
ca
n
b
e
g
en
er
ally
g
r
o
u
p
ed
in
to
d
if
f
er
e
n
t
ca
teg
o
r
ies.
R
o
b
u
s
t
m
eth
o
d
s
s
u
ch
as
s
lid
in
g
m
o
d
e
co
n
tr
o
l
[
5
]
,
[
6
]
,
p
ass
iv
ity
-
b
ased
c
o
n
tr
o
l
[
7
]
,
an
d
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
[
8
]
ar
e
k
n
o
wn
f
o
r
th
eir
r
o
b
u
s
tn
ess
ag
ain
s
t
d
is
tu
r
b
an
ce
s
an
d
p
ar
am
eter
v
ar
iatio
n
s
.
Ho
wev
er
,
th
e
y
ar
e
s
en
s
itiv
e
to
ch
atter
in
g
p
h
en
o
m
en
a
an
d
b
ec
o
m
e
m
o
r
e
c
o
m
p
lex
wh
en
an
ac
tu
a
to
r
f
a
u
lt
o
cc
u
r
s
.
T
r
a
d
itio
n
al
c
o
n
tr
o
ller
s
o
r
th
ei
r
s
u
b
m
e
r
g
in
g
ar
e
wid
ely
u
s
ed
,
s
u
ch
as
p
a
r
tial
f
ee
d
b
ac
k
lin
ea
r
izatio
n
co
n
tr
o
l
[
9
]
,
a
n
d
m
an
y
o
th
er
s
[
1
0
]
.
Yet,
th
e
y
ar
e
n
o
t
s
u
f
f
icien
tly
r
o
b
u
s
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
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8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
7
9
1
-
805
792
to
h
an
d
le
m
o
d
el
u
n
ce
r
tain
ties
an
d
f
a
u
lts
.
I
n
tellig
en
t
co
n
tr
o
ller
s
ar
e
also
u
s
ed
to
co
n
tr
o
l
u
n
d
er
ac
tu
ated
r
o
b
o
ts
,
s
u
ch
as
f
u
zz
y
co
n
tr
o
l
[
1
1
]
,
n
eu
r
al
n
etwo
r
k
co
n
tr
o
l
[
1
2
]
,
d
ata
-
d
r
iv
e
n
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
-
d
er
iv
ati
v
e
(
DD
-
PID
)
[
1
3
]
.
Nev
e
r
th
eless
,
s
o
m
e
o
f
t
h
ese
m
eth
o
d
s
r
eq
u
ir
e
tr
ain
in
g
,
o
th
e
r
s
d
ep
e
n
d
o
n
t
h
e
p
r
esen
ce
o
f
d
ata
an
d
o
p
tim
izatio
n
alg
o
r
ith
m
s
.
Mo
r
eo
v
er
,
c
o
m
b
in
in
g
co
n
tr
o
ller
s
ca
n
also
en
h
an
ce
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
m
er
g
ed
co
n
tr
o
ller
,
lik
e
s
lid
in
g
m
o
d
e
co
n
tr
o
l
b
ased
o
n
f
u
zz
y
lo
g
ic
an
d
n
e
u
r
al
n
etwo
r
k
s
[
1
4
]
,
n
o
n
f
r
ag
ile
p
r
escr
ib
ed
p
e
r
f
o
r
m
an
ce
co
n
tr
o
l
[
1
5
]
a
n
d
th
e
s
u
p
e
r
-
twis
tin
g
co
n
tr
o
l
m
eth
o
d
with
im
p
r
o
v
ed
p
o
ten
tial
en
er
g
y
f
u
n
ctio
n
[
1
6
]
,
wh
ich
ar
e
all
k
n
o
wn
f
o
r
th
eir
r
o
b
u
s
tn
ess
.
Ho
wev
er
,
m
a
n
y
o
f
th
e
co
n
tr
o
l
m
eth
o
d
s
m
en
tio
n
ed
b
elo
w
ar
e
estab
lis
h
ed
u
s
in
g
t
h
e
L
ag
r
an
g
e
-
E
u
ler
d
y
n
am
ic
m
o
d
el.
T
h
e
r
ef
o
r
e,
th
o
s
e
m
eth
o
d
s
ar
e
b
ased
o
n
o
n
e
d
y
n
am
ic
e
q
u
atio
n
th
at
r
eg
r
o
u
p
s
all
th
e
jo
in
ts
to
g
eth
er
.
So
,
wh
en
ev
er
an
ac
tu
at
o
r
f
au
lt
o
c
cu
r
s
in
o
n
e
jo
i
n
t,
it
ca
n
af
f
ec
t
th
e
co
n
tr
o
l
o
f
all
th
e
o
th
er
jo
in
ts
.
Fu
r
th
er
m
o
r
e,
ad
ap
tin
g
th
is
m
o
d
el
to
th
e
u
n
d
er
ac
tu
ated
s
y
s
tem
s
in
tr
o
d
u
ce
s
s
ig
n
if
ican
t
co
m
p
le
x
ity
d
u
e
to
th
e
n
ee
d
f
o
r
v
ar
io
u
s
p
ar
am
eter
s
an
d
f
o
r
s
o
m
e
c
o
n
tr
o
ller
s
,
th
e
n
ee
d
f
o
r
d
ata
a
n
d
o
p
tim
izatio
n
,
w
h
ich
lead
s
to
h
ig
h
co
n
tr
o
l
ef
f
o
r
t,
tim
e
co
n
s
u
m
p
tio
n
,
an
d
m
o
r
e
r
eso
u
r
ce
s
.
I
n
ad
d
itio
n
,
r
ec
e
n
t
ad
v
a
n
ce
d
co
n
tr
o
ller
s
wer
e
p
r
o
p
o
s
ed
,
s
u
ch
as
s
ig
m
o
id
PID
[
1
7
]
,
b
r
ain
em
o
tio
n
al
lear
n
in
g
-
b
ased
in
tellig
en
t
co
n
tr
o
ller
(
B
E
L
B
I
C
)
PID
[
1
8
]
,
an
d
n
e
u
r
o
en
d
o
cr
in
e
PID
[
1
9
]
,
b
u
t
th
ey
o
f
te
n
r
ely
o
n
ce
n
tr
alize
d
ar
c
h
itectu
r
es,
h
e
u
r
is
tic
tu
n
in
g
,
o
r
d
ata
-
d
r
i
v
en
tr
ain
in
g
.
I
n
t
h
e
m
ea
n
tim
e,
h
a
v
i
n
g
a
p
ass
iv
e
jo
in
t,
u
n
k
n
o
wn
u
n
ce
r
tain
ties
,
an
d
d
is
tu
r
b
an
ce
s
in
th
e
s
y
s
tem
i
n
cr
ea
s
in
g
ly
e
n
h
an
ce
s
t
h
e
co
m
p
licatio
n
an
d
th
e
co
m
p
u
tatio
n
al
b
u
r
d
en
.
T
o
m
a
n
ag
e
th
e
p
r
o
b
lem
s
m
e
n
tio
n
ed
ab
o
v
e,
a
n
ew
ad
a
p
tiv
e
co
n
tr
o
l
a
p
p
r
o
ac
h
b
ased
o
n
tim
e
d
elay
with
v
ir
tu
al
d
ec
o
m
p
o
s
itio
n
c
o
n
tr
o
l
(
T
D
-
VDC)
was
d
esig
n
ed
in
th
e
p
ap
er
[
2
0
]
to
c
o
n
tr
o
l
th
e
f
u
ll
-
ac
t
u
ated
r
o
b
o
t
m
an
ip
u
lato
r
.
I
n
co
n
tr
ast
to
th
e
r
ec
e
n
t
ad
v
a
n
ce
d
c
o
n
t
r
o
ller
s
d
is
cu
s
s
ed
ea
r
lier
,
th
e
p
r
o
p
o
s
ed
T
D
-
VDC
f
r
am
ewo
r
k
o
f
f
er
s
a
s
tr
u
ct
u
r
ed
,
d
ec
en
tr
alize
d
co
n
tr
o
l
s
ch
em
e.
T
h
is
ap
p
r
o
ac
h
allo
ws
ea
ch
j
o
in
t
to
b
e
r
eg
u
lated
in
d
ep
en
d
en
tly
,
e
n
h
an
cin
g
r
o
b
u
s
tn
ess
to
u
n
ce
r
tain
ties
an
d
s
ca
lab
ilit
y
.
Mo
r
eo
v
e
r
,
T
D
-
VDC
av
o
id
s
th
e
n
ee
d
f
o
r
co
m
p
lex
o
p
tim
izatio
n
p
r
o
ce
d
u
r
es
o
r
co
m
p
lete
d
y
n
am
ic
m
o
d
els,
s
u
ch
as
th
e
af
o
r
em
en
tio
n
ed
E
u
ler
-
L
ag
r
a
n
g
e
ap
p
r
o
ac
h
es,
m
ak
in
g
it
p
ar
tic
u
lar
ly
well
-
s
u
ited
f
o
r
co
n
tr
o
l
lin
g
u
n
d
er
ac
tu
ated
m
a
n
ip
u
lat
o
r
s
.
