TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.1, Jan
uary 20
14
, pp. 135 ~
140
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i1.3898
135
Re
cei
v
ed
Jun
e
15, 2013; Revi
sed Aug
u
st
22, 2013; Accepted Sept
em
ber 12, 20
13
Resear
ch on Tripod Gait of Bionic Hexapod Robot
Liu Ming-da
n*, LV Xiao-rong, Qi Xiang-jun, Wei jiang-shu
T
he Information & Engin
eer
in
g T
e
chnolo
g
y
Coll
eg
e Sich
ua
n Agricu
ltural
Univers
i
t
y
, 6
2
5
014
Sichu
an Ya
an, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: qxj
@
sica
u.ed
u.cn
A
b
st
r
a
ct
Based
on the
bio
n
ic the
o
ry a
nd the a
n
a
l
y
z
e
d
of
move
me
nt mec
han
is
m fo
r six-leg
ged
in
sect, the
princi
pl
e of trip
od g
a
it
mov
e
ment
for w
a
lki
n
g
robot w
a
s a
n
a
l
y
z
e
d
in this
pa
per, an
d b
a
sic
para
m
eters a
n
d
the pr
inci
ple
o
f
relativ
e
mov
e
ment th
eory
on
gait r
e
sear
ch w
e
re
discu
ssed. T
h
e
n
th
e h
e
xap
o
d
w
a
l
k
i
n
g
robot w
a
s asse
mb
le
d by usin
g
the compon
en
t of F
i
scherte
chnik. W
i
th the characters of s
i
mple c
onn
ecti
ve
structure, un
iq
ue d
e
si
gn, thi
s
robot c
an w
a
lk fo
rw
ard
an
d backw
ar
d a
nd ca
n
avoi
d
mi
ni-b
arrier. T
h
e
exper
iment sh
ow
ed that this robot
has
goo
d mo
bil
i
ty and st
abil
i
ty
.
Ke
y
w
ords
: bio
n
ic hex
ap
od ro
bot, tripod g
a
it, mech
an
is
m w
i
th four conn
ecting ro
d
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Bionic (bioni
c tech
nolo
g
y) is synth
e
siz
ed by two
words, Biol
ogy (Biology
) and
T
e
c
h
n
o
l
og
y (
t
e
c
hn
ica
l
)
.
R
e
s
e
ar
ch
is
us
ua
lly b
a
s
ed
on
the nature
science. In the past few yea
r
s,
resea
r
ch a
r
e
a
ha
s tou
c
h
ed u
pon
wa
lking
or ru
n
n
ing. Th
us,
the ro
bots
with le
gs
ha
ve
invented.
Such a walki
ng
machi
ne
can
wal
k
on
bu
mpy or
soft earth, even
cro
s
s ob
sta
c
l
e
s,
stairs, ditche
s, and
do
a
seri
es of difficult mo
vem
e
nts that
whe
e
ls
can’t d
o
.
This
rob
o
t ca
n be
use
d
in dan
g
e
rou
s
pla
c
e
such a
s
nu
cle
a
r po
we
r plan
ts, coal mine
s for rescu
e
[1].
With the bi
g
degree
s of freedom fo
r th
e foot,
the bi
onic
hexap
od
wal
k
ing
rob
o
t
is more
flexible and a
daptabl
e on u
neven g
r
ou
nd
. The touc
h a
r
ea to the g
r
o
und for th
e h
e
xapod
wal
k
i
ng
robot i
s
discrete compa
r
e
d
with th
e
wheel
rob
o
ts
o
r
tra
c
k robot
s. Small co
nta
c
t area
with t
h
e
grou
nd, you can
cho
o
se the be
st sup
p
o
rting poi
nt on the grou
nd.
Even under
the con
d
ition
of
the surfa
c
e i
s
very i
r
regu
lar, Robot i
s
also
abl
e t
o
wal
k
f
r
eel
y throug
h
strict
sele
ction
of
sup
portin
g
p
o
int. Walki
n
g
robot re
se
a
r
ch
ha
s be
come on
e of the most attractive area
s in
roboti
cs. The
study for multi-legg
ed walkin
g rob
o
t with indep
en
dently driven
system is m
o
re
focu
sed o
n
the gait desi
gn
[2] [3].
Wal
k
ing g
a
it is the way the
system to m
o
ve,
that is the order fo
r
wal
k
ing
syste
m
to lift
feet or p
u
t do
wn feet.
