TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 14, No. 2, May 2015, pp. 304 ~ 31
0
DOI: 10.115
9
1
/telkomni
ka.
v
14i2.772
3
304
Re
cei
v
ed Fe
brua
ry 3, 201
5; Revi
se
d March 25, 201
5
;
Accepte
d
April 10, 201
5
Robot Three Dimensional Space Path-planning
Applying the Improved Ant Colony Optimization
Zhao Ming*
1
,
Dai Yong
2
1
Appli
ed T
e
chn
o
lo
g
y
Col
l
eg
e
of Univers
i
t
y
of
Science a
nd T
e
chn
o
lo
g
y
Li
ao
nin
g
,
Ansha
n
, 114
05
1, Chin
a
2
School of Elec
tronic an
d Infor
m
ation En
gi
ne
erin
g,
Univers
i
ty of Scie
nce a
nd T
e
chnol
og
y Liao
nin
g
,
Ansha
n
, 114
05
1, Chin
a
*Corres
p
o
ndi
n
g
author, em
ail
:
as_zm
y
l
i
@1
6
3
.com
1
, 5789
1
613
5@q
q
.com
2
A
b
st
r
a
ct
T
o
mak
e
robot
avoid o
b
stacle
s in 3D space,
t
he Phero
m
on
e of Ant Colon
y
Optimi
z
a
ti
on
(ACO) in
F
u
zz
y
Contr
o
l
Upd
a
ting
is
put
forw
ard, the P
hero
m
one
U
p
d
a
ting
val
ue v
a
ri
es w
i
th T
he
nu
mb
er of
iterati
o
ns
and th
e p
a
th-p
l
ann
ing
le
ngth
by eac
h a
n
t . the i
m
prove
d
T
r
ansiti
on Pro
b
a
b
ility Fu
nction
i
s
also
pro
pose
d
,
w
h
ich makes
mor
e
sens
e for
each a
n
t cho
o
s
ing n
e
xt feas
i
b
le p
o
i
n
t .T
his pap
er firstly, describ
es the R
obo
t
W
o
rkspace M
o
deli
ng
an
d its
path-p
l
an
ni
ng basic method, w
h
ich
is
fol
l
ow
ed by
introd
uci
ng the
i
m
prov
e
d
desi
gni
ng of th
e T
r
ansitio
n Proba
bil
i
ty F
unction an
d
the me
thod of Pher
o
m
o
ne F
u
zz
y
C
ontrol U
pdati
n
g of
ACO in
detai
l.
At the sa
me
ti
me, th
e co
mpa
r
ison
of opti
m
i
z
a
t
i
on
betw
e
e
n
the
pr
e-i
m
pr
o
v
ed ACO
and
the
improve
d
ACO
is mad
e
. T
he simulati
on res
u
lt verifies
that the i
m
pr
oved A
C
O is feasibl
e
and av
ail
a
b
l
e.
Ke
y
w
ords
:
3D spac
e, ant colo
ny opti
m
i
z
ation (ACO), p
hero
m
one, tran
sition pr
oba
bi
lit
y function, path
-
pla
nni
ng
Copy
right
©
2015 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
It has
bee
n
a hot to
pic for
rob
o
t avoi
ding
ob
stacl
e
s in
3
D
spa
c
e in th
e field
of the
Optimal Sea
r
ch
Control in
recent yea
r
s. Ther
e are a
numb
e
r of
available re
search
m
e
tho
d
s,
su
ch a
s
A* Al
gorithm [1, 2]
、
Artificial P
o
tential Field
method [3, 4]
and G
eneti
c
algorith
m
[5, 6]
etc, but these method
s h
a
ve its own li
mitation to
some extent. By the time
of the early of the
ninth d
e
cade
of the t
w
ent
ieth century,
Italian
schol
ars M.Dorig
o
et al
pro
p
o
s
ed
Ant Col
ony
Algorithm [7,
8], This al
gorithm is a
n
an
other h
e
u
r
isti
c sea
r
ch
algo
rithm which i
s
u
s
ed to
sol
v
e
the optimi
z
ati
on p
r
obl
em.
