I
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S In
t
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na
l J
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Aut
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No
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2
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p
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2
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Ju
p
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b
o
t
h
a
s
m
a
d
e
a
g
re
a
t
imp
a
c
t
in
th
e
e
d
u
c
a
ti
o
n
a
l
fiel
d
with
i
ts
su
p
p
o
rt
f
o
r
a
u
t
o
n
o
m
o
u
s
n
a
v
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g
a
ti
o
n
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v
is
u
a
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p
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e
p
ti
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a
n
d
m
a
n
y
o
th
e
r
fe
a
tu
re
s
fro
m
it
s
a
rti
ficia
l
i
n
telli
g
e
n
c
e
p
latfo
rm
'
s
lea
rn
in
g
b
o
x
.
Th
is
stu
d
y
u
n
d
e
rta
k
e
s
a
k
in
e
m
a
ti
c
m
o
d
e
l
d
e
sig
n
o
f
Ju
p
it
e
r'
s
a
rm
to
a
id
t
h
e
ro
b
o
t'
s
m
o
ti
o
n
sta
b
il
it
y
.
T
h
is
p
ro
c
e
ss
in
v
o
lv
e
d
t
h
e
d
e
term
in
a
ti
o
n
o
f
a
h
o
m
o
g
e
n
e
o
u
s
tran
sfo
rm
a
ti
o
n
m
a
tri
x
,
f
o
ll
o
we
d
b
y
t
h
e
d
e
term
in
a
ti
o
n
o
f
o
rien
tatio
n
,
p
o
siti
o
n
,
a
n
d
Eu
ler
a
n
g
les
.
Ulti
m
a
tely
,
th
e
h
o
m
o
g
e
n
e
o
u
s
tran
s
fo
rm
a
ti
o
n
m
a
tri
x
wa
s
su
c
c
e
ss
fu
ll
y
d
e
riv
e
d
,
a
n
d
th
e
sim
p
l
ifi
c
a
ti
o
n
o
f
d
i
re
c
t
k
in
e
m
a
ti
c
m
a
tri
c
e
s
wa
s
a
c
h
iev
e
d
.
C
o
n
se
q
u
e
n
tl
y
,
t
h
e
k
in
e
m
a
ti
c
a
n
a
l
y
sis
f
o
r
Ju
p
it
e
r'
s
a
rm
wa
s
e
sta
b
li
sh
e
d
u
si
n
g
t
h
e
p
o
siti
o
n
De
n
a
v
it
–
Ha
rten
b
e
rg
m
e
th
o
d
,
o
rien
tati
o
n
,
a
n
d
Eu
ler
a
n
g
les
,
p
r
o
v
i
n
g
t
o
b
e
v
a
lu
a
b
le
in
th
e
c
o
n
t
e
x
t
o
f
t
h
is
re
se
a
rc
h
.
K
ey
w
o
r
d
s
:
An
aly
tical
s
o
lu
tio
n
s
Den
av
it
–
Har
ten
b
er
g
I
n
v
er
s
e
k
in
e
m
atics
J
u
p
iter
r
o
b
o
t
Kin
em
atic
an
aly
s
is
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
:
Om
ar
Sh
alash
C
o
lleg
e
o
f
Ar
tific
ial
I
n
tellig
en
ce
,
Ar
ab
Aca
d
em
y
f
o
r
Scien
ce
,
T
ec
h
n
o
l
o
g
y
a
n
d
Ma
r
itime
T
r
an
s
p
o
r
t
Alam
ein
,
E
g
y
p
t
E
m
ail: o
m
ar
.
o
.
s
h
alash
@
aa
s
t.e
d
u
1.
I
NT
RO
D
UCT
I
O
N
R
o
b
o
tics
,
th
e
in
ter
d
is
cip
lin
ar
y
f
ield
at
th
e
in
ter
s
ec
tio
n
o
f
m
ec
h
an
ical
en
g
in
ee
r
in
g
,
co
m
p
u
t
er
s
cien
ce
,
ar
tific
ial
in
tellig
en
ce
,
an
d
ele
ctr
o
n
ics,
h
as
r
a
p
id
ly
tr
an
s
f
o
r
m
ed
th
e
way
we
liv
e
an
d
wo
r
k
.
I
n
th
e
q
u
est
f
o
r
au
to
m
atin
g
task
s
an
d
im
p
r
o
v
i
n
g
ab
ilit
ies,
r
o
b
o
tics
h
as
b
ec
o
m
e
a
tech
n
o
lo
g
y
in
th
e
2
1
s
t
ce
n
tu
r
y
.
Or
ig
in
atin
g
f
r
o
m
t
h
e
r
ea
lm
o
f
s
cien
ce
f
ict
io
n
an
d
f
in
d
in
g
its
way
in
to
i
n
d
u
s
tr
ies
s
u
ch
,
as
m
a
n
u
f
ac
tu
r
in
g
an
d
h
ea
lth
ca
r
e
ar
tific
ial
in
tellig
en
ce
h
as
b
ec
o
m
e
wid
ely
p
r
ev
ale
n
t
[
1
]
–
[
1
3
]
.
T
h
e
s
tu
d
y
o
f
r
o
b
o
tics
h
as
b
ec
o
m
e
a
d
y
n
am
ic
an
d
cr
itical
ar
ea
o
f
r
esear
ch
,
o
f
f
er
in
g
in
s
ig
h
ts
in
to
d
esig
n
s
,
d
ev
elo
p
m
e
n
t
s
,
an
d
d
ep
l
o
y
m
en
t
s
o
f
in
tellig
en
t
m
ac
h
in
es.
T
h
e
f
ield
o
f
r
o
b
o
tics
h
as
m
ad
e
s
tr
id
es
th
an
k
s
to
ad
v
an
ce
m
en
ts
in
m
o
d
elin
g
tech
n
iq
u
es.
I
t
is
cr
u
cial
to
co
m
p
r
e
h
en
d
th
e
p
o
s
itio
n
in
g
an
d
o
r
ie
n
tatio
n
s
o
f
r
o
b
o
ts
s
u
ch
,
as
th
e
J
u
p
iter
r
o
b
o
t
in
o
r
d
er
to
ef
f
ec
tiv
ely
co
n
tr
o
l
an
d
in
ter
ac
t
with
th
e
m
in
en
v
ir
o
n
m
en
ts
.
T
wo
k
e
y
co
m
p
o
n
e
n
ts
,
f
o
r
war
d
k
in
e
m
atics
an
d
in
v
er
s
e
k
in
em
atics
p
lay
a
r
o
le
in
t
h
is
p
u
r
s
u
it.
Sig
n
if
ican
t
r
esear
ch
h
as
b
ee
n
d
e
v
o
ted
to
f
in
d
in
g
s
o
l
u
tio
n
s
f
o
r
d
eter
m
in
in
g
t
h
e
k
in
em
atics o
f
h
u
m
an
o
id
r
o
b
o
ts
.
I
n
th
e
p
ast r
esear
ch
er
s
p
r
im
ar
ily
u
tili
ze
d
Den
av
it
–
Har
ten
b
er
g
(
DH)
p
ar
am
ete
r
s
,
wh
ich
o
f
f
e
r
ed
a
s
tan
d
ar
d
ize
d
ap
p
r
o
ac
h
,
f
o
r
r
e
p
r
esen
tin
g
th
e
tr
a
n
s
f
o
r
m
atio
n
s
,
b
etwe
en
n
eig
h
b
o
r
in
g
lin
k
s
[
1
4
]
.
I
n
th
i
s
ap
p
r
o
ac
h
,
we
ass
ig
n
p
ar
am
eter
s
to
ea
ch
jo
in
t
allo
win
g
u
s
to
ca
lcu
late
th
e
p
o
s
itio
n
s
an
d
o
r
ien
tatio
n
s
o
f
th
e
e
n
d
e
f
f
ec
to
r
[
1
5
]
–
[
2
1
]
.
An
o
th
e
r
u
s
ed
tech
n
i
q
u
e
in
r
o
b
o
tics
is
th
e
h
o
m
o
g
en
eo
u
s
tr
an
s
f
o
r
m
atio
n
m
atr
ices
.
T
h
ey
p
r
o
v
id
e
a
f
r
am
ewo
r
k
,
f
o
r
ex
p
r
ess
in
g
th
e
p
o
s
i
tio
n
an
d
o
r
ien
tatio
n
tr
an
s
f
o
r
m
atio
n
s
o
f
r
o
b
o
tic
s
y
s
tem
s
[
2
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
1
-
1
0
2
T
h
ese
m
atr
ices
m
ak
e
co
m
p
u
t
atio
n
s
m
o
r
e
ef
f
icien
t,
b
y
co
n
tain
in
g
all
th
e
tr
a
n
s
f
o
r
m
atio
n
i
n
f
o
r
m
atio
n
with
in
a
m
atr
ix
[
2
3
]
–
[
2
8
]
.