Due
to the develo
p
ment n
eed
s
of wal
k
ing
ro
bot, McG
hee,
father of
rob
o
ts,
summ
ari
z
ing
the re
sults
on
previou
s
research o
n
ani
mal gait, syst
ematically p
r
ese
n
ts a
se
ri
es of
stri
ct mathe
m
atical d
e
fini
tion of description and
a
nalysi
s
of g
a
it.
After that, rese
arch
ers o
f
variou
s co
unt
ries
have got
many re
sults
in the stable
gait cycle
rul
e
s for fou
r
fe
et, six feet, eight
feet and othe
r multi-leg
g
e
d
walki
ng ma
chin
e re
se
a
r
ch. These results inclu
de a
variety of ga
it
cha
r
a
c
teri
stics an
d cla
s
sification,
su
ch
as tria
ngul
ar
gait, wave ga
it, free gait, tracking
gait, gait
para
m
eters a
nd their
relati
onship
s
. Ho
wever the
s
e st
udie
s
are limited in theory
of gait analyses;
take no a
ccount of spe
c
ific imple
m
entation.
Based o
n
the prin
ciple of
bioni
cs a
nd
the
comp
one
nt o
f
Fisch
er, a
wal
k
ing
Rob
o
t
with six
feet is asse
mble
d to impleme
n
t the theory
of
tripod gait.
2. Theor
y
an
d Design o
f
Tripod Gait for Hex
a
pod
Bionic Rob
o
t
2.1. Mo
v
e
ment Principle of Triangle
Gait
While "
C
la
ss
Hexap
o
d
s
” in
se
cts (co
c
kro
a
ch
es
a
nd a
n
t
s, etc.) walki
ng, gene
rally
not six
feet go forwa
r
d at same tim
e
, but go fo
rward
altern
at
el
y in form of th
ree
pairs of f
eet divided i
n
to
two g
r
oup
s a
nd form t
r
ian
gular
su
ppo
rti
ng st
ru
cture
s
.
The fro
n
t an
d rea
r
foot in
left side a
nd t
he
middle fo
ot in
right
sid
e
a
r
e
in a
gro
up. T
he fro
n
t
an
d rear fo
ot in
rig
h
t sid
e
an
d th
e middl
e foot
in
left side a
r
e i
n
anoth
e
r g
r
o
up. They co
mposed two
triang
ula
r
su
p
porting
struct
ure
s
sepa
rat
e
ly.
Whe
n
all the
feet in one t
r
i
angul
ar
sup
p
o
rting
stru
ctu
r
e lifted
simul
t
aneou
sly,
the feet in an
other
triangul
ar su
p
porting
struct
ure ke
ep still.
The
mi
ddl
e f
eet in two
sid
e
s a
r
e
the
su
pportin
g
p
o
int
to
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TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 135 – 1
4
0
136
sup
port th
e
weig
ht of in
sect b
ody. Th
e front tibi
a
muscle
co
ntraction,
pull th
e body fo
rwa
r
d, at
the same tim
e
, the rea
r
tibia mu
scle
contra
ction,
p
u
sh
the b
ody
forward.
So
the bo
dy slig
htly
rotates
aroun
d the middl
e
feet, letting the ce
nter of
inse
ct wei
g
ht shift from
three feet in
a
triangul
ar
su
pportin
g
stru
cture
to a
not
her th
re
e fee
t. And then
repeat th
e m
o
ve pe
riodi
cally.
Becau
s
e
of weig
ht cente
r
always
withi
n
triang
ular
frame, this wal
k
ing
style ea
sy let the insect
stop at anytime. This is a
typical triangl
e gait. The waveform of the gait is
2
1
＝
. Its
wal
k
ing path
is not straight
line but a zig
z
ag
curve to
move forward
.
Movement di
agra
m
for He
xapod ro
bot u
s
ing trip
od ga
it is sho
w
n in
Figure 1. Fee
t
that
touch the g
r
o
und (see the
black box) fo
rms a sta
b
le
triangul
ar st
ru
cture. Such
kin
d
of robot
woul
d rem
a
in
stable walki
n
g postu
re, not
easy to fell [4].
