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
R
A)
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
2
0
,
p
p
.
1
1
3
~
1
2
2
I
SS
N:
2089
-
4
8
5
6
,
DOI
: 1
0
.
1
1
5
9
1
/
i
jr
a
.
v9
i
2
.
pp
1
1
3
-
1
2
2
113
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
r
a
.
ia
esco
r
e.
co
m
Dy
na
mics
of t
ru
n
k t
y
pe robo
t
wit
h
spherica
l
piezo
elect
ri
c actu
a
tors
Ais
t
is
Aug
us
t
a
it
is
1
,
Vy
t
a
uta
s
J
urėna
s
2
1
De
p
a
rtme
n
t
o
f
In
fo
rm
a
ti
o
n
a
l
Tec
h
n
o
lo
g
ies
,
Viln
iu
s G
e
d
imin
a
s T
e
c
h
n
ica
l
Un
i
v
e
rsity
,
Li
t
h
u
a
n
ia
2
In
stit
u
te
o
f
M
e
c
h
a
tro
n
ics
,
Ka
u
n
a
s Un
iv
e
rsity
o
f
Tec
h
n
o
lo
g
y
,
Li
t
h
u
a
n
ia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Feb
7
,
2
0
2
0
R
ev
is
ed
Feb
2
4
,
2
0
2
0
Acc
ep
ted
Mar
1
0
,
2
0
20
Tru
n
k
ty
p
e
ro
b
o
ts
(T
TRs)
a
re
e
x
c
lu
siv
e
.
Th
e
se
ro
b
o
ts
c
a
n
p
r
o
v
id
e
a
h
ig
h
lev
e
l
o
f
m
a
n
e
u
v
e
ra
b
il
i
ty
a
n
d
h
a
v
e
a
p
o
te
n
ti
a
l
i
n
m
e
d
ici
n
e
o
r
h
i
g
h
risk
z
o
n
e
s.
TT
Rs
a
re
d
e
term
in
e
d
a
s
a
l
o
n
g
s
e
rial
li
n
k
a
g
e
o
f
sim
il
a
r
se
g
m
e
n
ts
.
Th
e
y
a
re
u
su
a
ll
y
c
o
n
n
e
c
ted
u
si
n
g
te
n
d
o
n
s
o
r
sm
a
ll
a
c
tu
a
to
rs.
A
sp
h
e
rica
l
a
c
tu
a
to
r
is
th
e
m
o
st
a
p
p
re
c
iab
le
o
p
ti
o
n
.
T
h
e
m
o
ti
o
n
o
f
re
a
l
sp
h
e
rica
l
a
c
tu
a
to
r
(RS
A)
c
a
n
b
e
e
a
sily
o
b
tain
e
d
a
p
p
ly
i
n
g
a
n
in
v
e
rse
p
iez
o
e
lec
tri
c
e
ffe
c
t.
It
h
a
s
th
re
e
in
d
e
p
e
n
d
e
n
t
s
p
in
n
in
g
a
x
e
s.
Th
e
se
a
x
e
s
a
r
e
p
e
rp
e
n
d
icu
lar
to
e
a
c
h
o
th
e
r
d
e
sp
it
e
t
h
e
h
ist
o
ry
o
f
e
x
c
it
a
ti
o
n
.
Kin
e
m
a
ti
c
s
a
n
d
d
y
n
a
m
ics
o
f
R
S
A
a
lmo
st
h
a
v
e
n
o
b
a
sic
s
re
g
a
rd
les
s
o
f
m
e
n
ti
o
n
e
d
fe
a
tu
re
s.
Th
is
sit
u
a
ti
o
n
c
a
n
b
e
e
x
p
lai
n
e
d
a
c
c
o
rd
i
n
g
to
c
o
m
m
o
n
d
isa
d
v
a
n
tag
e
s o
f
o
th
e
r
S
As
:
s
o
p
h
isti
c
a
ted
stru
c
tu
re
a
n
d
c
o
m
p
lex
c
o
n
tr
o
l.
Th
e
stru
c
t
u
re
s
a
n
d
a
b
il
it
ies
o
f
TT
Rs
a
re
re
v
iew
e
d
in
th
e
first
se
c
ti
o
n
o
f
th
is
a
rti
c
le.
At
th
e
b
e
g
i
n
n
i
n
g
o
f
th
e
fo
u
rt
h
se
c
ti
o
n
t
h
e
k
in
e
m
a
ti
c
s
o
f
p
iez
o
e
lec
tri
c
TT
R
wit
h
two
d
iffer
e
n
t
RS
As
is
in
tr
o
d
u
c
e
d
.
Its
re
su
lt
s
o
f
in
v
e
rse
d
y
n
a
m
ics
u
sin
g
E
u
ler
-
Lag
ra
n
g
e
e
q
u
a
ti
o
n
s
a
re
p
re
se
n
ted
a
t
th
e
e
n
d
o
f
t
h
e
fo
u
rt
h
se
c
ti
o
n
.
S
imilar
re
su
lt
s
a
re
d
e
riv
e
d
u
sin
g
a
n
a
n
a
l
y
ti
c
a
l
-
p
o
ten
ti
a
l
m
e
t
h
o
d
i
n
th
e
fift
h
se
c
ti
o
n
.
It
is
q
u
it
e
a
c
c
u
ra
t
e
a
n
d
e
ffe
c
ti
v
e
o
p
t
io
n
to
d
e
term
in
e
in
v
e
rse
d
y
n
a
m
ics
o
f
t
h
e
TT
R
e
m
p
lo
y
i
n
g
a
n
a
n
a
ly
ti
c
a
l
-
p
o
ten
t
ial
m
e
th
o
d
.
K
ey
w
o
r
d
s
:
E
u
ler
-
lag
r
a
n
g
e
d
y
n
am
ics
Kin
em
atics
Po
ten
tial to
r
q
u
e
Sp
h
er
ical
p
iezo
ac
tu
ato
r
T
h
is i
s
a
n
o
p
e
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
:
Ais
ti
s
Au
g
u
s
taitis
,
Dep
ar
tm
en
t o
f
I
n
f
o
r
m
atio
n
al
T
ec
h
n
o
lo
g
ies,
Viln
iu
s
Ged
im
in
as T
ec
h
n
ical
Un
iv
er
s
ity
,
Sau
lėtek
io
a
l.
1
1
,
Viln
iu
s
1
0
2
2
3
,
L
ith
u
a
n
ia.
E
m
ail:
ais.au
g
u
s
taitis
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
A
tr
u
n
k
ty
p
e
r
o
b
o
t
(
T
T
R
)
is
a
s
er
ial
ch
ain
o
f
lin
k
s
.
T
h
ey
ca
n
b
e
co
n
n
ec
te
d
with
ten
d
o
n
s
o
r
f
lex
ib
le
an
d
r
o
tar
y
ac
tu
ato
r
s
.
A
r
ea
l
s
p
h
er
ical
ac
tu
ato
r
(
R
SA)
h
as
t
h
r
ee
p
er
p
e
n
d
icu
lar
s
p
in
n
in
g
ax
es
an
d
th
is
s
ta
te
is
co
n
s
tan
t
d
esp
ite
th
e
h
i
s
to
r
y
o
f
ex
citatio
n
.
A
s
p
h
er
ical
ac
tu
ato
r
u
s
u
ally
h
as
v
er
y
s
o
p
h
is
t
icate
d
s
tr
u
ctu
r
e
an
d
is
h
ar
d
to
co
n
tr
o
l a
cc
u
r
ately
.
C
o
n
s
is
ten
tly
a
R
S
A
is
v
er
y
u
n
p
o
p
u
lar
in
p
r
ac
tical
an
d
th
e
o
r
e
tical
ca
s
es.
Gr
asp
in
g
ab
ilit
ies
o
f
T
T
R
ar
e
in
v
esti
g
ated
b
y
L
i,
T
en
g
,
Xi
ao
,
Kap
ad
ia,
B
ar
to
w
a
n
d
W
alk
e
r
in
2
D
wo
r
k
s
p
ac
e.
T
h
e
r
o
b
o
t is au
to
n
o
m
o
u
s
an
d
co
n
s
is
ts
o
f
f
lex
ib
le
p
n
eu
m
atic
ac
tu
ato
r
s
,
b
u
t h
as
n
o
en
d
ef
f
ec
to
r
an
d
clo
s
ed
lo
o
p
s
y
s
tem
to
o
.
T
h
e
n
u
m
er
ical
o
p
er
atio
n
s
f
o
r
tar
g
et
d
etec
tio
n
an
d
p
at
h
d
eter
m
in
ati
o
n
tak
e
o
n
l
y
0
.
2
s
.
T
h
e
tim
e
o
f
m
an
ip
u
latio
n
r
a
n
g
es
f
r
o
m
3
0
to
1
3
0
s
s
ee
k
in
g
to
av
o
id
u
n
welc
o
m
e
o
s
cillatio
n
s
b
ec
au
s
e
o
f
lo
w
s
tiff
n
ess
an
d
h
ig
h
in
e
r
tia
[
1
]
.
A
p
n
eu
m
atic
r
o
b
o
t
is
in
tr
o
d
u
c
ed
b
y
Ma
h
l,
Hild
eb
e
r
t
an
d
Sa
wo
d
n
y
.
I
t
co
n
s
is
ts
o
f
3
s
er
ial
s
tag
es
an
d
a
th
r
ee
-
f
in
g
e
r
ed
en
d
ef
f
ec
to
r
.
T
h
r
ee
ev
en
l
y
p
lace
d
f
lex
i
b
le
h
o
s
es
in
cir
cu
m
f
er
en
ce
d
ir
ec
tio
n
ar
e
u
s
ed
to
co
n
tr
o
l
o
n
e
s
tag
e.
E
v
e
r
y
s
tag
e
ca
n
b
e
b
en
d
e
d
i
n
d
ep
e
n
d
en
tly
.
A
t
o
tal
b
en
d
in
g
m
o
m
e
n
t
g
r
o
ws
u
p
f
r
o
m
th
e
en
d
p
o
in
t to
t
h
e
f
ir
s
t lin
k
o
f
th
e
r
o
b
o
t,
s
o
its
cr
o
s
s
-
s
ec
tio
n
s
ar
e
en
lar
g
ed
i
n
th
e
s
am
e
way
[
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
5
6
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l.
9
,
N
o
.
2
,
J
u
n
e
2
0
2
0
:
1
1
3
–
1
2
2
114
Nag
ar
ajan
,
Ku
m
ar
a
n
d
Kan
n
a
ar
e
m
ad
e
a
d
ir
ec
t
k
i
n
em
atic
r
esear
ch
f
o
r
a
T
T
R
with
ten
d
o
n
s
u
s
in
g
ADAM
S
an
d
ANSYS
m
o
d
elin
g
s
y
s
tem
s
.
T
h
ey
h
av
e
s
elec
ted
to
e
x
p
lo
r
e
th
e
r
o
b
o
t
with
f
o
u
r
i
n
d
ep
e
n
d
en
t
s
ec
tio
n
s
.
E
v
er
y
s
ec
tio
n
h
as
6
s
er
ially
co
n
n
ec
ted
d
is
k
s
an
d
u
n
iv
er
s
a
l
jo
in
ts
b
etwe
en
t
h
em
.
On
e
ten
d
o
n
is
ab
le
to
tr
an
s
f
er
th
e
f
o
r
ce
o
n
ly
in
o
n
e
d
ir
ec
tio
n
.
