Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
13
,
No.
1
,
Jan
uar
y
201
9
,
pp.
109
~
115
IS
S
N: 25
02
-
4752, DO
I: 10
.11
591/ijeecs
.v1
3
.i
1
.pp
109
-
115
109
Journ
al h
om
e
page
:
http:
//
ia
es
core.c
om/j
ourn
als/i
ndex.
ph
p/ij
eecs
Sp
ee
d an
d di
re
ction o
f a
n obst
ac
l
e using v
irtual wi
nd
ow
Hj. M
.A
.
H
j.
Mansor
Facul
t
y
of Electr
ic
a
l
Eng
ineeri
ng
,
MA
RA Unive
r
sit
y
of Te
chnol
o
g
y
40450
Shah
Alam,
Mal
a
y
s
ia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
A
ug
2
4
, 201
8
Re
vised Oct
15
, 2
018
Accepte
d Oct
28
, 201
8
A
virt
ual
windo
w
is
used
to
det
ermine
the
direct
i
on
and
spee
d
of
a
uniform
l
y
m
oving
obstac
l
e.
Two
in
te
rsec
ti
ons
with
the
virt
ual
window
at
differen
t
loc
a
ti
on
are
use
d
to
calc
ul
at
e
t
he
re
la
t
ive
pat
h
and
spe
ed
of
t
he
obsta
cle
.
Two
sim
ula
ti
ons
were
per
form
ed
using
Exc
el
2010.
The
firs
t
sim
ula
ti
on
sim
ula
te
s
a
pra
ct
i
ca
l
running
o
f
a
uniforml
y
m
oving
obstac
l
e,
while
the
sec
ond
has
th
e
obstac
l
e
m
oving
at
a
ver
y
high
s
pee
d.
The
result
show
s
tha
t
the
s
y
st
em
was
abl
e
to
d
et
ermine
the
re
la
t
ive
spe
e
d
and
pat
h
of
the
u
niforml
y
m
oving
obstac
l
e
accurately
.
Ke
yw
or
ds:
R
el
at
ive p
at
h
e
qu
at
io
n
R
el
at
ive sp
ee
d determ
inati
on
U
ni
form
l
y
m
ov
in
g obst
acl
e
V
irtual
wind
ow
Copyright
©
201
9
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed.
Corres
pond
in
g
Aut
h
or
:
Hj. M.
A
.
H
j
.
Ma
ns
or
,
Faculty
of Elec
tric
al
Engineer
ing
,
MARA
U
niv
er
sit
y of
Tec
hnol
og
y,
40450 S
hah A
l
a
m
, Mal
ay
sia
.
Em
a
il
:
pak
nga
h60@gm
ai
l.com
1.
INTROD
U
CTION
In
rece
nt
ye
ar
s
m
any
resear
ch
works
are
directed
to
t
he
so
luti
on
of
obsta
cl
e
av
oid
a
nce
in
pat
h
plan
ning.
T
his
is
du
e
to
the
i
nterest
in
aut
onom
ou
s
veh
ic
l
es,
su
c
h
as
D
A
RPA
U
rb
a
n
C
halle
ng
e
rs
[
1]
and
by
autom
otive com
pan
ie
s su
ch
a
s Merce
des
Be
nz,
A
ud
i,
Volv
o
a
nd Go
og
le
[
2
-
4].
An
aut
onom
ous
car
[5
]
is
a
ve
hicle
that
do
no
t
nee
d
hu
m
an
c
on
tr
ol
a
nd
it
basical
ly
dr
i
ve
s
it
sel
f.
It
is
al
so
call
ed
dri
ve
rless car
or
se
lf
-
dri
vi
ng
ca
r.
Au
t
onom
ou
s c
ars
util
ise
v
ari
ou
s
kind
of
tec
hn
i
qu
e
s to
se
nse
their
env
i
ronm
ent,
li
ke
rad
a
r,
la
ser
li
gh
t,
GPS,
od
om
et
er,
and
c
om
pu
te
r
visio
n.
Adva
nced
c
on
t
ro
l
syst
em
s
interp
ret
sens
or
y i
nfor
m
a
ti
on
to
ide
ntif
y appr
opriat
e na
vig
at
io
n paths
, as wel
l as
obs
ta
cl
es and r
el
e
van
t
sig
nag
e
[6
-
7].