This algo
rith
m ha
s
advant
age
s in
fast
converg
e
n
c
e,
being
not
ea
sy to
fall into lo
cal
optimum,
which
solves the p
r
o
b
lem
o
f
rob
o
t 3
D
p
a
th pla
nnin
g
better th
an
o
t
her
algorith
m
s [9
]. To the improveme
n
t of the conv
e
n
tio
nal Ant Colo
ny Algorithm,
Fuzzy Cont
rol
Pherom
one
Upd
a
ting m
e
thod
as well a
s
the
imp
r
ove
d
de
sig
n
of
T
r
an
sition P
r
o
bability Fun
c
t
i
on
is intro
d
u
c
ed
in this pa
pe
r. What i
s
improv
ed ma
ke
s the conventio
nal ACO
doe
s better i
n
pa
th
planni
ng and
redu
cin
g
the numbe
r of iteration
s
.
2.Robo
t Wor
kspac
e Mod
e
ling and its Path-plannin
g
Method
2.1 Robo
t Workspa
ce Mo
deling
Firstly, A 3D
environ
ment
with ob
sta
c
le
s
is
con
s
truct
ed and
sh
own by Figure
1. Then
this environm
ent is divid
e
d
equally into
M se
ction
s
, e
a
ch
se
ction i
s
in o
ne unit
averag
e g
r
id,
as
is sh
own by Figur e
2
, Figure 3. In this way,
the geometry sp
ace
ABCD-EF
G
H
is con
s
tru
c
ted.
hypothe
sis: AB=m, BC=n,
CG=v, The
discrete
p
o
int
in this environment can
be loo
k
ed o
n
as
P(i, j, k
)
, where i=
{0, 1,2, …,m}, j=
{0, 1,2,
…,
n}, k={
0
, 1,2, …,v},
therefore x=i, y=j,
z=
k .
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Rob
o
t Thre
e Dim
ensio
nal
Space Path
-p
lannin
g
Applying the Im
proved Ant… (Z
hao Ming
)
305
Figure 1. 3D
Environme
n
t with ob
stacl
e
s
Figure 2. Environm
ent Sections
Figure 3. The
gridde
d se
cti
o
n
2.2. Three Di
mensional Path
-planning
of Robo
t
w
i
th ACO
In the
grid
de
d three-dime
nsio
nal sp
ace,
a ce
rtain p
o
int
1
P
i
(i-1,j,k
) o
n
the
plan
e
1
Π
i
( i
taking valu
es
1,2, …, m) makin
g
a line t
o
a ce
rtain po
int
P
i
(i,j,k) on th
e plane
Π
i
(i taki
ng value
s
1,2, …, m) does not ke
ep i
n
touch with
any obsta
cle
s
, then the path from the poi
nt
1
P
i
(i-1,j,k) to
the point
P
i
(i,j,k) is called the feas
ible r
out
e, at the
sam
e
time, this fe
asibl
e
route i
s
store
d
in th
e
list
(i,
j
,
k
)
A
llowe
d
. ACO 3
D
p
a
th pla
n
n
ing i
s
simpl
y
that findin
g
out th
e fe
asibl
e
optim
al
path
（）
the sh
ortest path
f
rom the sta
r
ting point to
the target point In the gridde
d three-
dimensional
space. A
c
cording to the A
C
O
Transi
tion Probability
Function [10]
and Pherom
one
Upd
a
ting Rul
e
[10], under
the pre
-
condit
i
on of all passing p
o
ints b
e
longi
ng to
(i
,
j
,
k
)
A
llowe
d
, i
n
the O-XYZ coordi
nate sy
stem with obst
a
cle
s
, the
ro
bot can
set o
u
t from the starting poi
nt Son
0
Π
, to reach a
certain p
o
int
1
P
(1
, j, k
）∈
｛
０
(wh
e
r
e
j
,
１
, …,
ｎ｝
∈
｛
０
,k
,
１
, …, v
｝
), and then to
rea
c
h a ce
rtai
n
poi
nt
2
P
(2, j, k
)
(
w
h
e
re
j
∈｛
０
,
１
, …,
ｎ｝
,k
∈｛
０
,
１
, …,
v
｝
) fro
m
the
point
1
P
(1, j,
k
）
, taking turns re
aching a
certain p
o
int
1
P
m
（
m-1, j, k
）∈
｛
０
(w
her
e
j
,
１
, …,
ｎ｝
∈
｛
０
,k
,
１
, …,
v
｝
) on the plane
1
Π
m
,in the end, to reach the de
sti
natio
n point D fro
m
the point
1
P
m
（
m-1, j,
k
）
, Above all, a optimal path betwe
en the startin
g
po
int to the des
tination point i
s
co
nstructe
d
:
S
→
1
P
(1, j, k
）
→
2
P
(2, j, k
)
→
…
→
1
P
m
（
m-1, j, k
）
→
D.
