TELKOM
NIKA
, Vol. 11, No. 5, May 2013, pp. 2879 ~
2887
ISSN: 2302-4
046
2879
Re
cei
v
ed
Jan
uary 18, 201
3
;
Revi
sed Ma
rch 2
5
, 2013;
Acce
pted April 3, 2013
VSGA Method Based Trajectory Planning of a Novel
Limb-robot
Li Liu*
1
, Han-lin Yang
2
, Tie-feng Zha
n
g
2
, Ming Pang
2
, Jie Zhao
3
1
Manag
ement
Coll
eg
e, Harbi
n
Univ
ersit
y
of Commerce
2
Light Industr
y
Coll
eg
e, Harbi
n
Univ
ersit
y
of Commerce
3
Robot Res
ear
ch Institute, Ha
rbin Institute of
T
e
chnol
og
y
Harbi
n
, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: guan
gl
ongr
i
y
ue@
163.com
A
b
st
r
a
ct
A new
progres
sive ge
netic al
gorith
m
(PGA) w
a
s devel
o
p
e
d
for trajectory plan
nin
g
of a no
vel li
mb-
robot. T
he pr
o
pose
d
traject
o
ry pla
nni
ng
met
hod c
an b
e
a
p
p
lie
d to g
e
t an
opti
m
a
l
jo
ints trajectory fro
m
t
h
e
initia
l
to
t
he e
nd positi
on an
d
ori
entati
on. On
the basis
of the
gen
etic
alg
o
rith
m
a n
e
w
kind of v
a
ri
abl
e
structure ge
net
ic alg
o
rith
m (V
SGA) is prop
o
s
ed to so
lve t
he pr
obl
e
m
of
trajectory pl
a
nni
ng of th
e li
mb-
robot i
n
co
mp
li
cate env
iron
ments.
T
he VSGA chan
ges the
origi
nal struct
ure by a
b
a
ndo
nin
g
Elitist Mo
de
l
,
expectati
on
se
lectio
n, re
prod
ucin
g p
o
p
u
lati
on
an
d ch
an
gi
ng th
e
pro
bab
i
lity of cr
ossov
e
r a
n
d
mutatio
n
.
Experi
m
ents r
e
sults s
how
th
at the PG
A is
effective i
n
st
atic e
n
viro
n
m
e
n
ts an
d the
V
S
GA does
w
e
l
l
in
complic
ate env
iron
me
nts.
Ke
y
w
ords
:
limb-robot; trajectory pl
anning; VSGA m
e
thod
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
An increa
sin
g
intere
st in
the develo
p
m
ent of sp
ecial
climbin
g
robot
s ha
s bee
n
witne
s
sed in last de
cade
s.
The motivations b
ehi
nd it
are to incre
a
se o
peratio
n efficien
cy and
prote
c
t huma
n
health a
nd
safety in dan
gero
u
s ta
sks,
such a
s
cle
a
ning hig
h
-rise
building
s
, sp
ray
painting a
nd
san
d
bla
s
ting
of gas tan
k
s, inspe
c
ting a
nd maintaini
n
g nucl
e
a
r
faci
lities. Climbin
g
robot
s,
with
t
heir ca
pabiliti
e
s
to adhe
re to
wall su
rfaces
a
nd
m
o
ve
aro
und ca
rry
ing
ap
pro
p
ri
a
t
e
sen
s
o
r
o
r
too
l
s, are abl
e t
o
re
pla
c
e h
u
m
an
worke
r
s in the
s
e
da
ngerou
s d
u
ties
and
elimi
nate
c
o
s
t
ly erec
tion s
c
affolding
[1].
And at the same time, cli
m
bing robot
s shoul
d have
the operatio
n cap
ability. Jap
ane
se
resea
r
cher p
r
ofesso
r Nori
ho
Koyachi develop
ed
a
new
con
c
e
p
t
of limb stru
cture
of wal
k
ing
robot
s [2]. T
h
e maj
o
r
Ch
aracteri
stic of li
mb
stru
ctur
e
is that
the
“li
m
b”
of a
ro
bo
t can
be
u
s
e
d
to
both wal
k
an
d operate. Th
is pap
er intro
duces
su
ch a
limb-r
obot
.
