I
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S In
t
er
na
t
io
na
l J
o
urna
l o
f
Ro
bo
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ics a
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Aut
o
m
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t
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(
I
J
RA)
Vo
l.
14
,
No
.
4
,
Dec
em
b
er
20
25
,
p
p
.
4
7
2
~
4
8
2
I
SS
N:
2722
-
2
5
8
6
,
DOI
:
1
0
.
1
1
5
9
1
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jr
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.
v
14
i
4
.
pp
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-
482
472
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o
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fa
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g
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se
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rc
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m
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o
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tr
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De
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(S
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9
b
y
p
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m
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in
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c
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p
lex
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ig
h
-
risk
e
n
v
iro
n
m
e
n
ts.
K
ey
w
o
r
d
s
:
B
ac
k
war
d
walk
in
g
Hu
m
an
o
id
r
o
b
o
t
I
n
n
o
v
atio
n
Su
s
tain
ab
le
Dev
elo
p
m
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t G
o
al
I
n
v
er
s
e
k
in
e
m
atics
L
in
ea
r
q
u
a
d
r
atic
r
eg
u
lato
r
Su
p
p
o
r
t
p
o
ly
g
o
n
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
:
An
d
i D
h
ar
m
awa
n
Dep
ar
tm
en
t o
f
C
o
m
p
u
ter
Scie
n
ce
an
d
E
lectr
o
n
ics,
Facu
lty
o
f
Ma
th
em
atics a
n
d
Natu
r
al
Sci
en
ce
s
,
Un
iv
er
s
itas
Gad
jah
Ma
d
a
Yo
g
y
ak
ar
ta,
I
n
d
o
n
esia
E
m
ail:
an
d
i_
d
h
a
r
m
awa
n
@
u
g
m
.
ac
.
id
1.
I
NT
RO
D
UCT
I
O
N
Hu
m
an
o
id
r
o
b
o
ts
ar
e
d
esig
n
ed
to
em
u
late
h
u
m
a
n
ab
i
liti
es,
in
clu
d
in
g
walk
in
g
,
li
f
tin
g
,
an
d
p
er
f
o
r
m
in
g
task
s
in
co
m
p
le
x
e
n
v
ir
o
n
m
en
ts
[
1
]
.
T
h
e
y
ar
e
in
c
r
ea
s
in
g
ly
u
tili
ze
d
in
a
wid
e
r
a
n
g
e
o
f
ap
p
licatio
n
s
,
s
u
ch
as
s
u
p
p
o
r
tin
g
i
n
d
u
s
tr
ial
au
to
m
atio
n
,
h
ea
lth
ca
r
e
s
er
v
ic
es,
an
d
ass
is
tin
g
in
d
aily
h
u
m
an
task
s
[
2
]
.
T
h
ese
r
o
b
o
ts
o
f
f
er
s
ig
n
if
ican
t
a
d
v
a
n
tag
es
d
u
e
to
t
h
eir
h
u
m
an
-
lik
e
s
tr
u
ctu
r
e,
wh
ich
allo
ws
th
em
to
n
av
ig
at
e
en
v
ir
o
n
m
en
ts
b
u
ilt
f
o
r
h
u
m
a
n
s
[
3
]
.
Ho
wev
er
,
e
n
s
u
r
in
g
d
y
n
am
ic
s
tab
ilit
y
d
u
r
in
g
m
a
n
eu
v
er
s
lik
e
b
ac
k
war
d
walk
in
g
r
em
ain
s
a
cr
itical
ch
allen
g
e
[
4
]
.
I
s
s
u
es
s
u
ch
as
th
e
s
h
if
t
o
f
th
e
ce
n
ter
o
f
m
ass
(
C
o
M)
b
ey
o
n
d
th
e
s
u
p
p
o
r
t
p
o
l
y
g
o
n
an
d
th
e
lim
ited
r
an
g
e
o
f
m
o
tio
n
in
k
n
ee
jo
i
n
ts
lead
to
f
r
eq
u
en
t
in
s
tab
ilit
y
,
in
cr
ea
s
in
g
th
e
r
is
k
o
f
f
alls
an
d
lim
itin
g
t
h
eir
u
s
ab
ilit
y
in
r
ea
l
-
wo
r
ld
s
ce
n
ar
i
o
s
[
5
]
.
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
Hu
ma
n
o
id
r
o
b
o
t b
a
la
n
ce
c
o
n
t
r
o
l sys
tem
d
u
r
in
g
b
a
ck
w
a
r
d
w
a
lkin
g
… (
Mu
h
a
mma
d
A
r
s
yi
)
473
Alth
o
u
g
h
m
u
c
h
r
esear
ch
h
as e
x
p
lo
r
ed
h
u
m
an
o
id
r
o
b
o
t lo
co
m
o
tio
n
,
it h
as m
ain
ly
f
o
cu
s
ed
o
n
f
o
r
war
d
walk
in
g
an
d
s
tatic
b
alan
ce
[
6
]
,
[
7
]
.
E
x
is
tin
g
co
n
t
r
o
ller
s
s
u
ch
as
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
-
d
e
r
iv
ativ
e
(
PID
)
[
8
]
,
f
u
zz
y
lo
g
ic
[
9
]
,
an
d
o
th
er
co
n
v
en
tio
n
al
ap
p
r
o
ac
h
es
s
tr
u
g
g
le
with
d
y
n
am
ic
C
o
M
ad
ju
s
t
m
en
ts
r
eq
u
i
r
ed
f
o
r
b
ac
k
war
d
walk
in
g
,
o
f
ten
lac
k
i
n
g
th
e
p
r
ec
is
io
n
a
n
d
ad
a
p
tab
il
ity
f
o
r
m
ain
tain
in
g
s
tab
ilit
y
d
u
r
in
g
u
n
p
r
e
d
ictab
le
m
o
v
em
en
ts
[
1
0
]
,
[
1
1
]
.
T
h
is
h
ig
h
lig
h
ts
a
n
ee
d
f
o
r
co
n
tr
o
l
s
tr
ateg
ies
tailo
r
ed
s
p
ec
if
i
ca
lly
f
o
r
b
ac
k
war
d
walk
in
g
.