T
h
e
m
ain
id
ea
b
eh
in
d
th
e
g
e
n
er
al
v
ir
tu
al
d
ec
o
m
p
o
s
itio
n
co
n
tr
o
l
(
VDC)
[
2
1
]
is
to
d
ec
o
m
p
o
s
e
th
e
r
o
b
o
t
in
t
o
s
u
b
s
y
s
tem
s
(
lin
k
d
y
n
am
ics
an
d
j
o
in
t
d
y
n
am
ic
s
)
.
T
h
en
,
ea
ch
s
u
b
s
y
s
tem
is
co
n
tr
o
lled
in
d
ep
en
d
en
tly
wi
th
a
d
esig
n
ed
s
u
b
-
co
n
tr
o
ller
wh
ile
en
s
u
r
in
g
th
e
o
v
er
all
s
y
s
tem
s
tab
ilit
y
.
I
n
th
e
p
r
esen
t
p
ap
er
,
th
is
ap
p
r
o
ac
h
is
r
ec
o
n
f
ig
u
r
ed
to
s
u
it
th
e
d
y
n
am
ics
o
f
t
h
e
u
n
d
er
ac
tu
ated
r
o
b
o
t
m
an
ip
u
lato
r
wi
th
an
ac
tu
ato
r
f
au
lt.
T
h
e
r
ef
o
r
e
,
th
is
m
eth
o
d
lead
s
to
is
o
latin
g
a
n
d
r
ea
d
a
p
tin
g
th
e
p
ass
iv
e
jo
i
n
t
co
n
tr
o
ller
o
f
th
e
u
n
d
e
r
ac
tu
ated
r
o
b
o
t
i
n
d
ep
en
d
en
tly
with
o
u
t
im
p
ac
tin
g
th
e
s
u
b
-
co
n
tr
o
ller
s
o
f
t
h
e
ac
tiv
e
j
o
in
ts
.
As
a
r
e
s
u
lt,
u
s
in
g
VDC
s
im
p
lifie
s
th
e
co
n
tr
o
l
o
f
ea
ch
s
u
b
s
y
s
tem
o
f
t
h
e
u
n
d
er
ac
t
u
ated
r
o
b
o
t
ev
en
with
d
e
f
ec
tiv
e
jo
in
ts
.
Fu
r
th
e
r
m
o
r
e
,
to
d
ef
i
n
e
th
e
f
u
ll
d
y
n
am
ic
eq
u
atio
n
o
f
th
e
r
o
b
o
t,
th
e
well
-
k
n
o
wn
s
o
lu
tio
n
is
th
e
r
eg
r
ess
io
n
m
eth
o
d
[
2
2
]
.
Ho
wev
er
,
s
o
m
e
o
f
its
d
r
awb
ac
k
s
ar
e
th
e
d
if
f
icu
lt
y
o
f
d
esig
n
in
g
th
e
r
eg
r
ess
o
r
m
atr
ix
a
n
d
h
a
n
d
lin
g
t
h
e
u
n
ce
r
tain
ties
an
d
d
is
tu
r
b
an
ce
s
.
T
o
co
p
e
with
th
e
s
e
ch
allen
g
es,
th
e
tim
e
d
elay
e
s
tim
atio
n
(
T
DE
)
h
as p
r
o
v
e
d
its
d
esig
n
s
im
p
licity
an
d
ef
f
ec
tiv
e
n
ess
in
ap
p
r
o
x
im
atin
g
u
n
k
n
o
wn
u
n
ce
r
tain
ties
a
n
d
d
is
tu
r
b
a
n
ce
s
[
2
3
]
.
T
h
u
s
,
b
y
m
er
g
in
g
th
e
VDC
an
d
T
DE
,
we
estab
lis
h
th
e
ti
m
e
d
elay
esti
m
atio
n
b
ased
v
ir
tu
al
d
ec
o
m
p
o
s
itio
n
c
o
n
tr
o
l
(
T
D
-
VDC)
f
o
r
a
n
u
n
d
er
ac
tu
ate
d
r
o
b
o
t.
As
a
r
esu
lt,
it
p
r
esen
ts
m
an
y
ad
v
a
n
ta
g
es
s
u
ch
as
d
esig
n
s
im
p
licity
,
r
o
b
u
s
tn
ess
ag
ain
s
t
u
n
k
n
o
wn
d
y
n
am
ics,
an
d
h
ig
h
p
r
ec
is
io
n
in
tr
ajec
to
r
y
tr
ac
k
i
n
g
.
Fu
r
th
er
m
o
r
e
,
ev
alu
atin
g
o
u
r
s
u
g
g
ested
co
n
tr
o
ller
o
n
th
e
m
an
ip
u
lato
r
r
o
b
o
t
th
r
o
u
g
h
co
-
s
im
u
latio
n
r
ep
licates
th
e
ac
tu
al
r
o
b
o
t’
s
b
eh
av
io
r
b
ef
o
r
e
d
ep
lo
y
i
n
g
t
h
e
co
n
tr
o
ller
o
n
p
h
y
s
ical
h
ar
d
wa
r
e.
T
h
is
a
p
p
r
o
ac
h
s
im
p
lifie
s
th
e
p
r
o
ce
s
s
o
f
in
d
u
cin
g
j
o
in
t
d
ef
ec
ts
in
t
o
th
e
u
n
d
e
r
ac
tu
ated
r
o
b
o
t,
allo
w
in
g
m
o
r
e
ef
f
ec
tiv
e
o
b
s
er
v
atio
n
o
f
th
e
r
o
b
o
t'
s
p
er
f
o
r
m
an
ce
.
C
o
n
s
eq
u
en
tly
,
co
-
s
im
u
latio
n
test
in
g
o
f
th
e
co
n
tr
o
ller
h
elp
s
id
en
tify
th
e
b
est s
o
lu
tio
n
f
o
r
th
e
s
itu
atio
n
at
h
a
n
d
.
T
h
e
p
r
esen
t
p
ap
er
p
r
o
v
id
es
a
d
ee
p
er
u
n
d
er
s
tan
d
in
g
o
f
th
e
im
p
o
r
tan
ce
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
in
co
n
tr
o
llin
g
a
n
u
n
d
er
ac
tu
ated
m
an
ip
u
lato
r
.
Sectio
n
1
d
escr
ib
es th
e
d
y
n
am
ic
s
y
s
tem
o
f
a
n
n
-
Do
F u
n
d
er
ac
t
u
ated
m
an
ip
u
lato
r
with
an
i
th
d
ef
ec
tiv
e
jo
in
t.
Su
b
s
eq
u
en
tly
,
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
b
ased
o
n
T
D
-
VDC i
s
ad
ap
ted
to
a
r
o
b
o
t
m
an
ip
u
lato
r
with
p
as
s
iv
e
jo
in
ts
in
s
ec
tio
n
2
.
T
h
en
,
s
ec
tio
n
3
p
r
o
v
es
th
e
s
tab
ilit
y
an
aly
s
is
f
o
r
th
e
co
n
tr
o
ller
T
D
-
VDC.
I
n
s
ec
tio
n
4
,
a
ca
s
e
o
f
a
6
-
Do
F
u
n
d
er
ac
tu
ated
m
an
ip
u
lato
r
with
a
d
ef
ec
tiv
e
ac
tu
ato
r
is
p
er
f
o
r
m
ed
v
ia
a
co
-
s
im
u
latio
n
with
MA
T
L
AB
an
d
Simu
li
n
k
.
Mo
r
e
o
v
er
,
a
co
m
p
ar
is
o
n
an
aly
s
is
is
d
i
s
cu
s
s
ed
b
etwe
en
th
e
r
esu
lts
o
f
T
D
-
VDC
an
d
s
lid
in
g
m
o
d
e
co
n
tr
o
l
b
ased
o
n
p
ar
tial
f
ee
d
b
ac
k
li
n
ea
r
izatio
n
co
n
tr
o
l
(
SMC
-
PF
L
C
)
.
Fin
ally
,
th
e
co
n
clu
s
io
n
s
ar
e
estab
lis
h
ed
in
s
ec
tio
n
5
.
2.
T
H
E
P
RO
P
O
SE
D
M
E
T
H
O
D
2
.
1
.
Undera
ct
ua
t
ed
s
y
s
t
em
des
cr
iptio
n
T
h
e
u
n
d
er
ac
t
u
ated
m
an
ip
u
lato
r
r
o
b
o
t
is
a
co
m
p
lex
d
y
n
a
m
ic
s
y
s
tem
with
a
h
ig
h
er
n
u
m
b
er
o
f
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
th
an
ac
tiv
e
j
o
in
ts
.