Limb-robot
is
a joint type robot which is d
i
fficult
to plan its motion in dynamic
spa
c
es. The
probl
em
of m
o
tion pl
anni
n
g
with
ob
sta
c
le avoid
a
n
c
e
has be
en
extensively
studi
ed ove
r
th
e l
a
st
decade. The
main task o
f
motion plan
ning for r
obo
t end effecto
r
s is to find
an colli
sion
-free
trajecto
ry fro
m
an
initial
to a final
co
nfigur
atio
n.
Hen
r
ich et
a
l
. [3] pre
s
e
n
t
ed a
heu
ri
stic
hiera
r
chi
c
al
sea
r
ch meth
od for an i
n
dustri
a
l robot
with 6
deg
ree of freedo
m (DOF
). T
he
colli
sion
s are detecte
d in the Carte
s
ia
n worksp
ace
by a hiera
r
chi
c
al
distan
ce co
mputation ba
sed
on the give
n
CAD m
odel,
whi
c
h i
s
don
e
by adju
s
ting
the step
si
ze
of the se
arch
to the dista
n
c
e
betwe
en the robot an
d the
obsta
cle. Re
cently,
geneti
c
algo
rithm
s
(GAs) have b
een appli
ed to
robot p
a
th an
d motion pla
nning p
r
o
b
le
ms. Yano a
n
d
Tood
a [4] applie
d a ge
netic alg
o
rith
m to
solve th
e p
o
s
ition
and
m
o
vement of
a
n
en
d effe
ct
o
r
on
the
tip
of a two joi
n
t robot
arm.
H
e
defined o
b
je
ctive function
s in both Ca
rtesia
n
sp
ace
and joint sp
ace, an
d co
mbined the
m
to
optimiz
e the robot trajec
tory. Optimum solutions
with smo
o
th trajecto
rie
s
a
nd
mi
nimal
j
o
int
rotation were
obtained. Sh
intaku [5] pro
posed a sim
p
le method b
a
se
d on a ge
netic algo
rith
m,
whe
r
e a
poly
nomial a
ppro
x
imates time
histori
e
s
of
the traje
c
tory
in joint spa
c
e. The ge
net
ic
algorith
m
det
ermin
e
s the
para
m
eter
s o
f
the polynomial to minimize
the fitness of the obje
c
tive
function. P
a
ck d
e
velop
ed
a meth
od to
sea
r
ch fo
r val
i
d solution
in
config
uratio
n
spa
c
e
ba
se
d
on
geneti
c
al
gorithm. He fo
rmulated th
e
trajecto
ry
pl
a
nning
proble
m
with
point
ob
stacl
e
s.
His
method
can
also b
e
exten
ded to an n
-
dimen
s
ion
a
l spa
c
e. Lia
n
fa
ng Tian a
nd
Curti
s
Collins [6]
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ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2879 – 288
7
2880
also p
r
op
ose
d
a genetic
algorith
m
ba
sed tr
aj
ecto
ry planning
method for
a two degre
e
o
f
freedo
m rob
o
t
manipulato
r
who
s
e
workspace incl
ude
s several p
o
int
obsta
cle
s
.
In this
pape
r,
a novel
moti
on a
nd traje
c
tory plan
ning
method
for
a thre
e-lim
ed
rob
o
t’s
end effecto
r
s is develop
ed
. Unlike the
robots that
referred by the rese
arch
e
r
s a
bove (thei
r joi
n
t
hypothetically can rotate from 0 to 2
),
the motion planni
ng of the limb-rob
o
t is more diffi
cult
because of t
he restraint
of it
s joint. Especially in the dynam
i
c
environments this
will
bring
abortio
n
of
th
e alm
o
st
all i
ndividual
in t
he
cu
rre
nt p
opulatio
n. Fu
rtherm
o
re, th
e alg
o
rithm
can
easily
stop or oscillate at a local
pole. T
he
proposed
VSGA can be used
to
sol
v
e the problem
and find a fea
s
ible pl
annin
g
finally.