Figure 1. Trip
od Gait of Ro
bot
2.2. Assembl
ed for Hexa
p
od Robo
t Mike
Cra
n
k-a
nd-ro
cker m
e
chan
ism is
set a
s
si
x feet for Hexapo
d ro
bot Mike. An
d sma
r
t
interface boa
rd 310
02 is set for controll
er. The dr
ivin
g element co
nsi
s
ts of two small DC mot
o
r
with red
u
cer. Lwin
3.0 software which de
veloped
by company fisch
e
rtechni
k is p
r
og
ramm
ed a
nd
controlled.
The m
a
in p
a
rt of Fische
r
creative mod
e
l
is ma
de
of hi
gh q
uality nylon pla
s
tic,
wh
ich
with
the quality of size p
r
e
c
isi
o
n, not easy to we
a
r
, rep
e
a
ted setu
p a
nd disassem
bly but does
not
affect the a
c
curacy
of the
model. Th
e
patented
de
si
gn for
part
s
i
s
dovetail
groove which can
achi
eve part j
o
int in six-si
d
e
. This uniq
u
e
des
i
gn
can achi
eve
free combi
nation or
expan
ded.
Figure 2. The
Figure of rob
o
t Mike
The robot Mi
ke
with six fe
et is a
s
sembl
ed by
the pa
rts of Fische
r
as
sho
w
n in
Figure 2.
The whole
structure for the
robot in
clud
e
s
thre
e
pa
rts:
the mechani
cal pa
rt, the sensor p
a
rt an
d
control pa
rt. Mech
ani
cal p
a
rts a
r
e mainl
y
compo
s
ed
of the frame, two dc moto
rs, gear a
nd worm
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TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Tripo
d
Gait of Bionic He
xa
pod Robot
(Q
i Xiang-ju
n)
137
drive,
six sets of
four-b
ar
link
structu
r
e.
Wh
en
the
DC m
o
tor is worki
ng, th
e
spur ge
ar
whi
c
h
linked on the
motor
shaft will driv
e the
worm-shaft rot
a
tion. Rotati
on of
worm-shaft will drive t
h
e
three
worm
-wheel
s in one
side to rotate. Then drive t
h
e three fe
et to move
，
thus
the robot Mik
e
goe
s forward.
The foot of robot was d
e
signed a
c
co
rdi
ng to t
he the
o
ry of four-ba
r
link
stru
ctu
r
e whi
c
h
calle
d cran
k-and-ro
cker m
e
ch
ani
sm. Un
der the a
c
tion
of the cran
k, the gear
can
swi
n
g ba
ck a
n
d
forth. Adjust the dista
n
ce from the frame
to the bo
ttom of feet, in order that the move path of feet
of robot
wa
s
ellipse wh
en
cra
n
k
rotate.
Six cran
ks were a
s
sem
b
le
d for
six feet. Whe
n
thre
e feet
touch
the
ea
rth, the
cra
n
k of a
nothe
r t
h
ree
feet
rot
a
ted 1
8
0
-
deg
ree. T
hen
Mi
ke
we
nt
step
by
step, and fo
rm stable trip
o
d
gait.
2.3. Tripod Gait Analy
s
is
for He
xap
od Robo
t
For the
rob
o
t Mike, u
s
e tri
pod g
a
it to a
c
hieve
static
wal
k
ing. As
shown in Fig
u
re 3. The
1, 4, 5 feet is a gro
up. The
2,
3, 6 feet is anothe
r grou
p. The
two g
r
oup
s
did
coo
r
dinated m
o
tio
n
.
The
weig
ht shifted from
th
e re
set
state
of 2, 3, 6
fe
et
to initial
state of 1,
4, 5 f
eet (a
). Th
e f
i
rst
motion is the
swi
ngin
g
feet lifted and mo
ve forwa
r
d “o
ne step
” (b
).T
hen it becam
e
the sup
porti
ng
feet and
su
pp
orted th
e b
o
d
y
to move on
e ste
p
(c).
After that, an
othe
r g
r
oup
of
swi
nging fe
et we
nt
forwa
r
d
(d), t
hen
be
cam
e
sup
portin
g
fe
et to move
b
o
dy (e). F
r
o
m
the
diag
ra
m
we
see
th
at
the
locu
s of the
feet on x y plane i
s
alm
o
st irreg
u
lar.