T
h
er
ef
o
r
e
two
ten
d
o
n
s
ar
e
n
ee
d
ed
to
en
s
u
r
e
a
n
ac
tu
atio
n
o
f
s
in
g
le
DOF.
Fo
u
r
ev
en
ly
p
o
s
ted
ten
d
o
n
s
ar
e
u
s
ed
to
ac
tu
ate
a
s
in
g
le
s
ec
tio
n
.
Fo
u
r
ev
en
ly
p
o
s
te
d
s
p
r
in
g
s
h
as
b
e
en
em
p
lo
y
ed
f
o
r
ev
er
y
p
ai
r
o
f
d
is
k
s
to
en
s
u
r
e
th
e
s
tiff
n
ess
o
f
th
e
r
o
b
o
t.
T
h
e
au
th
o
r
s
h
av
e
p
r
o
v
ed
ag
ain
th
at
d
ef
o
r
m
atio
n
s
b
etwe
en
th
e
d
is
k
s
o
f
th
e
s
am
e
s
ec
tio
n
ar
e
d
is
tr
ib
u
ted
u
n
if
o
r
m
ly
[
3
]
.
A
s
p
ec
ial
d
esig
n
o
f
s
o
f
t
r
o
b
o
t
to
m
im
ic
th
e
m
o
tio
n
s
o
f
elep
h
a
n
t
t
r
u
n
k
o
r
s
n
ak
e
s
lith
er
in
g
is
g
en
er
ated
.
T
h
e
r
o
b
o
t
is
a
co
m
b
in
atio
n
o
f
f
ew
s
ec
tio
n
s
.
E
ac
h
s
ec
tio
n
is
a
g
r
o
u
p
o
f
tu
b
u
lar
a
n
d
h
elica
l
s
eg
m
en
ts
.
T
h
ey
ar
e
m
a
d
e
f
r
o
m
th
e
s
tr
ip
s
u
s
in
g
io
n
ic
p
o
ly
m
er
-
m
etal
n
an
o
co
m
p
o
s
ites
(
I
PMC
s
)
.
T
h
is
ty
p
e
o
f
s
eg
m
e
n
ts
ar
e
a
b
le
to
p
e
r
f
o
r
m
n
o
t
o
n
ly
v
ar
i
o
u
s
ac
tu
ati
o
n
s
(
lin
ea
r
ex
p
an
s
io
n
,
co
n
tr
a
ctio
n
,
b
e
n
d
in
g
a
n
d
twis
tin
g
)
,
b
u
t e
n
er
g
y
h
a
r
v
esti
n
g
an
d
m
o
tio
n
s
en
s
in
g
t
o
o
[
4
]
.
J
o
n
es a
n
d
W
alk
er
h
av
e
p
r
esen
ted
a
k
in
em
atic
th
eo
r
y
f
o
r
a
T
T
R
with
f
lex
ib
le
lin
k
s
.
I
t c
an
b
e
ac
tu
ated
em
p
lo
y
in
g
d
if
f
e
r
en
t
air
p
r
ess
u
r
es
in
g
o
f
f
er
r
e
d
h
o
s
es
o
r
d
i
f
f
er
en
t
len
g
th
s
o
f
ten
d
o
n
s
to
o
.
T
h
e
esti
m
atio
n
o
f
p
o
s
itio
n
an
d
o
r
ien
tatio
n
an
d
a
b
r
ief
r
e
p
o
r
t
a
b
o
u
t
its
s
in
g
u
lar
ities
ar
e
d
escr
ib
ed
c
o
m
p
r
e
h
en
s
iv
ely
.
T
h
e
lo
ca
l
p
ar
am
eter
s
o
f
p
r
ess
u
r
es
o
r
len
g
th
s
an
d
th
eir
f
ir
s
t
o
r
s
ec
o
n
d
d
er
iv
ativ
es
ca
n
b
e
esti
m
ated
ac
co
r
d
in
g
t
o
in
v
er
s
e
J
ac
o
b
ian
m
atr
ix
[
5
]
.
C
h
u
n
g
,
R
h
ee
,
Sh
im
,
L
ee
an
d
Par
k
h
a
v
e
a
n
aly
ze
d
d
o
o
r
o
p
en
in
g
r
o
b
o
ts
.
T
h
ese
r
o
b
o
ts
ca
n
b
e
u
s
ed
in
em
er
g
e
n
cy
s
itu
atio
n
s
to
s
h
i
f
t
h
u
m
a
n
s
.
T
h
ese
a
u
th
o
r
s
h
av
e
o
f
f
e
r
ed
a
n
ew
c
o
n
ce
p
tio
n
f
o
r
th
at
k
in
d
o
f
r
o
b
o
ts
.
T
h
ey
s
u
g
g
est
a
m
an
ip
u
lato
r
with
th
r
ee
f
in
g
e
r
s
an
d
th
e
f
o
r
ce
s
en
s
o
r
s
at
th
eir
tip
s
as
an
alter
n
ativ
e
f
o
r
a
wr
is
t
s
en
s
o
r
.
I
t
h
as
a
h
ig
h
p
r
ice
a
n
d
a
co
m
p
lex
s
tr
u
ct
u
r
e
to
o
.
A
te
s
ted
r
o
b
o
t
ca
n
b
e
s
ep
ar
ated
in
to
3
m
o
tio
n
s
tag
es:
o
m
n
id
i
r
ec
tio
n
al
ch
ass
is
,
m
an
ip
u
lato
r
with
6
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
(
DOFs
)
an
d
an
en
d
ef
f
e
cto
r
with
3
f
in
g
er
s
.
T
h
ese
s
tag
es
ar
e
ac
tu
ated
b
y
1
4
s
er
v
o
m
o
to
r
s
.
1
6
s
o
n
ar
,
1
6
in
f
r
a
r
ed
s
en
s
o
r
s
an
d
a
laser
r
an
g
e
f
in
d
e
r
ar
e
in
s
talled
to
en
h
a
n
ce
th
e
f
e
atu
r
es o
f
r
o
b
o
t v
is
io
n
[
6
]
.
A
T
T
R
o
f
s
er
ially
co
n
n
ec
ted
tu
b
es
with
in
clin
ed
en
d
p
lan
es a
t
o
n
e
s
id
e
is
p
r
esen
ted
b
y
Salo
m
o
n
an
d
W
o
lf
.
I
t
is
ab
le
to
p
er
f
o
r
m
1
6
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
.
T
h
e
s
am
e
ty
p
e
p
lan
es
o
f
th
e
tu
b
es
ar
e
c
o
n
ju
g
ated
to
g
eth
er
.
A
r
ev
o
lu
te
ac
tu
ato
r
g
o
es
af
ter
cy
lin
d
r
ical
-
in
clin
e
ac
tu
ato
r
a
n
d
s
o
o
n
.
T
h
is
r
o
b
o
t
p
r
o
v
id
es
h
ig
h
lev
el
f
ea
tu
r
es
lik
e
s
tiff
n
ess
an
d
p
o
s
itio
n
ac
cu
r
ac
y
.
I
t
p
o
s
s
ess
es
th
ese
d
im
en
s
io
n
s
:
d
iam
eter
o
f
tu
b
e
is
7
.
7
cm
,
to
tal
len
g
th
−
8
0
cm
a
n
d
a
m
ax
im
u
m
d
ev
iatio
n
an
g
le
1
8
0
°.
A
m
ax
im
u
m
tr
av
er
s
e
f
o
r
ce
at
th
e
e
n
d
o
f
th
e
r
o
b
o
t sh
o
u
ld
b
e
less
th
an
2
5
% o
f
its
o
wn
weig
h
t [
7
]
.
T
h
e
ab
ilit
ies o
f
m
o
tio
n
ar
e
in
v
esti
g
ated
an
d
test
ed
b
y
L
iljeb
äc
k
,
Hau
g
s
tu
en
an
d
Petter
s
en
f
o
r
a
s
n
ak
e
ty
p
e
r
o
b
o
t
(
STR).
T
h
is
r
o
b
o
t
is
co
m
p
o
s
ed
o
f
1
0
s
p
h
er
ical
s
eg
m
en
ts
.
T
h
e
y
ar
e
s
er
ially
co
n
n
ec
t
ed
with
s
h
o
r
t
f
lex
ib
le
lin
k
s
.
A
STR
h
as
a
s
im
ila
r
s
tr
u
ctu
r
e
ac
co
r
d
in
g
to
a
T
T
R
.
T
h
e
r
o
tatin
g
f
r
am
e
with
cr
o
s
s
wis
e
o
r
ien
ted
wh
ee
ls
ar
o
u
n
d
it
is
attac
h
ed
to
e
v
er
y
s
eg
m
en
t.
T
h
is
way
th
e
a
ctio
n
o
f
m
o
v
in
g
s
tr
aig
h
t
an
d
tr
a
n
s
v
er
s
ely
is
en
s
u
r
ed
f
o
r
e
v
er
y
s
eg
m
en
t
.
A
p
r
o
p
er
co
n
tr
o
l
o
f
th
e
r
o
b
o
t
is
ac
h
iev
ed
u
s
in
g
a
n
in
ter
n
al
f
u
n
ctio
n
o
d
e
4
5
in
MA
T
L
AB
s
o
f
twar
e.
A
co
m
b
in
ed
task
o
f
STR
is
to
d
etec
t
a
s
tr
aig
h
t
cu
r
s
o
r
lin
e
,
ch
a
n
g
e
its
d
ir
ec
tio
n
a
n
d
cr
awl
alo
n
g
th
e
lin
e
.
T
h
e
task
h
as b
ee
n
s
u
cc
ess
f
u
lly
im
p
lem
en
ted
u
s
in
g
a
n
o
v
el
s
tab
ilizatio
n
alg
o
r
ith
m
[
8
]
.
Kela
s
id
i,
J
esm
an
i,
Petter
s
en
an
d
Gr
av
d
ah
l
h
a
v
e
in
tr
o
d
u
ce
d
a
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
f
r
am
ewo
r
k
.
T
h
is
m
eth
o
d
is
ap
p
lied
to
in
v
esti
g
ate
th
e
ef
f
icien
cy
o
f
lo
co
m
o
tio
n
f
o
r
s
n
ak
e
ty
p
e
r
o
b
o
ts
em
p
lo
y
in
g
a
weig
h
ted
s
u
m
m
eth
o
d
.
A
Par
ticle
Swar
m
Op
ti
m
izatio
n
(
PS
O)
is
u
s
ed
f
o
r
d
if
f
er
en
t
s
et
o
f
weig
h
t
f
ac
to
r
s
.
T
h
e
co
n
s
u
m
e
d
p
o
wer
o
f
t
h
e
r
o
b
o
t
a
n
d
its
f
o
r
war
d
v
elo
city
ar
e
s
elec
ted
as
th
e
m
ain
p
a
r
am
eter
s
o
f
r
esear
ch
.
C
o
n
s
is
ten
tly
an
im
p
r
o
v
e
d
en
er
g
y
ef
f
icien
c
y
o
f
l
o
co
m
o
tio
n
ass
o
ciate
s
w
ith
th
e
d
ec
r
em
en
t
o
f
f
o
r
war
d
v
el
o
city
[
9
]
.
I
m
p
o
r
ta
n
t
p
r
o
ce
s
s
es
o
f
r
ed
u
n
d
an
t
r
o
b
o
ts
lik
e
m
o
tio
n
,
r
e
co
g
n
itio
n
o
f
o
b
jects,
f
etch
i
n
g
an
d
s
af
e
in
ter
f
ac
e
with
h
u
m
an
s
h
a
v
e
b
ee
n
wid
ely
in
v
esti
g
ated
b
y
L
u
o
an
d
Ku
o
.