This
w
ork
c
oncern
s
m
ob
il
e
r
obot,
bu
t
the
te
chn
i
qu
e
a
ppli
ed
can
be
us
e
d
i
n
aut
onom
ou
s
cars
as
well
.
Wh
e
n
a
car
or
a
m
ob
il
e
ro
bot
m
ov
es
in
a
n
unkn
own
a
nd
c
hangin
g
e
nvir
onm
ent,
the
m
ain
ai
m
is
to
get
to
its
go
al
with
ou
t
a
ny
colli
sion.
I
f
the
pat
h
ta
ke
n
happe
ns
to
be
op
ti
m
al
then
that
is
a
bonus.
Ob
sta
cl
e
a
vo
i
da
nce
is
the
basic
re
quirem
ent
of
autonom
ou
s
r
obot
nav
igati
on.
The
r
obot
nee
ds
to
ac
qu
ire
inf
or
m
at
ion
ab
ou
t
i
t
s
su
r
rou
nd
i
ngs
a
long
with
any
sta
ti
on
ary
a
nd
m
ov
ing
obsta
c
le
s
pr
ese
nt
so
that
a
na
vig
at
ion
syst
e
m
wit
h
pat
h
plan
ning
al
gor
it
h
m
is
able
t
o
guide
t
he
r
obot
to
the
ta
rg
et
wit
hout
c
olli
din
g
with
ob
sta
cl
es
with
in
the
env
i
ronm
ent.
Ther
e
a
re
m
any
path
pla
nn
i
ng
a
lg
or
it
hm
s
with
obsta
cl
e
avo
i
dan
ce
t
hat
has
bee
n
propose
d;
su
c
h
as
po
te
ntial
fiel
d
[8
-
10]
,
visibi
li
ty
gr
aph
s
[
11
-
12]
,
gri
d
m
et
hods
[
13]
,
a
nd
virt
ual
wi
ndow
[
14]
.
O
bs
ta
cl
e
avo
i
dan
ce
rese
arch
has
tra
diti
on
al
ly
bee
n
ha
nd
le
d
by
t
wo
t
echn
i
qu
e
s
[
15]
:
the
delibe
ra
ti
ve
ap
proac
h,
usual
ly
consi
sti
ng
of a
m
ot
ion
plan
ner, and t
he react
ive a
ppr
oach,
ba
sed o
n
the
ins
ta
ntaneous
sensed i
nfor
m
at
ion
.
The
re
searc
h
work
t
hat
is
r
eported
here
is
base
d
on
re
act
ive
ap
proac
h
util
isi
ng
virt
ual
wind
ow.
This
is
an
e
xte
ns
io
n
a
nd
im
pr
o
vem
ent
of
a
pr
e
vious
wor
k
descr
i
bed
in
[
16
]
.
U
nlike
[
17
-
18]
,
the
te
ch
nique
i
m
ple
m
ented
can
be
us
e
d
to
determ
ine
the
path
a
nd
sp
ee
d
of
a
m
ov
in
g
obst
acl
e.
In
this
work,
the
e
nv
ir
onm
e
nt
is
ass
um
ed
to
ha
ve
only
a
sin
gle
obsta
cl
e
m
ov
ing
in
a
strai
ght
li
ne
with
c
onsta
nt
sp
ee
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
13
, N
o.
1
,
Ja
nu
a
ry 20
19
:
109
–
115
110
The
te
ch
nique
is
us
ed
to
tra
ck
the
m
ov
em
ent
of
the
obs
ta
cl
e
by
cal
culat
ing
it
s
path
and
sp
ee
d
fro
m
two
cro
ssi
ngs
with
a
virtu
al
wind
ow.
This
vi
rtu
al
window
is
ge
ner
at
e
d
from
a
dev
ic
e
that
is
locat
ed
ei
ther
on
a
sta
ti
on
ary or
m
ov
i
ng
m
ob
il
e
r
obot.
When
t
he
directi
on
a
nd
sp
ee
d
of
the obstac
le
is
known
,
ap
pro
pr
ia
t
e
act
ion
can
be
ta
ke
n t
o av
oid
c
olli
sio
n.
Sp
ee
d
a
nd
pa
th of t
he ob
sta
cl
e are take
n
a
s
b
ei
ng
relat
ive
to the m
ob
il
e r
obot.
2.