Simp
lifie
d
d
y
n
am
ic
m
o
d
els
lik
e
th
e
lin
ea
r
in
v
er
ted
p
en
d
u
lu
m
[
1
2
]
o
f
f
er
a
p
r
o
m
is
in
g
f
o
u
n
d
atio
n
d
u
e
to
th
eir
lin
ea
r
ity
an
d
co
m
p
u
ta
tio
n
al
ef
f
icien
cy
[
1
3
]
,
th
o
u
g
h
ad
d
itio
n
al
r
ef
in
em
e
n
ts
ar
e
n
e
ce
s
s
ar
y
to
ad
d
r
ess
th
e
d
is
tin
ct
b
io
m
ec
h
an
ics
o
f
b
ac
k
war
d
m
o
tio
n
[
1
4
]
.
Stab
ilit
y
is
lar
g
ely
d
eter
m
in
ed
b
y
th
e
Z
er
o
Mo
m
en
t
Po
in
t
(
Z
MP)
,
d
er
iv
ed
f
r
o
m
C
o
M
p
r
o
jectio
n
[
1
5
]
,
[
1
6
]
,
an
d
s
h
o
u
l
d
r
em
ain
with
in
th
e
s
u
p
p
o
r
t
p
o
ly
g
o
n
f
o
r
m
ed
b
y
f
o
o
t c
o
n
tact
p
o
in
ts
[
1
7
]
,
[
1
8
]
.
B
ac
k
war
d
walk
in
g
is
cr
u
cial
in
ap
p
licatio
n
s
wh
er
e
s
p
ac
e
co
n
s
tr
ain
ts
o
r
s
u
d
d
en
en
v
i
r
o
n
m
en
ta
l
ch
an
g
es
ex
is
t,
s
u
ch
as
in
in
d
u
s
tr
ial
o
r
h
ea
lth
ca
r
e
s
ettin
g
s
[
1
9
]
.
T
o
im
p
r
o
v
e
p
er
f
o
r
m
an
ce
in
s
u
ch
s
ce
n
ar
io
s
,
th
is
s
tu
d
y
p
r
o
p
o
s
es
a
co
n
tr
o
l
f
r
am
ewo
r
k
c
o
m
b
in
i
n
g
lin
ea
r
q
u
ad
r
atic
r
eg
u
lato
r
(
L
QR
)
with
o
p
tim
ized
walk
in
g
p
atter
n
s
[
2
0
]
,
[
2
1
]
.
L
QR
en
a
b
les
s
tab
le,
r
ap
id
r
esp
o
n
s
es
in
MI
MO
s
y
s
tem
s
[
2
2
]
,
wh
ile
in
v
er
s
e
k
in
em
atics
en
s
u
r
es e
f
f
ec
tiv
e
C
o
M
tr
ajec
t
o
r
y
m
a
n
ag
em
en
t.
T
h
e
k
e
y
co
n
tr
ib
u
tio
n
s
ar
e
i)
d
ev
elo
p
m
en
t
o
f
an
L
QR
-
b
ased
co
n
tr
o
l
f
r
a
m
ewo
r
k
with
o
p
tim
ized
walk
in
g
p
atter
n
s
f
o
r
s
tab
le
b
a
ck
war
d
walk
in
g
a
n
d
ii)
ex
p
e
r
i
m
en
tal
v
alid
atio
n
s
h
o
win
g
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
co
m
p
ar
ed
to
tr
ad
itio
n
al
co
n
tr
o
l m
eth
o
d
s
,
th
er
e
b
y
a
d
d
r
ess
in
g
cr
itical
g
ap
s
in
h
u
m
a
n
o
id
r
o
b
o
t b
alan
ce
co
n
tr
o
l.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws:
Sectio
n
2
r
ev
iew
s
th
e
p
r
o
b
lem
s
tatem
en
t
an
d
r
esear
ch
p
r
elim
in
ar
ies.
Sectio
n
3
d
etails
th
e
m
eth
o
d
o
lo
g
y
,
in
clu
d
in
g
s
y
s
tem
d
esig
n
,
c
o
n
tr
o
l
s
tr
ateg
y
,
an
d
e
x
p
er
im
e
n
tal
s
etu
p
.
Sectio
n
4
p
r
esen
ts
th
e
r
esu
lts
an
d
p
er
f
o
r
m
an
c
e
an
aly
s
is
,
an
d
Sectio
n
5
co
n
clu
d
es
wi
th
im
p
licatio
n
s
an
d
d
ir
ec
tio
n
s
f
o
r
f
u
tu
r
e
r
esear
ch
.
2.
T
H
E
P
RO
P
O
SE
D
M
E
T
H
O
D
T
h
is
s
tu
d
y
ad
d
r
ess
es
th
e
u
n
d
e
r
ex
p
lo
r
e
d
p
r
o
b
lem
o
f
m
ain
tai
n
in
g
b
alan
ce
in
h
u
m
an
o
i
d
r
o
b
o
ts
d
u
r
in
g
b
ac
k
war
d
walk
i
n
g
,
a
m
an
e
u
v
er
th
at
is
co
n
s
id
er
ab
ly
m
o
r
e
u
n
s
tab
le
th
an
f
o
r
war
d
lo
c
o
m
o
tio
n
.
T
h
e
s
cien
tific
q
u
esti
o
n
in
v
esti
g
ated
is
:
C
an
th
e
in
teg
r
atio
n
o
f
o
p
tim
ized
walk
in
g
p
atter
n
g
en
e
r
atio
n
an
d
L
in
ea
r
Qu
ad
r
atic
R
eg
u
lato
r
(
L
QR
)
co
n
tr
o
l e
n
h
a
n
ce
s
tab
ilit
y
in
h
u
m
a
n
o
id
r
o
b
o
ts
walk
in
g
b
ac
k
war
d
?
B
ac
k
war
d
walk
in
g
in
tr
o
d
u
ce
s
s
p
ec
if
ic
ch
allen
g
es
th
at
ar
e
n
o
t
p
r
esen
t
in
f
o
r
war
d
m
o
tio
n
.
T
h
e
C
o
M
ten
d
s
to
s
h
if
t
b
e
y
o
n
d
th
e
s
u
p
p
o
r
t
p
o
ly
g
o
n
d
u
e
to
th
e
r
ev
e
r
s
ed
d
ir
ec
tio
n
o
f
m
o
v
em
en
t
an
d
lim
ited
ac
t
u
atio
n
r
an
g
e
in
t
h
e
k
n
ee
jo
in
ts
,
in
cr
ea
s
in
g
th
e
r
is
k
o
f
i
n
s
tab
ilit
y
an
d
f
alls
[
2
3
]
,
[
2
4
]
.
