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.
3, N
o
. 3
,
Sep
t
em
b
e
r
2014
, pp
. 19
1
~
20
0
I
S
SN
: 208
9-4
8
5
6
1
91
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
Mobile Robot Navigation
using Fuzzy L
ogi
c and
Wavelet Network
M
u
st
af
a I. Hamza
h
*, Turki
Y
.
Abda
ll*
*
* Departm
e
nt
of
Ele
c
tri
cal
Eng
i
n
eering
,
Univ
ers
i
t
y
of Bas
r
ah,
Bas
r
ah,
Iraq
**Departm
ent
of
Com
puter Eng
i
neering
,
Univ
ers
i
t
y
of
Bas
r
ah
, B
a
s
r
ah, Ir
aq
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 29, 2013
Rev
i
sed
Ap
r
10
, 20
14
Accepte
d
May 5, 2014
This paper presents the proposed
autonomous mobile robot navigation
scheme.
The n
a
vigation of
mobile
robot in unknown
envir
onment
with
obstacle avoid
a
nce is based o
n
usi
ng fuzzy
logic and wavelet network
.
Several cases are designed
and m
odeled in Simulink and MATLAB.
Simulation r
e
sults show good per
f
or
mance for
th
e proposed sch
e
me.
Keyword:
An
aut
o
n
o
m
o
u
s
m
obi
l
e
ro
bot
Navi
gat
i
o
n
Obstacle a
v
oidance
Particle swarm op
ti
m
i
zatio
n
Pat
h
Pl
a
nni
ng
Wavel
e
t
Ne
ura
l
net
w
or
k
Copyright ©
201
4 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
:
Mustafa I. Ha
mzah,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
Uni
v
e
r
si
t
y
of
B
a
sra
h
Basrah, Iraq
.
Em
ail: eng_m
ustafabgc@ya
hoo.com
1.
INTRODUCTION
An
au
ton
o
m
o
u
s
m
o
b
ile ro
botsh
av
e
b
een
used
in
m
a
n
y
ap
p
lication
s
du
e to
th
e h
i
gh
lev
e
l of
p
e
rform
a
n
ce an
d
reliab
ility s
u
ch
as m
o
v
i
ng
m
a
terial
in
u
n
k
nown
en
v
i
ronmen
t su
ch
as
wareho
u
s
es, offices
an
d ind
u
stries. Th
e ro
bo
t
h
a
s th
e ab
ility to
p
l
an
m
o
tio
n
an
d to
n
a
v
i
g
a
te
au
ton
o
m
o
u
s
ly
av
o
i
d
i
ng
an
y typ
e
of
obstacles in differe
nt environm
ents. This is a reac
tiv
e
strateg
y
wh
ich is co
m
p
letel
y
b
a
sed
on
sen
s
o
r
y
i
n
f
o
rm
at
i
on [1
]
.
The c
o
m
m
o
n
u
s
ed
sensi
n
g de
vi
ces
fo
r
obst
acl
e a
voi
d
i
ng a
r
e i
n
fra
re
d se
nso
r
,
ul
t
r
a
s
oni
c
sens
or,
l
a
ser
r
a
nge
fi
nde
r.
T
h
e ca
use
o
f
c
h
oosi
n
g IR
se
ns
ors
i
s
t
h
at
, IR
sens
or
are
si
m
p
l
e
, a
n
d
has t
h
e fast
resp
o
n
se t
i
m
e [2]
.
I
n
or
dert
o
achi
e
ve
aut
o
n
o
m
ous na
vi
gat
i
o
n
,
t
h
e m
obi
l
e
r
o
b
o
t
m
u
st
be
c
a
pabl
e
o
f
se
nsi
n
g
t
h
e
en
v
i
ron
m
en
t, p
l
ann
i
ng
a rou
t
e fro
m
an
i
n
itial to
a g
o
a
lp
o
s
ition
with o
b
s
tacle avo
i
d
a
n
c
e, and
con
t
ro
llin
g
th
em
o
b
ile ro
bo
ttu
rn
ing
an
g
l
e an
d
lin
ear
v
e
lo
city to
re
ach the target
. An aut
o
n
o
m
ous
r
o
b
o
t
can
avoi
d
obst
acl
es
o
n
t
h
e pat
h
an
d
sm
oot
hl
y
m
ove t
o
t
h
e t
a
r
g
et
[
3
]
.
Th
e pu
rpo
s
e of th
is p
a
per is to
d
e
sign
an
auto
no
m
o
u
s
m
o
b
ile ro
bo
t wh
ich
can
in
teract
an
d
p
l
an
its
m
o
ti
on i
n
u
n
k
n
o
w
n en
vi
r
o
n
m
ent
d
epe
ndi
n
g
o
n
capt
u
re i
n
f
o
rm
at
i
on fr
o
m
ni
ne IR
det
ect
i
on sens
o
r
s.