BRIEF
DISC
US
SI
ON OF
THE
V
I
RTU
AL WI
N
DOW
A
virtu
al
wind
ow
bas
ic
al
ly
act
s
as
a
se
ns
or
an
d
is
a
rectangula
r
pla
ne
that
is
pr
oj
ect
e
d
a
head
of
a
m
ob
il
e
ro
bo
t
f
or
the
pur
po
s
e
of
detect
in
g
obsta
cl
e.
Fig
ur
e
1
shows
a
m
ob
il
e
robo
t
hav
i
ng
a
virtu
al
wi
nd
ow
1
m
ahead
wi
th
a
s
quare
s
hap
e
(
1
m
by
1
m
)
ha
ving
a
pi
xel
res
olut
ion
o
f
10×
10.
De
pe
nd
i
ng
on
th
e
requirem
ents
of
the
w
ork,
the
sh
ape
ca
n
be
rectan
gu
la
r,
an
d
it
s
width
a
nd
heig
ht,
an
d
pi
xel
res
olu
ti
on
of
t
he
virtu
al
wind
ow can be
set
to o
ther val
ues
ot
he
r
tha
n
t
hat s
hown in Fi
gure
1.
In
a
visio
n
sy
stem
,
an
i
m
age
of
t
he
vie
w
fo
rw
a
r
d
of
the
m
ob
il
e
rob
ot
is
captur
e
d.
I
nt
ensive
a
nd
com
plex
i
m
age
processin
g
w
il
l
hav
e
to
be
a
pp
li
ed
i
n
orde
r
to
retrieve
t
he
releva
nt
inf
orm
at
ion
.
This
is
du
e
t
o
the
fact
that
t
he
captu
red
in
form
ation
co
ns
is
t
of
t
he
im
age
of
t
he
plane
of
interest
an
d
al
s
o
im
age
before
an
d
beyo
nd
th
at
plane,
al
beit
out
of
f
oc
us
(
3D
view
to
2D
im
age).
O
n
the
ot
her
ha
nd,
the
virtu
al
wi
ndow
will
return
only
the
i
m
age o
f
the
pl
ane
of interest
.
M
o
b
i
l
e
R
o
b
o
t
V
i
r
t
u
a
l
w
i
n
d
o
w
1
m
e
t
r
e
(
1
0
p
i
x
e
l
s
)
1
m
e
t
r
e
(
1
0
p
i
x
e
l
s
)
1
m
e
t
r
e
Figure
1. A
d
ia
gr
am
sh
owin
g a m
ob
il
e robo
t
with it
s
c
orres
p
on
ding
gen
e
r
at
ed
vi
rtual
window
This
virt
ual
w
indow
has
a
s
i
m
i
la
r
char
act
erist
ic
as
a
ca
m
era
in
that
it
has
a
disp
la
y
reso
luti
on.
This
disp
la
y
re
so
luti
on
ca
n
be
set
to
a
ny
va
lue
de
pe
nd
i
ng
on
the
nee
ds
of
the
w
ork
by
changin
g
t
he
a
m
ou
nt
of
data
th
at
is
read
from
the
plane
of
intere
st.
The
siz
e
of
the
vi
rtual
wi
ndow,
i.e.
t
he
le
ng
t
h
a
nd
wi
dth,
ca
n
al
so
be
set
to
any
value
that
is
req
uire
d.
I
deall
y,
the
siz
e
of
the
virt
ua
l
window
is
usual
ly
ren
de
re
d
a
litt
le
bigger
tha
n
the
size of
the r
ob
ot.
O
bv
i
ou
s
ly
this all
ow
s for
a b
igg
e
r
f
orwa
rd
im
age to
b
e
m
on
it
or
ed
an
d t
hu
s a
bigger
sa
fety
n
et
.
A
fu
ll
and c
om
plete
d
isc
us
sion
of
the
po
s
sible im
ple
m
e
ntati
on
of
the
vi
rtual w
in
dow ca
n
be
read f
ro
m
[
13]
.
3.
SIMULATI
O
N
As
was
descr
i
bed
in
[13],
a
la
ser
range
fi
nder
c
a
n
be
use
d
to
ge
ner
at
e
the
virt
ual
window.