3. The Improv
ed Designing ofACO
3.1. The Improv
ed Designing of th
e Transition Probabilit
y
Fu
nction
Acco
rdi
ng to geomet
ric p
r
i
n
cipl
es, co
nn
ection
(straig
h
t line)L from
the starting
point to
the target p
o
int is the
shorte
st p
a
th, und
er
the
pre
-
condition
that the
r
e
i
s
n
o
ob
stacl
e
s
forpa
ssi
ng directly. That is to say, selectinga
ce
rtai
n
point relatively close to the line L on the
next plane
ca
n app
roximat
e
ly approa
ch
to this line,
therefo
r
e the
distan
ce from
the point P on
the next plane to the line L has an
effect
not only
on t
he Transition
Probab
ility Function, but al
so
it plays a
de
cisive role in t
he conve
r
gen
ce of th
e alg
o
rithm,thu
s
th
e Di
stan
ce F
a
ctor con
c
ept
is
introdu
ce
d in this pap
er.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 14, No. 2, May 2015 : 304 – 310
306
Defini
tion:
T
he Di
st
an
ce
Fact
o
r
1
1
1
i
i
PL
D
P
L
, where
1
PL
i
is the di
st
ance from
th
e
point
1
P
i
(i+1,j,
k) belon
ging
to
(i
,
j
,
k
)
A
l
l
owed
to the
strai
g
h
t
-line L. T
he
Dista
n
ce Fa
ct
or
D pl
ays
a role in sele
cting the next
feasible p
o
in
t wh
ich a
ppro
x
imately approache
s to the optimal path L
(the sh
orte
st path).
The co
nventi
onal Tran
sition Prob
ability Function take
s
α
=
1,
β
= 1, then whi
c
h is
multiplied
by the
Dista
n
ce
Facto
r
. A b
r
a
nd n
e
w Tr
an
sition Pro
babili
ty Function
fo
r a
ce
rtain
poi
nt
P
i
(i,j,k
) on
Π
i
(i=0,
1, 2, …, m-1) getting to a certain poi
nt
1
P
i
(i+
1
,j,k) on
1
Π
i
is
f
o
rmed:
1
1
1
1
,1
1
(P
,
P
)
,
(
i,
j,
k
)
(P
,
P
)
0,
i
ii
ii
i
ii
ii
τ
d
DP
t
o
P
A
l
l
o
w
e
d
τ
P
d
el
s
e
(1)
Whe
r
e,
1
i
τ
is the Pherom
one
value of the point
1
P
i
(i+1,j, k)
on the plan
e
1
Π
i
1
(P
,
P
)
ii
d
i
s
the
distan
ce fro
m
the point
P
i
(i, j ,k
) to the point
1
P
i
(i+
1
, j, k
)
.
3.2. The Pheromone Fu
zz
y
Control Updating Me
thod
Ant Colon
y
Algorithm applied to
three-dimensional path pla
nninggenerally pu
ts
pheromo
n
e
s
on the co
nne
ction bet
wee
n
the grid
din
g
points, thi
s
sort of de
sig
n
ing for ACO
will
lead to a particularly large
amount of computat
ion. If the Pheromone is sim
p
ly placed on th
e
griddi
ng poi
nts inste
ad of the co
nne
ctio
n betwe
en
th
e grid
ding p
o
ints, then this desig
ning
wi
ll
not only great
ly reduce th
e computational
com
p
lexity
of the algorithm [11],
but al
so it will
be v
e
ry
con
v
e
n
i
e
nt f
o
r u
p
dat
in
g t
he P
h
e
r
o
m
o
ne v
a
l
u
e. F
u
zzy
Con
t
ro
l Ph
e
r
o
m
on
e
gl
ob
a
l
u
p
dat
i
ng
is
applied in
this pap
er, the u
pdating
formula from the p
e
riod t to
the
perio
d(t + n
)
:
(t
n)
(
1
)
(
t
)
Δ
t
ij
k
i
jk
i
j
k
τρ
τ
τ
(
2
)
Whe
r
e
(t
)
ijk
τ
repre
s
ent
s the no
t updated ph
erom
one val
ueon the p
o
i
n
t
P
(
i,
j,
k)
i
.
ρ
is the
Pherom
one Evaporatio
n Rate,
1
-
ρ
rep
r
esents the
Pherom
one
Re
sidu
eFa
c
tor, taki
ng
ρ
=
0.7.
