Intern
ati
o
n
a
l Jo
urn
a
l
o
f
R
o
botics
a
nd Au
tom
a
tion
(I
JR
A)
V
o
l.
4, N
o
. 1
,
Mar
c
h
20
15
,
pp
. 41
~52
I
S
SN
: 208
9-4
8
5
6
41
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJRA
A Brief Survey Paper on
Multi-Legged Robots
Mohammad B
e
hman
esh,
Eh
san
Amiri Te
hraniz
adeh
,
Mahmud
Iwan S
o
lihin
Department of
Mechatron
i
cs
En
gineer
ing,
UCSI University
, 5600
0, Cher
as, M
a
lay
s
ia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received J
u
n
3, 2014
Rev
i
sed
Sep
29
, 20
14
Accepted Oct 20, 2014
Thi
s
pape
r pre
s
ent
s
a b
r
i
e
f
s
u
r
v
ey
on
m
u
l
t
i
-
l
e
gge
d ro
b
o
t
s
an
d
t
h
ei
r
ap
p
lication
s
in
ag
ricu
ltu
re su
ch
as fo
r
h
a
rv
estin
g
.
Mu
lti-legg
ed
robo
ts
h
a
v
e
t
h
e b
e
n
e
fit o
f
m
o
re fl
ex
ib
ility an
d
ad
ap
t to
d
i
fferen
t rou
gh
t
e
rrai
n
i
n
a
bet
t
er way
.
T
h
ey
al
so
ha
ve
very
im
port
a
nt
ap
pl
i
cat
i
ons i
n
fu
lfillin
g th
e dan
g
e
ro
u
s
task
s
su
ch
as m
i
n
e
detectin
g
.
Keyword:
Dyn
a
m
i
c m
o
d
e
llin
g
Kin
e
m
a
tics
Legg
ed ro
bo
ts
Ro
bo
tics
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M
oham
m
ad B
e
hm
anesh,
Depa
rt
m
e
nt
of M
echat
ro
ni
cs En
gi
neeri
n
g
U
C
SI Un
iv
er
si
ty, 5
600
0
Cheras
, Malaysia
Em
a
il: m
o
h
a
mmad
b
e
h
m
an
esh
@
g
m
ail.co
m
1.
INTRODUCTION
It is
bee
n
a
long tim
e since t
h
e e
ngi
neers
a
n
d
scien
tifics h
a
v
e
b
e
en in
terested
i
n
ro
bo
tic
scien
ce. In
fact
r
o
b
o
t
s
ha
ve
fo
u
n
d
t
h
ei
r
ap
pl
i
cat
i
ons i
n
di
ffe
re
nt
asp
ect
s of
t
o
day
’
s l
i
f
e g
r
a
dual
l
y
.
To
day
t
h
e
r
e
i
s
n
o
facto
r
y
w
ithout so
m
e
k
i
nd
o
f
ro
bo
ts
h
e
lp
i
ng in
t
h
e
produ
ct lin
e.
Th
is is
du
e t
o
the cap
a
b
ilities o
f
ro
bots th
at
can m
a
ke t
h
e li
fe easie
r
since
the
robots ca
n
accom
p
lis
h the
da
ngerous
or
diffic
u
lt
tasks for hum
ankind. From
all d
i
fferen
t
typ
e
s of w
a
l
k
ing rob
o
t
s, th
e m
u
lti-leg
g
e
d
robot
is o
f
m
o
re in
terests, sin
ce it
d
e
m
o
n
s
trates a b
e
tter
m
o
v
e
m
e
n
t
o
v
e
r
ro
ugh
gr
oun
d, esp
ecially
when com
p
are
d
to the
wheele
d
or
track
e
d
m
o
b
ile ro
bo
ts. Th
e
m
u
l
ti-
leg
g
e
d
rob
o
t
s
sh
ow
b
e
tter
flex
ib
ility an
d
terrain
ad
ap
tab
ility at th
e co
st
of low sp
eed and
in
creased
con
t
ro
l
co
m
p
lex
ity [1
]
M
a
ny
resea
r
c
h
es h
a
ve
bee
n
do
ne
on t
h
e r
o
b
o
t
i
c
s i
ssue
f
r
om
di
ffere
nt
aspect
s.
Here
som
e
of t
h
e
n
o
v
e
l
u
n
d
e
rstan
d
i
n
g
s on
the
six
legg
ed ro
bo
ts are
presen
t
e
d
fro
m
th
e k
i
n
e
m
a
t
i
cs an
d
d
y
n
a
m
i
c
m
o
d
e
llin
g
vi
ews
.
2.
KINE
MATI
C
S
A
N
D
DY
NA
MIC
S
REVIE
W
I
n
a
no
v
e
l study Ro
y
et al
[2
] esti
m
a
ted
th
e o
p
tim
al
feet forces and
joi
n
t to
rqu
e
s fo
r
on
-
l
in
e con
t
ro
l
of
si
x-l
e
g
g
ed
r
o
b
o
t
.
They
ha
ve
obt
ai
ne
d
o
p
t
im
al
di
st
ri
b
u
t
i
ons
o
f
feet
f
o
r
ces an
d
val
u
es
of
j
o
i
n
t
t
o
r
q
u
e
s o
f
a
six
-
legg
ed
r
obo
t on-
lin
e.
I
n
t
h
is stud
y two
ap
pro
ach
es h
a
ve b
e
en
d
e
v
e
l
oped
:
Ap
pr
oac
h
I :
m
i
nim
i
zat
i
on of
t
h
e n
o
r
m
of fee
t
fo
rces
Ap
pr
oac
h
II:
m
i
nim
i
zat
i
on o
f
t
h
e
n
o
rm
of
j
o
i
n
t
t
o
r
ques
.
Accord
ing
to
th
is research
,
ap
pr
oach II de
m
onstrates
better
energy
efficiency in c
o
m
p
are with
app
r
oach
I.
Th
i
s
m
i
ght
be
bec
a
use
of a
bet
t
e
r
use
of
f
r
i
c
t
i
o
n
bet
w
ee
n t
i
p
s
o
f
t
h
e s
u
pp
o
r
t
i
n
g l
e
gs
an
d t
e
r
r
a
i
n
i
n
app
r
oach
II
. F
i
gu
re 1
di
s
p
l
a
y
s
t
h
e di
st
ri
bu
t
i
ons
of
feet
f
o
rces y
i
el
de
d
by
A
p
p
r
oache
s
I a
nd
II
o
v
e
r
t
w
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
4,
No
. 1,
M
a
rc
h 20
1
5
:
4
1
– 52
42
locom
o
tion cy
cles. As it ca
n be
seen the
forces a
r
e sy
mme
trical in left and ri
ght l
e
gs
because they are
t
o
l
e
rat
i
n
g
t
h
e
s
a
m
e
am
ount
of
f
o
rces
w
h
e
n
i
n
t
h
e s
u
pp
ort
p
h
a
se.