A
s
er
v
ice
-
o
r
ien
ted
m
u
ltiag
e
n
t
s
y
s
tem
(
So
MA
S)
is
u
s
ed
to
co
n
tr
o
l
an
d
an
aly
ze
th
e
r
o
b
o
t
wi
th
cy
b
e
r
-
p
h
y
s
ical
s
y
s
tem
(
C
PS
)
.
T
h
e
r
esu
lts
o
f
m
en
tio
n
e
d
o
p
e
r
atio
n
s
ap
p
r
o
v
e
th
e
ef
f
ec
tiv
e
n
ess
o
f
in
teg
r
ated
s
y
s
tem
s
r
eg
ar
d
in
g
to
h
i
g
h
p
o
s
itio
n
ac
cu
r
ac
y
an
d
f
ast
s
p
ee
d
.
Oth
e
r
h
i
g
h
q
u
ality
f
ac
to
r
s
o
f
th
e
r
o
b
o
t
in
c
o
m
p
ar
is
o
n
to
t
h
e
r
esu
lts
o
f
o
th
er
r
esear
c
h
er
s
ar
e
m
en
tio
n
ed
t
o
o
[
1
0
]
.
Sev
er
al
p
iezo
e
letr
ic
r
o
b
o
ts
ar
e
p
r
esen
ted
in
F
ig
u
r
es
1
a
n
d
2
.
T
h
ey
ca
n
b
e
n
am
ed
as
tr
u
n
k
t
y
p
e
r
o
b
o
ts
an
d
h
av
e
b
e
en
m
ad
e
in
Me
c
h
atr
o
n
ics
I
n
s
titu
te
o
f
KT
U.
Piezo
elec
tr
ic
T
T
R
s
ar
e
s
p
ec
ial
b
ec
au
s
e
o
f
s
m
all
d
im
en
s
io
n
s
(
to
tal
len
g
th
u
s
u
a
lly
is
less
th
an
2
0
cm
)
an
d
h
i
g
h
r
atio
o
f
o
u
tp
u
t
p
o
wer
to
m
ass
.
T
h
ey
p
o
s
s
ess
a
s
im
p
le
s
tr
u
ctu
r
e
an
d
a
h
ig
h
a
cc
u
r
ac
y
o
f
p
o
s
itio
n
t
o
o
.
T
h
ese
T
T
R
s
ca
n
b
e
s
ig
n
if
ican
t in
m
ed
icin
e
o
r
h
ig
h
r
is
k
zo
n
es.
An
ex
tr
a
f
r
ee
d
o
m
to
m
an
o
eu
v
r
e
is
ac
h
iev
e
d
em
p
lo
y
in
g
a
p
iezo
elec
tr
ic
s
p
h
e
r
ical
ac
tu
ato
r
with
3
in
d
ep
e
n
d
en
t
s
p
in
n
in
g
DOFs
.
A
p
iezo
elec
tr
ic
tu
b
e
F
ig
u
r
e
3
an
d
a
h
o
llo
w
b
all
ar
e
th
e
m
ain
s
tr
u
ctu
r
al
p
ar
ts
o
f
th
e
ac
tu
ato
r
.
T
h
e
b
all
is
a
p
ass
iv
e
lin
k
o
f
alu
m
in
iu
m
,
s
teel
o
r
o
th
e
r
m
ater
ial
with
h
ig
h
Yo
u
n
g
m
o
d
u
lu
s
.
Sev
er
al
lay
er
s
o
f
d
is
tin
ct
m
ater
ials
ar
e
a
p
o
s
s
ib
le
s
tr
u
ctu
r
a
l
o
p
tio
n
o
f
p
ass
iv
e
b
all
to
o
.
Sin
g
le
p
iezo
elec
tr
ic
tu
b
e
h
as
to
b
e
m
o
d
if
ie
d
in
o
r
d
er
to
p
r
o
v
id
e
th
r
ee
p
er
m
an
e
n
t
s
p
in
n
in
g
a
x
es.
T
h
er
e
f
o
r
e
a
n
in
ter
n
al
elec
tr
o
d
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4
8
5
6
Dyn
a
mics o
f tru
n
k
typ
e
r
o
b
o
t
w
ith
s
p
h
erica
l p
iezo
elec
tr
ic
a
c
tu
a
to
r
s
(
A
is
tis
A
u
g
u
s
ta
itis
)
115
o
f
th
e
tu
b
e
is
s
ep
ar
ated
in
to
th
r
ee
eq
u
al
s
ec
tio
n
s
.
Dr
iv
in
g
teeth
ar
e
em
p
lo
y
ed
to
d
e
f
in
e
ac
cu
r
ate
co
n
tact
zo
n
es
with
th
e
b
all.
C
o
n
tr
o
l te
ch
n
iq
u
es f
o
r
m
u
lti
-
ax
is
p
iezo
elec
tr
ic
ac
tu
ato
r
s
ar
e
alr
ea
d
y
d
ef
i
n
ed
[
1
1
]
.
T
h
e
aim
o
f
th
is
wo
r
k
is
to
d
eter
m
in
e
in
v
e
r
s
e
d
y
n
am
ics
o
f
T
T
R
with
two
d
if
f
er
en
t
s
p
h
er
ical
ac
tu
ato
r
s
.
T
h
is
r
o
b
o
t
h
as
a
m
ax
im
u
m
n
u
m
b
er
o
f
DOFs
f
o
r
3
D
m
a
n
ip
u
latio
n
.
T
h
e
d
e
ter
m
in
atio
n
o
f
r
o
b
o
t
d
y
n
am
ics
also
in
cl
u
d
es
th
e
esti
m
atio
n
o
f
C
o
r
io
lis
an
d
ce
n
tr
if
u
g
al
f
o
r
ce
s
.
T
h
ese
f
o
r
ce
s
a
r
e
h
ar
d
to
ev
alu
ate
in
an
aly
tical
way
.
Acc
o
r
d
in
g
to
th
at
i
s
s
elec
ted
to
u
s
e
a
u
n
iv
er
s
al
an
d
ef
f
ec
tiv
e
m
eth
o
d
o
f
E
u
ler
-
L
ag
r
a
n
g
e
eq
u
atio
n
s
an
d
an
a
n
aly
tic
-
p
o
ten
tial
m
o
d
el
to
o
.
T
h
e
r
esu
lts
o
f
p
r
ef
e
r
r
ed
m
eth
o
d
s
ar
e
alm
o
s
t
eq
u
al,
b
u
t
th
eir
o
p
er
atio
n
al
s
p
ee
d
s
ar
e
d
if
f
e
r
e
n
t.
Fig
u
r
e
1
.
Piezo
r
o
b
o
t
with
6
D
OFs
Fig
u
r
e
2
.
Piezo
r
o
b
o
t w
ith
1
5
DOFs
Fig
u
r
e
3
.
Stru
ctu
r
e
o
f
m
o
d
if
ied
p
iezo
elec
tr
ic
tu
b
e
2.
RE
VI
E
W
O
F
E
U
L
E
R
-
L
AG
RANG
E
DYN
AM
I
CS
E
u
ler
-
L
ag
r
a
n
g
e
(
E
-
L
)
m
eth
o
d
is
o
n
e
o
f
th
e
m
o
s
t
u
n
iv
er
s
al
an
d
s
im
p
lest
way
s
to
s
o
l
v
e
in
v
e
r
s
e
d
y
n
am
ics
o
f
m
ec
h
a
n
ical
s
y
s
tem
.
I
t
lets
u
s
e
d
if
f
er
en
t
c
o
o
r
d
in
ate
s
y
s
tem
s
(
C
Ss
)
an
d
co
n
s
is
ts
o
f
th
e
h
ig
h
est
in
teg
r
al
m
em
b
er
s
.
T
h
o
s
e
ar
e
p
o
ten
tial
P
i
an
d
k
in
etic
T
i
en
er
g
ies
o
f
th
e
lin
k
s
.
E
-
L
m
eth
o
d
is
b
ased
o
n
d
if
f
er
en
tial
ap
p
r
o
ac
h
.
T
h
er
ef
o
r
e
it
ca
n
p
r
o
v
id
e
all
p
o
s
s
ib
le
ac
tio
n
an
d
r
ea
ctio
n
f
o
r
ce
s
o
r
to
r
q
u
es.
I
t
lea
d
s
to
a
f
in
al
f
o
r
m
(
1
)
[
1
2
]
.
=
(
)
⋅
̈
+
(
,
̇
)
⋅
̇
+
(
)
(
1
)
wh
er
e:
f
–
v
ec
to
r
o
f
to
tal
t
o
r
q
u
es
f
o
r
ac
tu
atio
n
o
f
t
h
e
DO
Fs
;
,
̇
–
v
ec
to
r
s
o
f
lo
ca
l
r
o
b
o
t
co
o
r
d
in
ates
a
n
d
th
eir
f
ir
s
t
d
er
iv
ativ
es
r
esp
ec
ti
v
ely
;
(
)
̈
−
m
atr
ix
o
f
to
r
q
u
es
to
ev
alu
ate
in
er
tial
p
r
o
p
e
r
ties
;
(
,
̇
)
̇
−
m
atr
ix
o
f
to
r
q
u
es
to
esti
m
ate
th
e
ef
f
ec
ts
o
f
f
r
ictio
n
,
d
am
p
in
g
an
d
th
e
in
f
lu
en
ce
o
f
ce
n
t
r
if
u
g
al
an
d
C
o
r
io
lis
f
o
r
ce
s
also
;
g
(
q
)
–
m
atr
ix
o
f
to
r
q
u
es t
o
ev
alu
ate
th
e
e
f
f
ec
t o
f
g
r
a
v
ity
an
d
s
o
o
n
.
E
-
L
m
eth
o
d
ca
n
b
e
em
p
lo
y
ed
to
d
eter
m
in
e
th
e
d
y
n
am
i
cs
o
f
s
y
s
tem
s
wi
th
f
lex
ib
le
lin
k
s
[
1
3
]
an
d
to
im
p
lem
en
t
v
ar
i
o
u
s
r
e
s
tr
ictio
n
s
f
o
r
its
in
v
esti
g
atio
n
to
o
[
1
4
]
.
T
h
is
m
eth
o
d
is
s
elec
ted
to
ev
alu
ate
th
e
to
r
q
u
es
o
f
r
o
b
o
t
DOFs
at
p
ick
ed
tim
e
m
o
m
en
ts
.
T
h
e
d
ep
en
d
en
cies
o
f
th
e
to
r
q
u
es
o
n
tim
e
ca
n
b
e
ap
p
r
o
x
im
ated
t
o
o
.
Gen
er
al
E
u
ler
-
L
a
g
r
an
g
e
eq
u
atio
n
is
p
r
esen
ted
in
(
2
)
.
C
o
n
s
is
ten
tly
a
s
p
ec
ial
v
ar
iab
le
La
ca
lled
L
ag
r
an
g
ia
n
is
n
ee
d
ed
to
esti
m
ate
(
3
)
[
1
5
]
.
A
n
ew
a
n
d
m
o
r
e
co
m
p
r
eh
e
n
s
iv
e
f
o
r
m
u
la
o
f
E
-
L
(
4
)
ca
n
b
e
wr
itte
n
u
s
in
g
th
e
s
p
ec
ial
f
ea
tu
r
es
o
f
L
ag
r
an
g
ia
n
.