B
ased
o
n
t
h
e
E
u
ler
-
L
ag
r
an
g
e
a
p
p
r
o
ac
h
,
th
e
n
-
lin
k
u
n
d
er
ac
tu
ated
m
an
i
p
u
lato
r
r
o
b
o
t
is
ch
ar
ac
ter
ized
as
f
o
llo
ws,
with
a
p
r
ep
r
esen
tin
g
p
ass
iv
e
jo
in
ts
,
a
1
an
d
a
3
b
ein
g
ac
t
iv
e
jo
in
ts
,
an
d
th
e
to
tal
n
u
m
b
er
o
f
j
o
in
ts
s
atis
f
y
in
g
th
e
eq
u
atio
n
a
1
+
a
p
+ a
3
=
jo
in
ts
,
as m
en
tio
n
ed
in
[
1
0
]
:
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I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
V
ir
tu
a
l d
ec
o
mp
o
s
itio
n
w
ith
time
d
ela
y
co
n
tr
o
l fo
r
…
(
I
ma
n
e
C
h
eikh
)
793
(
̈
1
̈
̈
3
)
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(
1
̇
1
̇
3
̇
3
)
+
(
1
3
)
=
(
1
0
3
)
+
(
1
3
)
;
(
1
)
W
i
t
h
,
̇
j
,
̈
j
∈
ℜ
w
i
t
h
=
{
1
,
,
3
}
a
r
e
t
h
e
v
ec
t
o
r
s
o
f
th
e
i
n
i
t
i
al
a
c
ti
v
e
,
t
h
e
p
ass
i
v
e
,
an
d
t
h
e
l
a
s
t
a
c
ti
v
e
j
o
i
n
t
s
'
p
o
s
i
ti
o
n
s
,
v
e
l
o
c
it
i
es
,
a
n
d
a
c
c
e
l
e
r
a
ti
o
n
s
;
(
)
∈
ℜ
×
i
s
t
h
e
u
n
d
e
r
a
c
tu
a
t
e
d
r
o
b
o
t
i
n
e
r
t
i
a
m
a
t
r
i
x
,
a
n
d
i
t
is
d
i
v
i
d
e
d
i
n
t
o
6
s
u
b
-
m
a
t
r
ic
e
s
;
j
=
(
,
̇
)
̇
∈
ℜ
g
a
t
h
e
r
t
h
e
i
n
i
ti
a
l
,
t
h
e
p
as
s
i
v
e
,
a
n
d
t
h
e
l
as
t
a
c
ti
v
e
v
e
ct
o
r
s
o
f
t
h
e
C
o
r
i
o
l
is
a
n
d
c
e
n
t
r
i
p
e
t
a
l
t
o
r
q
u
e
s
;
j
=
(
)
j
∈
ℜ
j
d
e
n
o
t
e
t
h
e
g
r
a
v
i
t
a
ti
o
n
a
l
t
o
r
q
u
e
s
v
e
c
t
o
r
;
1
∈
ℜ
1
a
n
d
3
∈
ℜ
3
a
r
e
t
h
e
f
i
r
s
t
a
n
d
t
h
e
l
as
t
i
n
p
u
t
t
o
r
q
u
e
v
e
c
t
o
r
s
a
p
p
l
i
e
d
t
o
th
e
j
o
i
n
t
s
,
w
h
i
l
e
0
∈
ℜ
i
s
a
v
e
c
t
o
r
o
f
z
e
r
o
s
t
h
a
t
is
a
p
p
l
ie
d
t
o
t
h
e
p
a
s
s
i
v
e
j
o
i
n
t
a
n
d
∈
ℜ
p
r
e
s
e
n
t
t
h
e
d
is
t
u
r
b
a
n
c
e
v
e
c
t
o
r
.
2
.
2
.
Sy
s
t
e
m
d
ec
o
m
po
s
it
io
n
Similar
to
a
f
u
ll
-
ac
tu
ated
m
an
ip
u
lato
r
co
n
tr
o
l,
th
e
v
ir
tu
al
d
e
co
m
p
o
s
itio
n
o
f
an
n
-
Do
F
u
n
d
er
ac
tu
ated
r
o
b
o
t w
ith
an
i
th
p
ass
iv
e
jo
in
t is d
ef
in
ed
b
y
s
p
litt
in
g
th
e
lin
k
s
an
d
th
e
jo
in
ts
.
Fig
u
r
e
1
s
h
o
ws
th
e
r
ep
r
esen
tatio
n
o
f
th
e
v
ir
tu
al
d
ec
o
m
p
o
s
itio
n
o
f
an
u
n
d
e
r
ac
tu
ated
r
o
b
o
t
b
ase
d
o
n
th
e
o
n
e
f
o
r
th
e
f
u
ll
-
ac
tu
a
ted
r
o
b
o
t
s
h
o
w
n
in
th
e
p
ap
er
[
2
1
]
.
T
h
e
cu
ttin
g
p
o
in
t
ass
o
ciate
d
with
f
r
am
es
{B
i
},
an
d
{T
i+
1
}
is
r
elate
d
to
th
e
i
th
lin
k
,
wh
ile
th
e
cu
ttin
g
p
o
i
n
t a
s
s
o
ciate
d
with
f
r
am
es
{B
i
},
an
d
{T
i
}
is
r
elate
d
to
th
e
i
th
jo
in
t.
T
o
co
n
tr
o
l
th
e
u
n
d
er
ac
tu
ated
r
o
b
o
t,
ea
ch
s
u
b
s
y
s
tem
,
in
cl
u
d
in
g
th
e
n
lin
k
s
,
t
h
e
n
jo
in
ts
,
an
d
th
e
p
ass
iv
e
jo
in
t,
will
b
e
tr
ea
ted
in
d
ep
en
d
en
tly
.
T
o
d
o
s
o
,
we
will
n
ee
d
to
d
ef
in
e
th
e
r
eq
u
ir
ed
v
elo
cities
b
ef
o
r
e
ex
p
r
ess
in
g
th
e
lin
k
an
d
jo
in
t
d
y
n
am
ics
eq
u
atio
n
s
.
T
h
en
,
th
e
g
lo
b
al
s
y
s
tem
d
y
n
am
ic
eq
u
atio
n
will
b
e
co
m
p
u
ted
b
y
a
d
d
in
g
in
d
iv
i
d
u
a
l jo
in
ts
an
d
lin
k
s
to
r
q
u
es.
Fig
u
r
e
1
.
Vir
tu
al
d
ec
o
m
p
o
s
itio
n
o
f
an
u
n
d
er
ac
t
u
ated
m
an
i
p
u
lato
r
2
.
2
.
1
.
Required
v
elo
cit
ies
R
eq
u
ir
ed
v
elo
cities
ar
e
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
co
n
ce
p
ts
in
d
esig
n
in
g
th
e
VDC
co
n
tr
o
l
ler
f
o
r
th
e
u
n
d
er
ac
tu
ate
d
r
o
b
o
t.
T
h
ey
ar
e
ca
lcu
lated
b
ased
o
n
t
h
e
jo
i
n
t
p
o
s
itio
n
e
r
r
o
r
an
d
d
esire
d
v
elo
city
.
T
h
e
r
ef
o
r
e,
th
ey
allo
w
t
h
e
r
o
b
o
t
to
ad
h
er
e
to
th
e
d
esire
d
tr
ajec
to
r
y
wi
th
h
ig
h
p
r
ec
is
io
n
.
B
ased
o
n
t
h
e
p
a
p
er
[
2
1
]
,
th
e
eq
u
atio
n
s
b
elo
w
a
r
e
in
tr
o
d
u
ce
d
.
On
th
e
o
n
e
h
an
d
,
we
ca
n
e
x
p
r
ess
th
e
i
th
jo
in
t r
eq
u
ir
ed
v
elo
ci
ty
th
at
ca
n
b
e
ac
tiv
e
o
r
p
ass
iv
e:
̇
,
=
̇
,
−
(
)
;
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
7
9
1
-
805
794
W
h
e
r
e
,
,
̇
,
a
r
e
t
h
e
i
th
g
o
a
l
j
o
i
n
t
p
o
s
i
t
i
o
n
a
n
d
v
e
l
o
c
i
t
y
;
i
s
t
h
e
i
th
r
e
al
j
o
i
n
t
p
o
s
i
t
i
o
n
a
n
d
=
,
−
.
On
th
e
o
th
er
h
an
d
,
th
e
i
th
lin
k
r
eq
u
ir
ed
lin
ea
r
/an
g
u
lar
v
elo
cit
y
is
co
m
p
u
ted
in
(
3
)
:
=
̇
−
−
1
−
1
;
(
3
)
W
h
er
e
=
[
0
0
0
0
0
1
]
f
o
r
r
e
v
o
lu
te
jo
in
t
a
n
d
t
h
e
tr
an
s
f
o
r
m
atio
n
m
atr
ix
−
1
f
r
o
m
th
e
f
r
am
e
{B
i
-
1
}
to
th
e
f
r
am
e
{B
i
}
is
ex
p
r
ess
ed
as:
−
1
=
(
−
1
0
3
×
3
(
×
−
1
)
−
1
−
1
)
;
(
×
−
1
)
=
(
0
−
(
3
)
−
1
(
2
)
−
1
(
3
)
−
1
0
−
(
1
)
−
1
−
(
2
)
−
1
(
1
)
−
1
0
)
;
(
4
)
W
h
er
e
−
1
is
th
e
r
o
tatio
n
Ma
tr
ix
an
d
−
1
is
th
e
v
ec
to
r
o
f
t
r
an
s
f
o
r
m
atio
n
f
r
o
m
th
e
f
r
am
e
{B
i
-
1
}
to
th
e
f
r
am
e
{B
i
}.