Fi
gu
re
1. Di
st
ri
but
i
o
ns
o
f
feet
fo
rces o
b
t
a
i
n
ed
by
Ap
pr
oac
h
e
s
1 an
d 2 (i
n fi
r
s
t
p
h
ase,
t
h
e
l
e
gs:
2, 3
a
n
d 6
a
r
e
o
n
gro
und
,
wher
eas th
e leg
s
:
1
,
4
,
5 ar
e on
gr
oun
d in
second
p
h
a
se)
.
Besid
e
s th
e two
d
e
v
e
lop
e
d
ap
pro
ach
es i
n
th
e prev
iou
s
p
a
p
e
r, th
e en
erg
y
co
nsu
m
p
tio
n
an
d
stab
ility
of t
h
e r
o
b
o
t
ha
ve bee
n
st
udi
e
d
by
R
o
y
et
al
[3
]. In
th
is st
ud
y, th
e effects
o
f
walk
i
n
g
p
a
ra
m
e
ters, lik
e velo
city,
st
ro
ke an
d
d
u
t
y
fact
ors
ha
ve
been
co
nsi
d
e
r
ed. T
h
e
vari
at
i
ons
o
f
av
era
g
e
po
we
r co
ns
u
m
pti
on a
nd s
p
eci
fi
c
ener
gy
c
ons
um
pt
i
o
n
wi
t
h
t
h
e
vel
o
ci
t
y
an
d st
ro
ke a
r
e c
o
m
p
ared
f
o
r
f
o
u
r
di
ffe
rent
d
u
t
y
fa
ct
ors.
Fi
gu
re
2.
Gai
t
di
ag
ram
s
of t
h
e wa
ve
gai
t
wi
t
h
dut
y
fact
or
s (
a
)
1/
2,
(
b
)
2/
3
,
(
c
)
3/
4 a
n
d(
d)
5/
6.
Fi
gu
re
2 s
h
ow
s gai
t
di
ag
ram
s
f
o
r
di
f
f
ere
n
t
v
a
l
u
es
of
d
u
t
y
f
act
ors e
q
ual
t
o
1/
2
,
2/
3
,
3/
4 a
n
d
5/
6.
It
i
s
to be note
d that the placem
e
n
t and lifting
of a foot
that is the peri
od
of s
u
pport
pha
se is shown by the
d
a
rk
en
ed
lin
es
in
g
a
it d
i
agrams. As it can
be sh
own
appro
a
c
h
II is
m
o
re energy efficient in com
p
are wit
h
the
app
r
oach
I. B
e
si
des, a
p
pr
oac
h
I
I
has e
n
t
r
us
t
e
d l
e
ss va
ri
atio
n in
j
o
i
n
t torq
u
e
s of th
e rob
o
t
co
m
p
ared
with
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA
I
S
SN
:
208
8-8
7
0
8
A Brief Su
rvey
Pap
e
r
o
n
Mu
lti-Leg
g
e
d
Rob
o
t
s (Mo
hammad
Behman
esh
)
43
approach I. Al
so,
with t
h
e i
n
crease
in
du
ty facto
r
, th
e
max
i
m
u
m
v
a
lu
es
o
f
feet
forces and
jo
in
t t
o
rqu
e
s
dem
onstrate a
decrease
.
In
addition, the e
ffe
ct of
velo
city and stroke
on t
h
e ave
r
age
power cons
um
ption a
nd
speci
fi
c ene
r
g
y
cons
um
pt
i
on has bee
n
st
u
d
i
ed. The
res
u
l
t
s
indicate that for all duty fa
ctors, a
v
era
g
e
powe
r
con
s
um
pt
i
on a
nd
speci
fi
c e
n
ergy
c
ons
um
pt
i
on i
n
crease
w
i
t
h
t
h
e st
r
oke
at
a part
i
c
ul
ar
vel
o
ci
t
y
. Al
s
o
, Th
e
NESM
(Norm
a
lized
En
erg
y
Stab
ility Marg
in) in
creases
with
th
e in
cr
ease
i
n
d
u
t
y facto
r
.
In
an
ot
he
r st
ud
y
,
o
p
t
i
m
a
l
gai
t
fo
r
bi
o
-
i
n
s
p
i
r
e
d
cl
i
m
bi
ng r
o
b
o
t
s
usi
n
g
dry
a
dhe
si
o
n
was i
n
vest
i
g
at
ed
b
y
Bo
scario
l
et
al
[4]
.
A q
u
asi
-
st
at
i
c
i
nvest
i
g
at
i
on has bee
n
un
de
rg
o
n
e
t
o
s
o
l
v
e
i
n
ap
p
r
o
p
ri
at
e
redi
st
ri
but
i
o
n
o
f
fo
rces i
n
t
h
e
p
r
el
oadi
n
g
o
f
t
h
e
l
e
gs i
n
cl
i
m
bing
r
o
bot
s
w
h
i
c
h ca
n ca
use i
r
r
e
para
bl
e
det
achm
e
nt
of t
h
e
ro
bot
from
the vertic
al surface.
Fig
u
re
3
.
Op
timal p
o
s
ture
for a v
e
rtical wall: leg
1 lifted
.
Th
e
op
tim
a
l
p
o
s
ture
o
f
th
e ro
bo
t i
n
a v
e
rtical terrain is sh
own
i
n
Fi
g
u
re 3 wh
en
on
ly 5 leg
s
are
su
ppo
rting it.
Th
e
red
co
lor l
e
g
i
n
Fi
g
u
re
3
is in
swing
pha
s
e.
As a
res
u
lt
whe
n
t
h
e ce
nte
r
of m
a
ss is close t
o
th
e fron
t legs
an
d th
e
h
i
nd
l
e
g
s
are ex
tended
th
en
t
h
e
o
p
ti
m
a
l p
o
s
t
u
re is ach
iev
e
d. In
ad
d
ition
,
t
h
e
op
ti
m
a
l
post
u
re
ha
s t
h
e
be
nefi
t
of a
3
5
%
re
duct
i
o
n i
n
t
o
t
a
l
cost
.
Also Roy
et al
[
5
]
a
n
al
y
zed
t
h
e
ene
r
gy
c
ons
um
pt
i
on
of
a
s
i
x-l
e
g
g
e
d
r
o
b
o
t
d
u
ri
ng
i
t
s
t
u
r
n
i
n
g
m
o
t
i
o
n
o
v
e
r a
flat terrain
.
