Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 1
,
Febr
u
a
r
y
201
6,
pp
. 21
2
~
22
2
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
1.8
606
2
12
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
/
IJECE
Path Planning Based on Fuzzy
Decision Trees and Potential
Field
Iswanto*
,
**
, Oya
s
Wahy
ung
go
ro
*, A
d
ha
Ima
m
Ca
hy
adi*
* Department of
Electrical Eng
i
n
eering
and
Infor
m
ation
Technolo
g
y
, Universitas
Gadjah
Mada, Y
o
g
y
ak
arta, Indon
esia
** Departmen
t
o
f
Electr
i
cal
Engineering
,
Univ
ers
itas Muhammadiy
a
h
Yog
y
akarta
,
Yog
y
akart
a
,
Ind
ones
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
l 16, 2015
Rev
i
sed
No
v 2, 201
5
Accepted Nov 18, 2015
The fuz
z
y
log
i
c
algori
t
hm
is a
n
artif
ic
i
a
l inte
l
ligen
ce algori
t
h
m
that
uses
mathematical lo
gic to solve to by
the
data valu
e inputs which are not precise
in order
to reach an accur
a
te conclusi
on. In
this work, Fuzzy
d
ecision
tree
(FDT) has been
designed to
solv
e the path
plann
i
ng problem b
y
considering
all av
ailable inf
o
rmation and make th
e most ap
propriate decision given b
y
the inpu
ts. Th
e
FDT is often us
ed to make a p
a
th planning
decision in gr
aph
theor
y
. It has been applied in th
e previ
ous
res
ear
ches
in the field
of robotics
,
but it stil
l shows drawbacks in that th
e agen
t will stop at
the lo
cal m
i
nim
a
and is not able to find the shortest pa
th. Hen
ce,
t
h
is
paper com
b
i
n
es
the F
D
T
algorithm
with
t
h
e poten
tia
l fi
el
d algor
ithm. Th
e poten
tial field
algorithm
provides weigh
t
to the FDT
algorithm
which en
ables th
e agen
t to
successfully
avo
i
d th
e lo
cal minima and f
i
nd th
e
shortest path.
Keyword:
Fuzzy Decision
T
r
ees
L
o
c
a
mi
n
i
ma
N
o
n
-
Ho
lono
m
i
c
Pat
h
Pl
a
nni
ng
Po
ten
tial Field
Copyright ©
201
6 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
:
Iswa
nto
,
Depa
rt
em
ent
of El
ect
ri
cal
E
n
gi
nee
r
i
n
g a
n
d
I
n
f
o
rm
at
i
on Te
chn
o
l
o
gy
Uni
v
ersitas Ga
dja
h
M
a
da,
Yo
gy
aka
r
t
a
, In
do
nesi
a.
Em
a
il: iswan
t
o.s3
te1
3
@m
ail.
u
g
m
.ac.id
1.
INTRODUCTION
In
ge
neral
,
a
m
obi
l
e
rob
o
t
navi
gat
i
o
n
wh
i
c
h m
oves i
n
dy
nam
i
c envi
r
onm
ent
s
has
a
m
a
jor i
s
s
u
e
nam
e
ly
pat
h
pl
anni
ng
[
1
]
.
I
n
pat
h
pl
an
ni
n
g
pr
o
b
l
e
m
s
, t
h
e m
obi
l
e
rob
o
t
r
e
qui
res al
g
o
r
i
t
h
m
s
t
o
fi
n
d
a s
a
fe
pa
t
h
t
o
av
oi
d a c
o
l
l
i
s
i
on a
nd
nee
d
s an
opt
i
m
al
pat
h
i
n
ac
hi
evi
n
g t
h
e t
a
rget
s i
n
t
h
e
u
n
k
n
o
w
n
envi
ro
nm
ent
[2]
.
A
gra
p
h t
h
e
o
ry
al
go
ri
t
h
m
for
pat
h
pl
an
ni
n
g
i
s
n
eeded
t
o
o
v
erc
o
m
e
t
h
e pr
o
b
l
e
m
s
.
Th
ere are three typ
e
s o
f
g
r
ap
h
th
eo
ries, n
a
mely
v
i
sib
ility
, Vorono
i, and cell
d
eco
m
p
o
tio
n
graph
s
.
Som
e
researc
h
ers s
u
c
h
as
Li
u
an
d Z
h
a
n
g
[
3
]
ha
ve c
o
nd
uct
e
d
pat
h
pl
a
nni
n
g
researc
h
es
b
y
usi
n
g t
h
e t
h
e
o
ri
es.
Th
e Vorono
i diag
ram
fo
r th
e UAV p
a
t
h
p
l
an
n
i
n
g
h
a
s
b
e
en
u
s
ed
. By usin
g
a
g
l
ob
al v
i
ew, t
h
is g
r
aph
sp
lits
equally large
distance betwee
n obctacles
in
th
at th
e p
a
th
fo
r
UAV is obtain
e
d
.
W
i
t
h
th
e p
a
t
h
, th
e
UAV is
ab
le to
h
ead
t
o
th
e po
in
t
o
f
d
e
stin
atio
n
,
bu
t by ap
p
l
ying
m
e
rely th
is alg
o
r
it
h
m
, th
e rob
o
t
i
s
no
t ab
le to
p
a
ss th
e
lo
cal m
i
n
i
ma. Lo
ca m
i
n
i
m
a
a
con
d
ition
t
h
at
mak
e
s ro
bo
t st
o
p
s
at m
a
n
y
o
b
stacles
Th
e
v
i
sib
ility g
r
aph
algo
rithm
was u
s
ed
by Jan
d
t
et. Al
[4
] for m
o
b
ile robo
t p
a
t
h
p
l
an
n
i
n
g
. Th
is
algorithm
connects
not
only the a
n
gles
of one
obstacle to another
but al
so t
h
e a
ngl
es to t
h
e initi
al and
d
e
stin
ation
po
in
ts o
f
th
e rob
o
t. W
ith
th
is algo
rith
m
,
th
e
m
o
b
ile rob
o
t
is able to
m
o
v
e
to
t
h
e d
e
stin
ation
p
o
i
n
t
in
th
e
safest
p
a
th
bu
t
regrettably b
y
app
l
yin
g
th
is algo
rith
m
,
th
e rob
o
t
is
no
t ab
le to p
a
ss the lo
cal m
i
n
i
m
a
.