2
.
2
.
2
.
L
ink
s
dy
na
m
ics
Usi
n
g
th
e
r
eq
u
ir
ed
lin
ea
r
/an
g
u
lar
v
elo
city
in
(
3
)
,
th
e
e
q
u
at
io
n
o
f
th
e
r
e
q
u
ir
e
d
n
et
m
o
m
en
t
v
ec
to
r
∗
th
at
is
ex
er
ted
b
y
th
e
ith
-
1
lin
k
o
n
th
e
ith
lin
k
is
ex
p
r
ess
ed
a
s
f
o
llo
win
g
th
e
p
ap
er
[
2
1
]
:
∗
=
+
+
;
(
5
)
W
h
er
e
is
th
e
in
er
tial te
r
m
,
is
th
e
ce
n
tr
if
u
g
al
an
d
C
o
r
i
o
lis
ter
m
,
r
ep
r
esen
ts
th
e
g
r
av
itatio
n
a
l te
r
m
.
I
ter
ativ
ely
,
we
ca
n
f
in
d
th
e
g
e
n
er
alize
d
m
o
m
e
n
t
ap
p
lied
f
r
o
m
th
e
i
th+
1
b
o
d
y
o
n
th
e
i
th
b
o
d
y
with
th
e
f
o
llo
win
g
e
x
p
r
ess
io
n
as d
e
f
in
ed
in
th
e
p
ap
e
r
[
2
1
]
:
=
∗
;
−
1
=
−
1
∗
+
−
1
∗
;
.
.
.
−
1
=
−
1
∗
+
−
1
∗
;
=
[
2
,
…
,
−
1
]
(
6
)
Fin
ally
,
th
e
r
eq
u
i
r
ed
n
et
t
o
r
q
u
e
o
f
th
e
i
th
jo
in
t
to
war
d
th
e
lin
k
s
is
co
m
p
u
ted
with
th
e
u
s
e
o
f
(
6
)
:
,
=
;
(
7
)
2
.
2
.
3
.
J
o
ints dy
na
m
ics
B
ased
o
n
th
e
jo
in
t
r
eq
u
ir
ed
v
elo
city
in
(
2
)
,
th
e
i
th
jo
in
t
s
u
b
s
y
s
tem
d
y
n
am
ic
is
ex
p
r
ess
ed
with
th
e
eq
u
atio
n
o
f
th
e
r
eq
u
ir
e
d
n
et
to
r
q
u
e
,
as f
o
llo
ws,
as m
en
tio
n
ed
in
th
e
p
a
p
er
[
2
1
]
:
,
=
̈
,
+
(
̇
,
)
;
(
8
)
W
h
er
e
is
th
e
m
o
m
en
t o
f
in
er
ti
a
an
d
is
th
e
i
th
C
o
u
lo
m
b
f
r
ictio
n
co
ef
f
icien
t.
2
.
2
.
4
.
Sy
s
t
em
dy
na
m
ics
B
y
co
m
b
in
in
g
th
e
ex
p
r
ess
io
n
s
in
(
7
)
an
d
(
8
)
,
we
f
in
d
th
at
th
e
to
tal
to
r
q
u
e
f
o
r
an
n
-
D
o
F
r
o
b
o
t
is
as
d
escr
ib
ed
in
th
e
p
ap
er
[
2
1
]
:
=
,
+
,
;
(
9
)
I
n
th
is
s
ec
tio
n
,
th
e
jo
in
ts
'
an
d
lin
k
s
'
d
y
n
am
ics
f
o
r
a
r
o
b
o
t
m
an
ip
u
lato
r
h
av
e
b
ee
n
ex
p
r
ess
ed
u
s
in
g
th
e
v
ir
tu
a
l
d
ec
o
m
p
o
s
itio
n
co
n
tr
o
l.
T
h
e
n
ex
t
s
tep
is
to
d
esig
n
th
e
n
ew
co
n
tr
o
ller
f
o
r
th
e
u
n
d
er
ac
t
u
ated
r
o
b
o
t
with
a
p
ass
iv
e
jo
in
t.
T
h
er
ef
o
r
e,
a
n
e
w
co
n
tr
o
l
law
will
b
e
p
r
o
p
o
s
ed
in
th
e
n
ex
t
s
ec
tio
n
to
d
ef
in
e
th
e
VDC
f
o
r
an
u
n
d
er
ac
tu
ate
d
r
o
b
o
t m
a
n
ip
u
lat
o
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
V
ir
tu
a
l d
ec
o
mp
o
s
itio
n
w
ith
time
d
ela
y
co
n
tr
o
l fo
r
…
(
I
ma
n
e
C
h
eikh
)
795
3.
M
E
T
H
O
D
3
.
1
.
P
r
o
po
s
ed
co
ntr
o
ller
f
o
r
un
dera
ct
ua
t
ed
m
a
nip
ula
t
o
r
T
D
-
VDC
As
alr
ea
d
y
d
escr
ib
ed
in
s
ec
tio
n
2
,
t
h
e
jo
in
ts
an
d
lin
k
s
’
u
s
in
g
th
e
VDC
f
o
r
a
f
u
l
l
-
ac
tu
ated
m
an
ip
u
lato
r
r
o
b
o
t
h
av
e
b
ee
n
m
en
tio
n
ed
.
I
n
o
r
d
er
to
a
d
ap
t
th
is
co
n
tr
o
ller
to
th
e
u
n
d
er
ac
t
u
ated
d
y
n
am
ics,
a
n
ew
co
n
tr
o
l
law
is
d
esig
n
ed
in
th
e
f
o
llo
win
g
th
eo
r
e
m
f
o
r
th
e
u
n
d
er
ac
t
u
ated
r
o
b
o
t
b
a
s
ed
o
n
th
e
s
y
s
tem
d
ec
o
m
p
o
s
itio
n
.
T
h
en
,
th
e
n
ew
co
n
tr
o
ller
is
p
r
o
v
e
n
.
Th
eo
r
em
1
:
By
in
teg
r
atin
g
th
e
co
n
tr
o
l
law
f
o
r
th
e
u
n
d
er
ac
t
u
ated
r
o
b
o
t
ex
p
r
ess
ed
in
(
1
)
,
w
ith
th
e
to
tal
to
r
q
u
e
f
o
r
a
f
u
ll
-
ac
tu
ated
m
an
ip
u
lato
r
r
o
b
o
t,
th
e
n
ew
co
n
tr
o
l
t
o
r
q
u
e
in
p
u
t
f
o
r
t
h
e
n
-
Do
F
u
n
d
er
ac
tu
ated
m
an
ip
u
lato
r
with
p
p
ass
iv
e
jo
in
ts
is
d
esig
n
ed
as (
1
0
)
:
(
1
0
3
)
=
(
1
,
+
1
,
,
+
,
3
,
+
3
,
)
;
(
1
0
)
W
h
er
e
τ
a1
j
,
r
∈
ℜ
a1
an
d
τ
a3
j
,
r
∈
ℜ
a3
ar
e
th
e
f
ir
s
t
an
d
th
e
last
r
eq
u
ir
ed
n
et
to
r
q
u
e
v
ec
to
r
s
ap
p
lied
to
th
e
jo
in
ts
;
τ
a1
l
,
r
∈
ℜ
a1
an
d
τ
a3
l
,
r
∈
ℜ
a3
ar
e
th
e
f
ir
s
t
an
d
t
h
e
last
ac
tiv
e
r
eq
u
ir
ed
n
et
to
r
q
u
e
ap
p
lied
t
o
th
e
lin
k
s
;
τ
ap
l
,
r
,
τ
ap
j
,
r
∈
ℜ
ap
ar
e
th
e
p
ass
iv
e
r
eq
u
ir
ed
n
et
to
r
q
u
es
a
p
p
lied
to
lin
k
s
a
n
d
jo
in
ts
r
esp
ec
tiv
ely
.
Fr
o
m
(
1
0
)
,
we
d
ed
u
ce
th
e
n
ew
k
ey
co
n
ce
p
t
in
co
n
tr
o
llin
g
u
n
d
er
ac
tu
ate
d
r
o
b
o
ts
with
p
p
ass
iv
e
jo
in
ts
b
ased
o
n
VDC
an
d
wh
ich
ca
n
b
e
r
ep
r
esen
ted
as (
1
1
)
:
,
=
−
,
;
(
1
1
)
P
r
o
o
f
:
T
h
e
u
n
d
er
ac
tu
ated
r
o
b
o
t
is
ch
ar
ac
ter
ize
d
b
y
h
av
in
g
f
ewe
r
jo
in
t
ac
tu
ato
r
s
t
h
an
D
o
Fs
.
As
th
e
d
y
n
am
ic
(
1
)
m
en
tio
n
s
,
th
e
p
ass
iv
e
jo
in
t
ex
er
ts
a
n
u
ll
to
r
q
u
e
th
at
ca
n
n
o
t
b
e
co
n
tr
o
lled
.