Obst
acl
e
avoi
dance
a
n
d goal reachi
n
g algorithm
is propose
d
usi
n
g Fuzzy l
ogic. The
Ob
stacle
avoida
nce a
n
d
goal
reachi
ng c
o
ntrollersare c
o
nnected to a wa
velet netw
ork based m
o
tion controlle
r through m
obile robot
ki
nem
a
t
i
c
m
odel
t
o
get
com
p
l
e
t
e
aut
o
nom
ou
s m
obi
l
e
ro
bot
sy
st
em
.
2.
N
A
V
I
GA
TI
ON
OF
M
O
BI
LE R
O
BO
T
Th
e
n
a
v
i
g
a
tion o
f
a m
o
b
ile rob
o
t
can
b
e
co
nsid
ered
as a task
of
d
e
term
in
i
n
g
a co
llision
free p
a
t
h
th
at
en
ab
les th
e mo
b
ile ro
bo
t to trav
el th
ro
ugh
an
ob
stacle co
urse fro
m
an
in
itial co
n
f
ig
uratio
n
to
a g
o
a
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
19
1 – 20
0
19
2
con
f
i
g
urat
i
o
n
[4]
.
I
n
un
k
n
o
w
n e
n
vi
ro
nm
ent
we nee
d
at
l
east
t
h
e fol
l
o
wi
ng t
y
pes
o
f
react
i
v
e
nav
i
gat
i
o
n
b
e
h
a
v
i
ors (i) Mo
v
e
b
e
h
a
v
i
o
r
(ii) Obstacle
av
o
i
d
a
n
c
e
b
e
h
a
v
i
or. (iii) W
a
ll fo
llowing
b
e
h
a
v
i
or.
Mo
v
e
b
e
h
a
v
i
o
r
is to
m
a
k
e
th
e
robo
t m
o
v
e
in
free
env
i
ron
m
en
t. To
av
o
i
d
collisio
n
with
t
h
e ob
stacles,
o
b
s
tacle avo
i
dan
ce is
u
s
ed
.
Wall fo
llo
wi
ng
is a typ
i
cal
exam
ple of a
mission whe
r
e
reactive
na
vigation is
req
u
i
r
e
d
.T
he
m
o
ti
on c
ont
rol
of
m
obi
l
e
ro
b
o
t
s
am
ong
o
b
s
t
acl
es i
s
cl
assi
fi
ed t
o
t
h
ree
p
o
ssi
bl
e m
o
t
i
on t
a
sks a
s
fo
llows:
Poi
n
t
-
t
o
-p
oi
nt
mo
ti
on
(
g
oal
searchi
n
g)
:
The robot is assigne
d to reach
a desired goal
c
o
nfiguration
starting from
a give
n initial
co
nfigu
r
ation,
wh
ile av
o
i
d
i
ng co
llisio
n with
o
b
s
tacles
. Th
is task
is
so
m
e
ti
mes called
Path
p
l
ann
i
ng
.
Pa
th fo
llo
wing
:
The robot m
u
st reach a
nd foll
ow a
geom
etric path
in the C
a
rtesian space
starting from
a
give
n initia
l
co
nf
igu
r
ation (o
n or
o
f
f
t
h
e
path
)
.
Trajec
tor
y
tra
c
king
:
The robot m
u
s
t
reach and fol
l
ow
a traject
ory in the Cartes
ian space
(i.e., a geom
etric p
a
th with a
n
asso
ciated
tim
i
n
g law) starting
fro
m
a g
i
v
e
n
in
itial co
n
f
i
g
uratio
n
.
A
react
i
v
e
na
vi
gat
i
o
n
sy
st
em
base
d
fuzzy
c
o
nt
r
o
l
,
as
s
h
o
w
n
i
n
Fi
g
u
re
1
,
i
s
pr
o
pose
d
f
o
r
o
u
r
r
o
bot
.
T
h
e i
n
p
u
t
s
are th
e d
a
ta (si
g
n
a
ls) prov
id
ed
b
y
sensors in
fron
t, le
ft and right obstacle‘s ra
nge a
n
d the reac
h of the
goa
l
.
The out
puts are crisp
values
(comm
a
nds)
of the s
p
eed a
n
d the
orientati
on
of t
h
e ro
bot as it reacts with the
changing
of the environm
ent [5].
Fi
gu
re
1.
I
n
p
u
t
s
, O
u
t
p
ut
s
o
f
s
y
st
em
The c
o
m
pone
nt
s o
f
FLC
a
r
e an i
n
fere
nce
engi
ne a
nd a
set
of l
i
n
g
u
i
s
t
i
c
IF–T
HE
N
rul
e
s t
h
at
enc
ode t
h
e
beha
vi
o
r
of t
h
e m
obi
l
e
rob
o
t
, Ho
we
ver
,
t
h
e m
a
i
n
di
fficulty in
d
e
sign
ing
a fu
zzy log
i
c con
t
ro
ller is th
e
efficient form
ulation of the fuzzy IF–T
HE
N
rules [6]. Fi
gu
r
e
(2
) S
h
o
w
s t
h
at
Fuzzy
co
nt
r
o
l
l
e
r i
s
m
a
de up o
f
3
step
s: 1) Fu
zzificatio
n
:
conv
erts con
t
ro
ller in
pu
ts in
t
o
in
form
at
io
n
th
at the in
fere
nce m
e
chanism
can be use
d
to
activ
ate and ap
p
l
y ru
les.