T
h
e
f
o
r
m
u
la
k
n
o
wn
as
th
e
p
r
o
d
u
ct
o
f
ex
p
o
n
e
n
tials
wh
ich
was
in
tr
o
d
u
ce
d
b
y
Mu
r
r
ay
et
a
l
.
[
2
9
]
is
a
r
ep
r
esen
tatio
n
th
at
is
d
er
iv
ed
f
r
o
m
L
i
e
alg
eb
r
a.
I
t
p
r
o
v
i
d
es
a
co
m
p
ac
t
an
d
eleg
an
t
way
to
ex
p
r
ess
th
e
en
d
-
ef
f
ec
t
o
r
p
o
s
e
as
a
f
u
n
ctio
n
o
f
jo
in
t
v
ar
iab
les,
allo
win
g
f
o
r
ef
f
icien
t
an
d
ac
cu
r
ate
k
in
em
atic
co
m
p
u
tatio
n
s
[
3
0
]
–
[
3
3
]
.
Fin
d
in
g
eq
u
atio
n
s
,
f
o
r
p
ar
ticu
lar
r
o
b
o
t
co
n
f
ig
u
r
atio
n
s
is
esp
ec
i
ally
v
alu
ab
le
wh
en
d
ea
lin
g
with
r
o
b
o
ts
th
at
h
a
v
e
clea
r
ly
d
ef
in
ed
an
d
r
elativ
el
y
u
n
c
o
m
p
licated
s
h
ap
es
[
3
4
]
.
T
h
ey
o
f
f
er
ex
p
licit
eq
u
atio
n
s
f
o
r
d
eter
m
in
i
n
g
en
d
-
ef
f
ec
to
r
p
o
s
es
[
3
5
]
–
[
3
7
]
.
T
h
e
f
lex
ib
le
m
eth
o
d
o
f
in
v
e
r
s
e
k
in
em
atics
an
d
tr
ig
o
n
o
m
et
r
ic
m
eth
o
d
s
u
tili
ze
s
in
v
er
s
e
tr
ig
o
n
o
m
etr
ic
f
u
n
cti
o
n
s
to
ca
lcu
late
th
e
an
g
les
o
f
jo
in
ts
.
I
n
p
ar
ticu
lar
,
th
is
tech
n
iq
u
e
is
v
er
y
s
tr
aig
h
tf
o
r
war
d
,
as
t
h
e
co
r
r
esp
o
n
d
in
g
jo
in
ts
’
o
r
ie
n
tatio
n
s
ca
n
e
asil
y
d
eter
m
in
e
th
e
an
g
les
n
ee
d
e
d
t
o
ac
h
iev
e
ce
r
t
ain
tar
g
et
lo
ca
tio
n
s
o
f
an
en
d
-
ef
f
ec
to
r
[
3
7
]
–
[
3
9
]
.
A
r
ep
r
esen
tatio
n
b
ased
o
n
th
e
id
ea
o
f
Geo
m
etr
ic
in
te
r
p
r
etati
o
n
o
f
k
in
em
atics
clar
if
ies
to
u
s
h
o
w
th
e
m
o
tio
n
s
o
f
jo
in
ts
ar
e
r
elate
d
with
th
e
m
o
tio
n
o
f
th
e
e
n
d
ef
f
ec
to
r
.
I
t
i
s
a
way
o
f
c
o
n
ce
p
tu
alizin
g
r
o
b
o
t
m
o
tio
n
an
d
u
n
d
er
s
tan
d
in
g
h
o
w
ev
er
y
th
in
g
f
its
to
g
eth
er
[
4
0
]
,
[
4
1
]
.
C
u
r
r
e
n
tly
,
th
ese
s
o
lu
tio
n
s
h
av
e
b
ee
n
ex
p
an
d
ed
in
t
o
d
ea
lin
g
with
k
in
e
m
atica
lly
co
m
p
lex
s
tr
u
ctu
r
es
as
well
as
r
ed
u
n
d
a
n
t
s
y
s
tem
s
.
W
ith
th
is
d
ev
elo
p
m
en
t,
an
aly
s
is
s
o
lu
tio
n
s
h
a
v
e
tak
en
o
n
a
n
ew
d
im
en
s
io
n
; m
o
r
e
f
lex
ib
le
a
n
d
co
m
p
lex
r
o
b
o
tics
s
y
s
tem
s
.
Dete
r
m
in
in
g
th
e
an
g
les
o
f
j
o
in
ts
to
f
in
d
th
e
s
u
itab
le
p
o
s
itio
n
o
f
an
en
d
ef
f
ec
t
o
r
,
k
n
o
wn
as
k
in
em
atics,
h
as
b
ee
n
a
cr
u
c
ial
f
ield
o
f
s
tu
d
y
.
R
esear
ch
er
s
h
av
e
u
tili
ze
d
m
eth
o
d
s
,
lik
e
tech
n
iq
u
es
an
d
o
p
tim
izatio
n
alg
o
r
ith
m
s
,
to
ad
d
r
ess
th
is
co
m
p
lex
p
r
o
b
lem
.
T
h
ese
m
eth
o
d
s
h
av
e
s
h
o
wn
t
h
eir
ef
f
ec
tiv
en
ess
,
in
r
ea
l
-
tim
e
co
n
tr
o
l
an
d
p
lan
n
i
n
g
m
o
v
em
en
ts
[
4
2
]
.
I
ter
ativ
e
J
ac
o
b
ian
-
b
ased
m
et
h
o
d
s
ar
e
a
p
r
e
v
alen
t
ap
p
r
o
ac
h
in
s
o
lv
in
g
in
v
er
s
e
k
i
n
em
atics
[
4
3
]
.
T
h
e
y
u
s
e
th
e
m
atr
i
x
,
wh
i
ch
h
elp
s
d
eter
m
in
e
h
o
w
c
h
a
n
g
es,
in
v
elo
cities,
af
f
ec
t
th
e
v
elo
cities
o
f
th
e
en
d
ef
f
ec
to
r
[
4
4
]
.
Un
d
e
r
s
tan
d
in
g
th
e
r
elatio
n
s
h
ip
b
etwe
e
n
an
g
l
es
an
d
th
e
r
esu
ltin
g
ch
an
g
es
in
th
e
p
o
s
itio
n
an
d
o
r
ien
tatio
n
o
f
th
e
en
d
e
f
f
ec
to
r
i
s
ess
en
tial.
T
h
is
m
atr
ix
s
er
v
es
as
a
v
alu
ab
le
to
o
l,
f
o
r
th
at
p
u
r
p
o
s
e
[
4
5
]
.
B
y
m
ak
in
g
m
o
d
if
icatio
n
s
th
ese
tec
h
n
iq
u
es
g
r
a
d
u
ally
m
o
v
e
clo
s
er
,
to
th
e
in
te
n
d
ed
p
o
s
itio
n
s
k
illfu
lly
m
an
eu
v
er
i
n
g
th
r
o
u
g
h
t
h
e
r
an
g
e
o
f
s
o
lu
tio
n
s
an
d
s
tead
ily
m
o
v
in
g
to
war
d
s
th
e
o
b
jectiv
e
[
4
5
]
,
[
4
6
]
.
T
h
ey
p
e
r
f
o
r
m
well
in
ch
an
g
in
g
e
n
v
ir
o
n
m
en
ts
an
d
s
itu
atio
n
s
th
at
d
em
an
d
im
m
ed
iate
ad
ap
tatio
n
s
.
Ho
wev
er
,
th
eir
ef
f
icien
cy
ca
n
b
e
af
f
ec
te
d
b
y
f
ac
to
r
s
s
u
c
h
,
as
th
e
iter
atio
n
m
eth
o
d
u
s
ed
th
e
ac
cu
r
ac
y
o
f
ca
lcu
latin
g
th
e
J
ac
o
b
ian
,
an
d
th
e
o
cc
u
r
r
e
n
ce
o
f
s
in
g
u
lar
ities
[
4
4
]
.
R
eliab
le
co
n
v
er
g
en
ce
d
ep
en
d
s
o
n
ca
r
ef
u
l
p
ar
am
eter
tu
n
i
n
g
.
Ho
wev
er
,
t
h
e
ch
o
ice
b
etwe
en
t
h
e
I
ter
ati
v
e
J
ac
o
b
ian
-
b
ased
m
eth
o
d
s
a
n
d
o
th
er
tech
n
iq
u
es
d
ep
en
d
s
o
n
v
ar
io
u
s
co
n
s
id
er
a
tio
n
s
wh
ich
i
n
clu
d
e
r
o
b
o
t
s
tr
u
ctu
r
es,
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
,
an
d
o
p
er
atin
g
en
v
ir
o
n
m
en
t.