The re
st of
the pap
er i
s
org
ani
zed
a
s
fo
llo
ws. In
se
ction
1, the novel
me
cha
n
ical
stru
cture of th
e limb-rob
o
t is intro
d
u
c
ed i
n
brie
f. Sectio
n 2 presents t
he mathe
m
ati
c
al d
e
scri
ptio
n
of the path pl
annin
g
for th
e limb-rob
o
t, and then th
e motion pla
nni
ng usi
ng ge
n
e
tic algo
rithm
is
given. Sectio
n 3 VSGA is propo
sed t
o
solve
the
probl
em of motion plan
n
i
ng in dyna
mic
environ
ment.
Experime
n
ts result
s are
presented
in se
ction 4.
C
o
n
c
lu
s
i
on
s
a
r
e dr
awn
in
se
ction 5.
2. Mecha
n
ical
Structure
The
purpo
se
of the
limb
-
robot
is semi
-
auton
omo
u
s
re
co
nnai
ssa
n
ce
in dyna
mic and
unstructu
re
d environ
ment
s. We cho
o
se
a mechani
ca
l
stru
cture illu
strated i
n
Fig
u
re 1
with ni
ne
joints d
r
iven
by nine moto
rs
so th
at the
robot
ca
n walk a
nd o
perate flexibly. The dime
nsi
o
n
of
the prototype
robot is a
p
p
roximately
240mm in h
e
ight, 230m
m in width. The ro
bot weight,
without on
bo
ard ha
rd
wa
re
, is approxim
- ately 7700 gram.
Figure 1. The
limb-ro
bot wi
th
suctio
n cu
ps prototype
The
simulati
on expe
rime
nts in thi
s
p
aper
are re
a
lized i
n
the
human
-robot
interfa
c
e
based on
Jav
a
/Java3
D dev
elop platform. This interfa
c
e integrate
s
the com
m
an
d use
r
interfa
c
e
s
,
missi
on plan
ner, motion
planne
r, trajecto
ry
plan
ner, dynami
cs alg
o
rithm
and 3D virtual
environ
ment i
n
one, whi
c
h
make o
p
e
r
ato
r
easily control and supe
rvise the ro
bot.
3.
Motion Plan
ning of Limb-robo
t Ba
se
d on Progre
ssiv
e
Genetic Algorithm
3.1. Configur
ation Descri
p
tion
Define the
co
nfiguratio
n as follow:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
VSGA Method Based T
r
aj
ectory Plan
ni
ng of a No
vel
Lim
b
-robot (Li Liu)
2881
12
,,
,
ii
i
i
n
c
1,
,
im
(1)
Whe
r
e
n i
s
t
he n
u
mb
er
o
f
rob
o
t joint
s
, m i
s
th
e tot
a
l nu
mbe
r
of
the
amou
nt
of ro
bot
config
uratio
n in a path. The
n
the path ca
n be define
d
as:
12
,,
,
m
pc
c
c
(2)
Rob
o
t path pl
annin
g
is defi
ned a
s
follow:
(1)
Rob
o
t sho
u
ld move alo
ng the “p
” pat
h to arrive at the aim point.
(2) Implie
dly, ci ca
n rep
r
e
s
ent the config
uration of rob
o
t at any time.
(3) If the “p” p
a
th is acco
rd
ant with the
two ab
ove, then it is a feasi
b
le path.
(4) If the “p” path is
accorda
n
t with t
he optimi
z
ati
on rul
e
such
as
sho
r
test
path or
sho
r
test time,
then it is a optimization p
a
th.
3.2. Parameter Coding
GA is a
sea
r
ch e
ngine
ba
sed
on n
e
igh
borh
ood
co
ncept. We h
a
ve
the definition
:
on the
assumptio
n
t
hat c1
and
c2 i
s
two
o
f
the robot
config
uratio
n, wh
ere
11
1
1
2
1
,,
,
n
c
,
22
1
2
2
2
,,
,
n
c
.If a given angle
ε
is
acco
rdant with
the
con
d
ition
12
ma
x
ii
for
all the
element
of th
e sets
11
21
1
2
22
1
2
,,
,
,
,
,
nn
, then
c1
and
c2
is
neigh
borhoo
d
ea
ch
other.