In
this
arr
a
ng
em
ent,
the
set
-
up
f
or
the
virt
u
al
window
is
as
sho
wn
in
Fig
ur
e
2,
with
the
la
ser
range
fin
de
r
be
ing
on
the
m
ob
il
e
rob
ot.
The
ra
nge
of
the
virtu
al
window
is
the
range
w
her
e
a
ny
intersect
ion
or
colli
si
on
w
it
h
the
ob
sta
cl
e
is
co
nsi
der
e
d.
O
utsid
e
of
this
ra
nge,
any
occurri
ng
co
ll
isi
on
s
are
i
gnored
.
D
is
th
e
m
ini
m
u
m
dis
ta
nce
of
t
he
virtu
al
window
from
t
he
m
ob
il
e
r
obot,
d
is
th
e
wi
dth
of
the
ra
nge,
t
1
a
nd
t2
a
re
the
tim
es
that
li
ght
ta
kes
to
tra
vel
fr
om
the
m
o
bile
ro
bot
to
a
po
int
on
the
vw
1
a
nd
vw2,
res
pecti
vely
,
and
R
is
the
pix
el
reso
l
ution o
f
t
he
v
irt
ual w
i
ndow.
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Sp
ee
d a
nd d
ire
ct
ion
of an o
bst
acle u
si
ng virt
ua
l w
i
ndow
(
H
j. M.A
.
Hj.
M
a
n
s
o
r
)
111
M
o
b
i
l
e
R
o
b
o
t
D
m
R
a
n
g
e
o
f
t
h
e
v
i
r
t
u
a
l
w
i
n
d
o
w
d
m
t
1
t
2
R
,
p
i
x
e
l
r
e
s
o
l
u
t
i
o
n
v
w
1
v
w
2
Figure
2. A
d
ia
gr
am
sh
owin
g a m
ob
il
e robo
t
with it
s
virtu
al
window
ra
ng
e
and g
e
ne
ral p
a
ram
et
ers
Fo
r
t
his
w
ork,
it
is
assu
m
ed
t
hat
the
widt
h
of
the
ra
ng
e
,
or
d,
is
1
cm
.
The
m
ini
m
u
m
dist
ance
to
the
virtu
al
window
, D
, is set at
1 m
. Th
ese value
s ar
e set ar
bitra
rily
, i.e.
the val
ues
ca
n
be
c
ha
ng
e
d
to
ot
her
va
lues
su
bject
t
o
the
a
bili
ty
o
f
the
las
er r
a
nge
fin
der
to acc
urat
el
y m
easur
e the
ti
m
e d
iffe
ren
ce
s
.
Assum
ing
the
sp
ee
d
of
li
gh
t
in
ai
r
to
be
2
×
108
m
s
-
1,
the
n
the
tim
e
ta
ken
for
a
sin
gle
la
ser
beam
to
travel
to
a
poi
nt
on
the
pla
ne
of
inte
rest,
in
this
insta
nce
1
m
fr
om
the
m
ob
il
e
robo
t,
and
bac
k
is
about
10
ηsec
s.
T
he
ti
m
e taken
to
t
rav
e
l a f
ur
the
r 1 c
m
(
or
a total
of 2
.
02 m
)
is 1
0.1 ηsecs
.
Fo
r
a
total
pi
xe
l
count
of
100,
i.e.
the
res
olut
ion
of
th
e
vi
rtual
wi
ndow
be
ing
10
×
10
pix
e
ls,
the
total
tim
e
ta
ken
will
be
betwee
n
1
µsecs
and
1.01
µsecs.
For
co
m
par
ison
,
f
or
a
p
ixel
co
un
t
of
10,
000
(
100×
100)
,
the total
tim
e i
s 0
.
1
m
secs an
d 0.101 m
secs, r
es
pecti
vely
. If
the
virt
ual w
i
ndow is c
onsid
ered t
o be a
square
of
1
m
by
1
m
as
in
[13],
a
pi
xel
reso
l
ution
o
f
10×1
0
will
sti
l
l
detect
an
inters
ect
ion
or
colli
s
ion
w
it
h
an
obsta
cl
e
as
sm
a
ll
as
100
m
m
(o
r
10
c
m
)
in
siz
e,
ei
t
her
widt
h
or
he
igh
t.
C
urren
t
pr
act
ic
al
m
ob
ile
rob
ots
are
usual
ly
m
uch
big
ge
r
th
an
10
0
m
m
in
siz
es
[19
-
21]
.