The cel
l
deco
m
pot
i
t
i
on
was
use
d
by
R
y
an
[5]
.
T
h
i
s
al
g
o
r
i
t
h
m
di
vi
des t
h
e e
nvi
ro
nm
ent
i
n
t
o
sm
al
l
gri
d
s. T
h
e grids are use
d
to fi
nd the sa
fest path for m
u
lti-ro
bo
t. Th
e m
u
lt
i-robo
t h
e
ad
s to
th
e d
e
stin
ati
o
n
po
in
t
b
y
u
s
ing
th
e grid
lin
es. Graph th
eo
ry is u
s
ed fo
r
p
l
ann
i
ng
th
e safest p
a
t
h
.
Th
e weakn
e
ss
o
f
th
e algo
rit
h
m th
a
t
it is n
o
t
ab
le to find
t
h
e sh
ortest p
a
th.
W
i
t
h
th
e rem
a
in
in
g
p
r
ob
lem
s
, so
m
e
res
earch
ers h
a
v
e
co
m
b
in
ed
the g
r
ap
h
theory with
so
m
e
alg
o
rith
m
s
su
ch
as
Dijk
stra's
alg
o
rith
m
b
y
Feu
e
rstein
and
March
e
tti-Sp
acca
m
e
la [6
]. Th
is algo
rith
m
has b
e
en
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
21
2 – 22
2
21
3
appl
i
e
d
f
o
r
pl
anar
pat
h
pl
an
ni
ng
gr
ap
h t
h
e
o
r
y
. B
y
usi
ng t
h
i
s
al
go
ri
t
h
m
,
t
h
e ro
b
o
t
i
s
abl
e
t
o
fi
n
d
t
h
e s
h
ort
e
s
t
p
a
th
. Th
is alg
o
rith
m was also
i
m
p
l
e
m
en
ted
b
y
Peyer et al
[7
] to
search
th
e sho
r
test p
a
t
h
in
v
e
ry larg
e scale
in
teg
r
ation
(VLSI).
Th
e
d
r
awb
ack
o
f
t
h
e Di
j
k
stra’s alg
o
rith
m
is t
h
at it is n
o
t
ab
l
e
to
d
e
tect
o
b
s
t
acles wh
en
applied
to
th
e
m
obi
l
e
robot
pat
h
pl
a
nni
ng
.
It
has been
m
odi
fi
ed by
Li
u et
al
[8]
by
com
b
i
n
i
ng i
t
wi
t
h
t
h
e Fl
oy
d
alg
o
rith
m
.
Th
e Flo
y
d
algo
rithm is
u
s
ed
to
d
e
tect o
b
s
tacles wh
ile th
e Dij
k
str alg
o
rith
m is u
s
ed
to
find
th
e
shortest path.
Othe
r algorithm
s
such as A* can
also
d
e
termin
e th
e sho
r
t
e
st p
a
th
.
Th
is
alg
o
rith
m
h
a
s b
een
app
lied
by
C
h
e
n
g
Li
pi
ng
et
al
[
9
]
t
o
f
i
nd a
pa
rki
n
g l
o
t
,
but
i
t
i
s
al
s
o
not
a
b
l
e
t
o
d
e
t
ect
m
ovi
ng
o
b
st
acl
es. T
h
e
A*
a
n
d
Dijk
stra's algorith
m
s
were
no
t ab
le to
d
e
t
ect ob
stacl
es,
th
u
s
th
e t
w
o alg
o
rith
m
s
were co
m
b
in
ed with
th
e
artificial in
tell
i
g
en
ce al
g
o
rithm to
d
e
tect th
e
m
.
In
o
r
d
e
r
for A*
alg
o
rith
m to
b
e
ab
le to
be ap
p
lied
to
a
m
o
b
ile
robo
t, th
e algo
rith
m
h
a
s
been m
odified
by Ducho
ň
et al
[10] by adding
phi algorithm
.
In add
itio
n to
Dijk
stra's algorith
m
,
th
e research
er
h
a
s m
o
d
i
fied th
e cell d
eco
m
p
o
s
ition graph
t
h
eory
in
to
th
e tree grap
h
t
h
eo
ry [11]. Grap
h th
eo
ry is o
f
ten
u
s
ed
to
search
for th
e fastest
p
a
th. Th
is th
eo
ry
h
a
s b
e
en
sup
p
o
rt
e
d
by
a deci
si
on s
u
p
p
o
rt
sy
st
em
by
usi
n
g f
u
zzy
al
go
ri
t
h
m
.
Thi
s
al
go
ri
t
h
m
has
been
wi
del
y
u
s
ed t
o
search
d
a
ta and
d
ecision
m
a
k
e
rs
[12
]
-[15
]. In
add
itio
n, th
e fu
zzy alg
o
rith
m
h
a
s b
een
u
s
ed
as a search
p
a
th
an
d to
m
a
k
e
a
d
ecision
to
find
th
e shortest p
a
th
. Man
y
res
earche
r
s ha
ve applied
th
is al
gorithm
as the
search
algorithm
such as GH
Sha
h
Ha
m
zei et al [16]. They
use t
h
is
algo
rith
m
fo
r g
l
obal planning.