T
h
e
r
ef
o
r
e
,
th
e
to
tal
to
r
q
u
e
f
o
r
th
e
u
n
d
er
ac
t
u
ated
r
o
b
o
t
ca
n
b
e
ca
teg
o
r
ized
i
n
to
ac
tiv
e
an
d
p
ass
iv
e
to
r
q
u
es,
r
ep
r
esen
ted
as
1
,
3
f
o
r
th
e
ac
tiv
e
jo
in
ts
an
d
0
f
o
r
th
e
p
ass
iv
e
o
n
es.
=
(
1
0
3
)
;
(
1
2
)
B
y
r
ef
er
r
in
g
to
(
9
)
an
d
(
1
2
)
,
we
ca
n
d
er
iv
e
T
h
eo
r
em
1
co
n
ce
r
n
in
g
th
e
v
i
r
tu
al
d
ec
o
m
p
o
s
itio
n
co
n
tr
o
l
o
f
th
e
u
n
d
er
ac
tu
ate
d
r
o
b
o
t.
T
h
e
m
ai
n
r
esu
lts
o
f
th
e
th
eo
r
e
m
ar
e
g
i
v
en
in
(
1
0
)
an
d
(
1
1
)
.
T
h
ese
r
e
s
u
lts
will
b
e
u
s
ed
in
th
e
s
u
b
s
eq
u
en
t sectio
n
s
.
W
h
ile
VD
C
p
r
esen
ts
s
ig
n
if
ican
t
ad
v
an
tag
es
in
co
n
tr
o
llin
g
u
n
d
er
ac
tu
ated
m
a
n
ip
u
lato
r
s
,
ch
allen
g
es
r
em
ain
in
e
n
s
u
r
in
g
r
o
b
u
s
tn
ess
ag
ain
s
t
ex
ter
n
al
d
is
tu
r
b
an
ce
s
an
d
u
n
ce
r
tain
ties
in
s
y
s
tem
d
y
n
am
ics.
T
o
tack
le
th
ese
c
h
allen
g
es,
t
h
e
co
n
ce
p
t
o
f
T
DE
is
in
tr
o
d
u
ce
d
to
ac
co
u
n
t
f
o
r
d
y
n
am
ic
u
n
ce
r
tain
ties
.
T
h
is
en
h
an
ce
m
e
n
t
lead
s
to
th
e
p
r
o
p
o
s
ed
T
D
-
VDC
ap
p
r
o
ac
h
,
wh
ich
s
ig
n
if
ican
tly
im
p
r
o
v
es
b
o
th
s
tab
ilit
y
an
d
co
n
tr
o
l
e
f
f
icien
cy
f
o
r
u
n
d
er
ac
tu
ated
m
an
ip
u
lato
r
s
with
p
ass
iv
e
jo
in
ts
.
T
h
e
o
v
er
all
m
o
d
el
f
o
r
c
o
n
tr
o
llin
g
th
e
u
n
d
er
ac
tu
ate
d
m
a
n
ip
u
lato
r
b
a
s
ed
o
n
T
D
-
VDC
is
o
u
tlin
e
d
in
Fig
u
r
e
2
,
wh
ic
h
illu
s
tr
ates
th
e
co
r
r
esp
o
n
d
in
g
b
lo
ck
d
ia
g
r
am
.
B
y
s
ep
ar
atin
g
th
e
d
y
n
a
m
ics
o
f
th
e
lin
k
s
an
d
jo
in
ts
in
(
1
0
)
f
r
o
m
T
h
eo
r
em
1
,
th
e
n
ew
ap
p
r
o
ac
h
in
teg
r
ates
th
e
(
5
)
an
d
(
8
)
o
f
V
DC
alo
n
g
with
th
e
esti
m
atio
n
o
f
T
DE
as
alr
ea
d
y
g
iv
e
n
in
p
a
p
er
[
2
0
]
.
T
h
e
n
th
e
eq
u
atio
n
s
f
o
r
lin
k
s
an
d
jo
in
ts
ar
e
as:
Fo
r
lin
k
s
:
1
∗
=
1
̅
̅
̅
̅
̅
̅
̇
1
+
̂
1
,
+
1
,
1
;
∗
=
̅
̅
̅
̅
̅
̅
̇
+
̂
,
+
,
;
3
∗
=
3
̅
̅
̅
̅
̅
̅
̇
3
+
̂
3
,
+
3
,
3
;
(
1
3
)
Fo
r
jo
in
ts
:
1
,
=
,
1
̅
̅
̅
̅
̅
̅
̈
1
,
+
̂
1
,
+
1
,
1
;
,
=
,
̅
̅
̅
̅
̅
̅
̈
,
+
̂
,
+
,
3
,
=
,
1
̅
̅
̅
̅
̅
̅
̈
3
,
+
̂
3
,
+
3
,
3
;
;
(
1
4
)
W
h
er
e
̅
̅
̅
̅
̅
,
,
̅
̅
̅
̅
̅
ℎ
=
[
1
,
,
3
]
ar
e
co
n
s
tan
ts
ass
o
cia
ted
with
th
e
in
er
tial
ter
m
an
d
th
e
m
o
m
en
t
o
f
in
er
tia;
̂
,
ℎ
=
[
,
]
r
ef
er
to
th
e
esti
m
a
ted
v
ec
to
r
s
o
f
th
e
u
n
k
n
o
wn
d
y
n
am
ic
u
n
ce
r
tain
ties
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
7
9
1
-
805
796
d
is
tu
r
b
an
ce
s
,
o
f
lin
k
’
an
d
ac
tiv
e/p
ass
iv
e
jo
in
t’
s
y
s
tem
s
;
=
−
d
ef
i
n
es
th
e
tr
ac
k
i
n
g
ac
c
u
r
ac
y
er
r
o
r
;
=
̇
,
−
̇
d
ef
in
es th
e
tr
ac
k
in
g
jo
i
n
t e
r
r
o
r
; A
n
d
,
ar
e
p
o
s
itiv
e
g
ai
n
s
.
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
am
o
f
th
e
u
n
d
er
ac
t
u
ated
m
an
i
p
u
lato
r
’
s
co
n
tr
o
l
T
o
en
s
u
r
e
th
e
s
tab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
ller
,
we
m
ak
e
t
h
e
f
o
llo
win
g
ass
u
m
p
tio
n
s
:
a.
S1
:
th
e
v
ec
to
r
s
,
an
d
th
eir
d
er
iv
ativ
es
ar
e
g
lo
b
al
L
ip
s
ch
itz
f
u
n
ctio
n
s
.
C
o
n
s
eq
u
en
tly
,
th
eir
v
a
lu
es
at
th
e
p
r
esen
t tim
e
(
t)
an
d
at
th
e
p
ast tim
e
(t
-
T)
ar
e
n
ea
r
ly
eq
u
al
with
T
as a
lo
w
tim
e
d
elay
:
̂
,
(
)
=
̂
,
(
−
)
;
(
1
5
)
b.
S2
: T
h
e
co
n
s
tan
ts
̅
̅
̅
̅
̅
a
n
d
,
̅
̅
̅
̅
̅
ar
e
p
ick
ed
s
o
th
at:
|
−
(
)
̅
̅
̅
̅
̅
−
1
|
<
1
|
−
(
)
,
̅
̅
̅
̅
̅
−
1
|
<
1
(
1
6
)
Fo
r
s
im
p
lific
atio
n
,
let
u
s
co
n
s
i
d
er
an
n
-
Do
F u
n
d
er
ac
tu
ated
r
o
b
o
t w
ith
th
e
p
th
jo
in
t a
s
a
p
as
s
iv
e
jo
in
t.
T
h
en
,
we
f
in
d
lin
k
s
’
s
u
b
s
y
s
tem
s
b
ased
o
n
(
1
5
)
,
(
1
3
)
a
n
d
(
1
1
)
:
̂
,
(
)
=
[
,
(
−
)
−
̅
̇
(
−
)
−
,
(
−
)
]
;
.
.
.
̂
,
(
)
=
[
−
,
(
−
)
−
̅
̇
(
−
)
−
,
(
−
)
−
+
1
(
−
)
̂
+
1
,
(
−
)
+
̅
+
1
̇
(
−
)
+
1
+
+
1
,
+
1
(
−
)
]
;
.
.
.
̂
,
(
)
=
[
,
(
−
)
−
̅
̇
(
−
)
−
,
(
−
)
−
+
1
(
−
)
̂
+
1
,
(
−
)
+
̅
+
1
̇
(
−
)
+
1
+
+
1
,
+
1
(
−
)
]
;
(
1
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
V
ir
tu
a
l d
ec
o
mp
o
s
itio
n
w
ith
time
d
ela
y
co
n
tr
o
l fo
r
…
(
I
ma
n
e
C
h
eikh
)
797
T
h
e
ab
o
v
e
e
q
u
atio
n
s
s
h
o
w
th
a
t
th
e
̂
,
(
)
is
r
elate
d
d
ir
ec
tly
to
th
e
p
ass
iv
e
jo
in
t
to
r
q
u
e
,
wh
ich
h
as a
b
ig
im
p
ac
t o
n
ad
ju
s
tin
g
t
h
e
co
n
tr
o
ller
.