Kin
etic
en
er
g
y
o
f
s
p
in
n
in
g
lin
k
i
is
ev
alu
ated
b
y
(
5
)
an
d
p
o
ten
tial
en
er
g
y
o
f
th
e
s
am
e
lin
k
is
d
ete
r
m
in
ed
b
y
(
6
)
.
=
̇
−
(
2
)
=
∑
−
∑
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
5
6
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l.
9
,
N
o
.
2
,
J
u
n
e
2
0
2
0
:
1
1
3
–
1
2
2
116
=
̇
−
(
4
)
=
(
)
2
⁄
(
5
)
=
−
ℎ
(
6
)
wh
er
e:
,
–
a
s
in
g
le
d
er
i
v
atio
n
o
n
tim
e
an
d
a
p
a
r
tial
d
er
iv
atio
n
o
n
lo
ca
l
c
o
o
r
d
in
at
e
r
esp
ec
tiv
ely
;
La
−
s
u
b
s
titu
te
o
f
m
ec
h
an
ical
en
er
g
y
f
o
r
in
v
esti
g
ated
s
y
s
tem
(
L
ag
r
an
g
ian
)
;
t
–
tim
e;
T
i
,
P
i
–
k
in
etic
an
d
p
o
ten
tial
en
er
g
ies
o
f
lin
k
i
r
esp
ec
tiv
ely
;
Tr
a
ce
(
)
−
s
u
m
o
f
elem
en
ts
o
n
th
e
m
ain
d
iag
o
n
al
o
f
m
atr
ix
;
−
m
atr
ix
o
f
an
g
u
lar
s
p
ee
d
p
r
o
jectio
n
s
t
o
th
e
b
ase
C
S
r
eg
a
r
d
in
g
to
lin
k
i
;
,
m
i
,
h
i
–
m
o
m
en
t
o
f
in
er
ti
a,
m
ass
an
d
ce
n
ter
h
eig
h
t o
f
th
e
l
in
k
i
n
ac
co
r
d
an
c
e
to
th
e
g
r
o
u
n
d
ed
C
S;
g
–
ac
ce
ler
atio
n
o
f
g
r
av
ity
a
n
d
s
o
o
n
.
T
h
e
s
p
ee
d
o
f
a
n
y
r
o
b
o
t
p
o
in
t
ca
n
b
e
esti
m
ated
em
p
l
o
y
in
g
(
7
)
.
T
h
e
d
er
iv
ativ
e
o
f
s
in
g
le
o
r
ien
tatio
n
m
atr
ix
ca
n
b
e
d
eter
m
in
e
d
u
s
in
g
(
8
)
.
0
=
0
=
0
=
[
0
1
⋅
1
2
⋅
…
⋅
−
1
]
=
̇
0
1
1
2
⋅
…
⋅
−
1
+
0
1
̇
1
2
⋅
…
⋅
−
1
+
∙
…
∙
0
̇
(
7
)
−
1
=
−
1
̇
()
wh
er
e:
0
−
g
lo
b
al
s
p
ee
d
v
ec
to
r
o
f
s
elec
ted
lin
k
-
p
o
i
n
t
i
;
0
,
−
g
lo
b
al
an
d
in
itial
p
o
s
itio
n
v
ec
to
r
s
o
f
th
e
lin
k
-
p
o
in
t
r
esp
ec
tiv
ely
;
0
−
g
lo
b
al
o
r
ie
n
tatio
n
m
atr
i
x
o
f
th
e
lin
k
,
wh
ic
h
d
ir
ec
tly
ass
o
ciate
s
with
p
o
in
t
i
;
0
−
s
in
g
le
o
r
ien
tatio
n
m
atr
ix
f
r
o
m
t
h
e
f
ir
s
t
C
S
to
t
h
e
g
r
o
u
n
d
e
d
C
S;
−
lo
ca
l
co
o
r
d
in
ate
(
a
n
g
le)
o
f
lin
k
i
a
n
d
s
o
o
n
.
3.
P
ARAM
E
T
E
RS
O
F
DYN
A
M
I
CA
L
T
ASK
A
T
T
R
with
two
d
if
f
er
en
t
s
p
h
er
ical
ac
tu
ato
r
s
Fig
u
r
e
4
is
s
elec
ted
to
e
x
p
lo
r
e.
A
p
r
ef
er
r
e
d
s
p
h
er
ical
ac
tu
ato
r
co
n
s
is
ts
o
f
a
m
o
d
if
ied
p
iezo
elec
tr
ic
t
u
b
e
wit
h
th
r
ee
ev
en
ly
d
is
tr
ib
u
ted
in
ter
n
al
elec
tr
o
d
es
in
cir
cu
m
f
er
en
tial
d
ir
ec
tio
n
a
n
d
a
s
p
h
er
ical
s
eg
m
en
t.
T
h
r
e
e
lo
n
g
itu
d
in
al
zo
n
es
o
f
th
e
t
u
b
e
ca
n
b
e
ex
cited
in
d
ep
en
d
en
tly
,
b
u
t g
e
n
er
ated
d
is
p
lace
m
en
ts
ar
e
p
ar
tially
d
e
p
en
d
en
t
b
ec
au
s
e
o
f
a
m
o
n
o
lith
s
tr
u
ctu
r
e.
T
h
e
k
i
n
em
atica
l
len
g
th
s
o
f
th
e
f
ir
s
t
(
OO
1
)
an
d
s
ec
o
n
d
(
O
1
O
2
)
r
o
b
o
t
lin
k
s
ar
e
ch
o
s
en
to
b
e
eq
u
a
l
to
4
0
m
m
.
T
h
e
f
ir
s
t
lin
k
o
f
th
e
T
T
R
is
co
m
p
o
u
n
d
e
d
o
f
p
iez
o
elec
tr
ic
tu
b
e
an
d
two
cu
t
b
all
s
.
E
x
ter
n
al
r
ad
iu
s
es
o
f
th
e
b
alls
f
r
o
m
s
teel
ar
e
eq
u
al
to
1
0
m
m
an
d
th
eir
in
ter
n
al
r
ad
i
u
s
es
-
9
m
m
.
A
n
ex
ter
n
al
d
iam
eter
o
f
th
e
tu
b
e
is
1
0
m
m
,
its
in
ter
n
al
d
iam
eter
an
d
len
g
th
a
r
e
8
a
n
d
2
4
m
m
r
esp
ec
tiv
el
y
.
T
h
e
s
ec
o
n
d
lin
k
o
f
th
e
T
T
R
is
m
ad
e
o
f
p
iezo
elec
tr
ic
tu
b
e
to
o
.
I
ts
len
g
th
is
3
1
m
m
an
d
it
h
as
th
e
s
am
e
cr
o
s
s
-
s
ec
tio
n
d
im
en
s
io
n
s
.
T
h
e
tu
b
es
ar
e
m
ad
e
o
f
PZT
-
4
,
wh
ic
h
d
en
s
ity
is
tak
en
as
7
.
6
g
/cm
3
.
T
h
e
d
e
n
s
ity
o
f
s
teel
is
s
elec
ted
a
s
7
.
8
g
/cm
3
.
T
h
er
ef
o
r
e
th
e
m
ass
es
o
f
th
e
f
ir
s
t
an
d
s
ec
o
n
d
lin
k
s
ar
e
2
1
.
7
g
(
9
)
an
d
6
.
7
g
(
1
0
)
r
esp
ec
tiv
ely
.
≅
2
(
4
3
(
3
−
3
)
−
2
4
(
−
)
)
+
(
2
−
2
)
1
4
(
9
)
2
=
(
2
−
2
)
2
4
(
10
)
wh
er
e:
1
,
2
−
m
ass
es
o
f
th
e
f
ir
s
t
a
n
d
s
ec
o
n
d
lin
k
s
r
esp
ec
tiv
ely
;
−
Ar
ch
im
ed
es’
co
n
s
tan
t;
R
,
r
-
ex
ter
n
al
an
d
in
ter
n
al
r
ad
i
u
s
es
o
f
th
e
b
all;
D
,
d
–
ex
ter
n
al
an
d
in
ter
n
al
d
i
am
eter
s
o
f
p
iez
o
elec
tr
ic
tu
b
e;
ρ
st
,
ρ
PZT
-
d
en
s
ities
o
f
s
teel
an
d
PZT
-
4
r
esp
ec
tiv
ely
;
1
,
2
,
−
len
g
th
s
o
f
th
e
f
ir
s
t
an
d
s
ec
o
n
d
p
iez
o
elec
tr
ic
tu
b
es
r
esp
ec
tiv
ely
.
A
r
ef
er
en
ce
p
o
in
t
o
f
th
e
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O.
A
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ef
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en
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t lin
k
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t o
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An
ax
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a
v
ity
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ax
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to
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lo
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al
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k
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a
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o
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o
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in
ate
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s
o
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th
e
r
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ar
e
r
ig
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ly
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h
e
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d
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ec
o
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s
r
esp
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tiv
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ef
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co
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ig
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h
e
r
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ca
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b
e
n
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tifie
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as
in
itial,
wh
en
th
e
s
am
e
ty
p
e
ax
es
ar
e
m
ad
e
p
ar
allel
to
ea
ch
o
t
h
er
(
x
0
-
x
1
-
x
2
,
y
0
-
y
1
-
y
2
an
d
z
0
-
z
1
-
z
2
)
.
T
h
e
tu
b
e
o
f
th
e
f
ir
s
t
s
p
h
er
ical
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4
8
5
6
Dyn
a
mics o
f tru
n
k
typ
e
r
o
b
o
t
w
ith
s
p
h
erica
l p
iezo
elec
tr
ic
a
c
tu
a
to
r
s
(
A
is
tis
A
u
g
u
s
ta
itis
)
117
ac
tu
ato
r
is
its
p
r
im
ar
y
lin
k
with
d
ir
ec
t
co
n
tr
o
l
to
its
s
ec
o
n
d
ar
y
lin
k
.
T
h
e
tu
b
e
o
f
th
e
s
ec
o
n
d
s
p
h
er
ical
ac
tu
ato
r
is
its
s
ec
o
n
d
ar
y
lin
k
with
i
n
d
ir
ec
t
m
o
tio
n
.
I
t
p
r
o
v
id
es
t
wo
ac
tio
n
s
at
o
n
ce
:
ex
citati
o
n
an
d
m
o
v
em
en
t.
T
h
e
o
r
ien
tatio
n
s
o
f
tu
b
e
ax
e
s
ar
e
p
er
m
an
en
t,
b
ec
au
s
e
its
g
eo
m
etr
y
is
s
tatic.
T
h
er
ef
o
r
e
th
e
f
ir
s
t
s
p
h
er
ical
ac
tu
ato
r
ca
n
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e
r
ef
er
e
n
ce
d
as
d
ir
ec
t ty
p
e
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d
th
e
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ec
o
n
d
s
p
h
er
ical
ac
tu
ato
r
-
as in
v
er
s
e
ty
p
e
[
1
6
]
with
r
o
tatio
n
al
ax
es
x
2
-
y
2
-
z
2
p
lace
d
o
n
O
1
r
e
f
er
en
ce
p
o
i
n
t.
T
h
is
r
ep
etitio
n
o
f
O
2
co
o
r
d
in
ate
s
y
s
tem
is
i
m
p
o
r
tan
t
to
en
s
u
r
e
th
e
r
ig
h
tn
ess
o
f
ac
tu
atin
g
.
C
o
n
s
is
ten
tly
ev
alu
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m
et
h
o
d
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o
f
o
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s
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o
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ab
le
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k
s
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e
g
o
i
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to
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e
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if
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er
en
t.
Fig
u
r
e
4
.