The Fuzzy De
cision T
r
ee algorithm
faces a problem
when applied to t
h
e environm
ent which
has
man
y
o
b
s
tacles. At m
a
n
y
scen
ari
o
, t
h
e agent will sto
p
at
a lo
cal m
i
n
i
ma an
d is no
t ab
le to
fi
n
d
th
e sho
r
test
p
a
th
. Based
on
th
e prob
lems, th
is p
a
p
e
r co
m
b
in
es th
e Fuzzy Decision Tree algor
ithm with
p
o
t
en
ti
al field
alg
o
rith
m
.
Th
e p
o
t
en
tial field
alg
o
rith
m
p
r
ov
id
es
weigh
t
to
th
e
fu
zzy
d
e
cisio
n
tree al
go
rith
m
.
W
ith
th
e g
i
v
e
n
weigh
t
, th
e ag
en
tis exp
ected to
av
o
i
d
lo
cal
min
i
m
a
an
d
d
e
termin
e th
e sho
r
test
p
a
th
.
2.
R
E
SEARC
H M
ETHOD
Path
p
l
an
n
i
n
g
is an
alg
o
rithm th
at so
lv
es th
e prob
lem
o
f
m
o
v
i
n
g
an
ag
en
t fro
m
an
in
it
ial to
a g
o
a
l
p
o
s
ition
b
y
p
a
ssin
g
ob
stacles.
A research
m
e
t
h
od
b
y
m
e
rg
ing
sev
e
ral p
a
th
p
l
ann
i
ng
alg
o
ri
th
m
s
p
r
esen
ted th
is
pape
r a
r
e
gra
p
h t
h
e
o
ry
, f
u
zzy
deci
si
o
n
t
r
ee,
an
d th
e
po
ten
t
i
a
l field
algorith
m
s
.
2.
1.
Gra
ph T
h
eory
Al
gori
t
h
m
Thi
s
pa
per
pre
s
ent
s
gl
o
b
al
pa
t
h
pl
an
ni
n
g
m
e
t
h
o
d
t
o
est
a
bl
i
s
h an e
nvi
ro
n
m
ent
a
l
m
odel
.
Gl
o
b
al
pat
h
pl
an
ni
n
g
obt
ai
ns
dat
a
i
n
fo
rm
at
i
on t
h
at
i
s
t
h
e si
ze o
f
t
h
e e
n
vi
r
onm
ent
an
d
t
h
e dat
a
use
d
f
o
r
pat
h
pl
a
nni
n
g
s
u
ch
as
ag
en
t
po
sitio
n
,
po
sitio
n
o
f
ob
stacl
es an
d
go
al po
sitio
n
as show
n
in
f
i
gu
r
e
1. I
t
sho
w
s t
h
at in
the
en
v
i
ron
m
en
t th
ere is an
in
itial p
o
s
ition
d
e
no
t
e
d
b
y
a
b
l
u
e
st
ar, a
p
o
s
ition
of ob
stacle d
e
no
ted
b
y
a red
circle
and
a
goal
po
si
t
i
on o
f
a
g
e
n
t
d
en
ot
ed
by
a
sm
al
l
bl
ue ci
r
c
l
e
. The e
n
vi
r
onm
ent
m
odel
i
s
di
vi
ded
i
n
t
o
gri
d
s
whi
c
h
have
sa
m
e
si
ze.
Fig
u
re
1
.
Env
i
ro
n
m
en
t m
o
d
e
lin
g with cell d
e
co
m
p
o
s
itio
n
The en
vi
r
onm
ent
i
s
m
odel
e
d by
creat
i
n
g a
m
a
p di
vi
ded i
n
t
o
gri
d
s h
a
vi
ng s
a
m
e
si
ze usi
n
g
exact
cel
l
decom
posi
t
i
o
n
al
gori
t
h
m
wi
th so
urce c
o
d
e
pr
o
g
ram
as show
n i
n
fi
gu
re
2. It
sh
o
w
s t
h
a
t
(
I,J
) is th
e positio
n
o
f
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
Me
t
e
r
Me
t
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
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8-8
7
0
8
Pat
h
Pl
a
nni
n
g
Base
d
on
F
u
zz
y Deci
si
o
n
Tre
e
s a
n
d
P
o
t
e
nt
i
a
l
Fi
el
d (
I
sw
a
n
t
o)
21
4
the agent, (
X
G
,
Y
G
) is th
e g
o
a
l p
o
s
itio
n
o
f
the ag
en
t,
l
J
i
s
l
e
ngt
h of t
h
e
gri
d
,
l
I
i
s
wi
dt
h o
f
t
h
e gri
d
,
n
is size of
the environm
ent, and (
X
O
,
Y
O
) is th
e p
o
s
ition o
f
o
b
s
tacle. R
G
is th
e
form
ula of the
distance betwee
n the
agent
and t
h
e
g
o
al
p
o
si
t
i
ons
, R
o
1
is th
e fo
rm
u
l
a o
f
th
e d
i
stan
ce between
th
e ag
en
t an
d
t
h
e ob
stacle p
o
s
itio
ns.
Th
en
R
G
and
R
O4
are
summ
ed up t
o
becom
e
an
environ
m
en
t m
a
tri
x
v
a
lu
e.
Fi
gu
re
2.
S
o
u
r
ce co
de
pr
o
g
ra
m
for en
vi
r
o
n
m
ent
m
a
p
2
.
2
.
F
u
zzy
A
l
go
r
i
t
h
m
Fuzzy
al
g
o
r
i
t
h
m
was
di
sco
v
e
r
ed by
za
de
h
i
n
19
9
4
used
f
o
r r
o
b
o
t
navi
g
a
t
i
on pat
h
pl
a
nni
ng
.
S
o
m
e
researc
h
er
s su
ch as Vac
h
t
s
e
v
an
os a
nd
He
xm
oor [
17]
us
ed it for a wheeled robot pa
th
p
l
ann
i
ng
.