Fu
r
th
er
m
o
r
e,
we
r
em
ar
k
th
at
all
th
e
esti
m
atio
n
s
b
ef
o
r
e
o
n
e
o
f
th
e
p
ass
iv
e
jo
in
ts
̂
,
ar
e
r
elate
d
to
th
e
latter
esti
m
atio
n
.
T
h
is
im
p
li
es
th
at
th
e
to
r
q
u
e
co
n
tr
o
l
o
f
t
h
e
lin
k
s
b
ef
o
r
e
th
e
p
ass
iv
e
jo
in
t a
d
ap
ts
ea
s
ily
wh
en
ev
er
a
f
au
lt o
cc
u
r
s
.
Similar
ly
,
we
f
in
d
f
o
r
jo
in
ts
s
u
b
s
y
s
tem
s
:
̂
,
(
)
=
,
(
−
)
−
,
(
−
)
;
.
.
.
̂
,
(
)
=
,
(
−
)
−
,
(
−
)
;
(
1
8
)
T
h
er
ef
o
r
e,
b
ased
o
n
th
e
(
6
)
,
(
7
)
,
(
1
1
)
,
(
1
3
)
,
(
1
4
)
,
(
1
7
)
,
an
d
(
1
8
)
,
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
s
f
o
r
n
-
Do
F
u
n
d
er
ac
tu
ate
d
r
o
b
o
t w
ith
a
p
th
jo
in
t u
n
ac
tu
ated
ar
e
d
i
v
id
ed
in
to
two
ca
teg
o
r
ies:
-
Fo
r
ac
tiv
e
jo
in
t:
,
=
,
(
−
)
+
[
̅
̅
̅
̅
∆
(
̇
)
+
,
∆
(
)
+
+
1
̅
̅
̅
̅
̅
̅
̅
̇
+
1
(
−
)
+
+
1
,
+
1
(
−
)
+
∆
(
+
1
̂
+
1
,
)
+
−
1
(
+
1
̅
̅
̅
̅
̅
̅
̇
(
)
+
1
+
+
1
,
(
)
+
1
)
]
;
,
=
,
̅
̅
̅
̅
̈
,
+
,
(
−
)
+
,
∆
(
)
;
(
1
9
)
-
Fo
r
p
ass
iv
e
jo
in
t:
,
=
−
,
(
−
)
+
[
̅
̅
̅
̅
∆
(
̇
)
+
,
∆
(
)
+
+
1
̅
̅
̅
̅
̅
̅
̅
̇
+
1
(
−
)
+
+
1
,
+
1
(
−
)
+
∆
(
+
1
̂
+
1
,
)
+
−
1
(
+
1
̅
̅
̅
̅
̅
̅
̅
̇
(
)
+
1
+
+
1
,
(
)
+
1
)
]
;
,
=
,
̅
̅
̅
̅
̅
̈
,
+
,
(
−
)
+
,
∆
(
)
;
(
2
0
)
W
ith
∆
(
)
=
(
)
−
(
−
)
is
th
e
T
DE
er
r
o
r
[
2
2
]
.
Su
b
s
eq
u
en
tly
,
th
e
c
o
n
tr
o
l
to
r
q
u
es
ar
e
d
er
iv
ed
b
y
ad
d
in
g
th
e
jo
in
t
an
d
lin
k
t
o
r
q
u
es
in
(
1
9
)
a
n
d
(
2
0
)
as
s
h
o
wn
in
T
h
eo
r
em
1
.
T
h
e
n
ex
t
s
tep
is
to
d
em
o
n
s
tr
ate
th
e
s
tab
ilit
y
o
f
th
e
co
n
tr
o
ller
to
p
r
o
v
e
its
ef
f
ec
tiv
en
ess
.
T
h
en
,
th
e
n
ew
co
n
t
r
o
l to
r
q
u
es
will b
e
u
s
ed
to
co
n
t
r
o
l th
e
u
n
d
er
ac
tu
ated
r
o
b
o
t w
ith
a
p
ass
iv
e
jo
in
t.
3
.
2
.
T
D
-
VDC
s
t
a
bil
it
y
a
na
ly
s
is
T
o
p
r
o
v
e
th
e
s
y
s
tem
’
s
s
tab
il
ity
p
er
T
h
eo
r
e
m
1
,
a
n
o
n
-
n
e
g
ativ
e
to
tal
L
y
ap
u
n
o
v
ca
n
d
id
ate
V
T
is
d
ef
in
ed
.
T
w
o
n
o
n
-
n
e
g
ativ
e
L
y
ap
u
n
o
v
ca
n
d
i
d
ates a
r
e
s
u
m
m
e
d
u
p
,
t
h
e
f
ir
s
t o
n
e
f
o
r
lin
k
s
V
il
an
d
th
e
s
ec
o
n
d
o
n
e
f
o
r
jo
in
ts
V
ij
.
I
t
i
s
ex
p
r
ess
ed
as f
o
llo
ws f
o
r
=
{
1
,
.
.
.
,
,
.
.
.
,
}
[
2
1
]
:
=
∑
=
1
+
∑
=
1
;
(
2
1
)
W
ith
:
=
1
2
+
1
2
(
,
−
̂
,
)
2
(
2
2
)
=
1
2
,
2
+
1
2
(
,
−
̂
,
)
2
T
h
en
b
y
d
er
i
v
in
g
ea
c
h
L
y
ap
u
n
o
v
ca
n
d
id
ate,
we
h
a
v
e:
̇
=
−
,
+
(
∗
−
∗
)
+
∆
(
,
)
(
−
1
2
∆
(
,
)
)
(
2
3
)
̇
=
−
,
2
+
(
,
−
)
+
1
2
∆
(
,
)
2
W
h
er
e
is a t
e
rm
u
se
d
i
n
t
h
e
r
eg
r
ess
io
n
m
eth
o
d
.
As m
en
tio
n
ed
ab
o
v
e,
,
is
a
g
lo
b
al
L
ip
s
ch
itz
f
u
n
ctio
n
,
wh
ich
m
ea
n
s
th
at:
|
∆
(
,
)
|
≤
ℎ
>
0
(
2
4
)
Ho
wev
er
,
it is
n
ec
ess
ar
y
to
d
e
f
in
e
th
e
v
ir
t
u
al
p
o
wer
f
lo
ws co
n
ce
r
n
in
g
f
r
a
m
e
A
as
[
2
1
]
:
=
(
−
)
(
2
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
7
9
1
-
805
798
Acc
o
r
d
in
g
ly
,
th
is
lead
s
to
f
in
d
in
g
th
e
to
tal
v
ir
t
u
al
p
o
w
er
f
o
r
an
o
p
en
ch
ain
s
tr
u
ct
u
r
e,
as
we
h
a
v
e
a
m
an
ip
u
lato
r
r
o
b
o
t
:
∑
(
−
)
=
1
=
∑
(
∗
−
∗
)
=
1
=
0
(
2
6
)
Acc
o
r
d
in
g
t
o
(
2
2
)
,
(
2
3
)
,
(
2
4
)
,
an
d
(
2
6
)
,
we
o
b
tain
th
e
to
tal
L
y
ap
u
n
o
v
ca
n
d
id
ates a
s
:
∑
̇
=
1
≤
−
∑
(
,
+
1
2
=
1
)
∑
̇
=
1
≤
−
∑
(
,
2
=
1
+
1
2
)
(
2
7
)
Ho
wev
er
,
th
e
L
ip
s
ch
itz
co
n
s
tan
ts
,
an
d
th
e
g
ain
s
,
,
,
ar
e
s
tr
ictly
p
o
s
itiv
e
as
m
en
tio
n
ed
i
n
(
2
3
)
.
T
h
er
ef
o
r
e,
th
e
s
tab
ilit
y
o
f
th
e
clo
s
ed
-
lo
o
p
s
y
s
tem
is
p
r
o
v
ed
s
in
ce
̇
is
a
n
eg
ativ
e
-
d
ef
in
ite
f
u
n
ctio
n
:
̇
=
∑
̇
=
1
+
∑
̇
=
1
̇
<
0
(
2
8
)
T
h
e
f
in
ite
-
tim
e
co
n
v
er
g
en
ce
o
f
th
e
VDC
with
tim
e
d
el
ay
ca
n
b
e
g
iv
en
b
y
in
teg
r
at
in
g
th
e
L
y
ap
u
n
o
v
ca
n
d
id
ate:
∫
̇
0
≤
−
∑
∫
(
0
,
+
1
2
=
1
)
−
∑
∫
(
0
,
2
=
1
+
1
2
)
(
2
9
)
B
y
co
n
s
id
er
in
g
th
at
(
)
=
(
)
≅
0
,
we
d
ed
u
ce
:
(
)
+
(
)
−
(
0
)
−
(
0
)
≤
1
3
,
3
(
0
)
−
1
2
(
+
)
+
1
3
,
3
(
0
)
(
3
0
)
Fro
m
(
1
5
)
,
(
1
6
)
,
a
n
d
(
2
3
)
,
we
h
a
v
e
(
)
=
(
)
≅
0
.