2) Ru
le - Base: (a set of
If
-T
hen r
u
l
e
s). 3
)
Def
u
zzi
fi
cat
i
o
n:
Thi
s
c
o
nve
r
t
s
t
h
e
concl
u
sions of the
interf
ace m
echanism
into
actual
inputs for
the process
.
Figure 2.
FLC System
3.
THE
CONT
ROL
SYSTM OF A MOBIL
E
ROBOT
The control syste
m
of a
m
obile robo
t can
be
viewe
d
as a hierarc
h
ical
syste
m
o
f
th
ree con
t
ro
llers: th
e
m
o
t
i
o
n
p
l
ann
e
r, th
e
m
o
tio
n
con
t
ro
ller, and
the actu
a
to
r driv
er. Th
is stru
cture is illu
strated
in
Fig
u
r
e
3
.
At th
e
h
i
gh
est lev
e
l is th
e m
o
tio
n
plan
n
e
r. At th
is lev
e
l, wh
at
p
a
th
and
wh
at v
e
lo
city p
r
ofile th
e ro
bo
t is to
fo
llo
w
are determ
ined
[7].
The c
ont
r
o
l
l
e
r
at
t
h
e next
l
e
vel
t
a
kes t
h
e
i
n
f
o
rm
at
i
on o
f
t
h
e s
p
eed a
nd
p
o
si
t
i
on as
a refe
renc
e
(Desi
r
ed
inpu
t). At th
is lev
e
l, th
e actu
a
l p
o
s
it
io
n
and
v
e
l
o
city of the robot are m
eas
ured and c
o
m
p
ared to the
d
e
sired
po
sition
and
v
e
locity
(as d
e
term
in
ed b
y
th
e
m
o
tio
n p
l
an
n
e
r). Based
on
th
e errors b
e
tween
t
h
e actu
a
l
and
desire
d states, the cont
rol
l
er de
term
ines
what m
o
tor signals are neces
sary to achieve
the desire
d position
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Mo
bi
l
e
Ro
bot
N
a
vi
g
a
t
i
o
n
usi
n
g
F
u
zzy
Lo
gi
c
a
n
d
W
a
vel
et
N
e
t
w
ork (
M
ust
a
f
a
I.
Ha
mz
a
h
)
19
3
an
d
v
e
lo
city.
At th
e lowest lev
e
l are th
e act
u
a
tor driv
ers.
Th
ese co
n
t
ro
ll
ers m
o
to
r signals co
mman
d
s
fro
m
th
e
pre
v
ious level
cont
roller a
nd
determ
ine wha
t
actual veloc
ity and steeri
ng
angle to t
h
e motors are
neces
sary to
achi
e
ve
t
h
e des
i
red p
o
si
t
i
on o
r
r
o
t
a
t
i
onal
s
p
ee
d [8]
.
Fi
gu
re
3.
The
C
ont
r
o
l
Hi
erar
chy
o
f
a
m
obi
l
e
r
o
b
o
t
4.
WAVELET
NEURAL NETWORK
The wa
velet neural net
w
ork isshown in Figure
4.
It re
pres
ents the m
odel of m
u
lti-input
and m
u
lti-
out
put
(M
IM
O
)
WN
N
wi
t
h
t
h
ree
l
a
y
e
rs.
Th
e n
ode
n
u
m
b
er
o
f
t
h
e
i
n
put
l
a
y
e
r i
s
M
,
t
h
e
h
i
dde
n l
a
y
e
r i
s
K a
nd
t
h
e o
u
t
p
ut
l
a
y
e
r i
s
N
.
T
h
e i
m
pul
se
f
unct
i
o
n
of
hi
d
d
e
n
l
a
y
e
r
i
s
wa
vel
e
t
bas
i
s fu
nct
i
o
n.T
h
e
im
pul
se f
u
nct
i
o
n
o
f
out
put
l
a
y
e
r
i
s
si
gm
oi
d fu
nct
i
on
. T
h
e
fo
rm
ul
a f
o
r t
h
e c
o
m
put
at
i
on i
s
as
fol
l
ows
[
9
]
.
σ
u
(1
)
Fi
gu
re
4.
The
s
t
ruct
u
r
e
di
ag
ra
m
of
WNN
If th
e trai
n
i
ng sa
m
p
le set is
X=
X
,X
,……
.
,X
], th
e co
rrespo
nd
ing
act
u
a
l ou
tpu
t
is
y=
,
…….