W
i
t
h
th
is
algorithm
,
the robot could a
v
oid static obst
acles. The
ot
h
e
r resea
r
c
h
er,
Surm
ann et
al [18]
also use
d
fuzzy
al
go
ri
t
h
m
for m
obi
l
e
robot
p
a
t
h
pl
an
ni
n
g
. I
t
was used
fo
r a pat
h
pl
a
nni
n
g
i
n
an en
vi
r
o
nm
ent
t
h
at
has
m
a
ny
obstacles.
In a
ro
b
o
t
pat
h
pl
a
nni
ng
res
earch
, f
u
zzy
al
go
ri
t
h
m
has
m
a
ny
wea
kne
sse
s, so t
h
at
t
h
e a
l
go
ri
t
h
m
is
co
m
b
in
ed
with cell d
e
co
m
p
o
s
itio
n
to fi
n
d
th
e
fastest an
d
sh
or
test called FDT.
Th
e r
e
sear
ch of
d
e
termin
ing
t
h
e sh
ort
e
st
pat
h
usi
ng f
u
zzy
deci
si
o
n
tree has been carried out suc
h
as by
Ham
z
e
i
et a
l
[
19]. In his re
se
arch,
en
titled
Self-org
an
izing
Fu
zzy d
ecision
tree for R
o
bo
t
Nav
i
g
a
tio
n
:
An
On-lin
e Learn
i
n
g
Ap
pro
a
ch
, t
h
ey
im
pl
em
ent
e
d t
h
i
s
al
g
o
ri
t
h
m
t
o
sea
r
ch
r
o
bot
pat
h
a
n
d
fuzzy
rul
e
base t
o
det
ect
ob
st
acl
es.
Tur
n
bul
l
et
al
[20]
al
so
use
d
f
u
zzy decision tree algorithm
for
path
pl
an
ni
n
g
o
f
U
A
V
. T
h
i
s
al
go
ri
t
h
m
requ
ires a lo
t of d
a
ta u
s
ed
for train
i
ng
. Th
e train
i
n
g
en
ab
les UAV to
m
o
v
e
to
ward
th
e
go
al p
o
s
itio
n
and
av
oi
d
o
b
s
tacles. Th
is alg
o
rith
m
h
a
s a weak
n
e
ss th
at is it n
eed
s a
l
o
n
g
t
r
ai
ni
n
g
pr
ocess.
Due to the
weakness
a
ne
w
al
go
ri
t
h
m
i
s
devel
o
ped
wi
t
h
t
h
e p
r
i
n
ci
pl
e o
f
seei
ng
clo
s
e neig
hb
orh
ood
s.
Fu
zzy
decision tree algorithm
with
cl
ose
nei
g
hb
or
’s
opt
i
m
u
m
was de
vel
o
pe
d
by
Lert
w
o
rap
r
ach
ay
a [2
1]
.
Fi
gu
re
3.
The
e
nvi
ro
nm
ent
m
odel
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I
S
SN
:
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08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
21
2 – 22
2
21
5
Th
is p
a
p
e
r d
e
scrib
e
s fu
zzy
alg
o
rith
m
s
fo
r
path
p
l
an
n
i
ng
with
grid
v
a
lu
es as
th
e fu
zzy
inp
u
t
ob
tain
ed
fr
om
cel
l
deco
m
posi
t
i
on i
n
a
gl
o
b
al
pat
h
pl
anni
ng
a
n
d
t
h
e
f
u
zzy
o
u
t
put
i
s
m
o
t
i
on di
rec
t
i
on
of
a
n
a
g
e
n
t
t
h
at
t
h
e desi
g
n
i
s
sho
w
n i
n
fi
g
u
r
e
3. It
sh
ow
s t
h
a
t
t
h
e fuzzy
has
5 i
n
p
u
t
s
an
d 2
out
put
s i
n
whi
c
h t
h
e i
n
put
s a
r
e gri
d
values l
o
cated around t
h
e agent that is
in
t
h
e fr
on
t, i
n
45 d
e
gr
ee lef
t
,
45
d
e
gr
ee r
i
g
h
t
, lef
t
an
d
r
i
gh
t
o
f
t
h
e
g
r
id
s
.
W
h
i
l
e
th
e
o
u
t
p
u
t
o
f
th
e
f
u
z
z
y
i
s
th
e
val
u
e
of directi
o
n
for the
x and y
-
axis.
Fi
gu
re 4a sh
o
w
s m
e
m
b
er set whi
c
h ha
s a range
of 0
-
30
0 and t
h
ree m
e
mbers i
.
e. sm
al
l
(S)
,
m
e
di
u
m
(
M
)
,
an
d
larg
e
(
B
)
in
wh
ich
each
h
a
s a r
a
nge o
f
[0
90
] [
90 2
1
0
]
an
d
[
210 3
0
0
]
r
e
sp
ecti
v
ely. Th
e set o
f
f
u
zzy
out
put
has a ra
nge
of
-1 t
o
1
,
whi
c
h i
s
sh
ow
n i
n
Fi
g
u
r
e 4
b
.
It
sho
w
s t
h
at
t
h
e set
of m
e
m
b
ers
fo
r o
u
t
p
ut
hav
e
three m
e
m
b
ers, nam
e
ly the right
(R), t
h
e ce
nter (Z),
and
Left (L
) whic
h each
has
of a
range
[-1 -0.4] [-0.4
0.
4]
an
d
[0
.4
1
]
respect
i
v
el
y
.
Fi
gu
re
4.
F
u
zz
y
i
n
p
u
t
an
d
o
u
t
put
Th
e fu
zzy ru
le b
a
se is sho
w
n in
figu
re
5
.