T
T
R
with
two
d
i
f
f
er
en
t sp
h
er
ical
ac
tu
ato
r
s
Seek
in
g
to
p
r
o
p
er
ly
d
eter
m
i
n
e
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o
r
ien
tatio
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m
atr
ix
o
f
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e
s
elec
ted
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im
p
o
r
tan
t
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o
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alu
ate
its
ac
tu
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eq
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en
ce
.
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o
r
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lize
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h
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b
r
id
r
o
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n
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ax
is
a
n
d
to
en
s
u
r
e
a
p
r
o
p
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n
al
ex
citatio
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o
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s
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ted
DOFs
i
s
a
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er
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co
m
p
licated
tech
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ical
task
,
b
e
ca
u
s
e
o
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ite
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tiff
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o
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th
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all,
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ictio
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en
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o
n
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ee
d
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g
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n
tact
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air
o
r
th
e
ac
tio
n
o
f
e
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ter
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d
s
o
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e
m
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ip
u
latio
n
o
f
r
ea
l
s
p
h
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r
ical
ac
tu
ato
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ca
n
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e
ex
ec
u
te
d
m
o
r
e
ac
c
u
r
ately
o
n
ly
if
its
DOFs
ar
e
g
o
in
g
to
b
e
a
ctiv
ated
s
ep
ar
ately
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h
is
s
tatem
en
t
ca
n
b
e
p
r
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eg
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g
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im
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ler
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n
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o
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e,
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ich
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o
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d
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1
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d
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1
5
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ad
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d
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b
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t x
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d
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y
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les
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1
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d
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1
5
r
ad
r
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ec
tiv
ely
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o
r
ea
lize
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n
ex
t
r
o
b
o
t
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n
f
ig
u
r
ati
o
n
is
s
elec
t
ed
to
ac
tiv
ate
o
n
l
y
x
ty
p
e
o
f
a
x
es.
E
v
er
y
an
g
u
la
r
s
p
ee
d
d
ep
e
n
d
en
c
e
o
f
x
t
y
p
e
ax
es
o
n
ti
m
e
is
ch
o
s
en
t
o
b
e
a
tr
ian
g
le
ty
p
e
Fig
u
r
e
5
.
Am
p
litu
d
es
o
f
g
lo
b
al
an
g
u
lar
s
p
ee
d
s
f
o
r
ax
es
x
0
an
d
x
2
ar
e
s
elec
ted
to
b
e
0
.
1
an
d
-
0
.
0
5
r
ad
/s
r
esp
ec
tiv
ely
.
B
o
th
DOFs
ar
e
g
o
in
g
to
b
e
s
tar
ted
at
th
e
s
am
e
tim
e
an
d
th
eir
d
u
r
atio
n
s
ar
e
2
s
.
T
h
e
m
a
x
im
u
m
s
izes
o
f
l
o
ca
l
an
g
u
lar
s
p
ee
d
s
f
o
r
m
o
v
ab
le
lin
k
s
ar
e
eq
u
al
to
th
eir
m
ag
n
itu
d
es
o
f
p
er
m
an
en
t
ac
ce
ler
atio
n
s
(
0
.
1
an
d
-
0
.
1
5
r
ad
/s
2
r
esp
ec
tiv
ely
)
.
T
h
e
last
p
ar
am
eter
s
ca
n
b
e
ea
s
ily
esti
m
ated
an
d
ar
e
im
p
o
r
tan
t
f
o
r
esti
m
atio
n
o
f
k
in
etic
to
r
q
u
es i
n
r
o
b
o
t d
y
n
am
ics em
p
lo
y
in
g
a
n
an
aly
tical
way
.
A
ce
n
ter
o
f
lin
k
m
ass
is
tak
en
as
a
m
id
d
le
p
o
in
t
o
f
its
lo
n
g
itu
d
in
al
s
y
m
m
et
r
y
lin
e,
b
e
ca
u
s
e
ea
ch
r
o
b
o
t
lin
k
is
a
r
o
d
t
y
p
e.
A
m
ass
m
o
m
en
t
o
f
i
n
er
tia
in
a
cc
o
r
d
an
ce
to
p
ar
allel
a
x
es
o
f
b
o
d
y
is
p
r
esen
ted
in
(
11
)
.
T
h
e
f
ir
s
t
lin
k
m
o
m
en
t
o
f
i
n
er
tia
ab
o
u
t
x
1
o
r
y
1
ax
es
ca
n
b
e
ev
alu
ated
b
y
(
12
)
an
d
is
1
6
.
6
·
1
0
-
6
k
g
·
m
2
.
I
ts
m
o
m
en
t
o
f
in
er
tia
ab
o
u
t
z
1
ax
is
is
d
eter
m
in
ed
b
y
(
13
)
an
d
is
eq
u
al
to
1
.
4
·
1
0
-
6
k
g
·
m
2
.
T
h
e
s
ec
o
n
d
lin
k
m
o
m
en
t
o
f
in
er
tia
ab
o
u
t
x
2
o
r
y
2
ax
es
c
an
b
e
esti
m
ated
with
(
14
)
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d
is
4
.
6
·
1
0
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6
k
g
·
m
2
.
I
ts
m
o
m
en
t
o
f
in
er
tia
ab
o
u
t z
2
ax
is
is
d
eter
m
in
e
d
b
y
(
15
)
a
n
d
is
eq
u
al
t
o
0
.
6
·
1
0
-
6
k
g
·
m
2
.
_
=
_
+
2
(
11
)
1
_
=
1
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=
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1
2
12
+
1
_
1
2
+
2
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(
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−
5
)
5
(
3
−
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)
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(
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(
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)
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(
13
)
2
_
=
2
_
=
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2
2
12
+
2
2
2
⁄
(
14
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
5
6
I
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t
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wh
er
e:
I
c_a
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p_a
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m
ass
m
o
m
en
ts
o
f
in
er
tia
in
ac
co
r
d
an
ce
to
ce
n
ter
ax
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d
p
a
r
allel
m
o
v
ed
ax
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o
f
b
o
d
y
r
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tiv
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m
–
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o
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y
m
ass
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d
–
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r
m
al
d
is
tan
ce
b
etwe
en
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e
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o
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m
o
m
en
ts
o
f
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er
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ab
o
u
t
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a
x
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f
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e
f
i
r
s
t
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d
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e
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m
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d
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th
e
T
T
R
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r
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o
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ly
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o
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ate
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O.
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h
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ea
n
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th
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y
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n
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g
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o
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e
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S
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o
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g
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h
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ce
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ax
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ir
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.
An
an
aly
tic
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g
e
o
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ic
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h
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n
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e
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ate
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m
ass
m
o
m
en
t
o
f
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n
er
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o
r
f
r
ee
ch
o
s
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ax
is
(
MI
FC
A)
.
A
f
r
ee
ly
s
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ted
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o
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as
t
o
cr
o
s
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ter
o
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o
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K
an
d
b
e
ex
p
r
ess
ed
b
y
th
r
ee
s
p
atial
an
g
les
α
,
β
,
γ
in
ac
co
r
d
an
ce
to
its
p
r
in
cip
al
ax
es
x
,
y
an
d
z
Fig
u
r
e
6
.
A
g
en
er
al
f
o
r
m
u
la
o
f
th
e
MI
FC
A
is
in
tr
o
d
u
ce
d
in
(
16
)
.
C
en
tr
if
u
g
al
m
o
m
en
ts
I
yz
,
I
xz
an
d
I
xy
o
f
th
e
b
o
d
y
ar
e
eq
u
al
to
0
,
b
ec
au
s
e
it
is
f
u
lly
s
y
m
m
etr
ic
an
d
is
o
tr
o
p
ic
.
No
w
it
is
im
p
o
r
tan
t
to
m
en
tio
n
an
o
r
ien
tatio
n
m
atr
ix
(
1
7
)
o
f
b
o
d
y
K
ac
co
r
d
in
g
to
th
e
b
ase
C
S.
T
h
en
m
ass
m
o
m
en
ts
o
f
in
er
tia
f
o
r
th
e
b
o
d
y
ca
n
b
e
ap
p
a
r
en
tly
d
e
ter
m
in
ed
r
eg
ar
d
in
g
to
th
e
m
ain
C
S
ax
es
(
1
8
-
2
0
)
.
I
f
th
e
m
o
m
e
n
t
o
f
r
o
b
o
t
lin
k
is
esti
m
ated
in
ac
co
r
d
an
ce
to
ea
r
lier
s
p
h
er
ical
jo
in
t,
th
en
it is
im
p
o
r
tan
t to
ev
alu
ate
th
e
ad
d
itio
n
al
i
n
er
tial q
u
a
n
tity
o
f
s
h
if
ted
ax
es.
Fig
u
r
e
5
.
Sh
a
p
e
o
f
a
n
g
u
la
r
s
p
e
ed
d
ep
e
n
d
en
ce
o
n
tim
e
Fig
u
r
e
6
.
Ma
s
s
m
o
m
en
t
o
f
in
e
r
tia
f
o
r
f
r
ee
s
elec
ted
ax
is
=
(
c
os
)
2
+
(
c
os
)
2
+
(
c
os
)
2
−
2
c
os
c
os
−
2
c
os
c
os
−
2
c
os
c
os
(
16
)
0
=
[
0
0
0
0
0
0
0
0
0
]
(
17
)
_
0
=
(
0
)
2
+
(
0
)
2
+
(
0
)
2
(
18
)
_
0
=
(
0
)
2
+
(
0
)
2
+
(
0
)
2
(
19
)
_
0
=
(
0
)
2
+
(
0
)
2
+
(
0
)
2
(
20
)
wh
er
e:
−
m
ass
m
o
m
en
t
o
f
in
er
tia
f
o
r
b
o
d
y
K
r
e
g
ar
d
i
n
g
to
a
s
elec
ted
ax
is
OL
;
α
–
an
g
le
b
etwe
en
a
s
p
in
n
in
g
ax
is
OL
an
d
a
p
r
in
cip
al
ax
is
x
o
f
th
e
b
o
d
y
;
I
x
,
I
y
,
I
z
–
p
r
in
ci
p
al
m
o
m
en
ts
o
f
i
n
er
tia
f
o
r
b
o
d
y
K
;
0
,
0
,
0
−
p
r
o
jectio
n
s
o
f
p
r
in
cip
al
a
x
es
(
x
,
y
an
d
z
)
t
o
a
b
ase
a
x
is
x
0
;
_
0
,
_
0
,
_
0
−
m
ass
m
o
m
en
ts
o
f
in
er
tia
f
o
r
th
e
b
o
d
y
ac
co
r
d
i
n
g
to
th
e
m
ain
C
S a
x
es (
x
0
-
y
0
-
z
0
)
an
d
s
o
o
n
.
4.
AP
P
L
I
CA
T
I
O
N
O
F
E
UL
E
R
-
L
AG
RANG
E
DYNA
M
I
C
S
An
in
itial
o
r
ie
n
tatio
n
o
f
th
e
f
ir
s
t
lin
k
is
esti
m
ated
b
y
(
21
)
u
s
in
g
R
o
ll
-
Pit
ch
-
Yaw
m
eth
o
d
a
n
d
th
e
o
r
ien
tatio
n
o
f
th
e
s
ec
o
n
d
lin
k
-
by
(
22
)
[
1
7
]
.
T
h
e
last
eq
u
atio
n
ca
n
b
e
p
r
o
v
ed
em
p
lo
y
in
g
o
r
t
h
o
g
o
n
al
an
d
tr
an
s
p
o
s
itio
n
f
ea
tu
r
es
o
f
m
atr
i
ce
s
.