If predefine
a fixed angle
ε
which i
s
the maximum
angle move
ment of any
joint from o
n
e
config
uratio
n to other, then
any
configu
r
ation ca
n be repre
s
e
n
ted a
s
12
,,
,
n
s
ss
,
Whe
r
e
2,
0
,
2
i
s
rep
r
e
s
ent the
rotat
i
on directio
n
of joint i. So a co
mpleted
path of
robot can be
rep
r
e
s
ente
d
as:
11
1
2
1
2
1
2
2
2
1
2
,,
,
,
,
,
,
,
,
,
,
,
nn
m
m
m
n
ss
s
s
s
s
s
s
s
(3)
Each individ
u
a
l of GA population is
rep
r
esented by the vector
(3). When
0
and
m
, vector (3
) wi
ll steer the ro
bot to the aim position.
3.3. Fitness
Ev
aluation
Geneti
c
al
gorithm is an
op
timization
me
thod
with m
u
lti con
s
traine
d conditio
n
.
Fitness
function is e
s
sentially obj
ective functio
n
in
optimiza
t
ion probl
em. The optimization traje
c
to
ry
sho
u
ld be a
c
cordant with t
he rule a
s
foll
ow:
ma
x
F
it
ne
ss
C
d
(4)
Whe
r
e, d is t
he dista
n
ce o
f
the initial posit
ion an
d target positio
n o
f
robot end ef
fectors;
Cmax is
a pos
i
tive c
o
ns
tant.
3.4. Opera
t
o
r
Gene
tic Al
gorithm
Firstly fitne
s
s propo
rtion
method
is u
s
ed to
re
alize
re
pro
d
u
c
tion
. Accordi
n
g
to fitness
function, reproduction
probability
is
got
ten whi
c
h is
used to deci
de the
number of
offspri
n
g of
curre
n
t individual. The in
d
i
vidual that h
a
s a bi
gge
r copy pro
babilit
y would h
a
ve
more offspri
ng.
The in
dividua
l that ha
s sm
aller
copy
probabilit
y may
be elimi
nate
d
. Then
de
ci
de the
crossover
probability Pc, and construct the
ma
tching pool in term of P
c
. T
he individual
in the mat
c
hi
ng
pool is mat
c
hed ra
ndo
ml
y. The positi
on of crosso
ver is al
so d
e
cid
ed ra
ndo
mly. Finally,
the
individual ha
s the opportu
ni
ty of
the prob
ability Pm to
mutate.
3.5. Implement of Ge
netic
Algorithm
Thus th
e step
of the genetic algo
rithm is as follow:
Step 1: decid
e the rang
e o
f
each facto
r
and the len
g
th of the chro
moso
me cod
e
.
Step 2: rando
mly produ
ce
n individual to
con
s
tru
c
t the
initial populat
ion P(0).
Step 3: deco
de ea
ch indivi
dual an
d get
the fitness of each individu
al.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2879 – 288
7
2882
Step 4: operate the pop
ulation P(t)
accord
ing to
the repro
d
u
c
tion, crosso
ver and
mutation ope
rator, then pro
duce the pop
ulation P(t+1).
Step 5:
rep
e
a
t the
step
(3
) a
nd
step
(4
) until
the
current
pha
se
target
is a
c
hi
eved o
r
approa
che
d
.
Step 6: repea
t the step (1)~(5
) until
the
final positio
n is achieved.
Acco
rdi
ng to the algo
rithm
above, the joi
n
t trajecto
ry is gotten a
s
Fi
gure 2.
0
5
10
15
20
25
30
35
40
45
1
2
3
N
u
m
ber of
s
t
ep
Jo
i
n
t
3
0
5
10
15
20
25
30
35
40
45
1
1.
5
2
N
u
m
ber of
s
t
ep
Jo
i
n
t4
a
n
d
Jo
i
n
t5
0
5
10
15
20
25
30
35
40
45
1
1.