],
theexpected
output is D=
D
,D
,
…….,D
]
,
t
h
e t
r
ai
ned s
a
m
p
l
e
s num
ber i
s
N
, t
h
e sum
of t
h
e out
put
l
a
y
e
r
devi
at
i
o
ns
i
s
E (
N
) ,
Y
σ
u
σ
W
,
ψ
,
w
w
,
x
(2
)
1
,
2
,
3
,
…………N
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
19
1 – 20
0
19
4
EN
1
N
D
i
Y
i
…
3
(3
)
The
wavel
e
t
net
w
or
k
ope
ra
t
i
on co
nsi
s
t
s
of
t
w
o
phas
e
s.
In t
h
e fi
rst
p
h
ase, t
h
e net
w
o
r
k a
r
c
h
i
t
ect
ure i
s
det
e
rm
i
n
ed fo
r
cert
a
i
n
ap
pl
i
cat
i
on.
In t
h
e se
con
d
phas
e
t
h
e
param
e
t
e
r of t
h
e net
w
o
r
k are
up
dat
e
d s
o
t
h
at
t
h
e
approxim
a
tion errors
are
m
i
nimized.
4.
1.
A
Wa
vel
e
t N
e
ur
al
Ne
tw
ork B
a
sed
o
n
PSO
Th
e wav
e
let
neu
r
al
n
e
t
w
orks with PSO is sh
own
i
n
Figu
re 5. Th
e elem
e
n
ts
o
f
th
e lo
cat
io
n v
ect
o
r
in the Particle Swarm
s
is defined as the link weights
b
etwe
en each layer of the wa
velet neural networks and
t
e
l
e
scopi
c t
r
an
sl
at
i
on
pa
ram
e
t
e
r
and
. Fitness
fun
c
tion
is th
e Mean square erro
r
fun
c
t
i
o
n
E(
) of th
e
wavel
e
t
neu
r
al
net
w
or
ks.
As
s
een i
n
t
h
e
Eq
u
a
t
i
on
(4
).
E
1
N
e
and e
(
i
)=
(4
)
whe
r
e
y
(
i
) i
s
t
h
e m
odel
out
p
u
t
,
an
d
D
(
i
)
is t
h
e d
e
sir
e
d
ou
tput.
rep
r
esen
ts t
h
e to
tal train
i
ng
p
a
ttern
s.
4.
2. WN
N-
PS
O
T
r
ai
ni
n
g
Al
gori
t
hm Proce
ss:
(1) Set t
h
e in
itial v
a
lu
e
of telescop
ic facto
r
and
th
e tran
slation
facto
r
o
f
th
e
wav
e
let n
e
twork
s
param
e
ters.
(2) In
itiate th
e p
a
ram
e
ters o
f
th
e Particle Swarm
s
: Set th
e p
a
rticle n
u
m
b
e
r m
;
fitn
ess
th
resh
o
l
d
ε
; set th
e
maxim
u
m
allowable
num
b
er
of iterative st
e
p
Ma
xIter; set the
accelerating factor
,
; set th
e m
i
n
i
m
u
m
min
ω
an
d
ma
x
i
mu
m
m
a
x
of
ω
;
t
h
e
p
a
rticle lo
catio
n
; s
p
eed
initial to
th
e ran
d
o
m
n
u
m
b
e
r
b
e
t
w
een
0
and
1.
(3) Iterative update
the
location
x
and
th
e sp
e
e
d
of e
v
ery
pa
rticle according t
o
the
form
ula of the
Pa
rticle
Swarm
Opt
i
m
izat
i
on (
5
), (
6
)
and
(
7
),
rec
o
rd t
h
e hi
st
ory
opt
i
m
al
l
o
cat
ion
vect
o
r
o
f
ev
ery
p
a
rticle an
d
o
v
e
rall o
p
tim
a
l
lo
cation
v
ect
o
r
. Calcu
l
ate th
e fitn
ess
v
a
lue acco
r
d
i
ng to
Equ
a
tio
n
(4), reco
rd th
e fitness
v
a
lu
e Fitn
ess
and Fitness
corresponding t
o
and
.
(5
)
x
=
x
+
v
(6
)
(7
)
(4) Test if th
e fitn
ess v
a
l
u
e reach
to
th
e settin
g
v
a
lu
e,
an
d i
f
t
h
e i
t
e
rat
i
ons
num
ber reac
h t
o
t
h
e hi
ghest
.
I
f
t
h
e
Fitn
ess
≤
setting
v
a
lu
e
or th
e iteratio
n
s
nu
m
b
er reach
t
o
t
h
e
h
i
gh
est, t
h
e iteratio
n
s
ov
er,
o
r
go
to step (3
).
Fi
gu
re
(5
) s
h
o
w
s t
h
e
p
r
o
cess
of
t
r
ai
ni
ng
W
a
vel
e
t
net
w
o
r
k
param
e
t
e
rs an
d Sel
ect
opt
i
m
al
PID
s
val
u
es
usi
n
g
PSO algo
r
ithm
an
d
Figu
r
e
6
show
s th
e op
ti
m
i
zatio
n
b
a
sed
o
n
th
e
Particle Swarm
Op
ti
m
i
za
tio
n
.