T
o
o
v
e
r
co
m
e
th
ese
is
s
u
es,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
co
m
b
in
es two
k
ey
s
tr
ateg
ies
.
a.
W
alk
in
g
p
atter
n
o
p
tim
izatio
n
A
s
tab
le
walk
in
g
tr
ajec
to
r
y
is
g
en
er
ated
u
s
in
g
in
v
e
r
s
e
k
i
n
em
atics.
T
h
e
p
atter
n
co
n
s
is
ts
o
f
f
o
u
r
s
tr
u
ctu
r
ed
p
h
ases
:
s
h
if
tin
g
,
lif
tin
g
,
s
tep
p
in
g
,
a
n
d
p
lan
tin
g
.
T
h
ese
p
h
ases
ar
e
ca
r
ef
u
lly
co
o
r
d
in
ated
to
e
n
s
u
r
e
th
at
th
e
r
o
b
o
t’
s
C
o
M
r
e
m
ain
s
with
in
th
e
s
u
p
p
o
r
t
p
o
ly
g
o
n
d
u
r
in
g
ea
c
h
s
tep
.
T
h
e
p
atter
n
also
ac
co
u
n
ts
f
o
r
t
h
e
u
n
iq
u
e
b
io
m
ec
h
a
n
ical
co
n
s
tr
ai
n
ts
an
d
m
o
tio
n
tim
in
g
ass
o
ciate
d
with
b
ac
k
war
d
walk
in
g
[
2
5
]
–
[
2
7
]
.
b.
L
in
ea
r
q
u
a
d
r
atic
r
eg
u
lato
r
f
o
r
d
y
n
am
ic
b
alan
ce
L
QR
is
a
m
o
d
el
-
b
ased
o
p
tim
a
l
co
n
tr
o
l
m
eth
o
d
t
h
at
co
m
p
u
te
s
a
g
ain
m
atr
ix
to
m
in
im
ize
a
q
u
ad
r
atic
co
s
t
f
u
n
ctio
n
.
T
h
is
co
s
t
r
ef
lec
ts
th
e
tr
ad
e
-
o
f
f
b
etwe
en
s
tate
d
ev
iatio
n
s
(
e.
g
.
,
p
itch
a
n
d
r
o
l
l
an
g
le
e
r
r
o
r
s
)
an
d
co
n
tr
o
l e
f
f
o
r
ts
(
e.
g
.
,
a
n
k
le
jo
in
t to
r
q
u
e)
[
2
8
]
,
[
2
9
]
.
I
n
o
u
r
a
p
p
licatio
n
,
th
e
L
QR
co
n
tr
o
ller
is
d
esig
n
ed
b
ased
o
n
a
s
im
p
lifie
d
s
tate
-
s
p
ac
e
m
o
d
el
th
at
in
clu
d
es
i)
r
o
ll
an
g
le
an
d
an
g
u
lar
v
elo
city
an
d
ii)
p
itch
an
g
le
an
d
an
g
u
lar
v
elo
city
.
Usi
n
g
r
ea
l
-
tim
e
f
ee
d
b
ac
k
f
r
o
m
I
MU
s
en
s
o
r
s
,
t
h
e
L
QR
co
n
tin
u
o
u
s
ly
ad
ju
s
ts
th
e
an
k
le
jo
in
t
to
r
q
u
es
to
m
ain
tain
C
o
M
s
tab
ilit
y
,
es
p
ec
ially
d
u
r
in
g
tr
an
s
itio
n
s
b
etwe
en
th
e
s
win
g
an
d
s
tan
ce
p
h
ases
.
T
h
is
i
s
cr
itical
f
o
r
b
ac
k
war
d
walk
in
g
,
wh
er
e
v
is
u
al
an
d
p
r
o
p
r
io
ce
p
tiv
e
f
e
ed
b
ac
k
is
less
ef
f
ec
tiv
e,
an
d
b
alan
ce
r
elies
m
o
r
e
h
ea
v
ily
o
n
co
n
tr
o
l r
o
b
u
s
tn
ess
.
B
y
co
m
b
in
in
g
th
e
o
p
tim
ized
walk
in
g
p
atter
n
an
d
th
e
L
QR
co
n
tr
o
l,
th
e
h
u
m
an
o
id
r
o
b
o
t
c
an
r
esp
o
n
d
q
u
ick
ly
t
o
d
y
n
am
ic
c
h
an
g
es
an
d
d
is
tu
r
b
an
ce
s
wh
ile
walk
i
n
g
b
ac
k
war
d
.
T
h
e
c
o
n
tr
o
l
s
y
s
tem
was
tu
n
ed
v
ia
s
im
u
latio
n
u
s
in
g
a
lin
ea
r
i
n
v
er
ted
p
en
d
u
lu
m
m
o
d
el
b
ef
o
r
e
d
ep
lo
y
m
en
t
o
n
th
e
ac
tu
al
r
o
b
o
t.
T
h
e
r
esu
lt
is
a
s
y
s
tem
ca
p
ab
le
o
f
m
ain
tain
in
g
b
alan
ce
with
o
u
t
f
allin
g
,
ev
en
wh
en
th
e
C
o
M
m
o
m
en
tar
ily
ap
p
r
o
ac
h
es
t
h
e
b
o
u
n
d
ar
y
o
f
th
e
s
u
p
p
o
r
t p
o
ly
g
o
n
.
C
o
m
p
ar
ed
to
p
r
o
p
o
r
tio
n
al
co
n
tr
o
l,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
s
ig
n
if
ican
tly
im
p
r
o
v
es
s
tab
ilit
y
.
i)
C
o
M
d
ev
iatio
n
r
em
ain
s
with
in
5
%
o
f
th
e
p
o
ly
g
o
n
b
o
u
n
d
a
r
y
.
ii)
R
is
e
tim
e
is
b
elo
w
1
s
ec
o
n
d
,
an
d
s
ettlin
g
tim
e
i
s
b
elo
w
2
s
ec
o
n
d
s
.
iii)
N
o
f
alls
wer
e
o
b
s
er
v
e
d
d
u
r
in
g
m
u
lti
-
s
t
ep
b
ac
k
wa
r
d
walk
in
g
test
s
.
T
h
ese
r
esu
lts
p
r
o
v
id
e
ev
id
en
ce
th
at
t
h
e
in
teg
r
ate
d
L
QR
an
d
tr
ajec
to
r
y
o
p
tim
iza
tio
n
m
eth
o
d
is
ef
f
ec
tiv
e
f
o
r
m
ain
tain
in
g
r
o
b
u
s
t
b
alan
ce
d
u
r
in
g
b
ac
k
war
d
w
alk
in
g
.