I
n
m
ak
in
g
th
e
r
i
g
h
t
ch
o
ice
ab
o
u
t
v
a
r
io
u
s
m
eth
o
d
s
r
eg
ar
d
i
n
g
in
v
er
s
e
k
in
em
at
ics,
it
is
im
p
o
r
tan
t
to
u
n
d
er
s
tan
d
ea
c
h
m
eth
o
d
’
s
s
tr
o
n
g
p
o
in
ts
as
well
as
its
w
ea
k
p
o
in
ts
[
4
7
]
.
T
h
e
o
th
er
im
p
o
r
tan
t
ap
p
r
o
ac
h
is
th
at
th
e
C
C
D
alg
o
r
ith
m
h
as
b
ee
n
a
s
ig
n
if
ican
t
a
p
p
r
o
ac
h
f
o
r
in
v
e
r
s
e
k
in
em
atics.
T
h
r
o
u
g
h
a
n
iter
ativ
e
ad
ju
s
tm
en
t
o
f
ea
ch
s
ep
ar
ate
jo
in
t’
s
an
g
le,
C
C
D
is
d
ev
e
lo
p
ed
s
p
ec
if
ically
f
o
r
th
e
ar
ticu
lated
s
tr
u
ctu
r
es
p
o
s
s
ess
ed
b
y
s
ev
er
al
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
r
o
b
o
ts
[
4
8
]
.
T
h
e
o
p
er
atio
n
b
eg
in
s
o
n
its
b
ase
an
d
im
p
r
o
v
es
s
u
cc
ess
iv
e
an
g
les
o
n
th
e
k
in
et
ic
ch
ain
till
it
g
ets
to
th
e
p
o
s
itio
n
it
d
esire
s
f
o
r
th
e
e
n
d
ef
f
ec
to
r
.
T
h
is
tech
n
iq
u
e
tak
es
ad
v
an
tag
e
o
f
th
e
in
tr
i
n
s
ic
o
r
g
an
izatio
n
o
f
m
an
y
r
o
b
o
tic
s
y
s
tem
s
an
d
is
th
er
ef
o
r
e
h
ig
h
ly
u
s
ef
u
l
f
o
r
s
o
lv
in
g
co
m
p
licated
a
r
ticu
latio
n
s
lik
e
th
o
s
e
ch
ar
ac
ter
izin
g
h
u
m
an
o
id
r
o
b
o
ts
as
well
as
m
u
lti
-
lim
b
ed
r
o
b
o
tic
ar
m
s
[
4
9
]
.
Nev
e
r
th
eless
,
it’s
im
p
o
r
tan
t
to
ac
k
n
o
wled
g
e
th
at
wh
ile
C
C
D
ex
ce
ls
in
m
an
y
s
c
en
ar
io
s
,
it
m
a
y
f
ac
e
ch
allen
g
es
co
n
v
e
r
g
in
g
to
a
s
o
lu
tio
n
in
ca
s
es
in
v
o
lv
in
g
s
in
g
u
lar
ities
o
r
h
ig
h
ly
c
o
n
s
tr
ain
ed
en
v
ir
o
n
m
en
ts
[
5
0
]
.
Ad
d
itio
n
ally
,
th
e
o
r
d
er
o
f
jo
i
n
t
ad
ju
s
tm
en
ts
ca
n
im
p
ac
t
th
e
o
u
tco
m
e,
war
r
an
tin
g
th
o
u
g
h
t
f
u
l
co
n
s
id
er
atio
n
in
its
ap
p
licatio
n
.
Desp
ite
th
ese
co
n
s
id
er
atio
n
s
,
C
C
D
r
em
ain
s
a
v
alu
ab
le
an
d
p
r
ag
m
atic
to
o
l
f
o
r
ad
d
r
ess
in
g
co
m
p
lex
in
v
er
s
e
k
in
em
atics
c
h
allen
g
es
in
r
o
b
o
tics
as
r
ep
o
r
ted
in
T
ab
le
1
[
5
1
]
.
Gr
a
d
ien
t
-
b
ased
o
p
tim
izatio
n
ap
p
r
o
ac
h
es
in
v
er
s
e
k
in
em
atic
s
as
an
o
p
tim
izatio
n
ch
allen
g
e
,
em
p
lo
y
in
g
tech
n
iq
u
es
lik
e
g
r
ad
ien
t
d
escen
t
an
d
New
to
n
’
s
m
eth
o
d
to
m
in
im
iz
e
an
o
b
jectiv
e
f
u
n
ctio
n
,
h
en
c
e
co
n
v
er
g
i
n
g
to
war
d
s
o
p
tim
a
l
jo
in
t
an
g
les
[
5
2
]
.
T
h
e
p
r
o
ce
s
s
wh
er
eb
y
jo
in
t
a
n
g
les
ar
e
ad
ju
s
ted
i
n
cr
em
en
tall
y
m
o
v
in
g
t
h
e
s
y
s
tem
alo
n
g
th
e
p
ath
o
f
d
ec
r
ea
s
in
g
th
e
v
alu
e
o
f
th
e
o
b
jectiv
e
f
u
n
ctio
n
u
n
til
r
ea
ch
i
n
g
a
lo
ca
l
m
i
n
im
u
m
th
at
co
i
n
cid
es
with
th
e
tar
g
et
en
d
-
e
f
f
ec
to
r
p
o
s
itio
n
in
g
is
r
ef
er
r
e
d
to
as
g
r
ad
ien
t
d
ec
en
t.
I
t
h
as
b
ee
n
o
b
s
er
v
ed
th
at
s
o
m
e
co
m
p
lex
an
d
n
o
n
-
lin
ea
r
o
b
jectiv
e
f
u
n
ctio
n
s
,
c
o
u
ld
co
n
v
er
g
e
f
aster
th
an
f
ir
s
t
-
o
r
d
e
r
d
e
r
iv
ativ
es
u
s
in
g
New
to
n
’
s
m
eth
o
d
s
[
5
3
]
.
I
t
m
a
y
b
e
s
tr
o
n
g
b
u
t
y
o
u
n
ee
d
to
co
n
s
id
er
th
e
ch
o
ice
o
f
an
o
p
tim
izatio
n
alg
o
r
ith
m
,
a
co
n
v
er
g
e
n
ce
cr
iter
io
n
,
an
d
th
e
o
b
jectiv
e
f
u
n
ctio
n
d
ef
in
itio
n
.
Sin
ce
s
in
g
u
lar
ities
an
d
c
o
n
s
tr
ain
ed
en
v
ir
o
n
m
en
ts
r
e
q
u
ir
e
s
p
ec
ial
h
an
d
lin
g
[
4
9
]
.
Kn
o
wled
g
e
o
f
s
u
c
h
s
u
b
tletie
s
is
cr
u
cial
in
t
h
e
ef
f
ec
tiv
e
u
tili
za
tio
n
o
f
ad
d
r
ess
in
g
th
e
in
v
er
s
e
k
in
e
m
atics
p
r
o
b
lem
in
r
o
b
o
tics
.
Dam
p
e
d
least
s
q
u
ar
es
(
DL
S)
is
an
ap
p
r
o
ac
h
with
b
o
th
an
aly
ti
ca
l
an
d
n
u
m
er
ical
in
g
r
ed
ien
ts
ap
p
lied
with
in
in
v
er
s
e
k
in
em
atics
[
5
4
]
.
I
t
o
p
tim
i
ze
s
its
weig
h
ted
least
s
q
u
ar
e
t
o
s
o
lv
e
th
e
p
r
o
b
le
m
o
f
m
in
im
izin
g
th
is
d
if
f
er
e
n
ce
b
etwe
en
th
e
en
d
-
ef
f
ec
t
o
r
p
o
s
es.
T
h
er
ef
o
r
e,
o
n
e
s
h
o
u
ld
in
clu
d
e
th
is
d
am
p
in
g
f
ac
to
r
th
at
will
p
r
o
v
id
e
en
o
u
g
h
s
tab
ilit
y
th
at
m
a
k
e
th
e
s
o
lu
tio
n
co
r
r
ec
t
u
n
d
er
s
u
c
h
in
s
tab
ilit
ies
o
r
ar
is
in
g
in
co
n
s
is
ten
cies
[
5
0
]
.
T
h
e
ad
v
an
tag
e
o
f
Dam
p
ed
L
ea
s
t
S
q
u
ar
es
is
in
ac
c
u
r
ate
e
n
d
-
e
f
f
e
cto
r
p
o
s
es
f
o
r
th
e
s
y
s
tem
s
th
at
u
s
e
it.