It
is s
een that there are two ba
si
c ru
les th
at is th
e b
a
si
c
rul
e
s
of
f
u
zzy
X an
d
fo
r f
u
zz
y
Y. T
h
e ba
si
c rul
e
s
of
f
u
zzy
X p
r
ovi
des t
h
e val
u
e
of
di
re
ct
i
on f
o
r x
-
axi
s
w
h
i
l
e
t
h
e
basi
c r
u
l
e
s
o
f
fuzzy
X
p
r
ovi
des t
h
e
val
u
e
of
di
rect
i
o
n
f
o
r
x
-
axi
s
. T
h
e val
u
e
of
di
re
ct
i
on
of
x a
n
d
y
axi
s
m
ove t
h
e agen
t
t
o
war
d
s t
h
e
g
o
al
p
o
si
t
i
on a
n
d av
oi
d
ob
st
acl
es.Va
r
i
a
bl
e A
1
t
o
A5 i
s
a f
u
z
z
y
i
nput
nam
e
l
y
A1
is left inp
u
t
of
th
e
g
r
ids,
A2
i
s
45
d
e
g
r
ee left, A3
is a
fron
t inp
u
t
, A4 is
45
d
e
g
r
ee
righ
t,
an
d
A5
is
th
e righ
t
in
pu
t of t
h
e
g
r
i
d
s.
Fi
gu
re
5.
The
x a
n
d
y
r
u
l
e
ba
sed
fuzzy
2.3. Potential Field
Algorithm
Pot
e
nt
i
a
l
fi
el
d
al
go
ri
t
h
m
[22]
i
s
one
of
pat
h
pl
an
ni
n
g
al
g
o
r
i
t
h
m
s
whi
c
h
was de
vel
ope
d
by
K
h
at
i
b
fro
m
th
e
m
a
g
n
etic field
.
Th
e
eq
u
a
tion
of
p
o
t
en
tial field
algo
rith
m
is as fo
llo
ws:
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Pat
h
Pl
a
nni
n
g
Base
d
on
F
u
zz
y Deci
si
o
n
Tre
e
s a
n
d
P
o
t
e
nt
i
a
l
Fi
el
d (
I
sw
a
n
t
o)
21
6
whe
r
e
and
is th
e attraction and
repu
ls
ion. Attractiv
e force is th
e fo
rce th
at will cau
s
e th
e
ag
en
tto m
o
v
e
t
o
th
e d
e
stin
ation
.
Th
e attractive fo
rce equ
a
tion
is as fo
llows:
(
2
)
In w
h
ich
is th
e attractiv
e
po
ten
tial field
co
n
s
tan
t
. Th
e
valu
e of
is
0
1
.
shows t
h
e
dest
i
n
at
i
o
n
poi
nt
o
f
t
h
e a
g
ent
a
nd
shows
t
h
e coordinates of the
age
n
t.
Th
e repu
lsion
eq
u
a
tion
is
as fo
llo
ws:
(
3
)
In
w
h
ich
is t
h
e
repu
lsiv
e
po
ten
tial field co
n
s
tan
t
. Th
e
valu
e
o
f
is
0
1
.
shows
the
coordinates of the
a
g
enta
nd
sh
ow
s th
e po
in
t
of
t
h
e
ob
stacle. Man
y
r
e
search
ers
h
a
v
e
m
o
d
i
fied th
e po
ten
tial
fi
el
d al
g
o
r
i
t
h
m
suc
h
a
s
R
i
zqi
et
al
[
23]
w
h
o
h
a
s m
odi
fi
ed
re
pul
si
ve
pot
e
n
t
i
a
l
fi
el
d.
R
e
n
et
al
[
2
4]
has
m
odi
fi
e
d
pot
e
n
t
i
a
l
fi
el
d by
usi
n
g Ne
wt
on'
s l
a
ws an
d appl
i
e
d i
t
t
o
m
obi
l
e
age
n
t
s
.
Vel
a
gi
c et
al
[25]
has m
odi
fi
ed t
h
e
pot
e
n
t
i
a
l
fi
el
d i
n
or
der
t
o
a
v
oi
d l
o
cal
m
i
nim
a
.
In t
h
i
s
pa
pe
r,
t
h
e pot
ent
i
a
l
fi
el
d al
gori
t
h
m
was
m
odi
fi
ed t
o
pr
o
v
i
d
e
wei
ght
f
o
r t
h
e val
u
e
o
f
en
v
i
ron
m
en
t
m
atrix
e
s.
To
ob
tain
th
e weigh
t
v
a
lu
e,
th
e
Kh
atib
’s eq
u
a
tion
o
f
t
h
e attraction
p
o
t
en
tial field
was
m
o
d
i
fied
in
to th
e
fo
llowing
:
(
4
)
In
w
h
ich
is th
e attractiv
e po
ten
tial field co
n
s
tan
t
.
,
sh
ows th
e
d
e
stin
ati
o
n po
i
n
t of
t
h
e
agenta
nd
,
sho
w
s t
h
e c
o
or
di
nat
e
s o
f
t
h
e
age
n
t
.
Wh
ile Kh
ati
b
’s
rep
u
l
sion
po
ten
tial
field
e
qua
t
i
on
was m
odi
f
i
ed i
n
t
o
t
h
e
f
o
l
l
o
wi
ng:
(
5
)
In
whic
h
is t
h
e attractiv
e
po
ten
tial fiel
d
co
nstan
t
.
,
show
s th
e co
or
d
i
n
a
tes
of
t
h
e
obstacle with
is nu
m
b
er
of
obstacle.
2.
3.
E
n
vi
r
o
nm
ent M
o
del
Mo
di
fi
ed
Thi
s
st
udy
ex
p
l
ai
ns fuzzy
dec
i
si
on t
r
ee al
go
r
i
t
h
m
merg
ed
with
cell d
ecom
p
o
s
itio
n
alg
o
rith
m fo
r an
agent
pat
h
pl
a
nni
ng
. The a
g
e
n
t
m
oves t
h
e g
o
al
po
si
t
i
on i
n
an un
k
n
o
w
n envi
ro
nm
ent
.