T
h
e
n
,
w
e
r
e
p
la
ce
t
h
e
m
in
(
3
0
)
wit
h
th
ei
r
e
x
p
r
ess
i
o
n
f
r
o
m
(
2
2
)
:
≤
2
+
(
1
2
(
0
)
̅
̅
̅
̅
(
0
)
+
1
3
,
3
(
0
)
+
1
2
,
̅
̅
̅
̅
2
(
0
)
+
1
3
,
3
(
0
)
)
(
3
1
)
Hen
ce
,
th
e
a
b
o
v
e
r
esu
lt
g
u
a
r
an
tees
a
co
n
v
er
g
en
ce
tim
e
b
ased
o
n
T
D
-
VDC
ap
p
r
o
ac
h
l
ess
s
h
o
r
t
th
an
th
e
ex
p
r
ess
io
n
g
iv
e
n
in
(
3
1
)
.
I
n
th
is
s
ec
tio
n
,
th
e
n
ew
T
D
-
VDC
f
o
r
th
e
u
n
d
er
ac
tu
ated
r
o
b
o
t
h
as
b
ee
n
d
ev
elo
p
ed
an
d
its
s
tab
ilit
y
h
as
b
ee
n
p
r
o
v
ed
.
T
o
test
its
ef
f
ec
tiv
en
ess
,
a
ca
s
e
s
tu
d
y
is
in
tr
o
d
u
ce
d
in
th
e
n
e
x
t
s
ec
tio
n
u
s
in
g
th
e
r
o
b
o
t
m
an
ip
u
lato
r
UR
1
0
.
I
n
o
r
d
er
to
test
th
e
u
n
d
er
ac
tu
ated
co
n
t
r
o
l
ler
,
a
jo
in
t
f
au
lt
is
c
o
-
s
im
u
late
d
u
s
in
g
MA
T
L
AB
an
d
Simu
lin
k
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
Ca
s
e
s
t
ud
y
des
cr
iptio
n
T
o
illu
s
tr
ate
th
e
ef
f
ec
ti
v
en
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
y
,
th
is
s
ec
tio
n
p
r
esen
ts
a
c
ase
s
tu
d
y
p
er
f
o
r
m
ed
f
o
r
tr
ac
k
in
g
tr
ajec
to
r
y
,
in
C
ar
tesi
an
s
p
ac
e,
u
s
in
g
th
e
UR
1
0
r
o
b
o
tic
m
an
i
p
u
lato
r
[
2
4
]
.
T
h
e
in
ten
d
e
d
jo
in
t
an
g
les
ar
e
o
b
tain
e
d
b
y
c
o
n
v
er
tin
g
th
e
d
esire
d
en
d
-
ef
f
e
cto
r
p
o
s
itio
n
u
s
in
g
in
v
er
s
e
k
i
n
em
atics
[
2
5
]
.
T
h
e
m
an
ip
u
lato
r
r
o
b
o
t
is
co
n
s
id
er
ed
a
f
u
ll
-
ac
tu
ate
d
r
o
b
o
t.
Ho
w
ev
er
,
it
tr
an
s
itio
n
s
to
an
u
n
d
e
r
ac
tu
ated
s
tate
wh
en
th
e
f
if
th
jo
in
t
e
x
p
er
ien
ce
s
a
f
a
u
lt.
T
o
ad
d
r
ess
th
is
,
th
e
d
is
cu
s
s
ed
T
D
-
VDC
co
n
tr
o
ller
is
d
esig
n
ed
b
ased
o
n
th
e
m
o
d
el
d
ev
el
o
p
ed
i
n
s
ec
tio
n
s
2
an
d
3
,
an
d
th
e
r
o
b
o
t
m
o
d
e
l
is
co
-
s
im
u
lated
in
Me
ch
an
i
cs
E
x
p
lo
r
er
,
u
s
in
g
MA
T
L
AB
an
d
Simu
lin
k
So
f
t
war
e.
T
h
e
f
u
ll
-
ac
t
u
ated
UR
1
0
h
as
6
Do
Fs
,
wh
ile
th
e
c
o
n
s
id
er
ed
u
n
d
er
ac
t
u
ated
UR
1
0
h
as
a
f
if
th
p
ass
iv
e
jo
in
t,
with
th
e
r
em
ain
in
g
jo
i
n
ts
r
em
ain
in
g
ac
tiv
e.
T
h
e
r
ea
l
v
al
u
es
f
o
r
th
e
p
ass
iv
e
jo
in
t q
5
ar
e
o
b
tain
e
d
d
ir
ec
tly
f
r
o
m
th
e
c
o
-
s
im
u
latio
n
u
s
ed
with
Simu
lin
k
.
T
o
p
er
f
o
r
m
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
,
th
e
r
o
b
o
t
is
in
itially
f
u
lly
-
ac
tu
ated
a
n
d
is
co
n
tr
o
lle
d
u
s
in
g
t
h
e
TD
-
VDC.
Ho
wev
er
,
wh
en
a
n
ac
tu
ato
r
f
ails
at
a
ch
o
s
en
tim
e,
th
e
r
o
b
o
t
b
ec
o
m
es
u
n
d
er
ac
tu
ated
.
I
n
th
is
s
itu
atio
n
,
th
e
d
esig
n
e
d
co
n
t
r
o
l
ler
s
witch
es
au
to
m
atica
lly
to
t
h
e
u
n
d
er
ac
tu
ated
T
D
-
VDC
m
o
d
e,
wh
ich
ap
p
lies
T
h
eo
r
em
1
.
T
h
e
s
im
u
latio
n
m
o
d
el
is
d
ev
elo
p
ed
u
s
in
g
MA
T
L
AB
an
d
Simu
lin
k
as
s
h
o
wn
in
Fig
u
r
e
3
,
wh
ic
h
co
r
r
esp
o
n
d
s
to
th
e
b
l
o
ck
d
ia
g
r
am
s
h
o
wn
in
Fig
u
r
e
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
V
ir
tu
a
l d
ec
o
mp
o
s
itio
n
w
ith
time
d
ela
y
co
n
tr
o
l fo
r
…
(
I
ma
n
e
C
h
eikh
)
799
Fig
u
r
e
3
.
T
h
e
T
D
-
VDC co
-
s
im
u
latio
n
s
etu
p
As
d
ep
icted
in
Fig
u
r
e
3
,
th
e
u
s
er
in
p
u
t
b
lo
ck
d
ef
i
n
es
th
e
d
esire
d
tr
ajec
to
r
y
,
d
ep
e
n
d
in
g
o
n
ea
ch
ap
p
licatio
n
'
s
r
eq
u
ir
em
en
ts
.
T
h
e
co
n
tr
o
l
b
lo
c
k
co
r
r
esp
o
n
d
s
to
th
e
in
v
er
s
e
k
in
em
atics
m
o
d
u
le,
wh
o
s
e
o
u
tp
u
ts
ar
e
f
ed
in
to
th
e
r
o
b
o
t
c
o
n
tr
o
ll
er
to
co
m
p
u
te
th
e
jo
in
t
to
r
q
u
e
s
.
T
h
e
r
o
b
o
t
b
lo
c
k
r
ep
r
esen
ts
t
h
e
s
im
u
lated
r
o
b
o
t,
wh
ich
u
s
es
th
ese
to
r
q
u
es
an
d
p
er
f
o
r
m
s
th
e
tr
ac
k
in
g
tr
ajec
to
r
y
.
W
h
en
a
jo
in
t
f
ailu
r
e
o
cc
u
r
s
,
th
e
p
ass
iv
e
jo
in
t
p
o
s
itio
n
is
th
en
in
co
r
p
o
r
ated
i
n
to
th
e
in
v
er
s
e
k
in
em
atics m
o
d
el.
T
h
is
co
-
s
im
u
latio
n
aim
s
to
tr
ac
k
a
d
esire
d
p
o
s
itio
n
tr
aje
cto
r
y
in
ca
r
tesi
an
s
p
ac
e
with
th
e
f
u
ll
-
ac
tu
ated
UR
1
0
.
T
h
er
ea
f
ter
,
t
h
e
f
if
th
jo
in
t
b
ec
o
m
es
p
ass
iv
e
at
t
=2s
.
I
n
th
e
s
am
e
way
as
a
p
ick
-
an
d
-
p
lace
in
d
u
s
tr
ial
tr
ajec
to
r
y
,
th
e
en
d
-
ef
f
ec
to
r
d
esire
d
p
o
s
itio
n
s
,
=
{
,
,
,
,
,
}
with
=
[
0
,
…
,
4
]
s
tar
t
f
r
o
m
an
in
itial
g
o
al
p
o
s
itio
n
a
n
d
g
o
to
f
o
u
r
g
o
al
p
o
s
itio
n
s
,
r
esp
ec
tiv
ely
,
in
d
i
f
f
er
en
t d
esire
d
tim
e
s
o
f
ar
r
iv
al
an
d
v
elo
cities
̇
d
,
k
.