Fo
r th
is st
u
d
y
t
h
ey con
s
i
d
ered
th
e g
a
it
p
a
ram
e
ters on
en
erg
y
con
s
u
m
p
tio
n and
stab
ility o
f
th
e ro
bo
t. Th
e resu
lts ind
i
cat
e th
at
as it wa
s expected inc
r
em
ent in angu
lar
velocity increase
s
the a
v
era
g
e
po
we
r c
o
n
s
um
pt
i
o
n
f
o
r a
pa
rt
i
c
ul
ar
val
u
e
of
d
u
t
y
fact
o
r
. Besid
e
s, for
all d
u
t
y
factors bo
th th
e sp
ecific
resistance a
n
d
the ave
r
a
g
e
power cons
um
ption inc
r
ease
w
i
t
h
a
n
g
u
l
a
r
st
r
o
k
e
at
a gi
ve
n a
n
gul
a
r
vel
o
ci
t
y
.
Tabl
e 1 Ave
r
a
g
e val
u
e o
f
t
h
e
sq
uare
s of j
o
i
n
t
t
o
r
ques
during
turn
ing
m
o
ti
o
n
with d
i
fferen
t
du
ty fact
o
r
s.
Duty Fact
or (
)
Ave
r
a
g
e of
t
h
e
sq
uare
s of j
o
i
n
t
t
o
r
ques
(N.m
2
)
A
p
p
r
o
ach
I
Ap
pr
oac
h
II
1
/
2 7
.
2
513
4
.
0
773
2
/
3 5
.
5
217
2
.
9
939
3
/
4 4
.
9
860
2
.
6
133
5
/
6 4
.
5
577
2
.
2
946
Angu
lar
st
rok
e
=
8d
eg
. ,
An
gu
lar v
e
lo
city= 2
d
e
g./sec
Hei
g
ht
o
f
t
r
u
n
k
bo
dy
=
0.
1
3
m
, Turni
n
g
ra
di
us
=
1m
Tabl
e
1 s
h
o
w
s
t
h
e ave
r
a
g
e
val
u
es
of
t
h
e
sq
ua
res
of
j
o
i
n
t
t
o
r
que
s
of t
h
e
ro
b
o
t
f
o
r
ge
ne
rat
i
n
g
wa
ve
-
t
u
r
n
i
n
g
gai
t
pat
t
erns
wi
t
h
va
ri
ous
d
u
t
y
fact
or
s, as
o
b
t
a
ined
by approac
h
es
I a
n
d II. Res
u
lts indicate that for
bot
h a
p
proache
s
the i
n
crem
ent in
duty
factors g
i
v
e
s th
e in
cremen
t in
th
e av
e
r
age
val
u
e
of t
h
e s
q
uares
of
joint
to
rq
u
e
s during
o
n
e
co
m
p
lete lo
co
m
o
tio
n
cycle.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
4,
No
. 1,
M
a
rc
h 20
1
5
:
4
1
– 52
44
In add
ition
,
R
oy
et al
[6
]
predicted
stab
ility marg
in
and
energ
y
con
s
u
m
p
t
io
n in
t
u
rn
ing
g
a
its of
six
-
l
e
gge
d
r
o
b
o
t
s
by
usi
n
g
so
ft
c
o
m
put
i
n
g
-
base
d e
x
pert
sy
st
em
s. They
deve
l
ope
d
f
o
u
r
di
f
f
e
rent
so
ft
c
o
m
put
i
n
g
-
base
d ex
pe
rt
s
y
st
em
s (t
hat
i
s
, A
p
pr
oac
h
es
1 t
h
r
o
u
g
h
4
)
fo
r
pre
d
i
c
t
i
n
g
speci
fi
c e
n
er
gy
co
ns
um
pt
i
on a
n
d
stab
ility
m
a
rg
in
for t
u
rn
ing
m
o
t
i
o
n
o
f
a si
x
-
leg
g
e
d
ro
bo
t
.
App
r
o
a
ch
1
i
s
b
a
ck
prop
ag
atio
n
al
g
o
rith
m
-
tu
rn
ed
m
u
l
tip
le ad
ap
tiv
e
n
e
u
r
o-fu
zzy inferen
c
e syste
m
, wh
ile ap
pro
ach
2 is
GA-t
u
n
e
d m
u
ltip
le ad
ap
tiv
e
n
e
u
r
o-fu
zzy
i
n
fere
nce
sy
st
em
t
h
en ap
pr
oa
ch
3 i
s
G
A
-
t
u
n
e
d c
o
act
i
v
e
ne
ur
o-
f
u
zzy
i
n
fer
e
nce sy
stem
(GAC
AN
FI
S),
finally
t
h
e ap
pr
oac
h
4 i
s
GA
-t
u
n
e
d
bac
k
-
p
ro
pa
g
a
t
i
on ne
ur
al
net
w
or
k (
G
A
B
PNN
)
. B
y
c
o
m
p
ari
ng t
h
es
e fo
ur
app
r
oaches
, i
t
i
s
o
b
se
rve
d
t
h
at
a
p
p
r
oac
h
2
dem
onst
r
at
e
s
a
bet
t
e
r acc
uracy
i
n
pre
d
i
c
t
i
ons.
T
h
i
s
m
i
ght
be
because of a GA in
place of
BP algorithm
and
usi
ng t
w
o separate ANFIS
struct
ures
for the two
out
puts. For
th
e
g
e
n
e
ralized
b
e
ll-sh
ap
ed
me
m
b
ersh
ip
fu
n
c
tion
d
i
st
ribu
tio
ns, th
e m
e
m
b
ersh
ip
val
u
es are calculat
e
d as
fo
llows:
(1)
Whe
r
e I
k
is the in
pu
t, and
a
i
, b
i
and c
i
are th
e
p
a
ram
e
ters o
f
t
h
e m
e
m
b
ersh
ip fu
n
c
tion
for
i
th
l
i
ngui
st
i
c
t
e
rm
cor
r
es
po
n
d
i
n
g
t
o
an
i
n
put
.
Fig
u
re
4
.
Bell-sh
ap
ed m
e
m
b
e
r
sh
i
p
fun
c
tion
d
i
stribu
tio
ns for th
e inp
u
t
v
a
riab
les: (a) an
gular v
e
l
o
city (
), (b
)
an
gu
lar stro
k
e
(
), an
d
(c)
d
u
ty
facto
r
(
).