In
t
h
e sim
u
l
a
t
i
on, t
h
e
merg
er of
th
e two
al
g
o
rith
ms
are
un
ab
le t
o
find
th
e shortest p
a
th,
t
h
erefore it is
n
e
cessary to m
o
d
i
fy th
e
m
e
t
hod i
n
o
r
d
e
r f
o
r t
h
e pat
h
pl
a
nni
ng t
o
be o
p
t
i
m
al
in fi
ndi
ng t
h
e
sho
r
t
e
st
pat
h
.
The m
odi
fi
cat
i
on i
s
con
d
u
ct
ed
by
a
ddi
ng
p
o
t
e
nt
i
a
l
fi
el
d al
go
ri
t
h
m
i
n
t
h
e e
n
vi
ro
nm
ent
m
odel
wi
t
h
t
h
e
s
o
u
r
ce
co
de
pr
o
g
ram
sho
w
n
in
fi
gu
re 6.
Fi
gu
re
6.
S
o
u
r
ce co
de
pr
o
g
ra
m
for en
vi
r
o
n
m
ent
m
a
p wi
t
h
m
odi
fi
ed
pot
e
n
t
i
a
l
fi
el
d al
g
o
r
i
t
h
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
21
2 – 22
2
21
7
Fi
gu
re 6 s
h
ow
s t
h
at
d
x
F
is th
e attractiv
e o
f
p
o
t
ential field
s
as sh
o
w
n
in
eq
u
a
ti
on
s 4
wh
ile
O
x
F
is t
h
e
repu
lsiv
e
of fi
eld
po
ten
tial as shown
i
n
equ
a
tio
n 5.
A
K
is th
e con
s
tan
t
o
f
th
e
p
o
t
en
tial field
attractiv
e,
and
and
R
K
are th
e constan
t
o
f
th
e field
po
ten
tial repu
lsiv
e. Th
e sum o
f
p
o
t
en
tial field
force is u
s
ed
fo
r th
e wei
g
ht
v
a
lu
e
o
f
co
lum
n
s an
d
ro
ws
in
an
en
v
i
ronmen
t
m
a
trix
. If
t
h
e s
u
m
of at
t
r
at
i
v
e and
re
pul
si
ve i
s
a ve
ry
l
a
rge
,
th
en
a limit v
a
lu
e is
g
i
v
e
n
.
3.
R
E
SU
LTS AN
D ANA
LY
SIS
The resea
r
che
r
s used t
w
o so
f
t
wares nam
e
l
y
R
O
S (R
o
bot
Ope
r
at
i
n
g Sy
st
em
) and M
a
t
l
a
b. B
y
usi
n
g
th
e
m
a
tlab
,
th
e d
e
sign
and
si
m
u
latio
n
for th
e Fu
zzy
decisio
n
tree Artifial Po
ten
tial Field
s
(FDTAPF)
al
go
ri
t
h
m
coul
d be c
r
eat
ed
. E
xpe
ri
m
e
nt
s were car
ri
ed
out
wi
t
h
t
h
e
desi
g
n
envi
ro
nm
ent
that
was c
o
nd
u
c
t
e
d by
LI
ANG
[29
]
with
size o
f
10
0x
100
.
A
f
terw
ar
d, th
e en
v
i
r
onmen
t Matr
ix
der
i
v
e
d
fr
o
m
Lian
g’
s
w
a
s cr
eated
to
si
m
u
late th
e
mo
b
ile ro
bo
t. There were
2
experim
e
n
t
s cr
eate
d
ie in
en
v
i
ronmen
ts with
m
u
lti o
b
s
tacles an
d
in
en
v
i
ron
m
en
ts with
lo
cal m
i
n
i
ma.
Fi
gu
re
7.
Ex
pe
ri
m
e
nt
1 i
n
e
n
v
i
ro
nm
ent
1 wi
t
h
F
D
T
an
d
FD
TAPF
al
g
o
ri
t
h
m
In exp
e
rim
e
n
t
1 in
env
i
ro
nmen
t 1
,
th
e
go
al is to m
o
ve th
e ag
en
t fro
m
th
e in
itial po
in
t t
o
the
d
e
stin
ation
poin
t
as sh
own
in
Figu
re
7
with
FDT
an
d
FDTAPF al
g
o
rith
m
s
. It sh
ows th
at th
ere is an
envi
ronm
ent that has six obst
acles. The a
g
e
n
t is placed in
the
position of (30, 95) denot
e
d
by gree
n
sta
r
.
The
ag
en
tm
o
v
e
s toward
s th
e d
e
sti
n
atio
n po
in
t
(30
,
1
0
)
d
e
no
ted
b
y
b
l
ue star.
In th
e fi
g
u
re it can
be seen
th
at
th
ere
are t
w
o l
i
n
es,
nam
e
ly
red and bl
ue
. It
i
s
seen t
h
at
t
h
e FDTAPF algo
rith
m
with
red
lin
e is b
e
tter th
an
the FDT
algorithm
with blue
line i
n
term
of
that the
re
d line
has
a s
h
orter dista
n
ce t
o
reach the
final destination.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
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:
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8-8
7
0
8
Pat
h
Pl
a
nni
n
g
Base
d
on
F
u
zz
y Deci
si
o
n
Tre
e
s a
n
d
P
o
t
e
nt
i
a
l
Fi
el
d (
I
sw
a
n
t
o)
21
8
Fi
gu
re
8.
Ex
pe
ri
m
e
nt
2 i
n
e
n
v
i
ro
nm
ent
1 wi
t
h
F
D
T
an
d
FD
TAPF
al
g
o
ri
t
h
m
In th
e
fo
llowi
n
g
sim
u
latio
n
s
, th
e i
n
itial and
d
e
stin
ation
p
o
s
ition
po
in
t
o
f
th
e agn
e
t is ch
an
g
e
d
as
sh
own
i
n
Fi
g
u
re
8
with
FDT and
FDTAPF algo
rith
m
s
.