Her
ein
,
we
ch
o
o
s
e
to
u
s
e
th
e
cu
b
ic
p
o
ly
n
o
m
ial
tr
ajec
to
r
y
[
2
6
]
:
,
(
)
=
3
(
−
0
)
3
+
2
(
−
0
)
2
+
1
(
−
0
)
+
0
;
(
3
2
)
W
h
er
e
0
=
,
0
,
1
=
̇
,
0
,
2
=
3
2
(
,
k
−
,
0
)
−
2
̇
,
0
−
1
̇
,
,
an
d
3
=
2
3
(
,
k
−
,
0
)
−
1
2
(
̇
,
0
+
̇
,
)
ar
e
th
e
co
e
f
f
icien
ts
o
f
th
e
c
u
b
ic
p
o
ly
n
o
m
ial
tr
ajec
to
r
y
.
T
h
e
p
h
y
s
ical
p
ar
am
ete
r
s
o
f
t
h
e
m
an
ip
u
lato
r
r
o
b
o
t U
R
1
0
ar
e
d
escr
ib
ed
in
T
ab
le
1
[
2
7
]
.
T
h
o
s
e
p
ar
am
eter
s
ar
e
u
s
ed
in
T
D
-
VDC ca
lcu
latio
n
s
.
T
ab
le
1
.
Ph
y
s
ical
p
ar
a
m
eter
s
o
f
th
e
UR
1
0
r
obot
M
a
ss
(
K
g
)
Le
n
g
t
h
(
m)
C
o
u
l
o
m
b
f
r
i
c
t
i
o
n
c
o
e
f
f
i
c
i
e
n
t
(
N
.
m)
M
o
me
n
t
o
f
i
n
e
r
t
i
a
(
K
g
.
m
2
)
m
1=
7.778
l
1
=0.127
3
ξ
c1
=
0
.
5
i
m
,
1
=
0.042
01
m
2
=
12
.
930
l
2
=0.612
0
ξ
c2
=
0
.
5
i
m
,
2
=
1.614
3
m
3
=
3
.
87
0
l
3
=0.572
3
ξ
c3
=
0
.
5
i
m
,
3
=
0.422
5
m
4
=
1
.
96
0
l
4
=0.163
9
ξ
c4
=
0
.
5
i
m
,
4
=
0.017
5
m
5
=
1
.
96
0
l
5
=0.115
7
ξ
c5
=
0
.
5
i
m
,
5
=
0.008
7
m
6
=
0
.
202
l
6
=0.092
2
ξ
c6
=
0
.
5
i
m
,
6
=
0.000
5
Mo
r
eo
v
er
,
we
in
ject
th
e
u
n
ce
r
tain
ties
an
d
d
is
tu
r
b
an
ce
s
at
all
th
e
tr
ac
k
in
g
tr
ajec
to
r
y
tim
es a
s
:
(
)
=
{
−
5
∗
(
2
)
(
2
)
(
2
)
0
0
0
(
3
3
)
Fo
llo
win
g
th
e
clo
s
ed
-
lo
o
p
b
l
o
ck
d
iag
r
am
g
iv
e
n
in
Fig
u
r
e
2
,
we
u
s
e
a
tim
e
d
elay
eq
u
al
to
th
e
f
ix
ed
s
am
p
le
tim
e
=
10
−
4
(
s
)
.
T
h
is
ch
o
ice
en
h
a
n
ce
s
ac
cu
r
ac
y
an
d
p
r
ec
is
io
n
d
u
r
i
n
g
r
ea
l
-
tim
e
s
im
u
latio
n
in
Si
m
u
lin
k
.
Fu
r
th
er
m
o
r
e
,
th
e
c
o
n
s
tan
ts
̅
̅
̅
̅
̅
,
,
̅
̅
̅
̅
̅
ar
e
ch
o
s
en
ac
c
o
r
d
in
g
to
ass
u
m
p
tio
n
S2
.
N
o
f
o
r
m
al
o
p
tim
izatio
n
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
7
9
1
-
805
800
m
o
d
el
-
b
ased
tu
n
in
g
was
ap
p
li
ed
in
th
is
wo
r
k
.
Du
e
to
th
e
s
y
s
tem
’
s
co
m
p
lex
ity
a
n
d
t
h
e
a
b
s
en
ce
o
f
a
p
r
ec
is
e
an
aly
tical
m
o
d
el,
th
e
lin
k
s
an
d
jo
in
ts
co
n
tr
o
l
p
ar
am
eter
s
,
,
,
wer
e
d
eter
m
in
e
d
th
r
o
u
g
h
a
tr
i
al
-
an
d
-
er
r
o
r
p
r
o
ce
s
s
.
I
n
itial
g
ain
s
wer
e
c
h
o
s
en
,
th
en
r
ef
i
n
ed
v
ia
iter
ativ
e
s
im
u
latio
n
s
to
m
ee
t
th
e
s
u
itab
le
p
er
f
o
r
m
an
ce
g
o
als in
s
tab
ilit
y
an
d
tr
ajec
to
r
y
tr
ac
k
in
g
.
4
.
2
.
Co
-
s
im
ula
t
io
n
r
esu
lt
s
T
h
e
co
-
s
im
u
latio
n
r
esu
lts
ar
e
p
r
esen
ted
f
o
r
th
e
p
r
o
p
o
s
ed
T
D
-
VDC
co
n
tr
o
ller
an
d
th
e
SMC
-
PF
L
C
co
n
tr
o
ller
d
e
v
elo
p
e
d
in
th
e
p
a
p
er
[
4
]
o
n
th
e
task
s
p
ac
e.
T
h
e
s
am
e
tr
ajec
to
r
y
is
test
ed
f
o
r
b
o
th
co
n
tr
o
ller
s
to
b
etter
co
m
p
ar
e
th
e
r
esu
lts
o
f
th
e
co
n
tr
o
ller
s
.
Fu
r
th
er
m
o
r
e,
th
e
s
am
e
u
n
ce
r
tain
ties
an
d
d
is
tu
r
b
an
ce
s
ar
e
also
tak
en
in
to
ac
c
o
u
n
t a
s
m
en
ti
o
n
ed
in
(
3
3
)
.
Fo
r
th
at
p
u
r
p
o
s
e,
Fig
u
r
e
4
s
h
o
w
s
two
o
f
th
e
f
iv
e
r
ea
l
d
esire
d
p
o
s
itio
n
s
d
u
r
in
g
th
e
co
-
s
i
m
u
latio
n
,
d
em
o
n
s
tr
atin
g
h
o
w
t
h
e
UR
1
0
ef
f
ec
tiv
ely
tr
a
ck
s
th
ese
p
o
s
iti
o
n
s
in
ca
r
tesi
an
s
p
ac
e.
Fig
u
r
e
s
5
an
d
6
d
escr
ib
e
th
e
p
o
s
itio
n
er
r
o
r
s
f
o
r
th
e
s
ix
jo
in
ts
o
f
th
e
r
o
b
o
t
UR
1
0
u
n
d
er
th
e
T
D
-
VDC
an
d
SMC
-
PF
L
C
,
r
esp
ec
tiv
ely
.
Fig
u
r
e
s
7
(
a)
an
d
7
(
b
)
f
u
r
th
er
d
etail
th
e
tr
ac
k
in
g
tr
ajec
to
r
y
i
n
ca
r
tesi
an
s
p
ac
e
f
o
r
b
o
th
c
o
n
tr
o
ller
s
SMC
-
P
FLC
an
d
T
D
-
VDC,
h
i
g
h
lig
h
tin
g
t
h
e
p
er
f
o
r
m
a
n
ce
d
if
f
er
e
n
ce
s
.
Fu
r
th
er
m
o
r
e
,
jo
in
ts
’
to
r
q
u
es
ch
an
g
e
p
er
io
d
ically
with
h
ig
h
p
r
ec
is
io
n
d
u
e
to
th
e
ch
o
ice
o
f
T
s
.
Mo
r
eo
v
er
,
T
ab
le
2
r
e
p
r
esen
t
s
a
co
m
p
ar
ativ
e
s
tu
d
y
b
etw
ee
n
th
e
two
ap
p
r
o
ac
h
es
T
D
-
VDC
an
d
SMC
-
PF
L
C
to
co
n
tr
o
l
th
e
r
o
b
o
t
UR
1
0
th
at
is
f
u
ll
-
ac
tu
ated
u
n
til
th
e
tim
e
=
2
an
d
th
en
b
ec
o
m
es
u
n
d
er
ac
tu
ate
d
with
th
e
f
if
th
j
o
in
t
p
ass
iv
e.
Ad
d
itio
n
ally
,
th
e
r
o
o
t
m
ain
s
q
u
ar
e
(
R
MS)
is
ad
o
p
ted
to
ev
alu
ate
th
e
co
n
tr
o
ller
s
q
u
an
titativ
ely
a
n
d
is
d
ef
in
e
d
as:
(
)
=
√
1
∫
|
(
(
)
|
2
0
(
3
4
)
Fig
u
r
e
4
.
T
wo
ex
am
p
les o
f
co
-
s
im
u
lated
d
esire
d
p
o
s
itio
n
s
at
d
if
f
er
en
t tim
e
s
ca
les
Fig
u
r
e
5
.
E
r
r
o
r
tr
ac
k
in
g
u
s
in
g
th
e
T
D
-
VDC f
o
r
th
e
u
n
d
er
ac
t
u
ated
r
o
b
o
t U
R
1
0
Evaluation Warning : The document was created with Spire.PDF for Python.