In
a
not
her
st
ud
y
,
Wan
g
et al
[7
]
d
i
d th
e m
o
bilit
y an
alysis
on
t
h
e typ
i
cal
gait o
f
a
rad
i
al
sy
mmetrica
l
si
x-l
e
g
g
e
d
ro
b
o
t
.
T
h
ree t
y
pe
s o
f
si
x-l
e
gge
d
ro
b
o
t
s
are
stu
d
i
ed
; on
e is th
e in
sect-wav
e
g
a
it, secon
d
i
s
m
a
m
m
a
l
-
ki
ck
gai
t
an
d t
h
i
r
d
i
s
i
n
sect
-m
amm
a
l
m
i
xed gai
t
. It
can
be
ob
serve
d
fr
om
the Fi
g
u
r
e 5
t
h
at
t
h
e
m
a
m
m
a
l
-
ki
ck
gai
t
co
ns
um
es m
o
re ener
gy
i
n
c
o
m
p
are
wi
t
h
t
h
e t
w
o
ot
he
r
gai
t
s
.
The
c
o
nsum
pt
i
o
n
of
ener
gy
by the insect-wave
gait increases by
t
h
e i
n
crem
ent
of t
u
r
n
i
n
g a
ngl
e.
Al
so e
n
er
gy
c
ons
um
pt
i
ons
o
f
t
h
e
dy
nam
i
cs
m
odel
l
i
ng are
c
o
m
p
are
d
a
s
s
h
o
w
n i
n
Fi
gu
re
6.
This t
h
eoretical analysis
indicates that the
energy
co
nsu
m
p
tio
n
of th
e
ro
bo
t in th
e m
a
mmal-
k
i
ck
d
e
creas
es
, in t
h
e insect
wa
ve
gait increases a
n
d it stays
co
nstan
t
with
t
h
e insect-m
a
mmal
mix
e
d
g
a
it as
a
fun
c
tion
of in
creasing
t
h
e tu
rn
ing
ang
l
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA
I
S
SN
:
208
8-8
7
0
8
A Brief Su
rvey
Pap
e
r
o
n
Mu
lti-Leg
g
e
d
Rob
o
t
s (Mo
hammad
Behman
esh
)
45
Fi
gu
re
5.
Ene
r
gy
co
ns
um
pt
i
on
of
t
h
ree
gai
t
s
by
AD
AM
S
si
m
u
l
a
t
i
on (t
wo
st
ri
des:
0.
08
m
an
d
0.
10
m
)
.
Fi
gu
re
6.
Ene
r
gy
co
ns
um
pt
i
on
of
t
h
ree
gai
t
s
cal
cul
a
t
e
d t
h
r
o
u
g
h
ou
r
dy
na
m
i
cs
m
odel
(st
r
i
d
es:
0.
08
m
)
.
In
a
resea
r
ch
b
y
H
u
an
g
an
d
No
nam
i
[8]
hi
gh
i
n
st
rum
e
nt
at
i
on t
e
c
h
n
o
l
o
gi
es f
o
r
m
i
ne de
t
ect
i
on
was
devel
ope
d.
Fu
rt
herm
ore t
h
e
y
st
udi
ed m
i
ne det
ect
i
on st
r
a
t
e
gi
es usi
n
g
m
easuri
n
g eq
u
i
pm
ent
m
ount
ed
o
n
wal
k
i
n
g
ro
b
o
t
s
base
d
on
si
x-
l
e
gge
d t
e
l
e
o
p
e
r
at
ed
hi
g
h
t
e
c
h
n
o
l
o
gy
. T
h
ei
r
ro
b
o
t
nam
e
d C
O
M
ET-
I ca
n
wal
k
sl
owl
y
at
s
p
ee
d
10
0
–
2
0
0
m
per
ho
ur
wi
t
h
p
r
eci
se det
ect
i
o
n
m
ode usi
n
g
si
x m
e
t
a
l
det
ect
ors.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
4,
No
. 1,
M
a
rc
h 20
1
5
:
4
1
– 52
46
Fi
gu
re 7.
Con
t
ro
l system
with
h
ybrid
po
sitio
n/fo
rce n
e
uro con
t
ro
ller.
They
p
r
o
p
o
se
a hy
b
r
i
d
neu
r
o
cont
rol
sy
st
e
m
wi
t
h
po
si
t
i
on an
d
fo
rce c
o
nt
r
o
l
sy
st
em
as sh
ow
n i
n
Fi
gu
re
7
.
In
a
d
di
t
i
on,
C
O
M
E
T-1
ca
n
m
ove
24
h a
day
a
n
d
res
p
on
ses
o
f
s
canni
ng
m
o
ck
m
i
ne usi
n
g
t
h
e
ra
dar
sen
s
o
r
n
i
g
h
t
usin
g IR cam
era. Th
erefore, th
e
d
e
tected
area will in
crease with u
s
i
n
g rad
a
r sen
s
or
for
n
i
gh
t
s
and
m
e
t
a
l
det
e
ct
or
fo
r
day
s
fr
om
200
0 t
o
40
00
a day
M
i
ne det
ect
i
o
n
by
r
o
bot
s
has
been
o
f
i
n
t
e
res
t
s fo
r m
a
ny
res
earche
r
s,
suc
h
as G
onz
al
ez d
e
Sant
os
et
al
[
9
]
.
They
d
e
vel
o
ped
a wa
l
k
i
n
g
r
o
b
o
t
w
h
i
c
h ca
rri
es se
nso
r
s
fo
r
det
ect
i
ng a
nd l
o
ca
t
i
ng t
h
e m
i
nes i
n
a
n
effi
ci
ent
way
.
Thi
s
sy
st
em
b
e
nefi
t
s
fr
om
m
a
ny
t
o
ol
s
to create a
databa
s
e
s
of pote
ntial alarm
s
and e
q
uip the
ope
rat
o
r
wi
t
h
pr
o
p
o
r
t
i
onal
i
m
ages a
n
d
gra
phs
by
w
h
i
c
h
t
h
i
s
sy
st
em
do
m
i
nat
e
s t
h
e
d
r
awbac
k
s
of
pr
evi
o
us
min
e
d
e
tecto
r
leg
g
e
d
ro
bo
ts, su
ch
as weigh
t
, sp
eed
,
o
m
n
i
d
i
rectio
n
a
lity
an
d
efficiency.
On t
h
e ot
her
h
a
nd
, t
h
e
ro
b
o
t
s
have
ap
pl
i
cat
i
ons
n
o
t
o
n
l
y
o
n
t
h
e
gr
o
u
n
d
b
u
t
al
so
un
de
r t
h
e sea,
Shi
m
et al
[10
]
st
ud
ied a m
u
lti-leg
g
e
d sub
s
ea
robo
t system
i
n
con
s
id
eration
o
f
m
o
b
ility an
d ag
ility. By th
is
researc
h
,
they successfully derive
d
th
e
dyna
m
i
c and t
o
rque constrai
nt eq
uations.