PID
cont
rol
l
e
rs
are
use
d
t
o
i
m
prov
e res
p
onse
and
reduce lea
r
ni
ng cycle [11].
5.
PATH PLANNING
Wh
en
t
h
e m
o
bile rob
o
t
is t
r
av
elin
g toward
its fin
a
l targ
et
in
unk
nown en
v
i
ron
m
en
t with
d
i
fferen
t
sha
p
es o
f
ob
st
acl
es i
n
di
f
f
ere
n
t
l
o
cat
i
o
ns. T
w
o t
y
pe
s o
f
pl
anni
ng
t
a
sks a
r
e p
r
o
r
pose
d
,
one
f
o
r
g
o
al
re
achi
n
g
and t
h
e ot
her i
s
fo
r o
b
st
acl
e
avoi
dance
.
Ea
ch t
a
sk i
s
per
f
o
rm
ed by
o
n
e
fuzzy
c
ont
r
o
l
l
e
r .T
heo
b
st
acl
e
sense
out
put
signal is use
d
t
o
activat
e one
of these t
a
sks as
s
h
own
in Figure
7.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Mo
bi
l
e
Ro
bot
N
a
vi
g
a
t
i
o
n
usi
n
g
F
u
zzy
Lo
gi
c
a
n
d
W
a
vel
et
N
e
t
w
ork (
M
ust
a
f
a
I.
Ha
mz
a
h
)
19
5
Fi
gu
re
5.
M
o
bi
l
e
R
o
b
o
t
C
o
nt
r
o
l
sy
st
em
di
agram
usi
ng
PS
O
-
WNN
Fi
gu
re 6.
PS
O base
d WN
N
T
r
ai
ni
ng
Al
go
ri
t
h
m
Fi
gu
re
7.
O
b
st
acl
e avoi
da
nce
an
d
goal
reac
h
f
u
zzy
co
nt
r
o
l
sy
st
em
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
19
1 – 20
0
19
6
5.
1. Go
al
Rea
c
hi
ng
Wh
en
th
em
o
b
i
le ro
bo
t is travelin
g
toward
its fin
a
l targ
et in u
nkn
own
env
i
ron
m
en
t with
n
o
ob
stacles
det
ect
ed
by
IR
sens
o
r
s.
The
Goal
R
eac
hi
n
g
t
a
sk i
s
ex
pect
ed t
o
al
i
g
n t
h
e
ro
b
o
t
’
s
hea
d
i
n
g
wi
t
h
t
h
e
di
re
ct
i
on
of
the goal,
goal angle is t
h
e
orie
ntation
differe
n
ce
betwee
n the robot axel a
n
d the
goal. T
h
e
robot hea
d
ing
angl
e
θ
can be
det
e
rm
i
n
ed by
en
code
r
.
Th
e
f
u
zzy co
n
t
ro
ller
h
a
s on
e inpu
t
. It is u
s
ed
to
im
p
l
e
m
en
t t
h
e
n
a
v
i
g
a
tio
n
b
e
t
w
een
t
w
o
p
o
i
n
t
s, in
itial p
o
i
n
t
and
go
al po
in
t. Th
is con
t
ro
ller
h
a
s on
ly o
n
e
inpu
t (
dif
f
) the
di
ffe
re
nce
bet
w
een
t
h
e
Azi
m
ut
h
(t
he
m
obi
l
e
r
o
bot
he
adi
n
g
angl
e
)
,
an
d
t
h
e
g
o
al
an
gl
e
(
g
)
as sh
own in Fi
g
u
r
e
(8
).
The
o
u
tp
u
t
s of
this c
o
ntroller a
r
e
rig
h
t
w
h
eel an
d le
ft w
h
eel a
n
g
u
l
a
r s
p
eed
s. Fi
g
u
re
(
9
)
sh
o
w
sf
uzzy
infere
nce
sy
stem
for g
o
al
reac
hin
g
c
ont
roller
.
Fi
gu
re 8.
G
o
al
ori
e
nt
at
i
on si
g
n
al
s descri
pt
i
o
n
Figu
re
9.
F
u
zz
y
infere
nce
sy
stem
for
g
o
al re
achin
g
Fuzzy c
ont
roll
er
Th
e inp
u
t
v
a
ri
ab
le h
a
s
5
fu
zzy sets: Zero
(Z), Sm
all Po
siti
v
e
(SP), Big
Po
sitiv
e (BP), Small Neg
a
tiv
e
(SN
)
,
an
d B
i
g
Negat
i
v
e
(B
N)
as s
h
o
w
n i
n
F
i
gu
re
10
. Eac
h
o
u
t
p
ut
vari
abl
e
has
f
o
ur
f
u
zz
y
set
s
:
R
e
t
u
r
n
Sl
o
w
(RS), Ret
u
rn F
a
st (RF),
Ahea
d Slow (AS
)
,
and
Ahead Fa
st (
A
F)
as show
n
i
n
Figu
r
e
11
and
Figur
e 12
. Th
e
cont
rol
l
e
r r
u
l
e
base
i
s
gi
ve
n
i
n
Ta
bl
e 1.