T
h
is
wo
r
k
co
n
tr
ib
u
te
s
a
n
o
v
el
s
o
lu
tio
n
to
a
less
-
s
tu
d
ied
asp
ec
t
o
f
h
u
m
an
o
id
lo
co
m
o
tio
n
,
with
im
p
licatio
n
s
f
o
r
s
af
e
m
o
b
ilit
y
i
n
co
n
s
tr
ain
ed
o
r
d
y
n
am
ic
e
n
v
i
r
o
n
m
en
ts
.
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
.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
4
7
2
-
4
8
2
474
3.
M
E
T
H
O
D
T
h
e
s
tu
d
y
u
s
es
a
h
u
m
an
o
id
r
o
b
o
t
with
1
8
Do
F
(
1
2
in
le
g
s
,
6
in
ar
m
s
)
,
f
o
cu
s
in
g
o
n
leg
b
e
h
av
io
r
f
o
r
b
ac
k
war
d
walk
in
g
,
wh
er
e
m
a
in
tain
in
g
b
alan
ce
is
ch
allen
g
i
n
g
d
u
e
to
C
o
M
s
h
if
ts
.
C
o
M
is
esti
m
ated
u
s
in
g
f
o
r
war
d
k
in
em
atics
an
d
I
MU
d
ata.
A
L
i
n
ea
r
Qu
a
d
r
atic
R
eg
u
lato
r
(
L
QR
)
co
n
tr
o
ls
an
k
l
e
to
r
q
u
es
b
ased
o
n
p
itch
/r
o
ll
d
ev
iatio
n
s
an
d
an
g
u
l
ar
v
elo
cities
to
k
ee
p
C
o
M
o
n
tr
ac
k
.
I
n
v
e
r
s
e
k
in
em
atics
g
u
id
e
s
f
o
o
t
tr
ajec
to
r
ies.
Sy
s
tem
p
er
f
o
r
m
an
ce
c
r
iter
ia
in
clu
d
e:
C
o
M
with
in
5
% o
f
th
e
s
u
p
p
o
r
t p
o
ly
g
o
n
,
r
is
e
tim
e
≤
1
s
,
s
ettlin
g
tim
e
≤
2
s
,
an
d
p
itch
/r
o
ll o
v
er
s
h
o
o
t <
h
al
f
f
o
o
t le
n
g
th
/wid
th
—
en
s
u
r
in
g
s
tab
le
an
d
s
m
o
o
t
h
walk
in
g
.
3
.
1
.
Desig
n o
f
t
he
ba
ck
wa
rd
wa
lk
ing
pa
t
t
er
n
A
well
-
d
esig
n
ed
walk
in
g
p
atter
n
is
ess
en
tial
f
o
r
h
u
m
an
o
id
r
o
b
o
t
lo
c
o
m
o
tio
n
[
3
0
]
–
[
3
2
]
.
I
t
d
eter
m
in
es
jo
in
t
m
o
v
em
en
ts
an
d
ap
p
r
o
p
r
iate
co
n
tr
o
l
m
ec
h
a
n
is
m
s
.
T
h
e
b
ac
k
war
d
walk
in
g
p
atter
n
co
n
s
is
ts
o
f
f
o
u
r
k
ey
p
h
ases
,
as sh
o
wn
in
Fig
u
r
es 1
an
d
2
.
a.
Sh
if
tin
g
Ph
ase: T
h
e
ce
n
ter
o
f
m
ass
(
C
o
M)
s
h
if
ts
ab
o
v
e
th
e
s
u
p
p
o
r
t le
g
to
e
n
s
u
r
e
s
tab
ilit
y
.
b.
L
if
tin
g
Ph
ase: T
h
e
s
win
g
leg
i
s
lifte
d
,
r
eq
u
ir
in
g
p
r
ec
is
e
co
n
t
r
o
l to
m
ain
tain
b
alan
ce
.
c.
Step
p
in
g
Ph
ase: T
h
e
s
win
g
le
g
m
o
v
es b
ac
k
war
d
,
f
o
llo
wed
b
y
s
u
p
p
o
r
t le
g
a
d
ju
s
tm
en
ts
f
o
r
s
m
o
o
th
m
o
tio
n
.
d.
Plan
tin
g
Ph
ase: T
h
e
s
win
g
leg
is
p
lace
d
o
n
th
e
g
r
o
u
n
d
,
an
d
t
h
e
C
o
M
is
r
ea
d
ju
s
ted
to
r
esto
r
e
s
tab
ilit
y
.
Fig
u
r
es
1
an
d
2
illu
s
tr
ate
th
e
walk
in
g
p
atter
n
s
tar
tin
g
with
th
e
r
ig
h
t
an
d
lef
t
f
o
o
t,
r
esp
ec
t
iv
ely
.
B
y
p
r
o
g
r
ess
in
g
t
h
r
o
u
g
h
t
h
ese
p
h
ases
s
y
s
tem
atica
l
ly
,
th
e
r
o
b
o
t
m
ain
tain
s
its
C
o
M
with
in
th
e
s
u
p
p
o
r
t
p
o
ly
g
o
n
,
r
ed
u
cin
g
f
all
r
is
k
an
d
en
h
a
n
ci
n
g
s
tab
ilit
y
d
u
r
i
n
g
b
ac
k
war
d
walk
in
g
.
Fig
u
r
e
1
.
T
h
e
d
esig
n
o
f
th
e
b
a
ck
war
d
walk
in
g
p
atter
n
s
tar
ts
with
a
s
tep
f
r
o
m
th
e
r
ig
h
t f
o
o
t.
Fig
u
r
e
2
.
T
h
e
d
esig
n
o
f
th
e
b
a
ck
war
d
walk
in
g
p
atter
n
s
tar
ts
with
a
s
tep
f
r
o
m
th
e
lef
t
f
o
o
t.
3
.
2
.
Desig
n o
f
t
he
ba
ck
wa
rd
wa
lk
ing
a
lg
o
ri
t
hm
T
h
e
walk
in
g
alg
o
r
ith
m
aim
s
to
en
ab
le
p
r
ec
is
e
h
u
m
an
o
id
r
o
b
o
t
m
o
v
em
en
t
b
y
i
n
teg
r
at
in
g
s
en
s
o
r
s
etu
p
,
k
in
em
atics,
walk
in
g
p
at
ter
n
g
en
e
r
atio
n
,
a
n
d
L
QR
co
n
t
r
o
l.