The lo
cu
s o
f
the feet sh
ould b
e
a
cu
rve
becau
se the
knee joi
n
t is fixed when hip joi
n
t
is swi
ng. But it’s not contradi
ctory to
Figure 1.Be
cause in
p
r
o
c
ess of
movin
g
, the tri
angl
e gait
is not
deform
a
ti
on and wei
ght center
alway
s
within
supp
orting tri
angul
ar fram
e and therefo
r
e it’s also sta
b
le.
Figure 3. Tria
ngle gait of ro
bot Mike
Suppo
sed
we
ight supp
ortin
g
tria
ngle
is
A
，，
′
(x
a,y
a
)
B
′
(x
b,y
b
)
C
′
(xc,yc) in
coo
r
di
nate
system.
The weight
center of robot
Mike lo
cated
at orig
in of t
he co
ordinate
.
When Mi
ke
moves o
ne
step
to the left, the wei
ght center will move along x-axis
, also
within
the triangl
e. So it’s a stable
tripod
gait. T
he Mi
ke’
s
m
o
ving is al
so
coo
r
di
nated
becau
s
e
wei
ght su
ppo
rtin
g trian
g
le i
s
not
deform
ed wh
en moving [5].
Figure 4. Coo
r
dinate a
naly
z
e for tria
ngle
gait
A
B
C
O
X
Y
L
1
A′
B′
C′
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ISSN: 2302-4
046
TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 135 – 1
4
0
138
2.4. Kinematics Analy
s
is
Whe
n
the
wa
lking
ro
bot
we de
sig
ned
u
s
ed
trip
od
gai
t, the thre
e le
gs i
n
the
sam
e
g
r
ou
p
did the
same
moveme
nt a
t
anytime. Th
en the
three
leg
s
can
b
e
equival
ent t
o
on
e le
g. T
he
model is a
nal
yzed a
s
figure belo
w
:
Figure 5. Kinematics analy
s
is fo
r model
In order to facilitate the analysis
，
it a
s
sumes th
at the body qualit
y of the robot
focus
on
one sid
e
of the leg, and the mass of leg is negli
g
ib
le. M is the drive torque
which a
c
ted on
the
wal
k
ing rob
o
t.
F
x
and F
y
ar
e the re
active
force
whi
c
h
acted
by the
grou
nd. G i
s
the a
c
celeration
of gravity. L i
s
the l
ength
o
f
one le
g.
is t
he an
gle fo
rmed by the
suppo
rting le
g
and h
o
ri
zonta
l
dire
ction. Formulation can
be written a
s
[6]-[8]:
M
L
F
F
L
mg
F
y
m
F
x
m
y
x
y
x
cos
sin
'
'
..
Where
sin
cos
L
y
L
x
Substitute x and y then
si
mplify, mathematics
ex
pre
ssi
on for
moti
on mod
e
l of robot can b
e
get
[7]:
mg
mL
mL
M
Fy
Fx
mL
mL
L
L
.
2
.
2
..
sin
cos
1
0
cos
0
1
sin
cos
sin
1
2.5. Contr
o
l Program of
Hex
a
pod
Ro
bot
Rob
o
t shoul
d
be
program
med in
o
r
de
r to move.
LL
Win3.0
of Fi
sche
r i
s
th
e g
r
aphi
cal
prog
ram
m
ing
software, ca
n
a
c
hieve rea
l
-time c
ontrol
and e
a
sy to
u
s
e. Th
e la
dde
r p
r
og
ram
wa
s
use
d
wh
en in
telligent interf
ace b
oard 31
002 was a
ppl
ied.18 ki
nd
s of function m
odule
s
were i
n
the softwa
r
e
packag
e
, can be p
r
og
rammed in a
n
y combi
nation. It is gra
phical displa
y and
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TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Tripo
d
Gait of Bionic He
xa
pod Robot
(Q
i Xiang-ju
n)
139
automatic
co
nne
ction in
compute
r
. We
use the
digit
a
l cont
rol mo
del E1 an
d E2 to cont
rol t
he
feet to wal
k
.
Limit switch
E8 wa
s u
s
e
d
as
a re
set switch. Po
we
r of motor E2
wa
s suppli
e
d
by
VAR2.The m
o
tor M1 woul
d stop while l
i
mited swit
ch
switched o
n
. Motor M2 would sto
p
wh
en
swit
ch E2 swi
t
ched o
n
. The
prog
ram was sho
w
n a
s
Figure 6 [9].
Figure 6. Con
t
rolling p
r
og
ra
mmed of Ro
b
o
t Mike [9].