Δ
t
ij
k
τ
=Q/Nt, wh
ere
Nt is the number of point
s passe
d by the ant, Q rep
r
esents the to
tal amount
of each ant’
s
pheromo
ne,
Q pa
ramete
r is ve
ry imp
o
rtant, Thi
s
pape
r u
s
e
s
fuzzy rea
s
o
n
i
n
g
method
s to
control
the
am
ount of
ea
ch
Ant’s Q
in
order to g
e
t a
more
rea
s
on
able
amou
nt
of Q.
there
are t
w
o
v
alues dete
r
mines the
am
ount of
Q, the
first i
s
NC th
e nu
mbe
r
of
i
t
eration
s
of A
C
O
[12-14], an
d
the se
co
nd i
s
dthe l
engt
h of ea
ch
a
n
t’s path f
r
o
m
the sta
r
tin
g
point S to
the
destin
a
tion
p
o
int D.
Q th
e
amo
unt of
p
hero
m
on
e
ca
rrie
d
by
ea
ch
ant i
s
a fixe
d value
in
the
conve
n
tional Ant
Colony Algorithm,
it is
un
sci
entifi
c
. In the ea
rly period
of
the Pheromo
n
e
Upd
a
ting, if
Q is so la
rge
,
then the Ant Colony
Algo
rithmwill qui
ckly fall into local optimum,
on
the other
han
d, if the Q is
soli
ttle, then t
he convergen
ce
spe
ed of
t
he Ant Col
o
n
y
Algorithm will
be
slo
w
. ab
o
v
e all, the
be
st way is that
Q is
set li
ttle
when
NC is little, Q is set large when NC is
large. Fu
rthe
rmore, the pat
h (the straigh
t
line)
betwe
e
n
the target p
o
int and the
starting p
o
int is
the be
st
sho
r
test route, if t
her
e
i
s
d
the
length
of pat
h ma
de
by a
n
certai
n a
n
t
very cl
ose to
the
ideal
straig
ht-line L, the
n
the Q ofthis
ant sh
ouldb
e
set large
r
in
orde
r to imp
r
ove Pro
babil
i
ty
forothe
r
a
n
ts ch
oo
sing
thi
s
p
a
th, ma
ki
ng o
p
timizati
on a
gain
on
this
path
co
uld imp
r
ove
the
conve
r
ge
nce
spee
d. Accordin
g to the input
and
output rea
s
oning rule
sin
Fuzzy Cont
rol
Algorithm, M
e
mbe
r
ship F
u
nction
ap
plie
d trian
gula
r
[
15]. NC the
a
m
ount of
Iterations is the i
nput
taking val
u
e
s
from 0 to 1
00 times
(ex
perie
nce valu
e) in Fi
gure
4, d the len
g
t
h of the pat
h is
anothe
r in
put
takin
g
valu
e
s
from 2
0
(Fi
gure
1 th
e axi
a
l len
g
th i
s
th
e shorte
st) to
200
(exp
eri
e
nce
value) in Fig
u
r
e 5, Q the ca
rrying am
ount
of
pherom
on
e is the outpu
t shown in Figure 6.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Rob
o
t Thre
e Dim
ensio
nal
Space Path
-p
lannin
g
Applying the Im
proved Ant… (Z
hao Ming
)
307
Figure 4. NC
the iteration
s
input
Fi
gure 5. d the length of pa
th input
Figure 6. Q the carrying am
ount of phero
m
one
In this pape
r, mamda
n
i rea
s
oni
ng is a
ppl
ied, Fuzzy Re
aso
n
ing flo
w
diagram sho
w
n in
Figure 7:
Figure 7. Fuzzy Rea
s
o
n
ing
F
u
zz
y
R
e
as
on
in
g
r
u
les a
r
e
sh
ow
n in
Ta
b
l
e
1
,
F
i
gu
re
8 is a F
u
z
zy R
e
as
on
in
g
r
u
le ta
b
l
e
in grap
hic fo
rm.