Fo
o
ts
tep
p
lace
m
en
t
is
g
u
id
ed
b
y
C
o
M
an
d
en
d
-
ef
f
e
cto
r
p
o
s
itio
n
s
co
m
p
u
ted
v
ia
f
o
r
war
d
a
n
d
in
v
er
s
e
k
in
em
atics.
Fo
r
war
d
k
in
e
m
atics,
u
s
in
g
Den
a
v
it
-
Har
ten
b
e
r
g
m
atr
ices,
tr
ac
k
s
C
o
M
p
o
s
itio
n
a
n
d
o
r
ien
tatio
n
,
wh
ile
in
v
er
s
e
k
in
em
atics
d
eter
m
in
es
jo
in
t
an
g
les
f
o
r
d
esire
d
f
o
o
t
p
o
s
itio
n
s
,
en
s
u
r
in
g
a
cc
u
r
ate
m
o
tio
n
a
n
d
s
tab
ilit
y
.
Fig
u
r
e
3
illu
s
tr
ates
in
v
er
s
e
k
in
em
atics
p
r
o
jectio
n
s
o
n
th
e
r
o
b
o
t’
s
leg
f
r
o
m
b
o
th
s
id
e
in
Fig
u
r
e
3
(
a)
an
d
f
r
o
n
t
v
iews
in
Fig
u
r
e
3
(
b
)
.
I
n
v
er
s
e
k
in
em
atics
is
u
s
ed
to
d
eter
m
in
e
th
e
jo
in
t
a
n
g
les
b
ased
o
n
t
h
e
f
in
al
p
o
s
itio
n
o
f
th
e
e
n
d
-
e
f
f
ec
to
r
[
3
3
]
.
T
o
ca
lcu
late
th
e
in
v
e
r
s
e
k
i
n
em
atics
o
f
a
h
u
m
a
n
o
id
r
o
b
o
t'
s
leg
,
tr
ig
o
n
o
m
etr
ic
ca
lcu
latio
n
s
ar
e
r
eq
u
ir
ed
.
E
q
u
atio
n
s
(
1
)
to
(
5
)
ar
e
th
e
p
r
o
je
cted
ca
lcu
latio
n
f
o
r
th
e
in
v
er
s
e
k
in
em
atics
o
f
a
h
u
m
an
o
id
r
o
b
o
t'
s
leg
as
s
h
o
wn
in
Fig
u
r
e
3
.
B
ased
o
n
Fig
u
r
e
3
,
th
e
a
n
g
les
to
b
e
d
eter
m
i
n
ed
ar
e
th
e
h
ip
an
g
les
o
f
th
e
r
o
b
o
t
(
1
an
d
4
)
,
th
e
k
n
ee
a
n
g
le
(
2
)
,
an
d
t
h
e
an
k
le
a
n
g
les (
3
an
d
5
).
T
o
f
in
d
1
,
it c
an
b
e
d
er
iv
e
d
f
r
o
m
(
5
)
.
2
=
−
1
−
4
(
1
)
=
√
2
2
+
2
(
2
)
=
c
os
−
1
(
2
2
+
2
−
3
2
2
1
2
)
(
3
)
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
Hu
ma
n
o
id
r
o
b
o
t b
a
la
n
ce
c
o
n
t
r
o
l sys
tem
d
u
r
in
g
b
a
ck
w
a
r
d
w
a
lkin
g
… (
Mu
h
a
mma
d
A
r
s
yi
)
475
=
c
os
−
1
(
2
)
(
4
)
1
=
+
(
5
)
(
a)
(
b
)
Fig
u
r
e
3
.
Pro
jectio
n
s
o
f
in
v
er
s
e
k
in
em
atics o
n
th
e
h
u
m
a
n
o
id
r
o
b
o
t'
s
leg
: (
a)
s
id
e
v
iew
o
f
t
h
e
r
o
b
o
t a
n
d
(
b
)
f
r
o
n
t v
iew
o
f
th
e
r
o
b
o
t.
T
o
f
in
d
2
,
it c
an
b
e
d
er
iv
e
d
f
r
o
m
(
7
)
.
=
c
os
−
1
(
2
2
+
3
2
−
2
2
2
3
)
(
6
)
2
=
180°
−
(
7
)
T
h
e
p
itch
an
g
le
at
th
e
a
n
k
le
f
o
r
m
s
th
e
an
g
le
θ
3
,
wh
ich
is
o
b
t
ain
ed
u
s
in
g
(
1
2
)
.
=
√
2
+
4
2
(
8
)
=
c
os
−
1
(
)
(
9
)
=
s
in
−
1
(
4
)
(
10
)
=
180°
−
−
−
(
11
)
3
=
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−
−
(
12
)
T
o
f
in
d
4
,
it is
d
er
iv
ed
f
r
o
m
(
1
4
)
.
=
(
13
)
4
=
s
in
−
1
(
)
(
14
)
T
o
f
in
d
5
,
it is
d
er
iv
ed
f
r
o
m
(
1
6
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
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I
n
t
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R
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b
&
A
u
to
m
,
Vo
l
.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
4
7
2
-
4
8
2
476
=
c
os
−
1
(
)
(
15
)
5
=
180°
−
90°
−
(
16
)
Af
ter
th
e
f
o
o
t
co
n
tacts
th
e
g
r
o
u
n
d
an
d
b
ec
o
m
es
th
e
s
u
p
p
o
r
t
l
eg
,
th
e
d
o
u
b
le
s
u
p
p
o
r
t
p
h
ase
b
eg
in
s
.
T
o
m
ain
tain
b
alan
ce
,
t
h
e
I
MU
s
en
s
o
r
is
co
n
f
ig
u
r
ed
a
n
d
ca
lib
r
ated
to
f
u
n
ctio
n
o
p
tim
ally
.
Fo
r
war
d
k
in
e
m
atics
u
s
es
s
er
v
o
an
g
le
f
ee
d
b
ac
k
to
ca
lcu
late
th
e
r
o
b
o
t’
s
ce
n
ter
o
f
m
ass
(
C
o
M)
p
o
s
itio
n
.