In tabl
e 2 the m
obility and
ag
ility o
f
six-leg
g
e
d
robo
t consid
ering
d
i
fferen
t env
i
ron
m
e
n
t is d
e
m
o
n
s
trated
, th
ese d
a
ta
are d
e
riv
e
d
b
a
sed
on
the m
a
the
m
atic
al fram
e
work
with t
h
e
dyna
mic and cons
traint equations t
o
calc
u
la
te the
acceleration bound of
bo
dy
ce
nt
er.
Tab
l
e
2
.
M
o
b
i
l
ity an
d
ag
ility o
f
six-legg
ed ro
bo
t co
nsid
eri
n
g d
i
fferen
t
env
i
ro
n
m
en
t
Class
Ground case
Unde
rwater ca
se
Min
i
m
u
m Max
i
m
u
m
Min
i
m
u
m
Max
i
m
u
m
Mo
b
ility (m
/s
2
)
x
-
3
3
.
96 3
3
.96 -
4
8
.
78
4
.
7
8
y -
3
1
.
04
3
1
.04
-
2
6
.
7
2
6
.7
z
-
1
9
.
62 6
5
.46 -
1
5
.
62
6
1
.35
Ag
ility (rad
/
s
2
)
W
x
-
110
.4 1
1
0
.
4 -
9
9
.
25
3
7
.24
W
y
-7
7.
2
77
.2
-7
0.
7
8
70
.7
8
W
z
-
9
4
.
59 9
4
.59 -
8
6
.
04
8
6
.04
I
n
a
n
o
v
e
l study, Pr
atih
ar
et
al
[11]
est
a
bl
i
s
h
e
d t
h
e
opt
i
m
al
pat
h
wi
t
h
gai
t
gene
rat
i
o
ns o
f
a si
x l
e
gge
d
robot by m
eans of a
GA-fuz
zy approa
ch
.
Fo
r t
h
is aim
,
t
h
e six-legg
ed
robo
t sho
u
l
d
do
th
e fo
llowing
tasks
o
p
tim
all
y
, in
t
h
e shortest trav
ellin
g
tim
e
:
first it sh
ou
ld
mo
v
e
al
o
n
g
strai
g
h
t
lin
e
p
a
th
s, an
d
th
en
tak
e
sh
arp
ci
rcul
ar
t
u
rns
and
fi
nal
l
y
cr
oss-
di
t
c
hes
.
A
G
A
hel
p
s
t
h
e ro
bo
t t
o
f
i
nd th
e pr
op
er
r
u
les f
r
o
m
th
e
dif
f
e
r
e
n
t
co
d
e
s, t
h
erefo
r
e, th
e robo
t can
find
its p
a
t
h
an
d
g
a
it sim
u
lt
an
eou
s
ly i
n
an
o
p
tim
al way wh
ich m
ean
s wit
h
t
h
e
m
a
xim
u
m
average
ki
nem
a
ti
c m
a
rgi
n
o
f
t
h
e
gr
o
u
n
d
l
e
g
g
e
d
,
w
h
i
l
e
m
i
ni
m
u
m
nu
m
b
er
of l
e
g
g
ed
are
on
t
h
e
g
r
ou
nd
and
m
e
an
wh
ile th
e t
r
av
ellin
g
tim
e is min
i
m
u
m
as well.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA
I
S
SN
:
208
8-8
7
0
8
A Brief Su
rvey
Pap
e
r
o
n
Mu
lti-Leg
g
e
d
Rob
o
t
s (Mo
hammad
Behman
esh
)
47
B
e
si
des, C
h
en
an
d La
n
[1
2]
di
d t
h
e si
m
u
l
a
ti
on a
n
d st
i
f
fne
ss anal
y
s
i
s
f
o
r
he
xap
o
d
m
a
chi
n
es
. T
h
ey
success
f
ully de
rive
d ve
ry
detailed res
u
lts which
help
fo
r cal
culating t
h
e ins
t
antaneou
s
stiffness m
a
trix and the
defl
ect
i
o
n
of t
h
e en
d-e
ffect
or
of t
h
e
6–
6
he
x
a
po
ds
, f
o
r
an
e
a
sy
ada
p
t
i
o
n
.
F
u
rt
herm
ore t
h
e
sim
u
l
a
t
i
on
val
i
d
at
es
the correcti
o
n
of the m
a
the
m
atics and calculation res
u
lts.
On
t
h
e correctio
n
cap
a
b
ility o
f
a
d
e
p
l
o
y
ed tap
e
-sp
r
i
n
g
hex
a
pod
Aridon
et al
[
13]
p
r
edi
c
t
e
d
t
h
e
dy
nam
i
c beha
vi
o
u
r
of a t
a
pe-s
p
r
i
n
g he
x
a
po
d
usi
n
g t
w
o e
x
peri
m
e
nt
al
and n
u
m
e
ri
cal
appr
oac
h
e
s
. Thi
s
research
d
e
termin
es th
at an
ad
d
ition
a
l DOF b
y
u
s
ing
fl
ex
ural
b
l
ad
es is no
t n
ecessary
du
e to th
e
flex
ib
ility
feat
ure
o
f
t
a
pe-
s
pri
ngs
.
Fu
rt
h
e
rm
o
r
e,
Yang
[14
]
stu
d
ied
th
e h
e
x
a
p
o
d
ro
bo
ts with
a lo
ck
ed
jo
in
t failu
re con
s
id
erin
g
th
e
fau
l
t
to
leran
c
e. Th
e
failu
re
resu
lts in
a seriou
s m
o
b
ility lo
ss. Th
is research
ind
i
cates th
at th
is failu
re do
es
n
o
t
affect
the stability of a
gait
howe
ver it im
poses the
workplace of t
h
e
failed le
g.
The
solution th
at
the
y
ha
ve
in
trodu
ced
is t
h
at th
e
h
e
x
a
pod
sh
ou
ld
d
i
scon
tin
u
e
t
h
e m
o
ve
m
e
n
t
o
f
th
e
bo
d
y
with
resp
ect to
leg
swi
n
g wh
ile
t
h
e dam
a
ged
l
e
g i
s
s
w
un
g
pas
s
i
v
el
y
by
t
h
e
t
r
ansl
at
i
o
n
o
f
t
h
e b
ody
.