I
t
wo
r
k
s
o
u
t
to
b
e
a
g
o
o
d
c
h
o
ice
wh
en
it
co
m
es
t
o
r
o
b
o
tic
a
p
p
licatio
n
s
s
u
ch
as
m
an
ip
u
lato
r
ar
m
s
an
d
h
u
m
a
n
o
id
r
o
b
o
ts
[
5
5
]
.
R
esear
ch
er
s
h
av
e
d
el
v
ed
in
t
o
d
i
v
er
s
e
o
p
tim
izatio
n
-
b
ased
tech
n
iq
u
es,
s
u
ch
as
g
en
etic
alg
o
r
ith
m
s
,
s
im
u
lated
an
n
ea
li
n
g
,
an
d
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
,
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
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J
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&
A
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to
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N:
2722
-
2
5
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6
P
o
s
itio
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a
n
d
o
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ien
ta
tio
n
a
n
a
ly
s
is
o
f J
u
p
iter
r
o
b
o
t a
r
m
fo
r
n
a
vig
a
tio
n
s
ta
b
ilit
y
(
Oma
r
S
h
a
la
s
h
)
3
alter
n
ativ
e
av
e
n
u
es
f
o
r
tac
k
lin
g
in
v
er
s
e
k
i
n
em
atics
ch
allen
g
es
[
5
4
]
.
T
h
e
u
s
e
o
f
th
ese
m
eth
o
d
s
b
r
in
g
s
a
b
o
u
t
an
o
th
er
p
ar
ad
ig
m
b
ec
a
u
s
e
th
e
y
ap
p
ly
to
n
at
u
r
e
-
b
ased
s
ea
r
c
h
s
tr
ateg
ies.
Gen
etic
alg
o
r
ith
m
s
u
s
e
p
r
in
cip
les
o
f
n
atu
r
al
s
elec
tio
n
a
n
d
g
en
etic
s
f
o
r
e
x
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lo
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in
g
th
e
s
o
lu
tio
n
s
p
ac
e
an
d
h
en
ce
a
r
e
v
e
r
y
e
f
f
ec
tiv
e
in
s
o
lv
i
n
g
d
if
f
icu
lt,
m
u
ltid
im
e
n
s
io
n
al
o
p
tim
izatio
n
p
r
o
b
lem
s
[
5
6
]
.
T
h
ese
m
eth
o
d
s
o
f
f
er
d
iv
er
s
e
s
tr
ateg
ies
f
o
r
tack
lin
g
th
e
co
m
p
lex
p
r
o
b
lem
o
f
in
v
e
r
s
e
k
in
em
atics,
ea
ch
with
its
o
wn
s
tr
en
g
th
s
an
d
co
n
s
id
er
atio
n
s
.
T
h
eir
ap
p
licatio
n
d
ep
en
d
s
o
n
f
ac
to
r
s
s
u
ch
as
t
h
e
r
o
b
o
t’
s
s
tab
ilit
y
k
in
e
m
atic
s
tr
u
ctu
r
e,
c
o
m
p
u
tatio
n
al
r
es
o
u
r
ce
s
,
an
d
s
p
ec
if
ic
task
r
eq
u
ir
em
en
ts
.
T
h
is
r
esear
ch
c
o
n
tr
ib
u
tes
b
y
d
ev
elo
p
in
g
a
k
in
em
atic
m
o
d
e
l
f
o
r
th
e
J
u
p
iter
r
o
b
o
t,
en
h
a
n
c
in
g
its
ar
m
f
u
n
ctio
n
ality
i
n
s
ev
er
al
k
e
y
way
s
.
First,
th
e
m
o
d
el
allo
w
s
th
e
r
o
b
o
t'
s
ar
m
to
ex
ten
d
f
u
lly
,
p
r
o
v
id
i
n
g
an
ad
v
an
tag
e
in
co
m
p
etitiv
e
s
ettin
g
s
b
y
en
a
b
lin
g
f
aster
o
b
ject
-
g
r
ab
b
in
g
.
Seco
n
d
,
th
e
k
in
em
a
tic
m
o
d
el
im
p
r
o
v
es
th
e
s
tab
ilit
y
o
f
th
e
r
o
b
o
t'
s
m
o
v
em
en
ts
,
en
s
u
r
in
g
s
m
o
o
t
h
an
d
co
n
tr
o
lled
o
p
er
atio
n
.
T
h
ese
f
ea
tu
r
es
allo
w
th
e
J
u
p
iter
r
o
b
o
t
to
o
p
er
ate
at
m
a
x
im
u
m
s
p
ee
d
with
o
u
t
r
is
k
in
g
tip
p
in
g
o
v
er
,
wh
ile
s
wif
tly
r
ea
ch
in
g
a
n
d
g
r
asp
in
g
tar
g
et
o
b
jects.
2.
J
UP
I
T
E
R
B
ACK
G
RO
UN
D
T
h
e
J
u
p
iter
r
o
b
o
t
as
s
ee
n
in
Fig
u
r
e
1
,
cr
ea
ted
b
y
L
attel
R
o
b
o
tics
,
is
a
v
er
s
at
ile
h
o
m
e
ass
i
s
tan
t
weig
h
in
g
1
0
.
3
k
g
an
d
b
o
asti
n
g
ex
ter
n
al
d
im
en
s
io
n
s
o
f
3
5
2
×
352
×
9
2
0
m
m
,
with
a
g
r
o
u
n
d
c
lear
an
ce
o
f
1
5
m
m
.
L
attel
R
o
b
o
tics
,
a
co
m
p
an
y
d
ed
icate
d
to
p
r
o
m
o
tin
g
AI
-
f
o
cu
s
ed
r
o
b
o
tics
ed
u
ca
tio
n
,
i
s
h
ea
d
q
u
ar
ter
e
d
in
Sin
g
ap
o
r
e
a
n
d
Ma
lay
s
ia.
T
h
e
h
ea
r
t
o
f
th
e
J
u
p
iter
r
o
b
o
t
is
its
o
n
b
o
ar
d
co
m
p
u
ter
,
e
q
u
ip
p
e
d
with
an
I
n
tel
C
o
r
e
i5
-
1
0
2
1
0
U
p
r
o
ce
s
s
o
r
r
u
n
n
in
g
at
1
.
6
GHz
,
8
GB
o
f
R
AM
,
an
d
a
1
2
0
GB
SS
D
f
o
r
in
ter
n
al
s
to
r
ag
e.
I
t
als
o
f
ea
tu
r
es
a
W
i
-
Fi
r
em
o
te
co
n
tr
o
ller
with
a
s
wif
t
3
0
0
Mb
p
s
t
r
an
s
m
is
s
io
n
r
ate,
en
ab
lin
g
s
e
am
less
in
ter
ac
tio
n
.
Sp
ee
ch
in
ter
ac
tio
n
ca
p
ab
ilit
ies ar
e
in
co
r
p
o
r
ated
,
o
f
f
er
i
n
g
a
f
r
eq
u
en
cy
r
esp
o
n
s
e
b
etwe
en
5
0
Hz
an
d
1
6
k
Hz
f
o
r
clea
r
co
m
m
u
n
icatio
n
.
Fo
r
m
o
b
ilit
y
,
th
e
r
o
b
o
t
u
tili
ze
s
th
e
m
o
b
ile
b
ase
Ko
b
u
k
i
u
n
it,
allo
w
in
g
f
o
r
a
m
ax
im
u
m
p
ay
lo
ad
o
f
5
k
g
,
a
to
p
s
p
ee
d
o
f
0
.
5
m
/s
,
a
n
d
a
r
a
p
id
r
o
tatio
n
s
p
ee
d
o
f
1
6
0
d
e
g
r
ee
s
p
er
s
ec
o
n
d
.
Po
wer
in
g
th
is
r
em
ar
k
ab
le
m
ac
h
in
e
ar
e
s
tan
d
ar
d
4
4
0
0
m
Ah
L
i
-
I
o
n
b
atter
ies,
with
th
e
o
p
tio
n
f
o
r
ex
ten
d
ed
b
atter
y
life
u
s
in
g
a
n
ad
d
itio
n
al
4
4
0
0
m
A
h
L
i
-
I
o
n
u
n
it.
T
h
e
r
o
b
o
t
is
eq
u
ip
p
ed
with
an
ar
r
ay
o
f
s
en
s
o
r
s
,
in
c
lu
d
in
g
2
5
,
7
0
0
C
PR
en
co
d
er
s
,
a
r
ate
g
y
r
o
s
co
p
e
wi
th
a
f
ac
to
r
y
ca
lib
r
atio
n
o
f
1
1
0
d
eg
/s
,
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d
a
u
x
iliar
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s
en
s
o
r
s
(
3
x
f
o
r
war
d
b
u
m
p
,
3
x
C
liff
,
2
x
wh
ee
l
d
r
o
p
)
.