C
o
m
b
in
ed
with
I
MU
s
en
s
o
r
d
ata,
it
h
elp
s
d
ete
r
m
in
e
th
e
r
o
b
o
t'
s
tilt
an
d
en
s
u
r
es
th
e
C
o
M
r
em
ain
s
with
in
th
e
s
u
p
p
o
r
t
p
o
ly
g
o
n
to
p
r
ev
en
t
f
alls
.
Me
an
wh
ile,
in
v
er
s
e
k
in
em
atics
is
ap
p
lied
to
im
p
lem
en
t
th
e
walk
in
g
p
atter
n
an
d
c
o
o
r
d
in
ate
C
o
M
s
h
if
ts
d
u
r
in
g
b
ac
k
war
d
walk
in
g
.
3
.
3
.
Desig
n
o
f
t
he
ba
ck
wa
rd
wa
lk
ing
ba
la
nce
co
ntr
o
l sy
s
t
em
T
h
is
s
tu
d
y
f
o
cu
s
es
o
n
th
e
d
ev
elo
p
m
en
t
o
f
a
co
n
tr
o
l
s
y
s
tem
aim
ed
at
r
e
d
u
cin
g
th
e
r
o
b
o
t'
s
b
o
d
y
im
b
alan
ce
an
d
ac
h
iev
in
g
lo
w
er
r
o
r
v
al
u
es.
I
n
th
is
r
esear
ch
,
s
tates
ar
e
u
s
ed
as
th
e
f
u
n
d
am
en
tal
r
ef
er
en
ce
f
o
r
co
n
tr
o
l
p
ar
am
eter
s
.
T
h
ese
f
o
u
r
s
tates
f
o
r
m
th
e
b
asis
f
o
r
co
n
tr
o
llin
g
th
e
r
o
b
o
t
an
d
m
in
im
i
zin
g
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
d
esire
d
p
o
s
itio
n
an
d
th
e
r
o
b
o
t'
s
ac
tu
al
p
o
s
iti
o
n
:
r
o
ll
an
g
le
(
ϕ
)
,
p
itch
an
g
l
e
(
θ)
,
r
o
ll
an
g
u
la
r
v
elo
city
(
ϕ
̇
)
,
an
d
p
itch
a
n
g
u
la
r
v
elo
city
(
θ
̇
)
.
[
̇
̈
̇
̈
]
=
[
0
1
0
0
0
0
0
0
0
0
1
0
0
0
]
[
̇
̇
]
+
[
0
0
1
0
0
0
0
1
]
[
1
2
]
,
[
1
2
]
=
[
1
0
0
0
0
0
1
0
]
[
̇
̇
]
+
[
0
0
0
0
]
[
1
2
]
(
1
7
)
̇
wh
er
e
=
Pit
ch
an
g
le
̇
=
Pit
ch
an
g
u
lar
v
el
o
city
̈
=
Pit
ch
an
g
u
lar
ac
ce
ler
atio
n
=
R
o
ll a
n
g
le
̇
=
R
o
ll a
n
g
u
lar
v
elo
city
̈
=
R
o
ll a
n
g
u
lar
ac
ce
ler
atio
n
1
=
Pit
ch
ac
tio
n
2
=
R
o
ll a
ctio
n
=
Mo
m
en
t o
f
i
n
er
tia
o
n
th
e
x
-
ax
is
=
Mo
m
en
t o
f
i
n
er
tia
o
n
th
e
y
-
ax
is
=
Gr
av
itatio
n
al
f
o
r
ce
o
f
th
e
E
ar
t
h
1
=
Pit
ch
o
u
tp
u
t
2
=
R
o
ll o
u
tp
u
t
M
=
T
o
tal
m
ass
o
f
th
e
r
o
b
o
t
=
Dis
tan
ce
f
r
o
m
th
e
ce
n
te
r
o
f
m
ass
to
th
e
f
o
o
t so
le
Mo
m
en
t
o
f
in
er
tia
r
ef
e
r
s
to
an
o
b
ject'
s
ten
d
en
cy
to
m
ai
n
tain
its
p
o
s
itio
n
ag
ain
s
t
r
o
tatio
n
al
m
o
tio
n
.
I
n
th
is
s
tu
d
y
,
o
n
ly
m
o
v
e
m
en
ts
o
n
th
e
an
d
ax
es
ar
e
co
n
tr
o
lled
,
s
o
th
e
m
o
m
en
t
o
f
in
e
r
tia
o
n
th
e
-
ax
is
is
ig
n
o
r
ed
.
T
o
o
b
tain
th
e
m
o
m
e
n
t
o
f
in
er
tia
v
al
u
es
f
o
r
th
e
r
o
b
o
t
p
ar
ts
,
r
o
b
o
t
d
esig
n
ca
n
b
e
u
s
ed
in
Au
to
d
esk
I
n
v
en
to
r
s
o
f
twar
e.
Su
b
s
eq
u
en
tly
,
(
1
8
)
ca
n
b
e
u
s
ed
to
ca
lcu
l
ate
th
e
m
o
m
en
t
o
f
in
er
tia
o
n
t
h
e
x
an
d
y
a
x
es
o
f
th
e
r
o
b
o
t.
=
∑
=
1
(
+
(
2
+
2
)
)
,
=
∑
=
1
(
+
(
2
+
2
)
)
(
18
)
I
n
(
1
8
)
,
d
an
ar
e
th
e
m
o
m
en
ts
o
f
in
er
tia
o
n
th
e
an
d
ax
es
l
o
ca
ted
at
th
e
ce
n
ter
o
f
m
ass
o
f
ea
ch
r
o
b
o
t
p
ar
t;
an
d
ar
e
th
e
d
is
tan
ce
s
f
r
o
m
th
e
ce
n
ter
o
f
m
ass
o
f
ea
ch
r
o
b
o
t
co
m
p
o
n
en
t
to
th
e
f
o
o
t
s
u
p
p
o
r
t p
o
in
t o
n
th
e
an
d
ax
es,
r
esp
ec
tiv
ely
,
an
d
is
th
e
m
ass
o
f
ea
ch
r
o
b
o
t c
o
m
p
o
n
e
n
t.
Simu
latio
n
s
p
lay
a
v
ital
r
o
le
i
n
r
o
b
o
t
co
n
tr
o
l
s
y
s
tem
d
ev
elo
p
m
en
t
b
y
m
in
im
izin
g
r
is
k
s
b
ef
o
r
e
r
ea
l
-
wo
r
ld
im
p
lem
en
tatio
n
.