In exp
e
rim
e
n
t
2 in
t
h
e env
i
ron
m
en
t 1
,
th
e in
itial
position
of t
h
e
agnet is
placed in (10,
10) de
note
d
by
green
star
and the
destination
poi
nt
(90, 90) denoted
by
bl
ue st
ar.
In t
h
e fi
gu
re i
t
can be s
een that there are two lines, nam
e
ly ye
llow and gree
n. It is seen that the
FDTAPF algorith
m
with
yello
w lin
e is
better th
an
t
h
e FDT algo
rithm
with
g
r
een. By u
s
ing
FDTAPF
alg
o
rith
m
,
th
e ag
en
t can
find
th
e sh
ortest p
a
t
h
in bo
th exp
e
ri
m
e
n
t
s in
env
i
ro
n
m
en
t 1
.
Fi
gu
re
9.
Ex
pe
ri
m
e
nt
1 i
n
e
n
v
i
ro
nm
ent
2 wi
t
h
F
D
T
an
d
FD
TAPF
al
g
o
ri
t
h
m
In
t
h
e first ex
perim
e
n
t
in
en
viron
m
en
t 2
,
the g
o
a
l is to
m
o
v
e
t
h
e ag
en
t fro
m
th
e in
itial
p
o
i
n
t
to
th
e
d
e
stin
ation
poin
t
as sh
own
in
Figu
re
9
with
FDT
an
d
FDTAPF al
g
o
rith
m
s
. It sh
ows th
at th
ere is an
envi
ronm
ent that ha
s
obstacl
es. The a
g
e
n
tis placed in
the position of
(5, 5)de
note
d
by green star. The
agent
m
o
v
e
s to
wards th
e
d
e
stin
atio
n po
in
t
(95
,
9
5
)d
eno
t
ed b
y
bl
ue
st
ar.
Fr
o
m
t
h
e fi
g
u
re
that it can
be s
een tha
t
t
h
ere are t
w
o l
i
nes, nam
e
l
y
r
e
d an
d bl
ue. F
r
om
t
h
e fi
gur
e i
t
is seen
th
at t
h
e FDTAPF alg
o
rith
m
with
red
lin
e
is b
e
tter th
an
t
h
e FDT al
g
o
rith
m
with
b
l
u
e
l
i
n
e
in
term
o
f
th
at th
e red
line h
a
s sho
r
ter distan
ce to
reach
th
e
fin
a
l d
e
stin
ation
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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08
IJEC
E V
o
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.
6, No
. 1, Feb
r
uar
y
20
1
6
:
21
2 – 22
2
21
9
Fi
gu
re
1
0
. E
x
p
e
ri
m
e
nt
1 i
n
e
n
vi
r
onm
ent
2
wi
t
h
co
nt
o
u
r
Ex
peri
m
e
nt
1 i
n
envi
ro
nm
ent
2 wi
t
h
FD
T and
FDT
A
PF al
g
o
ri
t
h
m
can be a
n
al
y
zed by
u
s
i
n
g
cont
ou
rs as
sh
ow
n i
n
Fi
g
u
r
e
10
. I
n
t
h
e fi
gu
r
e
, t
h
e c
ont
ou
r
di
ffe
re
nce b
e
t
w
een
a wei
ght
ed e
nvi
r
o
nm
ent
wi
t
h
a
weigh
tless environ
m
en
t is v
i
sib
l
e. By add
i
ng
weigh
t
s pro
v
id
ed
b
y
p
o
t
en
tial alg
o
rith
m
,
sev
e
ral con
t
ou
rs ex
ist
in
th
e en
v
i
ronmen
t wh
ich
enab
le ag
en
t to
fin
d
th
e shorte
st p
a
th
. Th
e startin
g
po
i
n
t o
f
th
e ag
en
t is sh
own
i
n
red c
o
lor
whic
h ha
s a
high s
u
rface c
ont
our.
W
h
ile the
de
s
tination
poi
nt of t
h
e a
g
ent is
shown in bl
ue
color
whic
h has low surface c
ont
our. Thus
the agent will
m
o
ve to the goal
from
the higher contour towa
rds the
l
o
we
r c
ont
ou
r
so t
h
at
t
h
e
pat
h
p
l
ann
i
ng
ag
entis
m
o
re op
timal.
Fi
gu
re
1
1
. E
x
p
e
ri
m
e
nt
2 i
n
e
n
vi
r
onm
ent
2
wi
t
h
F
D
T a
n
d F
D
TAPF
al
g
o
ri
t
h
m
In
th
e
fo
llowi
n
g
sim
u
latio
n
s
, th
e in
itial an
d
d
e
stin
ation
p
o
s
ition
po
in
t
o
f
th
e ag
en
tis
ch
ang
e
d
as
sho
w
n i
n
Fi
g
u
r
e
11
wi
t
h
FDT
and
FD
TA
PF a
l
go
ri
t
h
m
s
. In e
xpe
ri
m
e
nt
2 i
n
envi
ro
nm
ent
2,
t
h
e i
n
i
s
i
a
l
p
o
si
t
i
on
poi
nt
of t
h
e ag
ent
(4
5,
2
5
)
de
not
e
d
by
g
r
ee
n
st
aran
d t
h
e de
st
i
n
at
i
on
poi
nt
(7
5,
80
) de
n
o
t
e
d by
bl
ue st
ar.
From
the figure that it can be seen
th
at th
ere are two
lin
es,
n
a
m
e
ly red
an
d
b
l
u
e
. Fro
m
th
e fig
u
re it is seen
th
at th
e
FDTAPF algorith
m
with
red
lin
e is b
e
tter th
an
th
e FDT al
g
o
rith
m
with
b
l
u
e
lin
e in
term o
f
th
at th
e red
lin
e
h
a
s sh
orter d
i
stan
ce to
reach
th
e fi
n
a
l d
e
stin
atio
n
.