Cli
m
b
i
n
g
robots h
a
v
e
b
e
en of a
gr
eat in
ter
e
st as
w
e
ll as th
e o
t
h
e
r typ
e
s
o
f
r
obo
ts,
sin
c
e they h
a
v
e
t
h
e
capabilities of m
oving on t
h
e large
bu
ildi
n
gs
or in the
pl
aces whe
r
e is
dange
r
ous for
hum
an. The
r
efore
a
researc
h
on le
gged clim
bing robot wh
ich
ha
s the application as m
a
intena
nce in
hazardous environm
ents was
do
ne by
Lu
k
et a
l
[1
5]
. T
h
i
s
ro
b
o
t
i
s
nam
e
d R
o
b
ug
II
s a
nd
has i
n
sect
-l
i
k
e st
ru
ct
ure
whi
c
h ca
n m
ove i
n
a
variety of t
h
e terrain. T
h
eir
m
e
thod s
u
cces
sfully was a
p
plied and t
h
e re
sults indi
cate a
sm
ooth a
nd a
ccurat
e
m
ovem
e
nt
of t
h
e
ro
b
o
t
,
whi
c
h t
h
e
G
A
-
f
u
zz
y
fu
nct
i
o
ns a
r
e
sh
ow
n i
n
Fi
g
u
r
e
8.
Fig
u
re 8
.
Th
e me
m
b
ersh
ip
fun
c
tio
ns
after GA o
p
tim
izat
io
n.
In
an
ot
he
r st
u
d
y
,
fo
r i
m
pro
v
i
n
g t
h
e
s
p
eed
co
nt
r
o
l
pa
rt
Yu
et al
[1
6
]
stu
d
i
ed
th
e mo
d
e
lling
and
co
n
t
ro
l
of a
sing
le-legg
e
d
robo
t. Th
ey aim
e
d
to
p
r
ov
id
e a
better m
e
th
o
d
to d
e
term
in
e th
e
co
n
t
ro
l
p
a
ram
e
ters.
A c
o
m
p
ari
s
on
bet
w
ee
n t
h
e
pr
o
pose
d
m
e
t
hod
an
d t
h
e R
a
i
b
ert
m
e
t
hod
sh
owe
d
t
h
at
t
h
e p
r
o
p
o
se
d
cont
rol
m
e
t
hod i
s
val
i
d a
n
d
feasi
b
l
e
whi
l
e
bei
n
g ea
sy
t
o
ac
hi
eve a
n
d
hi
gh
p
r
eci
si
on
.
In add
ition
Ai
ya
m
a
et al
[17
]
, inv
e
stig
ated
t
h
e coo
p
e
rativ
e
tran
sp
ortatio
n
b
y
two fo
ur-leg
g
e
d rob
o
t
s.
Th
eir strateg
y
i
s
th
at t
h
e
robo
ts shou
ld m
o
v
e
au
ton
o
m
o
u
s
ly
wh
ile coo
p
e
rate to
t
r
an
spo
r
t an
o
b
j
ect
ov
er a h
i
gh
place or
rough terrain. For t
h
is aim
they adopt a m
e
thod by
whic
h the
robots
get inform
ation only wit
h
i
m
p
licit co
mmu
n
i
cation
.
In
an
in
terestin
g
stud
y, Martín
et al
[18]
com
b
ined a
fuzzy-Markov
meth
od
an
d
a
po
pu
latio
n of
ex
tend
ed K
a
l
m
an
f
ilter
s
to
lo
calize th
e leg
g
e
d
r
obo
ts. Th
ey d
e
v
e
lop
e
d a n
e
w
ap
pro
a
ch
in case
o
f
a strong
ef
f
i
cien
cy r
e
quir
e
m
e
n
t
w
h
ich is r
obo
t v
i
sion
-b
ased
se
lf-localizatio
n
in
dyn
amic an
d
n
o
isy en
v
i
ron
m
e
n
ts for
leg
g
e
d
robo
ts. Th
e resu
lts
in
dicate
th
at
th
is n
e
w
appr
o
a
ch
is su
itab
l
e
for
th
e Robo
Cup
co
nd
itio
ns. Th
is n
e
w
app
r
oach
be
n
e
fi
t
s
f
r
om
ro
bust
i
n
n
o
i
s
y
en
vi
r
onm
ent
s
, c
o
n
v
er
gi
n
g
fr
om
scrat
c
h
and
rec
o
veri
n
g
fr
om
ki
d
n
ap
pi
n
g
.
M
eanw
h
i
l
e
,
A
n
sh
ar
an
d
W
i
l
l
i
a
m
s
[1
9]
st
ud
i
e
d a
not
her
a
p
pr
oac
h
t
h
at
i
s
fast
l
ear
n-t
o
-
w
al
k
fo
r
f
o
u
r
l
e
gge
d r
o
bot
s.
Thi
s
ap
p
r
oac
h
aim
s
t
o
decrea
se t
h
e wea
r
an
d t
ear
of
ro
b
o
t
m
o
t
o
rs,
j
o
i
n
t
s
and
ot
he
r
har
d
wa
re
.
They
r
u
n se
ver
a
l
t
e
st
s base
d
o
n
t
h
e
st
an
dar
d
GA
an
d t
h
e
res
u
l
t
s
can
be
see
n
i
n
Fi
g
u
r
e
9.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
4,
No
. 1,
M
a
rc
h 20
1
5
:
4
1
– 52
48
Fi
gu
re 9.
S
p
ee
d vs ge
nerat
i
o
n
base
d o
n
st
an
d
a
rd
G
A
.
Th
eir research
d
e
term
in
es th
at th
e ex
tend
ed
GA is
per
f
o
r
m
i
ng bet
t
e
r
t
h
a
n
f
itness
-
drive
n
search
a
n
d
standa
rd GA, because i
n
e
x
tended GA t
h
e
inc
o
rrect pa
ram
e
ters ca
n
be
pre
v
ented.
Also,
K
u
m
a
r
K
et
al
[2
0]
use
d
M
A
TL
AB
a
n
d
Si
m
u
l
i
n
k
t
o
d
o
dy
nam
i
c
m
odel
l
i
n
g
an
d
si
m
u
l
a
t
i
on
of
a
fou
r
-legg
e
d
j
u
m
p
in
g
ro
bo
t
with
co
m
p
atib
le leg
s
.
Acco
rd
ing
to th
eir sim
u
latio
n
,
t
h
e
robo
t can
run
at a sp
eed
of
1
.
5
m
/
s appro
x
i
m
at
el
y
,
fur
t
herm
ore t
h
ei
r
si
m
u
l
a
ti
on
w
a
s ani
m
at
ed t
o
gi
ve
a cl
ear
u
nde
rst
a
n
d
i
n
g
o
f
t
h
e
runn
ing
cycle.