Figure 10.
θ
mem
ber ship functions
Fi
gu
re 1
1
.
M
e
m
b
er
shi
p
f
unc
t
i
on of
Left
w
h
eel
out
put
va
ri
abl
e
Fi
g
u
re
1
2
.
M
e
m
b
er shi
p
f
unc
t
i
on
of
R
i
ght
w
h
eel
o
u
t
p
ut
va
ri
abl
e
Table
1.
Fuzzy
rules for go
al
reach fuzzy c
o
ntroller
Input
Outp
ut
dif
f
W
R
W
Z
AF
AF
SP
AS
RS
BP
AF
RF
SN
RS
AS
BN
RF
AF
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Mo
bi
l
e
Ro
bot
N
a
vi
g
a
t
i
o
n
usi
n
g
F
u
zzy
Lo
gi
c
a
n
d
W
a
vel
et
N
e
t
w
ork (
M
ust
a
f
a
I.
Ha
mz
a
h
)
19
7
5.
2.
M
o
bi
l
e
R
o
b
o
t E
n
vi
r
o
n
ment
an
d Se
n
s
ors
Arr
a
n
g
m
e
nt
The m
obi
l
e
ro
bot
has t
w
o e
n
code
rs
fi
xe
d o
n
axel
s
o
f
l
e
ft
and
ri
g
h
t
w
h
ee
l
used t
o
det
e
r
m
i
n
e t
h
e cu
rre
nt
p
o
s
ition
o
f
m
o
b
ile ro
bo
t.
Th
e m
o
b
ile rob
o
t
u
s
e
n
i
n
e
in
frared
sen
s
o
r
s (four in th
e left, fou
r
in
t
h
e
righ
t
an
d on
e
i
n
fr
ont
) t
o
det
ect
t
h
e surr
ou
n
d
i
n
g o
b
st
acl
es and fi
nd t
h
e
di
st
ance fr
om
robot
an
d o
b
st
acl
e and fi
n
d
t
h
e
angl
e
of
o
b
st
acl
e an
d
m
obi
l
e
ro
bot
.
The
IR
se
ns
ors
are m
o
u
n
t
e
d a
s
:
~
are m
o
un
ted
i
n
th
e left
o
f
t
h
e ro
bo
t.
are m
ount
e
d
i
n
t
h
e
fr
ont
o
f
t
h
e r
o
b
o
t
.
~
are m
o
u
n
t
e
d i
n
t
h
e
ri
ght
of
t
h
e
ro
b
o
t
.
The active range of
distance
between
obst
acle and m
obile robot can be
determ
ined for each IR se
nsor is
assum
e
d t
o
be
bet
w
ee
n 0~
1
m
.The di
st
an
ce fo
r ni
ne se
nso
r
s a
r
e de
n
o
t
ed by
D
,D
,D
,D
,………,D
.
A
si
m
u
latio
n
m
e
t
h
od
b
y
u
s
e o
f
Matlab
and
an
ex
p
e
rim
e
n
t
in
u
nkn
own
en
v
i
ro
n
m
en
ts will be g
i
v
e
n .Assume th
e
distance t
o
front, left a
n
d ri
ght obstacles a
r
e:
=
; The
front di
stance.
=m
i
n
{
,
}; The l
e
ft distanc
e
.
=m
i
n
{
,
};
The right distance.
Fi
gu
re
(1
3
)
s
h
ows
t
h
e
di
st
ri
b
u
t
i
o
n
o
f
t
h
e
ni
n
e
IR
se
ns
ors
ar
ou
n
d
t
h
e
m
obi
l
e
r
o
b
o
t
bo
dy
o
n
sem
i
ci
rcul
ar
sha
p
e.
The se
ns
or
s ar
e m
ount
ed
o
n
t
h
e l
e
ft
a
n
d ri
g
h
t
pl
at
fo
rm
at
22.
5° eac
h
ot
h
e
r
.
Fi
gu
re 1
3
. Sen
s
orsl
ocat
i
o
n on
m
obi
l
e
ro
bot
5.
3. Obs
t
acl
e
Av
oi
d
a
nce
When t
h
em
obile robot is traveling toward it
s final
target in unknown envi
ro
nm
ent, it faces different
sha
p
es of obsta
c
les in diffe
rent loca
t
i
on. O
b
s
t
acl
es are det
ect
ed by
ni
ne
IR
sens
ors
whi
c
h
sen
d
i
n
f
o
rm
at
ion
o
f
distance bet
w
e
e
n obstacle and m
obile
ro
bo
t to
a fu
zzy lo
gic co
n
t
ro
ller.Fu
zzy logic control (FLC
) is adopted
t
o
co
nt
r
o
l
t
h
e
m
ovem
e
nt
s of
t
h
e ri
g
h
t
an
d l
e
ft
w
h
eel
s. T
h
e t
w
o
out
put
s
are t
h
e m
o
t
o
r
com
m
a
nds t
o
bot
h t
h
e
left an
righ
t mo
tors.