5
2
N
u
m
ber of
s
t
ep
Jo
i
n
t6
a
n
d
J
o
i
n
t7
Figure 2. The
joint trajecto
ry computed b
y
the genetic
algorith
m
Joint 3,
4, 5,
6 and
7 a
r
e
u
s
ed to
realize
this
m
o
tion.
Our
obje
c
tive
is to l
e
t the robot en
d
effectors attai
n
the final po
sition.
Fig.3
shows that the
initial and
fin
a
l positio
n an
d orie
ntation
of
the limb-robot
.
(
a
)
(
b
)
Figure 3. The
initial and final positio
n an
d orientatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
VSGA Method Based T
r
aj
ectory Plan
ni
ng of a No
vel
Lim
b
-robot (Li Liu)
2883
4. VSGA
No
w let us su
ppo
se that an
obsta
cle app
ear
an
d the robot may colli
de with the o
b
sta
c
le.
The re
sult
s u
s
ing the g
ene
tic algorith
m
above are sh
own a
s
Figu
re 4.
0
10
20
30
40
50
60
70
80
90
1
2
3
N
u
m
b
e
r
of
s
t
ep
Jo
i
n
t
3
0
10
20
30
40
50
60
70
80
90
0
1
2
N
u
m
b
e
r
of
s
t
ep
J
o
i
n
t
4
an
d J
o
i
n
t
5
0
10
20
30
40
50
60
70
80
90
1
1.
5
2
N
u
m
b
e
r
of
s
t
ep
J
o
i
n
t
6
an
d J
o
i
n
t
7
Figure 4. The
joint trajecto
ry computed b
y
when ro
bot
Figure 5. The
robot o
scillat
e
at the obsta
cle area
In
Figure 4 we can see the
latter
traj
ectory
is an
oscillation at
a local
pol
e. This is
becau
se th
e i
ndividual
in t
he latter p
o
p
u
lation
are
all
abo
rted. T
o
solve th
e p
r
o
b
lem the
VS
GA is
develop
ed h
e
re. The alg
o
rithm chang
es the or
i
g
in
al stru
cture by abando
ni
ng Elitist Model,
expectatio
n
selectio
n, re
produ
cing
po
p
u
lation
and
changi
ng th
e
prob
ability of
cro
s
sover
a
n
d
mutation.
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7
2884
4.1. Fitness
Ev
aluation
Fitness fun
c
tion ca
n be def
ined a
s
follow:
4
ma
x
1
ii
i
F
it
n
e
ss
C
w
f
(5)
Whe
r
e, C
max
is a po
sitive consta
nt;
1
0,
1
f
represe
n
ts the eff
e
ctivene
ss of the curre
n
t
config
uratio
n; f
2
represent
s the amount
of collis
ion between robot
and obstacle; f
3
represents
the
di
stan
ce betwe
en rob
o
t
and obje
c
t
i
ve;
f
4
is the
step l
ength. I
n
the p
r
o
c
e
s
s of p
opul
ation
evolvement,
the individu
al
with hi
ghe
r
fitness wo
uld
have mo
re
cha
n
ce to p
a
r
ticipate
in th
e
comp
etition in the next
gene
ration; the indivi
dual
with lower
fitness
would
be eliminate
d
grad
ually.
4.2. Elitist Model and Re
produc
e Population
In the gen
etic alg
o
rithm
a
bove Elitist Model
will provide the mo
tion dire
ction
until the
robot g
e
ts to
the target a
r
e
a
. In dynamic environ
ment
s Elitist Mode
l will bri
ng forth an o
scillati
on
at a lo
cal
pol
e. So in
such
a ge
neration
Elit
ist
Model
sho
u
ld be ab
ando
ned.
In
addition, be
cause
of the restrai
n
t of joints and existen
c
e
of some
ob
stacl
e
s alm
o
st all the individual abo
rt. The
curre
n
t popul
ation will be repla
c
ed by a
new p
opulati
on pro
d
u
c
ed
rand
omly.