By
usi
n
g F
D
T
A
P
F
al
go
ri
t
h
m
,
the age
n
tcan
find the
sh
ortest
p
a
th
i
n
th
e en
v
i
ron
m
e
n
t 2.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Pat
h
Pl
a
nni
n
g
Base
d
on
F
u
zz
y Deci
si
o
n
Tre
e
s a
n
d
P
o
t
e
nt
i
a
l
Fi
el
d (
I
sw
a
n
t
o)
22
0
Fi
gu
re
1
2
. E
x
p
e
ri
m
e
nt
2 i
n
e
n
vi
r
onm
ent
2
wi
t
h
co
nt
o
u
r
Fi
gu
re 1
2
s
h
o
w
s t
h
at
t
h
e a
g
ent
p
at
h
pl
an
ni
ng e
n
vi
ro
nm
ent
can be a
n
al
y
zed usi
ng c
o
nt
ou
r. Fi
gu
re
A
i
s
pat
h
pl
an
ni
n
g
co
nt
o
u
r
t
h
at
do
not
u
s
e wei
ght
i
n
t
h
e e
nvi
ro
nm
ent
,
whi
l
e
fi
gu
re B
i
s
pat
h
pl
an
ni
n
g
co
nt
o
u
r
whi
c
h
uses
wei
ght
s i
n
t
h
e e
n
v
i
ro
nm
ent
.
The
st
art
i
ng
p
o
i
n
t of th
e ag
en
t is sh
own
in
red
colo
r
wh
ich
h
a
s a h
i
gh
surface c
ont
our.
While the
de
stination
poi
nt of t
h
e age
n
tishown in
blue color
whic
h ha
s low
surface c
ontour.
Thu
s
th
e ag
entwill
m
o
v
e
to
th
e go
al fro
m
th
e h
i
g
h
e
r conto
u
r toward
s t
h
e lower con
t
o
u
r so
th
at the p
a
th
pl
an
ni
n
g
a
g
e
n
t
i
s
m
o
re opt
i
m
al
.
Fi
gu
re
1
3
. E
x
p
e
ri
m
e
nt
3 i
n
e
n
vi
r
onm
ent
2
wi
t
h
F
D
T a
n
d F
D
TAPF
al
g
o
ri
t
h
m
In ex
pe
ri
m
e
nt 3 i
n
envi
r
o
n
m
ent
2 sho
w
n
i
n
fi
gu
re 13 t
h
e age
n
t
i
s
i
n
the en
vi
ro
nm
ent
wi
t
h
l
o
cal
min
i
m
a
. Th
e a
g
en
t stop
s if th
e agentcannot find the sm
a
lle
st weight. It
ca
n be o
v
erc
o
m
e
by
usi
ng a p
o
t
e
nt
i
a
l
field
algorith
m to
ob
tain
weigh
t
.
In th
e figure it is seen
th
at
th
ere are two
co
lor lin
es n
a
mely red
an
d blu
e
.
It
is seen
th
at th
e FDTAPF algorith
m with
th
e red
lin
e is
b
e
tter th
an
th
e FDT alg
o
r
ith
m
with
th
e b
l
u
e
lin
e. Th
e
ag
en
tin
t
h
e b
l
ue lin
e is n
o
t
able to
m
o
v
e
and av
o
i
d
lo
cal m
i
n
i
m
a
. W
h
ile the ag
en
tin
t
h
e red
lin
e is in
fluen
ced
b
y
repu
lsio
n an
d attractio
n of po
ten
tial field
in
th
at the ag
entis ab
le to
avo
i
d
lo
cal m
i
n
i
m
a
.
4.
CO
NCL
USI
O
N
Fuzzy
decision trees al
gorithm
has b
een us
ed in the
previ
ous
re
searc
h
es
to
fi
n
d
a m
o
b
ile ag
en
t
p
a
th
.
By ap
p
l
yin
g
t
h
e algo
rith
m
,
th
e ag
en
tis ab
l
e
to
m
o
v
e
to
th
e d
e
sti
n
atio
n
p
o
i
n
t
and
d
e
tect
m
u
ltip
le o
b
s
tacles.
Whe
n
a
p
pl
i
e
d
t
o
an
en
vi
r
o
n
m
ent
t
h
at
has
m
a
ny
ob
st
acl
es, howeve
r
, the algorithm
is not a
b
le to avoid l
o
ca
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
21
2 – 22
2
22
1
minim
a
. There
f
ore, t
h
is
pape
r presents
the
m
odificati
o
n
of th
e FDT algorith
m
with
po
ten
tial field
algo
rith
m
.
Po
ten
tial fiel alg
o
rith
m
p
r
ov
i
d
es
weigh
tto
FDT al
g
o
rith
m.
W
i
th
th
e
w
e
i
g
h
t
v
a
lu
e
s
p
r
o
v
id
e
d
b
y
th
e
p
o
t
e
n
t
i
a
l
field algorit
h
m, the
fuzzy deci
sion tr
ee algorith
m
is ab
le to
to
find
th
e shortest p
a
th and
avo
i
d
l
o
cal m
i
n
i
ma.
REFERE
NC
ES
[1]
K.
C.
Brat
a,
et
al,
L
o
c
a
t
i
on-Ba
se
d Augmented R
eality
In
formation for Bus Rout
e Planning
S
y
stem,
Internat
ion
a
l
Journal of Electrical and
Co
mputer
Eng
i
neer
ing
(
I
JECE)
, Vol. 5
,
No. 1
,
pp
. 142-1
49, Februar
y
20
15.
[2]
N.
Arman and
F.
Khamay
seh,
“A
Path-Compr
ession Approach
for Im
proving Shortest-Path
Algorithms,”
Int. J.
Ele
c
tr.
Comput.
Eng
., vol. 5
,
no
.
4, pp
. 772–781
,
2015.
[3]
L.
Liu
and
S. Zhang, “Voronoi
diagram
and GI
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