In
th
is
way, th
e m
o
b
ile
robo
t can avo
i
d
o
b
s
tacles au
t
o
no
m
o
u
s
ly.
Fi
gu
re
1
4
.
F
u
z
z
y
i
n
fere
nce
sy
st
em
for
O
b
st
a
c
l
e
avoi
da
nce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
19
1 – 20
0
19
8
The co
nt
r
o
l
st
r
u
ct
u
r
e gi
v
e
n i
n
Fi
gu
re (
1
4
)
i
s
base
d o
n
a t
a
sk f
o
r a
voi
di
n
g
obst
acl
es, t
h
e i
n
p
u
t
s
o
f
t
h
e
cont
rol system
are sensors
data and t
h
e outputs are th
e m
o
tor c
o
mm
ands. The fuzzy logi
c syste
m
has 3
inputs
and
2 outputs.
The three inputs are
the distances bet
w
een t
h
e robot and
t
h
e o
b
st
acl
e fr
o
m
9 i
n
frare
d s
e
ns
ors
and are expres
sed res
p
ectivel
y as S_L, S_F
and S_R. S_
F
i
s
t
h
e dat
a
fro
m
t
h
e
m
i
ddl
e sens
or, a
nd S
_
L
i
s
t
h
e
d
a
ta fro
m
th
e fo
ur sen
s
o
r
s on
th
e left side, and
S_
R is
ju
st lik
e S_
L.
A
.
F
u
zzy
S
e
t
s
For
S_
F i
n
p
u
t
,
2 m
e
m
b
ershi
p
f
u
nct
i
ons
(f
a
r
an
d
near
) ha
ve bee
n
defi
ne
d, a
nd
f
o
r S
_
L or
S_R
,
3
m
e
m
b
ershi
p
fu
nct
i
o
n
s
(
f
ar,
m
e
di
um
and
nea
r), a
n
d f
o
r
eve
r
y
o
u
t
p
ut
7 m
e
m
b
ershi
p
f
u
nct
i
ons
(R
eve
r
se
Fast
(Fast
)
, R
e
ver
s
e M
e
di
um
(-M
ed), R
e
verse
Sl
ow
(-Sl
o
w
)
, St
o
p
an
d F
o
rwa
r
d
Fast
(F
ast
)
, F
o
r
w
ar
d
M
e
di
um
(M
ed
), F
o
rwa
r
d Sl
ow
(Sl
o
w
)
)
.
S
_
F ca
n
be se
t
up
o
n
fo
u
r
l
e
vel
di
st
a
n
ces
r
e
spect
i
v
el
y
.
S
_
L an
d S
_
R
ca
n
be set
upon
five le
vel distances
. T
h
e
graphical re
presentatio
n of
me
m
b
er
sh
ip fun
c
tio
ns for
S_L and
S_
R
ar
e g
i
ven
by
Fi
g
u
r
es 15
, 16
, 17
.
Fi
gu
re
1
5
. M
e
m
b
er shi
p
f
unc
t
i
on
of
Fr
o
n
t
di
st
ance i
n
p
u
t
Fi
gu
re 1
6
.
M
e
m
b
er
shi
p
f
unc
t
i
on of
L
e
f
t
d
i
s
t
an
c
e
in
p
u
t
Fi
gu
re 1
7
.
M
e
m
b
er
shi
p
f
unc
t
i
on of
R
i
ght
di
st
ance i
n
p
u
t
The gra
p
hi
cal
rep
r
ese
n
t
a
t
i
o
n of
m
e
m
b
ers
h
i
p
f
unct
i
o
ns fo
r out
put
s ar
e
gi
ve
n by
Fi
gu
re 1
8
a
n
d
F
i
g
u
r
e
19
.
Fi
gu
re 1
8
.
M
e
m
b
er
shi
p
f
unc
t
i
on of
R
i
ght
w
h
eel
o
u
t
p
ut
va
ri
abl
e
Fi
gu
re 1
9
.
M
e
m
b
er
shi
p
f
unc
t
i
on of
R
i
ght
w
h
eel
o
u
t
p
ut
va
ri
abl
e
B. Fuz
z
y
Infer
e
nce Pr
ocess
The fuzzy
c
o
nt
rol rules
are gi
ven
in Table 2 and
Ta
ble
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
Mo
bi
l
e
Ro
bot
N
a
vi
g
a
t
i
o
n
usi
n
g
F
u
zzy
Lo
gi
c
a
n
d
W
a
vel
et
N
e
t
w
ork (
M
ust
a
f
a
I.
Ha
mz
a
h
)
19
9
Table 2.