4.3. Expecta
t
ion Selectio
n Method
Expectation selectio
n meth
od is sho
w
n a
s
follow:
(1)
Comp
ute the expe
ctatio
n
i
f
of the fitness
1
1
n
ii
i
f
f
n
(6)
(2)
Comp
ute the expe
ctatio
n of
each in
di
vidual in the popul
ation
i
i
i
f
R
f
(7)
4.4. Adjusting the Probabilit
y
of Crossov
e
r and Mu
tation
The
pro
babili
ty of sel
e
ctio
n an
d m
u
tation
can
be
a
d
juste
d
a
dapt
ively acco
rdi
ng to
the
formulatio
n a
s
follow:
c
,c
,
m
i
n
cc
0
k
,
m
ax
,
m
in
1
1
i
i
tt
tt
ff
PP
ff
e
(8)
m
,m
,
m
i
n
mm
0
k
,m
a
x
,
m
i
n
1
1
i
i
tt
tt
ff
PP
ff
e
(9)
Whe
r
e
,c
i
t
f
is th
e bigg
er fitne
ss
one
betwe
en the t
w
o
crossover indiv
i
dual;
,m
i
t
f
is the
fitness of the
individual th
at are goi
ng
to mutate; P
c
is crossover probability; P
m
is
mutation
probability; P
c0
is initial crossover
probability; P
m0
is initial mutation probability; K
c
is con
s
t
a
nt,
deci
ded by e
x
perime
n
ts; K
m
is con
s
tant, decid
ed by e
x
perime
n
ts.
4.5. Experiments
Resul
t
s
In allu
sion to
the environm
ent refe
rred
a
bove
we u
s
e
d
the
pro
p
o
s
ed VSGA to
plan th
e
robot’
s
motio
n
. Figu
re 6
is the final
po
si
tion and
o
r
ien
t
ation of the li
mb-robot
and
Figu
re 7
is the
joints
trajec
tory.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
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ISSN:
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046
VSGA Method Based T
r
aj
ectory Plan
ni
ng of a No
vel
Lim
b
-robot (Li Liu)
2885
Figure 6. The
final position
and ori
entatio
n
0
5
10
15
20
25
30
35
40
45
1
2
3
N
u
m
ber
of
s
t
ep
Jo
i
n
t
3
0
5
10
15
20
25
30
35
40
45
0.
5
1
1.
5
N
u
m
ber
of
s
t
ep
Jo
i
n
t
4
a
n
d
Jo
i
n
t
5
0
5
10
15
20
25
30
35
40
45
1
1.
5
2
N
u
m
ber
of
s
t
ep
J
o
i
n
t6
a
n
d
J
o
i
n
t7
Figure 7. The
joints traje
c
tory co
m
puted
by variable structu
r
e GA
Simulation
s result
s sh
ow
that the VSGA can
solv
e the motion
plannin
g
problem in
dynamic environm
ents. The joints trajectory has s
lim
oscillation in
some phase
seen from Figure
6. These osci
llation ca
n be
eliminated e
a
sily.
Experiment
s photo
s
sh
own in Figure 8
indicate
that
the VSGA is effective in a motion
planni
ng of the three limb robot.
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TELKOM
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Vol. 11, No
. 5, May 2013 : 2879 – 288
7
2886
a)
b)
c)
d)
h)
g)
f)
e)
i)
j)
k)
l)
Figure 8. The
experime
n
t of the combine
d
motion
5. Conclu
sion
This p
ape
r p
r
opo
sed a
nov
el limb-rob
o
t with nine j
o
int
s
drive
n
by ni
ne moto
rs in
orde
r to
both wal
k
an
d ope
rate fle
x
ibly. A novel pro
g
re
ssive geneti
c
al
gorithm i
s
d
e
velope
d for the
motion pla
n
n
i
ng of the li
mb-robot. Si
mulation
exa
m
ple sho
w
s
the feasibility
of the gene
tic
algorith
m
. Th
e VSGA is
prop
osed to
reali
z
e m
o
tio
n
plan
ning
o
f
the limb-ro
bot in dyn
a
m
ic
environ
ment
s. Experiments result
s show
the va
lidity of
this kin
d
of genetic al
gorit
hm.
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046
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r
aj
ectory Plan
ni
ng of a No
vel
Lim
b
-robot (Li Liu)
2887
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