3. Parameter
Descrip
tion
s for Gait o
f
Hex
a
pod
Ro
bot
McG
hee,
wh
o is the
fathe
r
of robot, de
fines the
pa
rameter i
n
the
motion
su
ch
as
step
length supp
orting factor a
n
d
the pha
se i
n
itially,
suppo
sed that any
gait can b
e
d
e
scrib
ed by lag
in pha
se
of e
a
ch fo
ot’s m
o
tion and
wei
g
ht sup
p
o
r
ti
ng
factor
of ea
ch
foot, whi
c
h p
r
ovide th
e ma
th
foundatio
n for gait research. Hexapod robot gait is
the seq
uen
ce
of feet’s up
and do
wn in the
workin
g
syste
m
. The fe
et o
f
wal
k
ing
ro
b
o
t ca
n b
e
se
en a
s
t
w
o
sta
t
e com
pon
ent
s. The
tra
n
sf
er
pha
se
of the
feet i
s
the
p
e
riod
of l
eavi
ng the
g
r
ou
n
d
, whi
c
h
p
r
o
g
ramm
ed
a
s
1. T
he
su
pp
ort
pha
se
of the
feet is th
e
pe
riod
of tou
c
hi
ng th
e
g
r
ou
n
d
an
d
com
p
e
lling the
bo
dy forward, whi
c
h
prog
ram
m
ed
as
0. Th
e
period g
a
it T i
s
time for o
ne f
oot finish
all t
he m
o
tion i
n
one
cycl
e. Th
e
perio
d gait mean
s all feet spe
n
t the sa
me time
in the motion cycl
e and ea
ch fo
ot’s motion p
e
riod
doe
s
n
o
t cha
nge as
time
is cha
ngin
g
. Duty
facto
r
i
s
the time
p
r
o
portion
that
o
ne feet
supp
o
r
ting
weig
ht on the
groun
d in wh
ole motion pe
riod [9]-[14].
4. Experimental Re
sults
and An
aly
s
is
The functions of hexapod
robot
for go forward,
go
backward, turn t
o
left; turn to
right
and avoi
d the
obsta
cle
had
been te
sted.
The result
shows that the
robot
wal
k
s
smoothly a
n
d
can cro
s
s the small barrie
r
. When the shield in
the front of the robot touch the
big obsta
cle,
the limited switch turn on,
give the robot a cont
rol
si
gnal then rob
o
t will avoid the ob
stacle. In
order to prev
ent the trip
when the model turn l
e
ft, the left foot of
the
robot step sm
all pace
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then the righ
t foot step a big pace. Then t
he ro
bo
t would turn
and the trip
od gait wa
s
controlled
wel
l
by program.
But if
the rob
o
t walks for a
long distan
ce,
it will emerge the uncoo
rdinate
d
gait. This
phen
omen
on
is due to the motion was
realized by
linkag
e
mechan
ism, whi
c
h h
a
ve mech
ani
c
and ele
c
tri
c
d
i
fferences, ca
n’t maintain the wal
k
ing p
hase of left and right foot same in
whol
e
pro
c
e
ss.
Wh
en the
differences a
c
cum
u
late u
p
to
some
deg
ree,
the u
n
coo
r
di
nated
gait
wi
ll
emerge [10].
5. Conclusio
n
On the
ba
sis
of the bio
n
ics prin
cipl
e, the
tripod
gait p
r
incipl
e of the
hexapo
d rob
o
t and
stability wa
s
analyzed in t
h
is the
s
i
s
. Th
e hexap
od
ro
bot wa
s a
s
se
mbled by Fi
sche
r pa
ckag
e
and
prog
ram
m
ed
on compute
r
.
After that the experi
m
ent
wa
s do
ne. T
he rel
a
tion
shi
p
between th
e
gait para
m
et
er and th
e ro
bot wa
s de
scribed in the
o
ry
. The result
sho
w
s that the robot
can
walk
in stri
ct acco
rdan
ce
with tripod
gait, re
alize t
he fu
n
c
tion of movi
ng straight, turnin
g, avoidi
ng
barrier, an
d h
a
ve good mo
bility and stab
ility.
Ackn
o
w
l
e
dg
ements
Found
ation
item: Supp
ort
ed by
the
National
Natu
ral Sci
e
n
c
e
F
ound
ation
of Chi
na
(511
052
61)
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