A PD con
t
ro
l alg
o
rith
m
was im
p
l
e
m
en
ted
to th
e sim
u
lated
m
o
d
e
l to
con
t
ro
l th
e
fo
rward
sp
eed
.
Sin
ce it is v
e
ry i
m
p
o
r
tan
t
to kno
w th
e exact lo
catio
n
o
f
a ro
bo
t esp
eci
ally in
task
s su
ch as m
i
n
e
d
e
tectin
g, Coban
o
et al
[2
1]
de
vel
o
ped
D
G
PS
(
D
i
ffe
re
n
t
i
a
l
Gl
obal
P
o
si
t
i
oni
n
g
Sy
st
e
m
) ant
e
nna a
n
d t
h
e
DGPS
receive
r syste
m
for SILO4
(Figure
10) legged robot
.
Figure
10. T
h
e
SIL
O
4 system
.
The e
xpe
rim
e
nts showe
d
that
the data ac
quired
of
t
h
e electrom
a
gnetic com
p
ass in conc
ern
with t
h
e
od
om
et
ry
dat
a
can achi
e
ve t
h
e ade
q
uat
e
as
sessm
ent
of t
h
e ro
bot
’s p
o
si
t
i
on.
Thi
s
pape
r det
e
rm
i
n
es t
h
at
t
h
e
p
o
s
ition
o
f
th
e
robo
t in
ou
tdoo
r env
i
ro
n
m
en
t can
b
e
l
o
cated with
an
accuracy o
f
abou
t ±20
mm
.
In
ad
d
ition
,
the rob
o
t
s
h
a
v
e
fo
und
th
eir ap
plicatio
n
in
th
e
ag
ricu
ltu
ral ind
u
s
t
r
y, su
ch
as h
a
rv
esting.
D
e
sign
and
con
t
ro
l of an ap
ple h
a
rv
esting ro
bo
t
w
a
s stud
i
e
d
b
y
D
e
-An
et a
l
[22].
T
h
ey success
f
ully de
signe
d
a ro
bo
t
(Fi
g
ure 11
)
wh
ich
h
a
s th
e
cap
ab
ilitie
s to d
e
tect, lo
ca
te and
p
i
ck the fru
it
with
no
d
a
m
a
g
e
on
t
h
e fru
i
t
or t
h
e t
r
ee.
F
o
r
det
ect
i
on a
nd l
o
cal
i
z
i
ng
t
h
e fr
ui
t
,
a
vi
si
on
-ba
s
ed m
odul
e i
s
used
b
y
t
h
e ro
b
o
t
,
a
nd
f
o
r
app
r
oachi
n
g
an
d
pi
cki
n
g t
h
e
fr
ui
t
s
, a c
o
nt
rol
s
y
st
em
consi
s
t
e
d
of
m
a
ni
pul
at
or
an
d t
h
e e
n
d
-
effect
o
r
i
s
use
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA
I
S
SN
:
208
8-8
7
0
8
A Brief Su
rvey
Pap
e
r
o
n
Mu
lti-Le
g
g
e
d
Rob
o
t
s (Mo
hammad
Behman
esh
)
49
Figure 11
.
Har
v
est
i
n
g e
xpe
ri
m
e
nt
s i
n
a
n
orc
h
ar
d.
Also, Ji
et al
[
23]
i
n
vest
i
g
at
e
d
a
gui
de sy
st
em
for a
p
pl
e ha
rvest
i
n
g
by
m
e
ans
of a
n
d aut
o
m
a
t
i
c
vi
si
on
syste
m
. Their
sim
u
lation on
Visual C++
indicates th
at
us
i
ng SVM
(
S
u
p
p
o
r
t
Vect
or Machine)
for apple
h
a
rv
esting
resu
lts in a h
i
g
h
e
r
recogn
itio
n rate th
an
u
s
ing
o
n
l
y t
h
e sh
ap
e or co
l
o
r ch
ar
acteristics of t
h
e fru
i
t
,
besi
des
t
h
e
ha
r
v
est
i
n
g t
i
m
e i
n
t
h
i
s
m
e
t
hod i
s
sho
r
t
e
r
.
Fu
rt
h
e
rm
o
r
e, th
e
robo
ts
h
a
v
e
ap
p
lication
in th
e
h
a
rv
esting
n
o
t
on
ly fo
r the tree
fru
its bu
t
also
fo
r the
field fruits s
u
c
h
as stra
wberry. Hayashi
et al
[2
4]
eval
uat
e
d a r
o
bot
f
o
r
har
v
est
i
n
g st
ra
wbe
rry
i
n
a
fi
e
l
d. T
h
e
robo
t was su
ccessfu
lly
d
e
signed
with
t
h
e ab
ilities to
o
p
er
at
e at n
i
g
h
t
s,
h
a
nd
le pedun
cle an
d sh
aring tasks with
hum
an w
o
rke
r
s.
In add
ition
,
Rath
an
d
Kawo
llek
[25
]
i
n
v
e
sti
g
ated a
G
e
rb
er
a
Jam
e
s
o
n
ii
(
k
i
n
d of
fl
o
w
er
) har
v
est
i
n
g
ro
b
o
t
.
T
h
i
s
ro
bot
det
ect
s t
h
e
pe
di
cel
s
by
i
m
ages o
f
o
n
e
cam
e
ra, t
h
e
n
a
t
h
ree
-
di
m
e
nsional
m
odel
i
n
g
o
f
c
u
t
-
fl
o
w
er
pe
di
cel
s are
pe
rf
o
r
m
e
d,
by
m
eans
o
f
usi
n
g t
h
e sec
o
nd
cam
era images. Analyzing
bot
h im
ages from
ca
m
e
ra en
ab
les th
e au
to
m
a
tic
h
a
rv
esting
b
y
al
m
o
st 9
7
%
of co
rrect h
a
rv
estin
g.
A s
u
r
v
ey
of
d
e
si
gn
aspect
s
and
t
ech
nol
o
g
i
e
s f
o
r
cl
im
bi
ng
ro
b
o
t
s
wa
s
un
de
rg
o
n
e
by
Schm
i
d
t
and
B
e
rns
[2
6]
si
n
ce i
t
i
s
st
il
l
an uns
ol
ved
pr
o
b
l
em
. They
exa
m
i
n
ed t
h
e ap
pl
i
cat
i
ons an
d re
qui
rem
e
nt
s for
ro
bot
lo
co
m
o
tio
n as
well as for attractio
n to th
e
vertical struct
ures a
r
e
disc
usse
d. T
h
eir res
u
lts indicate t
h
at
so fa
r
t
h
ere i
s
no
s
y
st
em
whi
c
h
coul
d m
eet
the gi
ve
n re
q
u
irem
en
ts. Only fo
r a
sp
ecific setu
p
or
certain
envi
ronm
ents there
are
specia
l
so
lu
tion
s
fo
r ro
bo
tic
pro
t
o
t
ypes.