Much
sm
al
le
r
m
ob
il
e
ro
bo
ts
can
be
c
onside
red,
howe
ve
r
this
will
hav
e
s
om
e i
m
p
act
o
n t
he
ti
m
e
n
ee
ded to
proc
ess the i
nfor
m
at
ion
.
If
the
re
ha
pp
e
ns
to
be
an
ob
st
acl
e
at
the
plane
of
interest
within
the
ra
nge,
the
beam
that
i
s
ref
le
ct
ed
within
t
he
s
pec
ifie
d
ra
nge
of
t
i
m
e
will
be
co
ns
ide
red.
Ou
tsi
de
of
t
his
ra
ng
e
of
tim
e
per
io
d,
it
is
ass
um
e
d
that
no co
ll
isi
on
o
c
cur
s
w
it
h t
he o
bs
ta
cl
e.
Since
t
her
e
is
a
ra
ng
e
of
ti
m
e
that
the
obsta
cl
e
will
be
co
ns
i
der
e
d
as
inte
rs
ect
ing
t
he
virtua
l
wind
ow
,
there
is
a
n
ass
ociat
ed
m
axi
m
um
sp
eed
that
the
obsta
cl
e
ca
n
tra
vel
that
w
il
l
sti
l
l
al
low
the
syst
em
to
hav
e
th
e
two
interse
ct
io
n
s
with
the
virt
ual
windows
.
Othe
rw
ise
,
on
l
y
on
e
intersect
ion
will
be
det
ect
ed,
an
d
that
sing
le
inf
or
m
at
ion
do
not
al
low
for
the
syst
em
t
o
cal
culat
e
the
path
a
nd
s
pe
ed
of
the
obsta
cl
e.
This
m
a
xim
u
m
relat
ive spee
d
dep
e
nds
on
the
p
a
ram
et
ers
sh
own
i
n
Fi
gure
2
a
nd is s
how
n i
n
the
(
1)
bel
ow:
v
=
cd
2R
(
2D
+
d
)
(1)
wh
e
re
c
is
the
sp
eed
of
li
ght
in
ai
r.
Taki
ng
the
values
s
ta
te
d
above,
v
=
4
,
975
.
124
m
/s
.
This
is
equ
i
valent
to
17,91
0.45km
/hr.
As
a
com
par
iso
n,
if
R
is
i
ncr
ease
d
to
10
,000
(
100×
100
pix
el
s),
the
s
pe
ed
is
179.1
km
/hr.
T
hese tim
es are in
cl
us
ive
of
processin
g
ti
m
e.
Table
1
s
how
s
the
relat
ionship
betwe
en
the
relat
ive
sp
ee
d
of
t
he
ob
sta
cl
e
a
nd
it
s
distance
travell
ed f
or
:
t
T
=
t
1
+
t
2
(2)
wh
e
re
tT
is
the
total
scan
ni
ng
ti
m
e
of
th
e
virtu
al
wi
ndow,
with
t1
,
a
t
first
intersec
ti
on
an
d
the
s
econd
intersect
io
n
at
t2.
In
this
sit
ua
ti
on
,
only
the
sp
eed
of
the
obsta
cl
e
is
var
ie
d,
w
hile
the
rest
of
the
par
a
m
et
er
s
rem
ai
n
con
sta
nt
.
Table
1
.
Re
la
ti
on
s
hi
ps
betwee
n
Re
la
ti
ve
S
pe
ed
of
O
bs
ta
cl
e
and
Dista
nce
be
tween t
he
tw
o
I
ntersecti
ons
(secon
d
)
Sp
eed
r
elativ
e
(
m
/s)
Distan
ce
tr
av
el
(c
m
)
1
0
.00
0
0
0
1
0
1
4
0
0
0
.0
0
0
0
.80
4
0
0
2
0
.00
0
0
0
1
4
9
7
5
.1
2
4
1
.00
0
0
0
5
0
0
0
.0
0
0
1
.00
5
0
0
5
2
0
0
.0
0
0
1
.04
5
2
0
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
13
, N
o.
1
,
Ja
nu
a
ry 20
19
:
109
–
115
112
As
ca
n
be
see
n,
the
li
m
it
of
the
relat
ive
s
peed
is
4975.