F
u
zz
y
rules f
o
r S_
F
(
F
a
r )
I
nputs
Outputs
S_L S_R
WL
WR
Far
Far
Fast
Fast
Far
Med
i
u
m
Med
i
u
m
Fast
Far
Near
Slow
Fast
Med
i
u
m
Far
Fast
Med
i
u
m
Med
i
u
m
Med
i
u
m
Med
i
u
m
Med
i
u
m
Med
i
u
m
Near
-
Slo
w
Fast
Near
Far
Fast
Slow
Near
Med
i
u
m
Fast
-
Slo
w
Near
Near
-Fast
-Fast
Table 3.
Fuzz
y
rules for S_F
( Near
)
I
nputs
Outputs
S_L
S_R
WL
WR
Far
Far
-Fast
Fast
Far
Med
i
u
m
- Med
i
u
m
Fast
Far
Near
Slow
Med
i
u
m
Med
i
u
m
Far
Fast
- Med
i
u
m
Med
i
u
m
Med
i
u
m
-Fast
Fast
Med
i
u
m
Near
Slow
Med
i
u
m
Near
Far
Med
i
u
m
Slow
Near
Med
i
u
m
Med
i
u
m
Slow
Near
Near
-Fast
-Fast
6.
RESULTS
Matlab
\
si
m
u
lin
k
e
nv
iron
m
e
n
t
co
m
p
u
t
es th
e lo
catio
n
o
f
th
e
g
o
a
l
and
ob
stacles, sim
u
late t
h
e sen
s
o
r
y
data, find the
distance from
the obstacles and
feed th
is inform
at
io
n
to
th
e fu
zzy co
n
t
ro
ller th
at m
a
k
e
th
e
m
o
v
e
m
e
n
t
d
e
cisio
n
(sp
eed an
d orien
t
ation
)
and
u
s
ed
for t
e
stin
g
t
h
e ab
ility o
f
au
tono
mo
u
s
m
o
b
ile rob
o
t
fo
r
goal
reac
hi
n
g
wi
t
h
st
at
i
c
obst
acl
e av
oi
da
nce
i
n
t
h
e
way
toward
t
h
e goal. Two fuzzy logic controllers are us
e
d
fo
r pat
h
pl
a
n
ni
ng t
o
na
vi
g
a
t
e
am
ong st
at
i
c
obst
acl
es;
one c
ont
rol
l
e
r i
s
use
d
fo
r g
o
al
reac
hi
n
g
an
d anot
h
e
r fo
r
obst
acl
e av
oi
d
a
nc de
pe
ndi
ng
on se
nsi
n
g i
n
f
o
rm
at
i
on fr
om
un
k
n
o
w
n en
vi
ro
nm
ent
.
The
navi
gat
i
on
fr
o
m
st
art
poi
nt to end
(t
arget) poi
n
t. T
h
e m
obile robot stops
when
it
arrives
the
g
oal poi
n
t withi
n
0.03 m
accuracy of
di
st
ance
bet
w
e
e
n t
h
e ce
nt
er
o
f
t
h
e
m
obi
l
e
r
o
bot
(
,
) and the targ
et
po
in
t
(
,
).
Fig
u
re
(
2
0)
sho
w
s
the
n
a
v
i
g
a
tio
n of
m
o
b
ile ro
bo
t fro
m
startin
g
po
in
t
(0,0) to
ward
targ
et
po
int (12
,
16
) and
t
h
e m
o
b
ile ro
bo
t can
m
ove am
ong
t
h
e
ob
st
acl
es wi
t
h
o
u
t
hi
t
.
Fi
gu
re
2
0
.
A
u
t
o
n
o
m
ous m
obi
l
e
ro
b
o
t
na
vi
ga
t
i
on
In t
h
e Fi
gu
re
(
2
1
)
a
not
her
g
o
a
l
poi
nt
i
s
sel
e
ct
ed an
d al
s
o
t
h
e m
obi
l
e
ro
b
o
t
can
m
ove a
m
ong t
h
e
o
b
st
acl
es
with
ou
t
h
it from
start p
o
i
n
t
(0,0) to go
al
p
o
i
nt (0,16
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
4
:
19
1 – 20
0
20
0
Fi
gu
re
2
1
.
A
u
t
o
n
o
m
ous m
obi
l
e
ro
b
o
t
na
vi
ga
t
i
on
7.
CO
NCL
USI
O
N
In t
h
i
s
pape
r,
an effi
ci
ent
aut
o
nom
ous
m
obi
l
e
robot
navi
gat
i
on sc
h
e
m
e
usi
ng f
u
z
z
y
l
ogi
c an
d
wavel
e
t
net
w
o
r
k i
s
desi
gne
d
and i
m
pl
em
ented. T
h
e m
e
t
h
o
d
i
s
t
e
st
ed i
n
u
n
k
o
w
n e
nvi
ro
n
m
ent
and gi
ves
go
od
p
e
rform
a
n
ce
for n
a
v
i
g
a
tio
n
toward
t
h
e g
o
a
l with
ou
t h
ittin
g
an
y o
b
stacle.
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NC
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z
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A. Sanchez,
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