Dir
ec
t
test
in
g
with
o
u
t
s
im
u
latio
n
m
ay
lead
to
s
y
s
tem
d
am
a
g
e
d
u
e
to
u
n
m
ea
s
u
r
ab
le
er
r
o
r
s
an
d
lac
k
o
f
c
o
n
tr
o
l
o
v
er
r
ea
l
-
tim
e
b
eh
av
io
r
.
T
h
e
r
ef
o
r
e
,
s
im
u
latio
n
is
ess
en
tial
f
o
r
v
alid
atin
g
th
e
co
n
tr
o
l
s
y
s
tem
d
esig
n
.
I
n
th
is
s
tu
d
y
,
th
e
L
QR
co
n
tr
o
l
s
y
s
tem
is
s
im
u
lated
u
s
in
g
Py
t
h
o
n
,
wh
er
e
Q
a
n
d
R
m
atr
ices
ar
e
v
ar
ied
to
d
eter
m
i
n
e
th
e
o
p
tim
al
g
ai
n
K
[
3
4
]
,
[
3
5
]
.
T
h
is
g
ain
is
ap
p
lied
to
a
two
-
d
im
en
s
io
n
al
lin
ea
r
in
v
er
te
d
p
en
d
u
l
u
m
m
o
d
el.
T
h
e
o
p
tim
a
l
g
ain
K
is
th
en
im
p
le
m
en
ted
in
th
e
ac
tu
al
r
o
b
o
t
to
e
n
s
u
r
e
ac
cu
r
ate
an
d
s
tab
le
walk
in
g
co
n
tr
o
l.
T
h
e
b
lo
ck
d
i
ag
r
am
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
y
s
tem
is
s
h
o
wn
in
Fig
u
r
e
4
.
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
Hu
ma
n
o
id
r
o
b
o
t b
a
la
n
ce
c
o
n
t
r
o
l sys
tem
d
u
r
in
g
b
a
ck
w
a
r
d
w
a
lkin
g
… (
Mu
h
a
mma
d
A
r
s
yi
)
477
Fig
u
r
e
4
.
T
h
e
b
lo
c
k
d
iag
r
am
o
f
th
e
co
n
t
r
o
l sy
s
tem
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
s
tu
d
y
ev
alu
ated
th
e
r
o
b
o
t's
b
ac
k
war
d
walk
i
n
g
s
tab
ilit
y
b
y
test
in
g
its
walk
in
g
alg
o
r
ith
m
an
d
co
n
tr
o
l
s
y
s
tem
.
I
MU
s
en
s
o
r
s
an
d
f
o
r
war
d
k
in
em
atics
wer
e
u
s
ed
t
o
tr
ac
k
C
o
M,
wh
ile
in
v
er
s
e
k
in
e
m
atics
en
s
u
r
ed
c
o
r
r
ec
t
j
o
in
t
m
o
v
em
en
t.
Me
ch
an
ical
lim
itatio
n
s
a
f
f
ec
ted
s
tab
ilit
y
d
u
r
in
g
leg
liftin
g
an
d
s
tep
p
i
n
g
p
h
ases
.
W
ith
o
u
t
L
QR
,
th
e
r
o
b
o
t
f
r
eq
u
e
n
tly
f
ell.
W
ith
L
Q
R
,
tu
n
ed
u
s
in
g
a
lin
ea
r
in
v
er
ted
p
en
d
u
l
u
m
m
o
d
el
,
an
k
le
ad
ju
s
tm
en
ts
im
p
r
o
v
ed
p
itch
/r
o
ll c
o
n
tr
o
l,
m
ain
tain
in
g
b
alan
ce
an
d
k
ee
p
in
g
th
e
C
o
M
with
in
a
s
af
e
r
an
g
e.
4
.
1
.
B
a
c
k
wa
rd
wa
lk
ing
ro
bo
t
us
ing
pro
po
rt
io
na
l c
o
ntr
o
l
m
et
ho
d
T
h
e
t
e
s
t
i
n
g
b
e
g
i
n
s
w
i
t
h
t
h
e
r
o
b
o
t
i
n
a
n
u
p
r
i
g
h
t
p
o
s
i
ti
o
n
,
f
e
e
t
p
a
r
a
l
l
e
l
.
I
t
t
h
e
n
p
e
r
f
o
r
m
s
b
a
c
k
w
a
r
d
s
t
e
p
s
f
o
llo
win
g
t
h
e
d
esig
n
e
d
p
atter
n
:
th
e
lef
t
f
o
o
ts
tep
s
f
ir
s
t,
s
u
p
p
o
r
ted
b
y
t
h
e
r
ig
h
t
f
o
o
t,
f
o
llo
w
ed
b
y
th
e
r
ig
h
t
f
o
o
t
s
tep
p
in
g
b
ac
k
wh
ile
th
e
lef
t su
p
p
o
r
ts
.
T
h
is
s
eq
u
e
n
ce
co
n
tin
u
es f
o
r
s
ix
s
tep
s
,
ea
ch
p
h
ase
las
tin
g
2
s
ec
o
n
d
s
.
T
h
e
m
o
tio
n
p
atter
n
in
clu
d
es
a
d
o
u
b
le
s
u
p
p
o
r
t
p
h
ase,
wh
er
e
th
e
r
o
b
o
t
b
alan
ce
s
b
ef
o
r
e
s
h
if
tin
g
its
C
o
M.
T
ests
wer
e
co
n
d
u
cted
to
d
eter
m
i
n
e
th
e
o
p
tim
al
d
u
r
atio
n
f
o
r
t
h
is
p
h
ase
t
o
e
n
h
an
ce
s
tab
ilit
y
b
ef
o
r
e
s
tep
p
in
g
.
I
n
itially
,
p
r
o
p
o
r
tio
n
al
co
n
tr
o
l
was
u
s
ed
with
o
u
t
s
tab
ilizin
g
m
ec
h
an
is
m
s
.
T
h
e
r
o
b
o
t
f
ailed
t
o
co
m
p
lete
th
e
b
ac
k
wa
r
d
walk
i
n
g
task
with
o
u
t
f
allin
g
,
as
t
h
e
C
o
M
ex
ce
ed
e
d
th
e
s
u
p
p
o
r
t
p
o
ly
g
o
n
b
o
u
n
d
ar
ies.
C
o
M
d
ata
o
n
th
e
-
an
d
-
ax
es wa
s
an
aly
ze
d
to
ass
es
s
s
tab
ilit
y
.