I
t
als
o
f
ea
tu
r
es
a
3
D
s
ter
eo
ca
m
er
a
with
a
r
eso
lu
tio
n
o
f
6
4
0
p
x
x
4
8
0
p
x
,
r
ec
o
r
d
in
g
at
3
0
f
p
s
,
an
d
a
Slam
tec
A2
m
8
-
R
4
R
P L
i
DAR
s
y
s
tem
.
W
ith
a
ll th
ese
f
ea
tu
r
es,
th
e
J
u
p
iter
r
o
b
o
t is eq
u
ip
p
ed
wit
h
v
ar
io
u
s
s
u
p
p
o
r
t
f
o
r
au
to
n
o
m
o
u
s
n
av
ig
atio
n
,
v
is
u
al
p
er
ce
p
tio
n
,
s
p
ee
ch
i
n
ter
ac
tio
n
,
m
o
b
il
e
m
an
ip
u
latio
n
an
d
AI
,
m
ac
h
i
n
e
lear
n
in
g
,
an
d
cl
o
u
d
co
m
p
u
tin
g
,
h
e
n
ce
p
r
o
v
e
n
to
b
e
ess
en
tial
in
th
e
ed
u
c
atio
n
al
f
ield
,
wh
ic
h
en
ab
led
th
e
r
o
b
o
t to
b
e
t
h
e
co
r
e
elem
en
t in
R
o
b
o
C
u
p
@
Ho
m
e
E
d
u
ca
tio
n
c
o
n
test
[
5
7
]
.
Fig
u
r
e
1
.
J
u
p
iter
r
o
b
o
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
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2
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8
6
I
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b
&
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u
to
m
,
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l
.
1
4
,
No
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1
,
Ma
r
ch
20
2
5
:
1
-
1
0
4
J
u
p
iter
’
s
ar
m
s
y
s
tem
as
s
ee
n
i
n
Fig
u
r
e
1
is
co
m
p
r
is
ed
o
f
5
s
er
v
o
s
,
in
clu
d
i
n
g
t
h
e
en
d
e
f
f
e
cto
r
s
er
v
o
,
alo
n
g
with
4
lin
k
s
.
I
ts
ex
ter
n
al
d
im
en
s
io
n
s
(
L
×
W
×
H)
ar
e
3
2
×
50
×
4
0
m
m
,
an
d
it
o
f
f
e
r
s
an
i
m
p
r
ess
iv
e
ac
cu
r
ac
y
o
f
0
.
2
9
d
eg
r
ee
s
[
5
7
]
.
T
h
is
r
o
b
o
tic
wo
n
d
er
s
ea
m
less
ly
in
teg
r
ates
a
b
len
d
o
f
f
ea
t
u
r
e
s
,
in
clu
d
in
g
r
o
b
o
t
in
tellig
en
ce
,
n
atu
r
al
in
ter
ac
tio
n
,
co
m
p
u
te
r
v
is
io
n
,
m
o
b
ile
p
l
atf
o
r
m
ca
p
ab
ilit
ies,
an
d
o
b
ject
m
an
ip
u
latio
n
.
T
h
e
r
o
b
o
t’
s
AR
M
is
a
4
DOF
(
f
o
u
r
d
e
g
r
ee
s
o
f
f
r
ee
d
o
m
)
s
y
s
tem
.
I
t
c
o
m
p
r
is
es
f
o
u
r
jo
in
ts
,
e
ac
h
with
its
u
n
iq
u
e
r
o
tatio
n
:
J
o
in
t
1
:
Yaw
r
o
tatio
n
,
J
o
in
t
2
:
Pit
ch
r
o
tatio
n
,
J
o
in
t
3
:
Pit
ch
r
o
tatio
n
,
J
o
in
t
4
:
Pit
ch
r
o
tatio
n
,
T
h
ese
f
o
u
r
jo
in
ts
co
llectiv
ely
en
d
o
w
th
e
r
o
b
o
t’
s
ef
f
ec
to
r
with
f
o
u
r
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
,
en
ab
lin
g
m
o
tio
n
in
th
e
x
,
y
,
an
d
z
ax
es,
as we
ll a
s
p
itch
an
d
y
aw
r
o
tatio
n
.
3.
M
E
T
H
O
DO
L
O
G
Y
T
h
e
tr
an
s
f
o
r
m
atio
n
m
atr
ix
f
o
r
jo
in
t ‘
i‘
with
r
esp
ec
t to
an
ad
ja
ce
n
t jo
in
t ‘
i‘
in
th
r
ee
-
d
im
e
n
s
io
n
al
s
p
ac
e
is
in
(
1
)
.
=
[
(
)
−
(
)
0
−
1
(
−
1
)
(
)
(
−
1
)
(
)
−
(
−
1
)
−
(
−
1
)
(
−
1
)
(
)
(
−
1
)
(
)
(
−
1
)
(
−
1
)
0
0
0
1
]
(
1
)
T
h
e
tr
an
s
f
o
r
m
atio
n
f
r
o
m
j
o
in
t
‘
i‘
to
jo
in
t
‘
j‘
,
wh
e
r
e
‘
i‘
r
a
n
g
e
s
f
r
o
m
1
t
o
‘
N‘
,
a
n
d
‘
j‘
r
an
g
es
f
r
o
m
‘
i+1
‘
to
‘
N‘
,
is
g
iv
en
b
y
(
2
)
.
=
+
1
⋅
+
1
+
2
⋅
…
⋅
−
1
(
2
)
Fo
r
th
e
ca
s
e
o
f
a
5
-
j
o
in
t
r
o
b
o
t
ic
ar
m
as
o
b
s
er
v
e
d
in
Fig
u
r
e
2
,
th
e
tr
a
n
s
f
o
r
m
atio
n
m
atr
ices
ar
e
f
illed
f
o
r
ea
c
h
jo
in
t
(
2
)
,
an
d
t
h
e
m
u
ltip
licati
o
n
is
p
r
o
ce
s
s
ed
s
eq
u
e
n
tially
to
o
b
tain
t
h
e
tr
an
s
f
o
r
m
atio
n
f
r
o
m
th
e
b
ase
to
th
e
en
d
-
ef
f
ec
t
o
r
f
r
am
e
(
3
)
.
4
0
=
[
11
0
4
12
0
4
13
0
4
0
4
21
0
4
22
0
4
23
0
4
0
4
31
0
4
32
0
4
33
0
4
0
4
0
0
0
1
]
(
3
)
I
n
o
r
d
er
to
p
r
e
p
ar
e
th
e
DH
m
o
d
el
f
o
r
J
u
p
iter
’
s
a
r
m
,
s
ee
Fig
u
r
e
2
f
o
r
illu
s
tr
atio
n
,
th
e
m
o
d
el’
s
p
ar
a
m
eter
s
(
th
e
lin
k
len
g
th
(
a
i
)
,
lin
k
o
f
f
s
et
(
d
i
)
,
r
o
tatio
n
a
n
g
le
(
θ
i
)
,
an
d
lin
k
twis
t
(
α
i
)
)
ar
e
ca
lcu
lat
ed
an
d
p
r
esen
ted
in
T
ab
le
1
.
So
lv
in
g
th
e
in
v
er
s
e
k
in
em
atic
p
r
o
b
lem
d
e
p
en
d
s
o
n
ea
c
h
r
o
b
o
t’
s
d
esig
n
.
I
ter
ativ
e
n
u
m
er
ica
l
m
eth
o
d
s
m
ay
ev
en
tu
ally
lead
to
a
s
o
lu
tio
n
,
b
u
t
th
ey
ar
e
p
r
o
n
e
to
en
co
u
n
ter
i
n
g
s
in
g
u
lar
ities
,
r
esu
ltin
g
in
p
o
ten
tial
f
ailu
r
es
ev
en
wh
e
n
a
v
alid
s
o
lu
tio
n
is
p
o
s
s
ib
le.
Fu
r
th
er
m
o
r
e
,
th
eir
p
er
f
o
r
m
a
n
ce
is
g
en
e
r
ally
s
u
b
-
o
p
tim
al.
O
n
th
e
o
th
er
s
id
e,
an
aly
tical
s
o
lu
t
io
n
s
ar
e
s
wif
t
an
d
h
ig
h
ly
p
r
ec
i
s
e,
y
et
u
n
co
v
er
in
g
th
em
n
ec
ess
itates
a
s
u
b
s
tan
tial
am
o
u
n
t
o
f
ef
f
o
r
t.
Fig
u
r
e
2
.