Table 1. Q va
lue of Fuzzy Rea
s
o
n
ing
dS
dM
dB
NCS
NCM
NCB
QM
QM
QB
QS
QS
QM
QS
QS
QS
N
C
Itera
tion
s
Q
Carry
ing
phero
m
o
n
e
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Vol. 14, No. 2, May 2015 : 304 – 310
308
Figure 8. Fuzzy Rea
s
o
n
ing
rule table in
grap
hic fo
rm
4. The Desig
n
ing for th
e Fuzz
y
ACO
Steps of the algorith
m
is a
s
follows:
Step 1:
T
he
3D spa
c
e en
vironme
n
t with obsta
cle
s
i
s
initialized , establi
s
h th
e linear
equatio
n fro
m
the startin
g
point to the destinati
on
point, cal
c
ula
t
e PL the length of each p
o
int
belon
ging to
(i
,
j
,
k
)
A
llowe
d
to the straight
line L.
Step 2:
A
ccordin
g to fo
rmula
(1) u
s
e
roul
ette met
hod to
dete
r
mine the
nex
t point of
each a
n
t, ant
s
rea
c
hin
g
th
e targ
et poi
nt
apply Fu
zzy
Control Ph
eromone
Updat
ing formula
(2
) to
update the p
h
e
rom
one.
Step 3:
Dete
rmine
wh
ethe
r ea
ch
set of
all the ant
s
have complet
ed path
plan
ning, if
not, go to step 2.
Step 4:
Det
e
rmin
es whe
t
her th
e
stop
ping
co
nditio
n
of thi
s
al
g
o
rithm i
s
me
t, if it is,
output the opt
imal path and
end,
otherwi
se, go to step
2.
5. Simulation Resul
t
s
As sho
w
n in
Figure 1, A robot in a three dime
n
s
ion
a
l terrain with ob
stacl
e
s ap
plie
s fuzzy
Ant Colony Al
gorithm to fin
d
out an
opti
m
al path fr
om
the sta
r
ting p
o
int (0,10,
0) t
o
thede
stinati
on
point (20,8,0
)
. Hypothe
si
s: The
r
e
are 2
0
ants in
ea
ch
set, ma
ke
an
experim
ental
comp
ari
s
o
n
o
f
conve
n
tional
Ant Colony Algorithm a
nd the impr
oved
Ant Colony Algorithm, Matl
ab 200
8 obtai
ns
the simulatio
n
results
sho
w
n in Figu
re
9 and Figu
re
10.
These re
sult
s clearly sho
w
that the impro
v
ed algorith
m
not only gets a better path
in th
e
path plan
nin
g
, but also
redu
ce
s app
roximately An
t Colony Alg
o
rithm iterations to the h
a
lf
amount of
work, the
co
nverge
nce rate
also im
pr
oves a lot. Spe
c
i
f
ic experi
m
en
tal data re
sul
t
s
are sho
w
n in
Table 2:
Figure 9. The
conventio
nal
ACO for path
-
plan
ning
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Rob
o
t Thre
e Dim
ensio
nal
Space Path
-p
lannin
g
Applying the Im
proved Ant… (Z
hao Ming
)
309
Figure 10. Th
e improve
d
ACO for p
a
th-p
lannin
g
Table 1. Co
m
pari
s
on of two algorith
m
s
algorithm comparison
Experiment
1
Experiment
2
Experiment
3
Average
improved ACO
Best path
length
iterations
35.032
43
34.871
46
34.904
50
34.936
47
conventional
ACO
Best path
length
iterations
44.381
90
45.082
88
45.128
85
44.864
88
6. Conclusio
n
The imp
r
ove
m
ent of the
Tran
sition
Proba
bility Functio
n
and
Pherom
one
Upd
a
ting
method
s in convention
a
l Ant Colony Alg
o
rithm great
ly incre
a
ses th
e conve
r
ge
nce rate of the Ant
Colony Algori
t
hm, reduces the num
ber
of iterations, effectively
avoids fallingint
o local
optim
al
probl
em, e
n
a
b
les ant
sto fi
nd the
first
pathwith
go
o
d
re
sult
s. In
addition, th
e
location
of the
pheromo
ne i
s
o
n
the
po
intsin
stead
o
f
the c
onne
ction
betwee
n
the
points, whi
c
h g
r
e
a
t
ly
improve
s
the
comp
utationa
l spe
ed.
Cl
ea
rly, the impro
v
ement of An
t Colony Alg
o
r
ithm can b
e
tter
improve
the
rate of three
-
d
i
mensi
onal
p
a
th pla
nning
and optimization.
The
r
efo
r
e,
this de
sign
ing
can p
r
ovide b
r
oad p
r
o
s
p
e
ct
s for furthe
r o
p
timization of
three-dimen
s
ional ro
bot pa
th plannin
g
.
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ces
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e
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a
t
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ang
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i
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h
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al
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aa S
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