An
o
r
ien
tatio
n
o
f
th
e
f
ir
s
t
lin
k
at
th
e
f
ir
s
t
an
d
s
ec
o
n
d
h
alv
es
o
f
ac
tu
atio
n
ca
n
b
e
ev
alu
ated
b
y
(
2
3
an
d
2
5
)
r
esp
ec
tiv
ely
.
An
o
r
ien
tatio
n
o
f
th
e
s
ec
o
n
d
lin
k
at
th
e
f
ir
s
t
an
d
s
ec
o
n
d
h
alv
es
o
f
ac
tu
atio
n
ca
n
b
e
d
ete
r
m
in
ed
b
y
(
2
4
an
d
2
6
)
r
esp
ec
tiv
e
ly
.
I
n
o
r
d
e
r
to
esti
m
ate
a
T
T
R
co
n
tr
o
l
f
u
n
ctio
n
o
f
an
y
DOF
is
s
elec
ted
to
u
s
e
th
r
ee
m
ain
tim
e
p
o
in
ts
(
in
itial,
m
ed
iu
m
an
d
f
in
al)
o
f
its
ex
citatio
n
p
er
io
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4
8
5
6
Dyn
a
mics o
f tru
n
k
typ
e
r
o
b
o
t
w
ith
s
p
h
erica
l p
iezo
elec
tr
ic
a
c
tu
a
to
r
s
(
A
is
tis
A
u
g
u
s
ta
itis
)
119
L
o
ca
l
s
p
ee
d
d
ep
e
n
d
en
cies
o
n
tim
e
o
f
t
h
e
f
ir
s
t
lin
k
ca
n
b
e
d
eter
m
in
ed
em
p
lo
y
in
g
th
ese
f
o
r
m
s
:
1
(
0
≤
Δ
≤
1
)
=
1
Δ
,
1
(
1
≤
Δ
≤
2
)
=
Ω
1
−
1
Δ
,
1
(
Δ
≥
2
)
=
0
.
T
h
e
s
p
ee
d
d
ep
e
n
d
en
cies
o
f
th
e
s
ec
o
n
d
lin
k
c
an
b
e
wr
it
ten
u
s
in
g
t
h
e
s
am
e
way
.
Glo
b
al
s
p
ee
d
s
o
f
th
e
f
i
r
s
t
an
d
s
ec
o
n
d
h
al
v
es
r
eg
ar
d
in
g
to
th
e
f
ir
s
t
lin
k
ar
e
esti
m
ated
b
y
(
2
7
-
2
8
)
.
T
h
e
s
p
ee
d
s
o
f
th
e
f
ir
s
t
an
d
s
ec
o
n
d
h
alv
es
ac
co
r
d
in
g
to
th
e
s
ec
o
n
d
lin
k
ar
e
e
v
alu
ate
d
b
y
(
29
-
30
)
.
0
1
=
⋅
(2
1
)
1
2
=
(
⋅
)
−
1
=
⋅
(2
2
)
0
1
(
<
1
)
=
(
1
⋅
2
2
⁄
)
⋅
(
1
)
⋅
(
1
)
(2
3
)
0
2
(
<
1
)
=
(
1
⋅
2
2
⁄
)
⋅
(
1
)
⋅
(
1
)
⋅
(
2
)
⋅
(
2
)
⋅
(
2
⋅
2
2
⁄
)
(2
4
)
0
1
(
>
1
)
=
(
0
.
05
+
0
.
1
−
1
⋅
(
−
1
)
2
2
⁄
)
⋅
(
1
)
⋅
(
1
)
(2
5
)
0
2
(
>
1
)
=
(
0
.
05
+
0
.
1
⋅
−
1
⋅
(
−
1
)
2
2
⁄
)
⋅
(
1
)
⋅
(
1
)
⋅
(
2
)
⋅
(
2
)
⋅
(
−
0
.
075
−
0
.
15
⋅
−
2
⋅
(
−
1
)
2
2
⁄
)
(2
6
)
1
=
0
1
1
2
⋅
2
⋅
(
1
)
⁄
(2
7
)
1
=
0
1
1
−
(
−
1
)
2
⋅
2
⋅
(
Ω
1
−
1
(
−
1
)
)
⁄
(2
8
)
2
=
0
2
1
2
⋅
2
⋅
(
1
)
⁄
+
0
2
2
2
⋅
2
⋅
(
2
)
⁄
(2
9
)
2
=
0
2
1
−
(
−
1
)
2
⋅
2
⋅
(
Ω
1
−
1
(
−
1
)
)
⁄
+
0
2
1
−
(
−
1
)
2
⋅
2
⋅
(
Ω
2
−
2
(
−
1
)
)
⁄
(
30
)
wh
er
e:
-
s
in
g
le
o
r
ien
tatio
n
m
a
tr
ix
ab
o
u
t
ax
is
x
;
-
tr
an
s
p
o
s
e
m
atr
ix
o
f
;
1
2
-
o
r
ien
tatio
n
m
atr
i
x
f
r
o
m
th
e
s
ec
o
n
d
C
S
to
th
e
f
ir
s
t
C
S;
1
,
2
-
v
ar
iab
les
o
f
an
g
u
lar
ac
ce
ler
atio
n
s
ab
o
u
t
x
ax
es
f
o
r
t
h
e
f
ir
s
t
an
d
s
ec
o
n
d
lin
k
s
r
esp
ec
tiv
ely
;
1
,
1
-
s
elec
ted
an
g
u
lar
m
o
v
em
en
ts
o
f
th
e
f
ir
s
t
lin
k
ab
o
u
t
x
0
a
n
d
y
0
a
x
e
s
(
0
.
1
2
an
d
0
.
1
5
r
ad
r
esp
ec
tiv
ely
)
;
1
,
1
-
an
g
u
lar
s
p
ee
d
s
o
f
th
e
f
ir
s
t
lin
k
at
t
h
e
f
ir
s
t
an
d
s
ec
o
n
d
h
alv
es
r
es
p
ec
tiv
ely
;
Ω
1
,
Ω
2
-
am
p
litu
d
es o
f
g
lo
b
al
an
g
u
lar
s
p
ee
d
s
ab
o
u
t a
x
es x
0
,
(
r
ep
lac
ed
)
x
2
r
esp
ec
tiv
el
y
an
d
s
o
o
n
.
A
to
tal
k
in
etic
en
er
g
y
o
f
th
e
s
y
s
tem
is
e
s
t
im
ated
em
p
lo
y
in
g
(
3
1
)
.
Kin
etic
en
er
g
y
o
f
th
e
s
e
co
n
d
lin
k
is
d
eter
m
in
ed
b
y
(
31
)
a
n
d
k
in
etic
en
er
g
y
o
f
th
e
f
i
r
s
t
lin
k
-
by
(
33
)
.
A
m
ass
m
o
m
en
t
o
f
in
er
tia
f
o
r
th
e
f
ir
s
t lin
k
ab
o
u
t a
x
is
x
0
is
e
v
alu
ated
b
y
(
34
)
an
d
th
e
m
o
m
en
t o
f
th
e
s
ec
o
n
d
lin
k
ab
o
u
t x
0
-
by
(
35
)
.
=
1
+
2
(3
1
)
2
=
(
2
⋅
2
)
⋅
(
2
_
2
2
⁄
)
2
⁄
(3
2
)
1
=
(
1
⋅
1
)
⋅
(
1
_
0
2
⁄
+
2
_
0
2
⁄
)
2
⁄
(3
3
)
1
_
0
=
(
0
1
(
1
.
1
)
)
2
⋅
1
_
1
+
(
0
1
(
1
.
2
)
)
2
⋅
1
_
1
+
(
0
1
(
1
.
3
)
)
2
⋅
1
_
1
(3
4
)
2
_
0
=
(
0
2
(
1
,
1
)
)
2
⋅
2
2
+
(
0
2
(
1
,
2
)
)
2
⋅
2
2
+
(
0
2
(
1
,
3
)
)
2
⋅
2
2
+
2
(
(
0
1
(
3
.
3
)
⋅
1
)
2
+
(
0
1
(
2
.
3
)
⋅
1
)
2
)
(3
5
)
wh
er
e:
T
1
,
T
2
–
k
in
etic
en
e
r
g
ies
o
f
th
e
f
ir
s
t
an
d
s
ec
o
n
d
lin
k
s
r
esp
ec
tiv
ely
;
I
1_x0
,
I
2
_x0
-
m
ass
m
o
m
en
ts
o
f
in
er
tia
o
f
th
e
f
ir
s
t a
n
d
s
ec
o
n
d
lin
k
s
r
esp
ec
tiv
ely
in
ac
c
o
r
d
a
n
ce
to
x
0
a
x
is
an
d
s
o
o
n
.
T
h
e
to
tal
p
o
ten
tial
en
er
g
y
o
f
th
e
r
o
b
o
t
is
esti
m
ated
with
(
36
)
.
T
h
e
p
o
ten
tial
en
er
g
ies
o
f
th
e
f
ir
s
t
an
d
s
ec
o
n
d
lin
k
s
ar
e
d
eter
m
in
ed
b
y
(
37
-
38
)
r
esp
ec
tiv
ely
.
=
1
+
2
(3
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
5
6
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l.
9
,
N
o
.
2
,
J
u
n
e
2
0
2
0
:
1
1
3
–
1
2
2
120
1
=
−
1
(
0
1
(
3
.
3
)
⋅
1
2
⁄
)
(3
7
)
2
=
−
2
(
0
1
(
3
.
3
)
⋅
1
+
0
2
(
3
.
3
)
⋅
2
2
⁄
)
(3
8
)
wh
er
e:
P
1
,
P
2
-
p
o
ten
tial
en
e
r
g
ies
o
f
th
e
f
i
r
s
t
an
d
s
ec
o
n
d
lin
k
s
r
esp
ec
tiv
ely
;
L
2
-
k
in
em
atica
l
len
g
th
o
f
th
e
s
ec
o
n
d
lin
k
(
4
0
m
m
)
a
n
d
s
o
o
n
.
Dy
n
am
ical
r
esu
lts
ar
e
esti
m
at
ed
an
d
p
r
esen
ted
in
T
a
b
le
1
a
n
d
F
ig
u
r
e
7
in
r
e
g
ar
d
to
E
u
ler
-
L
ag
r
an
g
e
m
eth
o
d
a
n
d
s
elec
ted
p
ar
a
m
eter
s
o
f
m
o
tio
n
.
T
ab
le
1
.