Fiv
e
-
jo
i
n
t r
o
b
o
tic
ar
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
P
o
s
itio
n
a
n
d
o
r
ien
ta
tio
n
a
n
a
ly
s
is
o
f J
u
p
iter
r
o
b
o
t a
r
m
fo
r
n
a
vig
a
tio
n
s
ta
b
ilit
y
(
Oma
r
S
h
a
la
s
h
)
5
T
ab
le
1
.
DH
-
m
o
d
el
p
ar
a
m
eter
s
i
αi
−
1
ai
−
1
d
i
θ
i
1
0
0
a
1
θ
1
2
−
9
0
°
0
0
θ
2
3
0
L
2
0
θ
3
4
0
L
3
0
θ
4
5
0
L
4
0
0
3
.
1
.
G
eo
m
e
t
ric
s
o
lutio
n
T
h
e
g
e
o
m
etr
ic
s
o
lu
tio
n
f
o
r
in
v
er
s
e
k
in
em
atics
was
c
h
o
s
en
ac
co
r
d
in
g
to
two
f
ac
to
r
s
.
Firs
t,
it
is
an
E
f
f
icien
t
s
o
lu
tio
n
f
o
r
s
im
p
le
s
tr
u
ctu
r
es
with
clo
s
ed
-
f
o
r
m
s
o
lu
tio
n
s
,
th
u
s
g
r
ea
tly
r
ed
u
ci
n
g
m
an
y
ca
lc
u
latio
n
s
an
d
in
cr
ea
s
in
g
ef
f
icien
c
y
.
Se
co
n
d
,
th
e
g
e
o
m
etr
ic
s
o
lu
tio
n
is
ad
ap
tab
le,
allo
win
g
m
o
r
e
m
o
d
if
icatio
n
s
to
th
e
ar
m
with
o
u
t
r
e
q
u
ir
in
g
an
y
ch
an
g
es
to
th
e
i
n
v
er
s
e
k
in
e
m
atics
m
o
d
el,
as
lo
n
g
as
t
h
e
p
ar
am
eter
s
an
d
co
ef
f
icien
ts
s
tay
th
e
s
am
e.
I
n
co
m
p
ar
is
o
n
t
o
o
th
er
m
eth
o
d
s
,
s
u
ch
as th
e
alg
eb
r
aic
tr
ac
k
,
th
e
g
eo
m
etr
ic
s
o
lu
tio
n
is
v
alu
ed
f
o
r
its
ef
f
icien
c
y
in
less
co
m
p
lex
s
tr
u
ctu
r
es.
W
h
ile
th
e
al
g
eb
r
aic
m
eth
o
d
b
o
asts
g
r
ea
ter
v
er
s
atility
an
d
ca
n
h
an
d
le
a
b
r
o
a
d
er
s
p
ec
tr
u
m
o
f
r
o
b
o
tic
s
y
s
tem
s
,
it
m
ay
g
r
ap
p
le
with
ch
alle
n
g
es,
p
ar
ticu
lar
ly
i
n
s
ce
n
ar
io
s
th
at
in
v
o
lv
e
h
ig
h
ly
n
o
n
lin
ea
r
s
y
s
tem
s
[
5
8
]
.
M
o
r
e
o
v
er
,
wh
en
co
m
p
ar
e
d
to
n
u
m
er
ical
s
o
lu
tio
n
s
s
u
ch
as
n
eu
r
o
-
f
u
zz
y
m
o
d
els,
asid
e
f
r
o
m
b
ei
n
g
k
n
o
wn
f
o
r
th
eir
a
d
ap
tab
ilit
y
,
th
ey
in
t
r
o
d
u
ce
co
m
p
lex
ities
r
elate
d
to
co
m
p
u
tatio
n
al
c
o
s
ts
,
in
ter
p
r
et
ab
ilit
y
,
an
d
d
ata
r
e
q
u
ir
em
e
n
t
s
.
T
h
e
d
ec
is
io
n
to
ch
o
o
s
e
o
n
e
o
f
th
ese
m
o
d
els
d
ep
en
d
s
o
n
t
h
e
n
ee
d
s
o
f
th
e
r
o
b
o
tic
s
y
s
tem
.
Nec
ess
itatin
g
a
ca
r
e
f
u
l
b
alan
ce
b
etwe
en
ad
ap
tab
ilit
y
,
co
m
p
u
tatio
n
al
r
eq
u
i
r
em
en
ts
,
a
n
d
in
ter
p
r
etab
ilit
y
[
5
9
]
an
d
co
m
p
ar
is
o
n
with
n
ew
tech
n
i
q
u
es,
s
u
ch
as
th
e
u
s
e
o
f
PS
O.
co
m
b
in
ed
with
POSIX
th
r
ea
d
s
f
o
r
in
v
er
s
e
k
in
e
m
atics.
W
h
ile
th
is
in
n
o
v
ativ
e
s
tr
ateg
y
h
o
l
d
s
p
r
o
m
is
e
b
y
f
ac
ilit
atin
g
p
ar
allelis
m
an
d
p
o
ten
tial
s
p
ee
d
u
p
,
it
p
r
esen
ts
ch
allen
g
es
r
elate
d
to
th
r
ea
d
s
y
n
ch
r
o
n
izatio
n
,
lo
ad
b
alan
cin
g
,
an
d
s
y
s
tem
co
m
p
l
ex
ity
.
R
ig
o
r
o
u
s
test
in
g
an
d
v
alid
atio
n
u
n
d
e
r
v
ar
io
u
s
co
n
d
i
tio
n
s
is
es
s
en
tial
to
ac
cu
r
ately
ev
alu
ate
its
p
er
f
o
r
m
an
ce
[
5
9
]
.
Af
ter
ca
r
ef
u
ll
y
c
o
n
s
id
er
in
g
t
h
ese
f
ac
to
r
s
,
th
e
g
eo
m
etr
ic
s
o
lu
tio
n
ap
p
r
o
ac
h
em
er
g
e
d
as
th
e
p
r
e
f
er
r
ed
ch
o
ice
in
th
is
s
tu
d
y
.
I
ts
ef
f
icien
cy
in
h
an
d
lin
g
s
im
p
le
s
tr
u
ctu
r
es
an
d
clo
s
ed
f
o
r
m
s
o
lu
tio
n
s
,
an
d
t
h
e
ad
ap
tab
ilit
y
o
f
t
h
e
g
eo
m
e
tr
ic
s
o
lu
tio
n
allo
w
f
o
r
d
y
n
a
m
ic
ch
an
g
es
in
lin
k
len
g
th
s
o
r
th
e
e
n
d
-
e
f
f
ec
to
r
w
h
ile
m
ain
tain
in
g
th
e
s
am
e
co
n
f
ig
u
r
atio
n
.
T
h
is
f
ea
tu
r
e
is
p
a
r
ticu
lar
ly
b
en
e
f
icial
in
s
ce
n
ar
io
s
wh
e
r
e
alter
atio
n
s
to
t
h
e
r
o
b
o
t’
s
s
tr
u
ctu
r
e
ar
e
r
eq
u
ir
ed
.
I
t
is
th
e
m
o
s
t
f
it
s
o
l
u
tio
n
f
o
r
J
u
p
iter
’
s
r
o
b
o
tic
s
y
s
tem
an
d
its
u
n
iq
u
e
r
eq
u
ir
em
e
n
ts
.
T
h
e
to
p
v
ie
w
o
f
th
e
r
o
b
o
tic
ar
m
,
th
e
v
a
lu
e
o
f
r
1
,
u
s
in
g
th
e
Py
th
ag
o
r
ea
n
th
eo
r
e
m
in
(
5
)
.
Giv
en
th
at
y
o
is
th
e
p
o
s
itio
n
o
f
th
e
en
d
e
f
f
ec
to
r
alo
n
g
th
e
y
-
ax
is
an
d
x
o
is
th
e
p
o
s
itio
n
o
f
th
e
en
d
ef
f
ec
to
r
alo
n
g
th
e
x
-
ax
is
.
θ
4
=
ta
n
−
1
(
)
(
4
)
θ
1
r
ep
r
esen
ts
th
e
r
o
tatio
n
al
jo
i
n
t
o
f
th
e
ar
m
(
b
ase
jo
in
t)
.
Gi
v
en
th
at,
z
0
is
th
e
d
is
tan
ce
th
e
en
d
ef
f
ec
to
r
alo
n
g
th
e
z
-
ax
is
,
an
d
a
0
is
th
e
b
ase
li
n
k
len
g
t
h
.