124m
/s,
as
cal
culat
ed,
wh
e
re
the
distance
travell
ed
betw
een
the
tw
o
int
ersecti
ons
is
1
c
m
.
High
e
r
rel
at
ive
sp
ee
d
will
no
t
al
low
t
he
syst
e
m
eno
ug
h
tim
e
to
proce
ss
the
inf
or
m
at
ion
since
the
ra
ng
e
of
t
he
virtu
al
w
in
dow
was
s
et
at
1
cm
apar
t
Fig
ure
2
.
O
f
co
ur
se
,
this can
b
e
r
ect
ifie
d by incr
ea
sing t
he ran
ge.
Si
m
ulati
on
s
ar
e
per
f
or
m
ed
usi
ng
E
xcel
2010
to
cal
culat
e
the
distance
travell
ed
by
a
un
if
or
m
ly
m
ov
ing
ob
sta
c
le
in
the
ge
ne
r
al
directi
on
of
the
m
ob
il
e
rob
ot.
T
he
s
peed
and
pat
h
is
ta
ke
n
as
relat
ive
to
th
e
m
ov
ing
m
ob
il
e
robo
t.
The
ti
m
e
per
io
d
of
the
cal
culat
ion
is
ta
ken
to
be
the
total
tim
e
that
the
syst
e
m
need
s
t
o
scan
the
w
ho
l
e
virtu
al
w
in
dow
at
the
t
wo
intersect
io
ns
F
ig
ure
3
.
This
i
s
a
valid
ass
um
pt
ion
since
t
he
tw
o
intersect
io
ns
ta
ke
rou
gh
ly
t
he
su
m
of
the
tw
o
sca
nnin
g
ti
m
e.
It
is
sta
te
d
a
s
bei
ng
r
oughl
y
beca
us
e,
the
exact
tim
e d
epends a
t wh
ic
h pixel t
he
inte
rsecti
on
occurs.
O
b
s
t
a
c
l
e
O
b
s
t
a
c
l
e
S
e
c
o
n
d
i
n
t
e
r
s
e
c
t
i
o
n
b
e
t
w
e
e
n
v
i
r
t
u
a
l
w
i
n
d
o
w
a
n
d
o
b
s
t
a
c
l
e
T
i
m
e
t
o
s
c
a
n
v
i
r
t
u
a
l
w
i
n
d
o
w
,
T
v
w
2
=
1
µ
s
e
c
F
i
r
s
t
i
n
t
e
r
s
e
c
t
i
o
n
b
e
t
w
e
e
n
v
i
r
t
u
a
l
w
i
n
d
o
w
a
n
d
o
b
s
t
a
c
l
e
T
i
m
e
t
o
s
c
a
n
v
i
r
t
u
a
l
w
i
n
d
o
w
,
T
v
w
1
=
1
.
0
1
µ
s
e
c
1
c
m
T
o
t
a
l
t
i
m
e
t
o
s
c
a
n
,
T
v
w
=
T
v
w
1
+
T
v
w
2
=
2
.
0
1
µ
s
e
c
v
m
/
s
Figure
3
.
A
f
ig
ur
e
sho
wing th
e p
a
ram
et
e
rs
con
si
der
e
d
i
n
th
e sim
ulatio
n
4.
RESU
LT
S
AND DI
SCUS
S
ION
Figure
4
s
hows
a
m
od
el
dem
on
strat
in
g
the
si
m
ulati
o
n
that
was
pe
rfor
m
ed
for
this
researc
h.
The
obsta
cl
e
is
m
ov
ing
t
owar
ds
t
he
gen
e
ral
directi
on
of
th
e
m
ob
il
e
robo
t
.
T
he
relat
ive
s
peed
of
t
he
m
ov
i
ng
ob
sta
cl
e
is
v
m
/s,
and
the
first
intersect
i
on
with
the
vi
r
tual
wind
ow
was
ass
um
ed
to
be
at
co
ordi
nate
(98, 1
01). Ti
m
e p
e
rio
d
f
or the
calc
ulati
on of
the sim
ulati
on
starts f
ro
m
that m
o
m
ent o
n.
y
(
c
m
)
x
(
c
m
)
1
m
1
0
1
1
0
0
v
m
/
s
O
b
s
t
a
c
l
e
Θ
=
4
5
°
F
i
r
s
t
i
n
t
e
r
s
e
c
t
a
t
(
9
8
,
1
0
1
)
t
1
=
0
0
M
o
b
i
l
e
r
o
b
o
t
v
t
c
o
s
(
ϑ
)
v
t
s
i
n
(
ϑ
)
y
=
x
+
3
S
t
a
r
t
i
n
g
c
o
o
r
d
i
n
a
t
e
(
1
2
0
,
1
2
3
)
Fig
ure
4
.