As s
h
o
wn
in
Fig
u
r
e
5
,
s
ev
er
al
C
o
M
p
o
s
itio
n
s
d
u
r
in
g
th
e
f
ir
s
t
s
tep
f
ell
o
u
ts
id
e
th
e
s
u
p
p
o
r
t
p
o
ly
g
o
n
,
t
h
o
u
g
h
th
e
r
o
b
o
t
r
em
ain
ed
u
p
r
i
g
h
t.
I
n
th
e
s
ec
o
n
d
s
tep
,
th
e
r
o
b
o
t
-
m
ain
tain
ed
s
tab
ilit
y
.
Ho
wev
er
,
in
th
e
th
ir
d
s
tep
,
th
e
C
o
M
d
r
o
p
p
ed
to
ze
r
o
,
in
d
icatin
g
a
f
all
an
d
s
en
s
o
r
s
h
u
td
o
w
n
.
T
h
is
test
h
ig
h
lig
h
ts
th
e
im
p
o
r
tan
ce
o
f
C
o
M
m
o
n
ito
r
in
g
an
d
co
n
tr
o
l
f
o
r
m
ain
tain
in
g
b
alan
c
e
d
u
r
in
g
b
ac
k
war
d
walk
in
g
.
Fig
u
r
e
5
.
B
ac
k
war
d
walk
in
g
t
est o
n
th
e
-
ax
is
u
s
in
g
p
r
o
p
o
r
ti
o
n
al
co
n
tr
o
l
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
.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
4
7
2
-
4
8
2
478
Nex
t
is
th
e
b
ac
k
wa
r
d
walk
in
g
test
o
n
th
e
-
ax
is
u
s
in
g
p
r
o
p
o
r
ti
o
n
al
co
n
tr
o
l
th
at
is
s
h
o
wn
in
Fig
u
r
e
6
.
I
n
th
is
f
ig
u
r
e,
th
e
lo
wer
b
o
u
n
d
o
f
th
e
s
u
p
p
o
r
t
p
o
l
y
g
o
n
r
ep
r
esen
ts
th
e
r
ig
h
t
s
id
e
o
f
th
e
r
o
b
o
t'
s
b
o
d
y
,
wh
ile
th
e
u
p
p
er
b
o
u
n
d
r
e
p
r
esen
ts
th
e
lef
t
s
id
e.
B
ased
o
n
th
e
test
r
esu
lt
g
r
ap
h
,
th
er
e
ar
e
s
till
C
o
M
p
o
s
itio
n
p
o
in
ts
o
n
th
e
-
ax
is
th
at
f
all
o
u
ts
id
e
th
e
s
u
p
p
o
r
t p
o
ly
g
o
n
ar
ea
.
Fig
u
r
e
6
.
B
ac
k
war
d
walk
in
g
t
est o
n
th
e
-
ax
is
u
s
in
g
p
r
o
p
o
r
ti
o
n
al
co
n
tr
o
l
As
s
ee
n
in
Fig
u
r
e
5
d
a
n
Fig
u
r
e
6
,
th
e
b
alan
ce
an
d
s
tab
ilit
y
o
f
th
e
r
o
b
o
t
wh
ile
walk
in
g
b
a
ck
war
d
ar
e
in
ad
eq
u
ate,
m
a
k
in
g
it
p
r
o
n
e
to
f
allin
g
.
T
h
is
co
n
d
itio
n
is
d
u
e
to
th
e
cu
r
r
e
n
t
u
s
e
o
f
a
co
n
v
e
n
tio
n
al
p
r
o
p
o
r
tio
n
al
co
n
tr
o
l
s
y
s
tem
,
wh
ich
is
n
o
t
r
ig
id
an
d
o
p
tim
al
en
o
u
g
h
to
m
ain
tain
th
e
s
tab
ilit
y
o
f
th
e
h
u
m
an
o
id
r
o
b
o
t
wh
e
n
walk
in
g
b
ac
k
war
d
.
T
h
e
p
o
ten
tial
f
o
r
f
allin
g
is
h
ig
h
er
wh
e
n
walk
in
g
b
ac
k
war
d
b
ec
au
s
e
t
h
e
p
r
im
ar
y
s
u
p
p
o
r
t
o
n
th
e
f
o
o
t so
le
is
o
n
ly
at
th
e
h
ee
l.
4
.
2
B
a
ck
w
a
rd
wa
lk
ing
ro
bo
t
us
ing
L
Q
R
co
ntr
o
l m
et
ho
d
T
h
e
n
ex
t
test
u
s
es
th
e
L
QR
m
eth
o
d
.
I
n
v
er
s
e
k
i
n
em
atics
is
u
s
ed
to
p
lan
th
e
en
d
-
ef
f
ec
to
r
’
s
p
ath
,
wh
ile
L
QR
en
s
u
r
es
th
e
ac
tu
ato
r
s
,
p
ar
ticu
lar
ly
th
e
an
k
le
s
er
v
o
s
,
f
o
llo
w
th
at
p
ath
p
r
ec
is
ely
an
d
ef
f
icien
tly
.
T
h
e
o
p
tim
al
g
ain
K
is
d
eter
m
in
ed
b
y
tu
n
in
g
th
e
Q
m
atr
ix
an
d
o
b
s
er
v
in
g
h
o
w
clo
s
ely
th
e
r
o
b
o
t’
s
C
o
M
f
o
llo
ws
th
e
r
ef
er
en
ce
tr
ajec
to
r
y
.
Sm
aller
d
ev
iatio
n
s
in
d
icate
b
etter
s
y
s
tem
r
esp
o
n
s
e.
T
est
r
esu
lts
ar
e
s
h
o
wn
in
Fig
u
r
e
7
(
-
ax
is
)
an
d
Fig
u
r
e
8
(
-
ax
is
)
.
T
h
e
r
o
b
o
t
s
u
cc
ess
f
u
lly
p
er
f
o
r
m
ed
b
ac
k
war
d
walk
i
n
g
with
o
u
t
f
al
lin
g
—
u
n
lik
e
in
t
h
e
p
r
o
p
o
r
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RE
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E
R
E
NC
E
S
[
1
]
C
.
R
.
d
e
L
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a
,
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.
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.
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.
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a
x
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H
u
ma
n
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[
2
]
I
.
R
a
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sa
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,
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.
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o
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a
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.
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[
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4
]
Q
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6
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[
7
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8
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1
2
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1
4
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.
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[
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6
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.
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1
7
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A
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[
1
8
]
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.
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