T
h
e
s
id
e
v
iew
o
f
th
e
r
o
b
o
t
’
s
ar
m
:
1
=
√
0
2
+
2
;
2
=
0
−
0
;
3
=
√
1
2
+
2
2
(
5
)
B
y
ap
p
ly
in
g
t
h
e
co
s
in
e
r
u
le
(
6
)
o
n
th
e
r
3
lin
k
(
3
2
=
1
2
+
2
2
−
2
⋅
1
⋅
2
⋅
c
os
α
)
(
6
)
T
h
e
an
g
le
α
ca
n
b
e
d
en
o
ted
b
y
(
7
)
/
c
os
α
=
1
2
+
2
2
−
3
2
2
⋅
1
⋅
2
(
7
)
θ
2
an
d
α
ar
e
s
u
p
p
lem
en
tar
y
an
d
ca
n
b
e
o
b
tain
e
d
b
y
(
8
)
.
θ
2
=
(
π
−
α
)
;
c
os
θ
2
=
−
c
os
α
;
θ
2
=
c
os
−
1
(
1
2
+
2
2
−
(
1
2
+
2
2
)
2
⋅
1
⋅
2
)
(
8
)
T
h
en
,
ap
p
ly
in
g
(
SOHC
AHT
O
A)
tr
ig
o
n
o
m
etr
ic
f
u
n
ctio
n
s
(
9
)
to
d
ed
u
ce
th
e
an
g
les eq
u
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
1
-
1
0
6
θ
1
=
γ
−
β
;
t
a
n
β
=
2
sin
θ
2
1
+
2
cos
θ
2
;
t
a
n
γ
=
2
1
;
β
=
t
a
n
−
1
(
2
sin
θ
2
1
+
2
cos
θ
2
)
;
γ
=
t
a
n
−
1
(
2
1
)
(
9
)
T
h
is
r
ep
r
esen
ts
th
e
r
esu
lt o
f
s
u
b
s
titu
tin
g
p
r
ev
io
u
s
eq
u
atio
n
s
t
o
r
esu
lt in
(
1
0
)
.
1
=
ta
n
−
1
(
2
1
)
−
ta
n
−
1
(
2
s
in
2
1
+
2
c
os
2
)
(
10
)
Fin
ally
,
we
ca
lcu
late
th
e
an
g
l
es
o
f
m
o
v
em
e
n
t
in
th
e
eq
u
atio
n
s
b
elo
w
wh
er
e
θ
base
r
ep
r
esen
ts
th
e
b
ase
r
o
tatio
n
an
g
le,
an
d
φ
is
th
e
E
u
ler
a
n
g
le
.
be
nc
=
ta
n
−
1
(
)
;
=
1
+
2
+
3
;
3
=
−
(
1
+
2
)
(
11
)
4.
RE
SU
L
T
S
A
s
et
o
f
to
o
ls
an
d
lib
r
ar
ies
h
av
e
b
ee
n
u
s
ed
to
im
p
lem
e
n
t
an
d
test
th
e
r
o
b
o
t’
s
ar
m
in
a
s
im
u
latio
n
.
First,
a
v
is
u
aliza
tio
n
o
f
th
e
r
o
b
o
t’
s
r
o
b
o
tic
a
r
m
u
s
in
g
t
h
e
”Visu
alize
Kin
em
atics”
lib
r
ar
y
o
n
Py
th
o
n
as seen
in
Fig
u
r
e
.
I
n
th
is
lib
r
ar
y
in
Py
th
o
n
,
th
e
k
in
em
atics
m
o
d
el
is
i
m
p
lem
en
ted
a
n
d
test
ed
.
T
h
e
r
o
b
o
t’
s
en
d
-
ef
f
ec
to
r
is
g
iv
e
n
a
lo
ca
tio
n
an
d
o
r
ien
tatio
n
,
th
ese
c
o
o
r
d
i
n
ate
s
ar
e
co
m
p
ar
e
d
with
th
e
o
r
ig
in
co
o
r
d
in
ate
f
r
a
m
e
to
p
r
o
v
e
ac
cu
r
ac
y
.
Fig
u
r
e
3
.
Kin
em
atics
v
is
u
aliza
tio
n
I
n
th
e
p
r
o
p
o
s
ed
s
tu
d
y
,
we
em
p
lo
y
ed
a
v
er
s
atile
r
o
b
o
t
eq
u
ip
p
ed
with
an
ad
v
an
ce
d
a
r
m
an
d
a
m
u
lti
-
Ast
r
a
d
ep
th
ca
m
er
a.
T
h
e
ex
p
er
im
en
ts
wer
e
co
n
d
u
cted
in
d
iv
er
s
e
en
v
ir
o
n
m
e
n
ts
,
s
u
ch
as
k
itch
en
an
d
liv
in
g
r
o
o
m
s
ettin
g
s
,
to
ass
ess
th
e
r
o
b
o
t’
s
a
b
ilit
y
to
au
to
n
o
m
o
u
s
ly
n
av
ig
ate,
d
etec
t
d
i
f
f
er
en
t
tar
g
et
o
b
jects
with
d
if
f
er
en
t
d
im
e
n
s
io
n
s
an
d
g
r
as
p
in
g
p
o
in
ts
an
d
ce
n
te
r
o
f
m
ass
,
an
d
p
er
f
o
r
m
p
r
ec
is
e
ar
m
m
an
ip
u
latio
n
s
,
f
o
r
th
e
ar
m
’
s
p
o
s
itio
n
s
ee
Fig
u
r
e
3
.
T
h
e
r
o
b
o
t’
s
en
d
ef
f
ec
to
r
was
d
e
s
ig
n
ed
f
o
r
ad
ap
ta
b
ilit
y
,
allo
wi
n
g
f
o
r
th
e
g
r
asp
in
g
o
f
v
ar
i
o
u
s
o
b
jects a
n
d
th
eir
d
e
liv
er
y
to
th
e
u
s
er
.
No
tab
ly
,
th
e
r
o
b
o
t’
s
en
d
ef
f
ec
to
r
is
a
m
o
d
u
lar
c
o
m
p
o
n
e
n
t
th
at
ca
n
b
e
c
h
an
g
e
d
o
r
m
o
d
if
ied
t
o
p
er
f
o
r
m
v
a
r
io
u
s
task
s
.
T
h
e
ad
ap
tatio
n
also
in
v
o
lv
es
twea
k
i
n
g
o
f
th
e
lin
k
len
g
th
s
wh
ic
h
i
s
p
o
s
s
ib
le
b
u
t
d
o
es
n
o
t
p
o
s
e
an
y
is
s
u
e
f
o
r
in
v
e
r
s
e
k
in
em
atics.
W
ith
r
esp
ec
t
t
o
th
is
f
ea
tu
r
e,
th
e
r
o
b
o
t
b
ec
o
m
es
m
o
r
e
f
lex
ib
le
,
p
er
f
o
r
m
in
g
d
iv
er
s
e
o
p
e
r
atio
n
s
in
v
ar
io
u
s
s
ettin
g
s
with
h
ig
h
a
cc
u
r
ac
y
an
d
p
e
r
f
o
r
m
an
ce
.
4
.
1
.
F
ina
l
t
a
s
k
Sen
s
o
r
s
co
u
p
led
with
alg
o
r
ith
m
s
en
ab
led
th
e
r
o
b
o
t
to
m
o
v
e
p
r
ec
is
ely
to
th
e
p
r
ed
ef
in
e
d
wa
y
p
o
in
t.
At
th
is
p
o
in
t,
th
e
r
o
b
o
t
s
tar
ted
3
D
lo
ca
lizatio
n
o
f
t
h
e
b
all
o
n
th
e
s
p
o
t
b
y
m
u
ltip
le
astra
-
d
ep
th
ca
m
er
as
wit
h
r
esp
ec
tiv
e
x
,
y
,
an
d
z
co
o
r
d
i
n
ates.
Su
b
s
eq
u
en
tly
,
th
e
r
o
b
o
t
s
ea
m
less
ly
tr
an
s
itio
n
ed
to
ar
m
m
an
ip
u
latio
n
,
em
p
lo
y
in
g
in
v
er
s
e
k
in
em
atics to
ca
lcu
late
jo
in
t a
n
g
les f
o
r
an
ac
cu
r
ate
g
r
asp
a
n
d
r
elo
ca
tio
n
o
f
th
e
b
all.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
P
o
s
itio
n
a
n
d
o
r
ien
ta
tio
n
a
n
a
ly
s
is
o
f J
u
p
iter
r
o
b
o
t a
r
m
fo
r
n
a
vig
a
tio
n
s
ta
b
ilit
y
(
Oma
r
S
h
a
la
s
h
)
7
4
.
2
.
Va
lid
a
t
i
o
n
Valid
atin
g
th
e
ac
cu
r
ac
y
a
n
d
r
eliab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
in
v
e
r
s
e
k
in
em
atics
m
o
d
el
is
cr
u
cial
to
en
s
u
r
e
its
ap
p
licab
ilit
y
an
d
ef
f
ec
tiv
en
ess
in
p
r
ac
tical
s
ce
n
ar
io
s
.