Dy
n
am
ical
r
esu
lts
o
f
th
e
T
T
R
Ti
me
mo
me
n
t
(
s)
Q
u
a
n
t
i
t
y
M1
(
N
m)
M2
(
N
m)
0
T
o
t
a
l
P
o
t
e
n
t
i
a
l
K
i
n
e
t
i
c
1
1
,
1
2
·
1
0
-
4
1
1
,
0
8
·
1
0
-
4
3
,
7
8
1
·
1
0
-
6
-
2
,
8
4
4
·
1
0
-
4
-
2
,
8
3
7
·
1
0
-
4
-
6
,
6
9
7
·
1
0
-
7
0
,
3
3
P
o
t
e
n
t
i
a
l
1
1
,
6
2
·
1
0
-
4
-
3
,
0
0
6
·
1
0
-
4
0
,
6
7
P
o
t
e
n
t
i
a
l
1
3
,
3
0
·
1
0
-
4
-
3
,
5
3
2
·
1
0
-
4
1
,
0
0
T
o
t
a
l
P
o
t
e
n
t
i
a
l
K
i
n
e
t
i
c
1
5
,
8
9
·
1
0
-
4
1
6
,
0
0
·
1
0
-
4
-
1
1
,
3
4
·
1
0
-
6
-
4
,
3
5
0
·
1
0
-
4
-
4
,
3
7
0
·
1
0
-
4
2
,
0
0
9
·
1
0
-
6
1
,
3
3
P
o
t
e
n
t
i
a
l
1
8
,
6
7
·
1
0
-
4
-
5
,
1
8
8
·
1
0
-
4
1
,
6
7
P
o
t
e
n
t
i
a
l
2
0
,
3
0
·
1
0
-
4
-
5
,
6
8
0
·
1
0
-
4
2
,
0
0
T
o
t
a
l
P
o
t
e
n
t
i
a
l
K
i
n
e
t
i
c
2
0
,
8
2
·
1
0
-
4
2
0
,
8
2
·
1
0
-
4
0
-
5
,
8
3
6
·
1
0
-
4
-
5
,
8
3
6
·
1
0
-
4
0
wh
er
e:
M1
,
M2
-
to
tal
to
r
q
u
es
ab
o
u
t
x
ax
es
o
f
th
e
f
i
r
s
t
an
d
s
ec
o
n
d
s
p
h
er
ical
ac
tu
ato
r
s
r
esp
ec
tiv
el
y
Fig
u
r
e
7
.
Dep
e
n
d
en
cies o
f
to
t
al
to
r
q
u
e
o
n
tim
e
5.
DYNA
M
I
CS O
F
ANA
L
Y
T
I
CAL
-
P
O
T
E
NT
I
A
L
M
E
T
H
O
D
An
aly
tical
-
p
o
ten
tial
m
et
h
o
d
h
as
b
ee
n
s
elec
ted
to
ass
u
r
e
th
e
co
r
r
ec
t
n
ess
o
f
d
escr
ib
ed
E
-
L
alg
o
r
ith
m
an
d
its
r
esu
lts
.
T
h
e
o
r
ie
n
tatio
n
s
o
f
r
o
b
o
t
lin
k
s
at
th
e
in
itial,
m
ed
iu
m
a
n
d
f
i
n
al
co
n
f
ig
u
r
ati
o
n
s
ar
e
d
eter
m
in
ed
by
(
23
-
26
)
to
o
.
T
h
e
c
o
n
tr
o
l
o
f
th
e
f
ir
s
t
lin
k
is
b
ased
o
n
th
e
m
ain
co
o
r
d
in
ate
s
y
s
tem
O.
I
ts
z
0
ax
is
is
co
in
cid
en
t
with
a
g
r
av
itatio
n
al
ax
is
.
T
h
er
ef
o
r
e
a
n
ev
alu
at
io
n
o
f
p
o
te
n
tial
to
r
q
u
e
f
o
r
th
e
f
ir
s
t
SP
A
is
q
u
ite
s
im
p
le
(
3
9
)
.
A
v
alu
e
o
f
to
r
q
u
e
ab
o
u
t
x
ax
is
is
r
ated
as
p
o
s
itiv
e,
wh
en
th
e
d
ir
ec
tio
n
o
f
lin
k
s
y
p
r
o
jectio
n
g
o
es
f
r
o
m
y
a
x
is
to
z
ax
is
(
u
p
war
d
in
th
e
m
ai
n
q
u
ar
ter
o
f
y
–
z
p
lan
e
o
r
d
o
wn
war
d
in
-
y
–
z
p
lan
e)
.
E
v
er
y
s
in
g
le
m
ag
n
itu
d
e
o
f
p
o
ten
tial
to
r
q
u
e
s
h
o
u
ld
b
e
m
u
ltip
lied
b
y
-
1
in
o
r
d
er
to
r
ea
lize
an
o
p
p
o
s
ite
d
ir
ec
tio
n
o
f
g
r
a
v
itatio
n
al
f
o
r
ce
o
r
t
h
e
s
en
s
e
(
n
eg
ativ
e
to
p
o
s
itiv
e)
o
f
its
elb
o
w.
1
_
=
−
(
0
1
(
2
.
3
)
⋅
1
2
⁄
+
2
(
0
1
(
2
.
3
)
⋅
1
+
0
2
(
2
.
3
)
⋅
2
2
⁄
)
)
(3
9
)
wh
er
e:
1
_
−
to
r
q
u
e
ab
o
u
t x
0
ax
is
b
ec
au
s
e
o
f
g
r
a
v
ity
.
T
o
ev
al
u
ate
a
p
o
ten
tial
to
r
q
u
e
o
f
th
e
s
ec
o
n
d
lin
k
f
ir
s
tly
th
e
o
r
ien
tatio
n
o
f
s
p
in
n
in
g
ax
is
x
2
t
o
th
e
g
lo
b
al
ar
ea
x
0
-
y
0
h
as
to
b
e
d
eter
m
in
ed
.
T
h
is
ca
n
b
e
d
o
n
e
em
p
l
o
y
in
g
ar
ctan
g
en
t
f
u
n
ctio
n
(
4
0
-
4
2
)
,
wh
ich
d
ep
e
n
d
s
o
n
p
r
o
jectio
n
s
s
en
s
es
o
f
m
en
tio
n
ed
ax
es
Fig
u
r
e
8
.
T
h
en
an
ap
p
ar
en
t
to
r
q
u
e
(
4
3
)
o
f
th
e
lin
k
an
d
its
o
r
ien
tatio
n
(
44
-
4
6
)
to
g
l
o
b
al
ar
ea
x
0
-
y
0
h
av
e
to
b
e
esti
m
ated
.
Fin
ally
a
p
er
p
en
d
icu
la
r
ity
o
f
ap
p
ar
en
t
to
r
q
u
e
to
ax
is
x
2
ca
n
b
e
ev
alu
ated
an
d
a
p
er
p
en
d
icu
la
r
ity
o
f
th
e
s
am
e
ax
is
to
a
g
r
av
itatio
n
al
ax
is
z
0
to
o
.
T
h
e
last
two
s
tep
s
ar
e
ess
en
tia
l in
th
e
esti
m
atio
n
o
f
t
h
e
to
r
q
u
e
ab
o
u
t a
r
ep
lace
d
a
x
is
x
2
(
4
7
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4
8
5
6
Dyn
a
mics o
f tru
n
k
typ
e
r
o
b
o
t
w
ith
s
p
h
erica
l p
iezo
elec
tr
ic
a
c
tu
a
to
r
s
(
A
is
tis
A
u
g
u
s
ta
itis
)
121
1
,
1
=
(
0
2
(
1
.
1
)
0
2
(
2
.
1
)
⁄
)
,
if
0
2
(
1
.
1
)
>
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an
d
0
2
(
2
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1
)
>
0
(4
0
)
1
,
2
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+
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1
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0
2
(
2
.
1
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,
if
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d
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r
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0
2
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(
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.
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2
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(
0
2
(
2
.
3
)
)
2
)
1
2
⁄
⋅
2
2
⁄
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(4
3
)
2
,
1
=
(
0
2
(
1
.
3
)
0
2
(
2
.
3
)
⁄
)
,
if
0
2
(
1
.
3
)
>
0
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d
0
2
(
2
.
3
)
>
0
(4
4
)
2
,
2
=
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2
(
1
.
3
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0
2
(
2
.
3
)
⁄
)
,
if
0
2
(
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.
3
)
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0
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d
0
2
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.
3
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0
o
r
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2
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1
.
3
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,
0
2
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2
.
3
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0
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5
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2
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3
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,
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3
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d
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6
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−
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,
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⋅
(
(
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(
1
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1
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2
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(
2
.
1
)
)
2
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1
2
⁄
(4
7
)
w
h
e
r
e
:
,
−
a
r
c
t
a
n
g
e
n
t
f
u
n
c
t
i
o
n
t
o
e
s
t
i
m
a
t
e
t
h
e
d
i
r
e
c
t
i
o
n
(
i
-
m
a
r
k
f
o
r
s
e
n
s
e
o
f
o
r
i
e
n
t
a
t
i
o
n
a
n
d
j
-
i
n
d
e
x
f
o
r
a
p
p
l
i
c
a
b
l
e
f
u
n
c
t
i
o
n
)
;
N
2
_
x
,
M
2
_
x
–
a
p
p
a
r
e
n
t
a
n
d
r
e
a
l
t
o
r
q
u
e
s
a
b
o
u
t
a
r
e
p
l
a
c
e
d
a
x
i
s
x
2
b
e
c
a
u
s
e
o
f
g
r
a
v
i
t
y
a
n
d
s
o
o
n
.
Nu
m
er
ical
an
d
g
r
ap
h
ical
r
es
u
lts
ar
e
g
en
er
ated
T
a
b
le
2
,
Fig
u
r
e
9
in
ac
co
r
d
an
ce
t
o
a
r
ec
en
tly
d
escr
ib
ed
m
eth
o
d
o
f
in
v
er
s
e
d
y
n
am
ics.
I
t
is
b
ased
o
n
t
h
e
ac
tio
n
o
f
g
r
a
v
ity
r
eg
a
r
d
i
n
g
to
th
e
a
d
eq
u
ate
p
ar
am
eter
s
o
f
m
o
tio
n
.
Fig
u
r
e
8
.
Pro
jectio
n
o
f
r
o
b
o
t li
n
k
o
r
ax
is
in
ar
ea
x
0
-
y
0
T
ab
le
2
.
R
esu
lts
o
f
th
e
an
aly
ti
c
-
p
o
ten
tial r
esear
ch
Ti
me
mo
me
n
t
(
s)
M1
*
(
N
m)
M2
*
(
N
m)
0
1
1
,
0
8
·
1
0
-
4
-
2
,
8
3
7
·
1
0
-
4
0
,
3
3
1
1
,
6
2
·
1
0
-
4
-
3
,
0
0
6
·
1
0
-
4
0
,
6
7
1
3
,
3
0
·
1
0
-
4
-
3
,
5
3
2
·
1
0
-
4
1
,
0
0
1
6
,
0
0
·
1
0
-
4
-
4
,
3
7
0
·
1
0
-
4
1
,
3
3
1
8
,
6
7
·
1
0
-
4
-
5
,
1
8
8
·
1
0
-
4
1
,
6
7
2
0
,
3
0
·
1
0
-
4
-
5
,
6
8
0
·
1
0
-
4
2
,
0
0
2
0
,
8
2
·
1
0
-
4
-
5
,
8
3
6
·
1
0
-
4
M1
*
,
M2
*
:
p
o
ten
tial
to
r
q
u
es
ab
o
u
t
x
ax
es
o
f
th
e
f
ir
s
t
an
d
s
ec
o
n
d
s
p
h
er
ical
ac
tu
ato
r
s
r
esp
ec
tiv
ely
Fig
u
r
e
9
.
Dep
e
n
d
en
cies o
f
p
o
t
en
tial to
r
q
u
e
o
n
tim
e
6.
CO
NCLU
SI
O
N
T
h
e
r
esu
lts
o
f
E
u
ler
-
L
ag
r
an
g
e
d
y
n
am
ics
ar
e
p
ar
tly
co
n
f
ir
m
ed
b
y
th
e
r
esu
lts
o
f
an
aly
ti
c
-
p
o
ten
tial
m
eth
o
d
.
Kin
etic
to
r
q
u
es
o
f
E
-
L
m
eth
o
d
ca
n
b
e
co
n
f
ir
m
e
d
b
y
th
e
o
r
etica
l
way
to
o
.