I
n
a won
d
e
r
f
ul stud
y,
Zh
ang et al
201
4
[
2
7
]
d
e
v
e
l
o
p
e
d
a b
i
on
ic
h
e
x
a
p
od rob
o
t
fo
r
w
a
lk
ing
on
unst
r
uct
u
re
d t
e
rrai
n
. I
n
t
h
i
s
p
a
per
,
t
h
ey
e
xpl
ai
ned i
n
det
a
i
l
s
t
h
e de
si
g
n
ed
m
e
t
hod
ol
o
g
y
a
n
d
co
nt
r
o
l
sy
st
em
of
the
aforem
entione
d robot, HITCR
-II
. T
h
e
Figu
re
12
sh
o
w
s t
h
e st
ructure of the
robot
trunk.
Figu
re
1
2
. T
h
e
struct
ure
o
f
HI
TCR-II
tr
un
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
4,
No
. 1,
M
a
rc
h 20
1
5
:
4
1
– 52
50
Th
ey
o
p
tim
ize
d
the stru
cture p
a
ram
e
ters, th
en
analyzed the
relations
hip
bet
w
een dexterity a
nd
stab
ility
m
a
rg
in
. Th
e sim
u
latio
n and exp
e
rimen
t
resu
lts ind
i
cate th
at
th
e
robo
t is cap
a
b
l
e of wal
k
ing
on
t
h
e
unst
r
uct
u
re
d t
e
rrai
n
.
Recently
the num
b
er
of pa
pe
rs for designing
a
ro
bot has increase
d
,
for in
stance Pa
a
n
d Wu
[28]
have
p
ubl
i
s
h
e
d
t
h
ei
r n
ovel
de
si
gn e
xpe
ri
m
e
nt
of a
he
xap
o
d
r
o
b
o
t
wi
t
h
a
serv
o co
nt
r
o
l
and a m
a
n-m
a
chi
n
e
interface
. As
s
h
own in Fi
gure 13. T
h
e gait sequences
of
th
e ro
bo
t were well d
e
sign
ed. Th
ei
r exp
e
ri
men
t
d
e
term
in
es th
at th
e
h
e
x
a
po
d ro
bo
t is cap
a
b
l
e of walk
ing
and
th
e h
i
g
h
l
y sen
s
itiv
e
d
e
tectio
n
o
f
ob
stacles.
Fig
u
r
e
13
G
a
it sequ
en
ce of
the h
e
x
a
pod
r
obo
t.
Whi
l
e
i
n
an
ot
her
st
u
d
y
,
a
n
un
de
rwat
er
he
xap
o
d
ro
b
o
t
A
Q
U
A
was
si
m
u
l
a
t
e
d
by
Ge
o
r
gi
a
d
es et
al
20
0
9
[
29]
.
T
h
e
m
o
t
i
on
of
t
h
e
ro
b
o
t
base
d
o
n
i
t
s
pad
d
l
e
osci
l
l
a
t
i
on
was
si
m
u
l
a
t
e
d.
T
h
en
t
h
e si
m
u
l
a
t
i
on re
sul
t
s
were app
lied
on
th
e exp
e
rim
e
n
t
al ro
bo
t, the
resu
lts
were to
i
m
p
r
ov
e th
e m
o
v
e
m
e
n
t
of th
e robo
t und
erwater b
y
havi
ng a
better force a
n
d torque
distri
bution
according t
o
the pa
ddle
oscillation.
Also
,
d
y
n
a
m
i
c
an
alysis o
f
a
hex
a
pod
rob
o
t
was carried
o
u
t
u
s
ing
th
e co
n
c
ep
t o
f
m
u
ltib
od
y d
y
n
a
m
i
cs
b
y
Mah
a
p
a
tr
a
et al [3
0
]
. Th
ey b
e
n
e
f
ited fr
om
CA
D
,
ADAMS and
CA
TIA
so
f
t
w
a
r
e
s to do
th
e an
alysis. Th
e
resu
lts ind
i
cate th
at retraction
p
h
a
se re
q
u
i
res
m
u
ch
h
i
gh
er torqu
e
th
an
p
r
o
t
ractio
n
p
h
a
se
for all th
e jo
in
ts.
It is
because
of t
h
e
weight of t
h
e trun
k body
ca
rri
ed out by
the
l
e
gs.
In
add
itio
n, th
e recon
f
i
g
uratio
n
o
f
t
h
e
six
-
legg
ed
rob
o
t
is
op
ti
m
i
zed
b
y
u
s
i
n
g h
e
x
a
-q
uad
t
r
ans
f
o
r
m
a
ti
on
[3
1]
. T
h
ey
pr
op
ose
d
t
h
i
s
m
e
t
h
o
d
fo
r a ce
rt
ain
situ
ation
s
t
h
at a leg can do
th
e o
t
h
e
r legs task
s
and s
o
m
e
legs are
disabled. T
h
ey s
u
ccessfully sim
u
late
d in
real tim
e
and
verified t
h
e
res
u
lt num
erically.
3.
CO
NCL
USI
O
N
In th
is
p
a
p
e
r,
a sho
r
t
rev
i
ew
o
n
m
u
lti-leg
g
e
d
robo
ts
as well as so
m
e
applicatio
n
s
h
a
s
been
do
n
e
.
It
h
a
s been
un
d
e
rsto
od
th
at th
e l
e
g
g
e
d
robo
t h
a
v
e
so
m
u
ch
b
e
n
e
fits and
m
o
re flex
ib
ility co
m
p
ared
to
o
t
h
e
r typ
e
s
of
r
o
b
o
t
s
.
The
y
al
so are
ca
pa
bl
e o
f
m
ovi
n
g
i
n
r
o
ug
h t
e
r
r
ai
n.
Fu
rt
he
rm
ore, f
o
r
ri
s
k
y
an
d
dan
g
e
r
o
u
s t
a
s
k
s su
c
h
as min
e
d
e
tectio
n, or for tall b
u
ild
i
n
gs and
u
n
d
e
rwater
t
a
s
k
s t
h
ey
are
ve
r
y
go
od
o
p
tio
ns. In
so
m
e
research
it
Evaluation Warning : The document was created with Spire.PDF for Python.