T
o
in
itiate
th
e
v
alid
atio
n
,
an
e
x
p
e
r
im
en
tal
s
etu
p
was
d
esig
n
ed
b
y
m
an
u
ally
p
o
s
itio
n
in
g
th
e
en
d
ef
f
ec
to
r
to
a
p
r
ed
ef
in
ed
p
o
in
t
in
s
p
ac
e
an
d
m
ea
s
u
r
in
g
th
e
jo
in
an
g
les
θ
1
,
θ
2
an
d
θ
4
,
th
en
cr
o
s
s
-
v
alid
atin
g
th
e
m
ea
s
u
r
ed
v
al
u
e
s
with
th
e
p
r
o
p
o
s
ed
m
o
d
el.
T
h
e
en
d
ef
f
ec
to
r
was
p
lace
d
at
p
o
in
t
(
1
0
,
0
,
1
4
)
in
s
p
ac
e
w
h
ich
co
r
r
esp
o
n
d
s
to
x
,
y,
z
c
o
o
r
d
in
ates
r
esp
ec
tiv
ely
,
th
en
th
e
jo
in
t a
n
g
les we
r
e
m
ea
s
u
r
ed
θ
1
= 0
°
,
θ
2
=
9
0
°
an
d
θ
4
= 0
°
an
d
g
iv
en
th
e
lin
k
len
g
th
s
o
f
th
e
r
o
b
o
t
ar
m
l
1
=
10
cm
,
l
2
=
1
0
cm
an
d
a
0
=
4
cm
.
we
s
u
b
s
titu
te
in
(
4
)
,
(
8
)
,
(
9
)
to
o
b
tain
th
at
th
e
r
esu
lt
o
f
th
e
jo
in
t a
n
g
les
θ
1
=
0
°
,
θ
2
=
9
0
°
a
n
d
θ
4
=
0
°
,
s
ee
Fig
u
r
e
1
.
5.
CO
NCLU
SI
O
N
I
n
o
r
d
e
r
to
d
ev
elo
p
a
r
o
b
u
s
t
k
in
em
atic
m
o
d
el
f
o
r
J
u
p
iter
’
s
r
o
b
o
tic
ar
m
,
we
p
r
esen
ted
an
ex
ac
t
f
o
r
war
d
a
n
d
i
n
v
er
s
e
k
in
e
m
atics
s
o
lu
tio
n
,
en
co
m
p
ass
in
g
a
s
tep
-
by
-
s
tep
d
er
iv
atio
n
o
f
a
h
o
m
o
g
en
eo
u
s
tr
an
s
f
o
r
m
atio
n
m
atr
ix
,
d
eter
m
in
atio
n
o
f
o
r
ien
tatio
n
,
p
o
s
itio
n
,
an
d
E
u
ler
an
g
les,
cu
lm
in
at
ed
in
a
s
tr
ea
m
lin
e
d
d
ir
ec
t
k
in
em
atic
s
o
lu
tio
n
,
f
o
ll
o
wed
b
y
th
e
s
im
p
lific
atio
n
o
f
d
ir
ec
t
k
in
em
atic
m
atr
ices.
T
h
is
co
n
tr
ib
u
tio
n
n
o
t
o
n
ly
im
p
r
o
v
es
th
e
r
o
b
o
t’
s
m
o
tio
n
c
o
n
tr
o
l
b
u
t
also
alig
n
s
with
its
ed
u
ca
tio
n
al
o
b
jectiv
es
b
y
f
ac
ilit
atin
g
au
to
n
o
m
o
u
s
n
av
ig
atio
n
an
d
e
n
h
an
cin
g
lear
n
in
g
ex
p
e
r
ien
ce
s
.
W
h
ile
th
is
s
tu
d
y
p
r
esen
ts
a
s
o
lid
f
o
u
n
d
atio
n
,
f
u
tu
r
e
w
o
r
k
co
u
ld
ap
p
ly
th
e
k
in
em
atic
m
o
d
el
to
r
ea
l
-
life
s
ce
n
ar
io
s
an
d
a
d
ap
tiv
e
lear
n
i
n
g
m
ec
h
an
is
m
s
to
f
u
r
th
er
a
d
v
an
ce
J
u
p
iter
’
s
ed
u
c
atio
n
al
co
n
tr
ib
u
tio
n
s
.
RE
F
E
R
E
NC
E
S
[
1
]
M
.
S
.
K
a
i
ser,
S
.
A
l
M
a
mu
n
,
M
.
M
a
h
mu
d
,
a
n
d
M
.
H
.
Ta
n
i
a
,
“
H
e
a
l
t
h
c
a
r
e
r
o
b
o
t
s
t
o
c
o
m
b
a
t
C
O
V
I
D
-
1
9
,
”
i
n
L
e
c
t
u
re
N
o
t
e
s
o
n
D
a
t
a
En
g
i
n
e
e
ri
n
g
a
n
d
C
o
m
m
u
n
i
c
a
t
i
o
n
s
T
e
c
h
n
o
l
o
g
i
e
s
,
v
o
l
.
6
0
,
S
p
r
i
n
g
e
r
S
i
n
g
a
p
o
r
e
,
2
0
2
1
,
p
p
.
8
3
–
9
7
.
d
o
i
:
1
0
.
1
0
0
7
/
9
7
8
-
9
8
1
-
15
-
9
6
8
2
-
7
_
1
0
.
[
2
]
J.
H
o
l
l
a
n
d
e
t
a
l
.
,
“
S
e
r
v
i
c
e
r
o
b
o
t
s
i
n
t
h
e
h
e
a
l
t
h
c
a
r
e
s
e
c
t
o
r
,
”
R
o
b
o
t
i
c
s
,
v
o
l
.
1
0
,
n
o
.
1
,
M
a
r
.
2
0
2
1
,
d
o
i
:
1
0
.
3
3
9
0
/
r
o
b
o
t
i
c
s
1
0
0
1
0
0
4
7
.
[
3
]
I
.
M
.
G
a
b
e
r
,
O
.
S
h
a
l
a
sh
,
a
n
d
M
.
S
.
H
a
mad
,
“
O
p
t
i
mi
z
e
d
i
n
t
e
r
-
t
u
r
n
s
h
o
r
t
c
i
r
c
u
i
t
f
a
u
l
t
d
i
a
g
n
o
si
s
f
o
r
i
n
d
u
c
t
i
o
n
m
o
t
o
r
s
u
s
i
n
g
n
e
u
r
a
l
n
e
t
w
o
r
k
s wi
t
h
Le
Le
R
U
,
”
F
e
b
.
2
0
2
3
.
d
o
i
:
1
0
.
1
1
0
9
/
C
P
E
R
E
5
6
5
6
4
.
2
0
2
3
.
1
0
1
1
9
6
1
8
.
[
4
]
A
.
K
h
a
l
e
d
,
O
.
S
h
a
l
a
s
h
,
a
n
d
O
.
I
smae
i
l
,
“
M
u
l
t
i
p
l
e
o
b
j
e
c
t
s
d
e
t
e
c
t
i
o
n
a
n
d
l
o
c
a
l
i
z
a
t
i
o
n
u
si
n
g
d
a
t
a
f
u
s
i
o
n
,
”
D
e
c
.
2
0
2
3
.
d
o
i
:
1
0
.
1
1
0
9
/
I
C
A
R
C
E
5
9
2
5
2
.
2
0
2
4
.
1
0
4
9
2
6
0
9
.
[
5
]
O
.
S
h
a
l
a
s
h
,
“
D
e
s
i
g
n
a
n
d
d
e
v
e
l
o
p
me
n
t
o
f
a
u
t
o
n
o
m
o
u
s
r
o
b
o
t
i
c
m
a
c
h
i
n
e
f
o
r
k
n
e
e
a
r
t
h
r
o
p
l
a
st
y
,
”
P
h
.
D
.
d
i
ssert
a
t
i
o
n
,
D
e
p
a
r
t
m
e
n
t
o
f
B
i
o
me
d
i
c
a
l
E
n
g
i
n
e
e
r
i
n
g
,
U
n
i
v
e
r
si
t
y
o
f
S
t
r
a
t
h
c
l
y
d
e
,
2
0
1
8
.
[
6
]
S
.
K
.
K
a
v
o
u
s
si
,
K
.
M
.
K
a
v
o
u
ss
i
,
a
n
d
D
.
I
.
Le
b
o
v
i
c
,
“
R
o
b
o
t
i
c
-
a
ss
i
st
e
d
t
u
b
a
l
a
n
a
st
o
m
o
si
s
w
i
t
h
o
n
e
-
s
t
i
t
c
h
t
e
c
h
n
i
q
u
e
,
”
J
o
u
rn
a
l
o
f
Ro
b
o
t
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