Actu
ato
r
s
d
ep
e
n
d
en
cies
o
f
to
tal
to
r
q
u
e
o
n
lar
g
e
tim
e
s
tep
s
ca
n
b
e
ap
p
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Evaluation Warning : The document was created with Spire.PDF for Python.
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RE
F
E
R
E
NC
E
S
[1
]
J.
Li
,
e
t
a
l.
,
“
Au
to
n
o
m
o
u
s
Co
n
t
in
u
u
m
G
ra
sp
in
g
,
”
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
In
telli
g
e
n
t
Ro
b
o
t
s
a
n
d
S
y
ste
ms
,
p
p
.
4
5
6
9
-
4
5
7
6
,
2
0
1
4
.
[2
]
T.
M
a
h
l,
e
t
a
l.
,
“
F
o
rwa
rd
Ki
n
e
m
a
ti
c
s
o
f
a
Co
m
p
li
a
n
t
P
n
e
u
m
a
ti
c
a
ll
y
Ac
tu
a
ted
Re
d
u
n
d
a
n
t
M
a
n
i
p
u
lat
o
r,
”
IEE
E
Co
n
fer
e
n
c
e
o
n
In
d
u
stri
a
l
El
e
c
tro
n
ics
a
n
d
A
p
p
li
c
a
ti
o
n
s
,
p
p
.
1
2
6
7
-
1
2
7
3
,
2
0
1
2
.
[3
]
A.
Na
g
a
ra
jan
,
S
.
K.
R.
Ka
n
n
a
a
n
d
V.
M
.
Ku
m
a
r,
"
M
u
lt
ib
o
d
y
d
y
n
a
m
ic
sim
u
latio
n
o
f
a
h
y
p
e
r
re
d
u
n
d
a
n
t
r
o
b
o
ti
c
m
a
n
ip
u
lat
o
r
u
sin
g
AD
AMS
a
n
sy
s
in
tera
c
ti
o
n
,
"
In
ter
n
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
Al
g
o
rith
ms
,
M
e
t
h
o
d
o
l
o
g
y
,
M
o
d
e
ls
a
n
d
Ap
p
li
c
a
ti
o
n
s i
n
Eme
rg
i
n
g
T
e
c
h
n
o
lo
g
ies
(ICA
M
M
AE
T
)
,
p
p
.
1
-
6
,
C
h
e
n
n
a
i,
2
0
1
7
.
[4
]
S
.
E
.
Ta
b
a
tab
a
ie
a
n
d
M
.
S
h
a
h
in
p
o
o
r,
“
Artifi
c
ial
S
o
ft
R
o
b
o
ti
c
El
e
p
h
a
n
t
Tru
n
k
M
a
d
e
wit
h
I
o
n
ic
P
o
ly
m
e
r
-
Me
tal
Na
n
o
c
o
m
p
o
si
tes
(IP
M
Cs),”
In
ter
n
a
ti
o
n
a
l
R
o
b
o
ti
c
s &
A
u
to
m
a
ti
o
n
J
o
u
rn
a
l
,
v
o
l
.
5
,
n
o
.
4
,
p
p
.
1
3
8
-
1
4
2
,
2
0
1
9
.
[5
]
B.
A.
Jo
n
e
s
a
n
d
I.
D.
Walk
e
r,
"
K
in
e
m
a
ti
c
s
fo
r
m
u
lt
ise
c
ti
o
n
c
o
n
ti
n
u
u
m
ro
b
o
ts,
"
in
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
R
o
b
o
ti
c
s
,
v
o
l.
2
2
,
n
o
.
1
,
p
p
.
4
3
-
5
5
,
F
e
b
.
2
0
0
6
.
[
6
]
W
.
C
h
u
n
g
,
C
.
R
h
e
e
,
Y
.
S
h
i
m
,
H
.
L
e
e
a
n
d
S
.
P
a
r
k
,
"
D
o
o
r
-
O
p
e
n
i
n
g
C
o
n
t
r
o
l
o
f
a
S
e
r
v
i
c
e
R
o
b
o
t
U
s
i
n
g
t
h
e
M
u
l
t
i
f
i
n
g
e
r
e
d
R
o
b
o
t
H
a
n
d
,
"
i
n
I
E
E
E
T
r
a
n
s
a
c
t
i
o
n
s
o
n
I
n
d
u
s
t
r
i
a
l
E
l
e
c
t
r
o
n
i
c
s
,
v
o
l
.
5
6
,
n
o
.
1
0
,
p
p
.
3
9
7
5
-
3
9
8
4
,
O
c
t
.
2
0
0
9
.
[7
]
O.
S
a
lo
m
o
n
a
n
d
A.
W
o
lf,
“
In
c
li
n
e
d
Li
n
k
s
Hy
p
e
r
-
Re
d
u
n
d
a
n
t
E
lep
h
a
n
t
Tr
u
n
k
-
Li
k
e
Ro
b
o
t
,
”
M
e
c
h
a
n
isms
a
n
d
Ro
b
o
ti
c
s
,
v
o
l.
4
,
n
o
.
4
,
2
0
1
2
.
[8
]
P
.
Li
l
jeb
a
c
k
,
I.
U.
Ha
u
g
stu
e
n
a
n
d
K.
Y.
P
e
tt
e
rse
n
,
"
P
a
t
h
F
o
ll
o
win
g
C
o
n
tr
o
l
o
f
P
lan
a
r
S
n
a
k
e
Ro
b
o
ts
Us
in
g
a
Ca
sc
a
d
e
d
Ap
p
ro
a
c
h
,
"
i
n
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
Co
n
tro
l
S
y
ste
ms
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
2
0
,
n
o
.
1
,
p
p
.
1
1
1
-
1
2
6
,
Ja
n
.
2
0
1
2
.
[9
]
E.
Ke
las
id
i,
e
t
a
l.
,
“
Lo
c
o
m
o
ti
o
n
Eff
icie
n
c
y
Op
t
imiz
a
ti
o
n
o
f
Bi
o
l
o
g
ica
ll
y
I
n
sp
ir
e
d
S
n
a
k
e
Ro
b
o
ts,”
A
p
p
li
e
d
S
c
ien
c
e
s
,
v
o
l.
8
,
n
o
.
1
,
2
0
1
8
.
[1
0
]
R.
C.
Lu
o
a
n
d
C
.
Ku
o
,
"
In
tell
ig
e
n
t
S
e
v
e
n
-
Do
F
R
o
b
o
t
Wi
th
Dy
n
a
m
ic
Ob
sta
c
le
Av
o
id
a
n
c
e
a
n
d
3
-
D
Ob
jec
t
Re
c
o
g
n
it
i
o
n
fo
r
In
d
u
str
ial
Cy
b
e
r
–
P
h
y
sic
a
l
S
y
ste
m
s
in
M
a
n
u
fa
c
tu
rin
g
Au
t
o
m
a
ti
o
n
,
"
in
Pro
c
e
e
d
in
g
s
o
f
th
e
I
EE
E
,
v
o
l.
1
0
4
,
n
o
.
5
,
p
p
.
1
1
0
2
-
1
1
1
3
,
M
a
y
2
0
1
6
.
[1
1
]
R.
Ba
n
se
v
i
č
iu
s
a
n
d
V.
Ka
rg
a
u
d
a
s,
“
Atti
tu
d
e
Co
n
tro
l
o
f
M
icr
o
-
a
n
d
Na
n
o
sa
telli
tes
Us
in
g
M
u
lt
i
-
De
g
re
e
-
of
-
F
re
e
d
o
m
P
iez
o
e
lec
tri
c
Ac
tu
a
to
rs,”
Vi
b
r
a
ti
o
n
p
r
o
b
lem
s ICOVP
,
v
o
l.
1
3
9
,
p
p
.
3
7
9
-
3
8
4
,
2
0
1
1
.
[1
2
]
J.
Iq
b
a
l,
“
M
o
d
e
r
n
C
o
n
tr
o
l
Law
s
fo
r
a
n
Artic
u
late
d
R
o
b
o
ti
c
Arm
:
M
o
d
e
li
n
g
a
n
d
S
imu
lati
o
n
,
”
En
g
in
e
e
rin
g
,
T
e
c
h
n
o
l
o
g
y
&
A
p
p
li
e
d
S
c
ien
c
e
R
e
se
a
rc
h
,
v
o
l
.
9
,
n
o
.
2
,
p
p
.
4
0
5
7
-
4
0
6
1
,
2
0
1
9
.
[1
3
]
Ch
u
n
x
ia
Z.
,
e
t
a
l.
,
“
Eff
e
c
t
o
f
L
i
n
k
s
De
fo
rm
a
ti
o
n
o
n
M
o
ti
o
n
P
re
c
isio
n
o
f
P
a
ra
ll
e
l
M
a
n
i
p
u
lat
o
r
Ba
se
d
o
n
F
lex
i
b
le
Dy
n
a
m
ics
,
”
In
d
u
stria
l
Ro
b
o
t
,
v
o
l.
4
4
,
n
o
.
6
,
p
p
.
7
7
6
-
7
8
7
,
2
0
1
7
.
[1
4
]
D.
Do
p
ico
,
e
t
a
l.
,
“
Dire
c
t
S
e
n
siti
v
it
y
An
a
ly
sis
o
f
M
u
l
ti
b
o
d
y
S
y
ste
m
s
with
Ho
l
o
n
o
m
ic
a
n
d
No
n
h
o
lo
n
o
m
ic
Co
n
stra
in
ts
v
i
a
a
n
I
n
d
e
x
-
3
A
u
g
m
e
n
ted
Lag
ra
n
g
ia
n
F
o
rm
u
latio
n
with
P
r
o
jec
ti
o
n
s,”
No
n
li
n
e
a
r
Dy
n
a
mic
s
,
v
o
l
.
9
3
,
p
p
.
2
0
3
9
-
2
0
5
6
,
2
0
1
8
.
[1
5
]
D.
Ba
lea
n
u
,
e
t
a
l.
,
“
Th
e
M
o
ti
o
n
o
f
a
Be
a
d
S
li
d
in
g
o
n
a
Wi
re
i
n
F
ra
c
ti
o
n
a
l
S
e
n
se
,
”
Acta
P
h
y
si
c
a
Po
l
o
n
ica
A
,
v
o
l.
1
3
1
,
v
o
l.
6
,
p
p
.
1
5
6
1
-
1
5
6
4
,
2
0
1
7
.
[1
6
]
A.
Au
g
u
sta
it
is,
e
t
a
l.
,
“
Ki
n
e
m
a
ti
c
s
o
f
Tru
n
k
-
Li
k
e
Ro
b
o
ts
with
P
iez
o
Ac
tu
a
to
rs,”
M
e
c
h
a
n
ics
,
v
o
l.
2
4
,
n
o
.
2
,
p
p
.
2
5
4
-
2
5
9
,
2
0
1
8
.
[1
7
]
Y.
H.
Hw
a
n
g
,
e
t
a
l.
,
“
An
El
e
c
tro
rh
e
o
lo
g
ica
l
S
p
h
e
rica
l
Jo
in
t
A
c
tu
a
to
r
fo
r
a
Ha
p
ti
c
M
a
ste
r
wit
h
Ap
p
li
c
a
ti
o
n
to
Ro
b
o
t
-
As
siste
d
Cu
tt
in
g
S
u
rg
e
r
y
,
”
S
e
n
s
o
rs
a
n
d
Actu
a
to
rs
A:
Ph
y
sic
a
l
,
v
o
l.
2
4
9
,
p
p
.
1
6
3
-
1
7
1
,
2
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.
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s
.
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