A
m
od
el
r
e
pr
e
sentin
g
the
sim
ulat
io
n
set
ti
ng that
w
as co
ns
ide
re
d
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Sp
ee
d a
nd d
ire
ct
ion
of an o
bst
acle u
si
ng virt
ua
l w
i
ndow
(
H
j. M.A
.
Hj.
M
a
n
s
o
r
)
113
Fo
r
e
ver
y
ti
m
e
per
io
d,
t
he
tim
e
it
ta
kes
for
the
syst
em
to
sweep
or
scan
the
virtua
l
window,
it
s
locat
ion
in
the
x
and
y
directi
on
was
cal
culat
ed.
S
how
n
an
d
disc
us
se
d
in
this
r
eport
are
two
resu
lt
s
ob
ta
ine
d from
the sim
ulati
on
. Tab
le
2
a
da
n 2b
sho
ws
t
wo s
a
m
ples o
f
the
re
su
lt
of the
sim
ulati
on
.
Table
2a
.
A
T
a
ble S
howing
t
he
Re
su
lt
s
f
r
om
the
Sim
ulati
on
with
Tim
e Perio
d
at
2.01 µ
sec
s
No
t (
seco
n
d
)
T
vw
(
seco
n
d
)
x
(
c
m
)
y
(
c
m
)
1
0
.00
0
0
0
0
0
0
0
.00
0
0
0
1
0
1
0
9
8
.00
0
0
0
1
0
1
.0000
0
2
0
.00
0
0
0
2
0
1
0
.00
0
0
0
1
0
1
0
9
7
.96
4
4
7
1
0
0
.9644
7
3
0
.00
0
0
0
4
0
2
0
.00
0
0
0
1
0
0
9
9
7
.92
8
9
4
1
0
0
.9289
4
Table
2b
.
A
Ta
ble S
howing
t
he
Re
su
lt
s
f
r
om
the
Sim
ulati
on
with
Tim
e Perio
d
at
0.9 µse
cs
No
t (
seco
n
d
)
T
vw
(
seco
n
d
)
x
(
c
m
)
y
(
c
m
)
1
0
.00
0
0
0
0
0
0
0
.00
0
0
0
1
0
1
0
9
8
.00
0
0
0
1
0
1
.0000
0
2
0
.00
0
0
0
0
9
0
0
.00
0
0
0
1
0
1
0
9
7
.98
4
0
9
1
0
0
.9840
9
3
0
.00
0
0
0
1
8
0
0
.00
0
0
0
1
0
1
0
9
7
.96
8
1
8
1
0
0
.9681
8
The
la
st
tw
o
colum
ns
of
T
able
2
gi
ve
t
he
x
-
an
d
y
-
di
sta
nce
of
the
obsta
cl
e
f
rom
the
ori
gi
n,
resp
ect
ively
.
T
he
relat
ive
s
pe
ed
is
assum
ed
to
be
25
0
m
/
s,
an
gle
θ
at
45
,
s
peed
of
li
gh
t
at
2
×
108
m
/s,
and p
i
xel r
es
ol
ution o
f 1
0×10
. T
he
siz
e
of th
e v
irt
ual w
i
ndow is set at
1×
1m
.
Row
1
an
d
co
lum
n
Tvw
of
Table
2a
s
ho
ws
t
hat
the
fir
st
scan
tim
e
of
the
virtu
al
w
indow
ta
kes
0.000
001010
s
ecs.
That
is
a
lso
the
fir
st
intersect
io
n
of
the
ob
sta
cl
e
with
the
virtua
l
window,
th
us
t=
0.
Af
te
r
0.000
00201
sec
onds
la
te
r,
the
seco
nd
intersect
io
n
with
the
virt
ua
l
window
occ
ur
s
.
As
can
be
seen,
the
ch
oice
of
t
he
tim
e
per
iod
is
log
ic
al
as
there
is
enou
gh
t
i
m
e
fo
r
the
firs
t
scan
to
finis
h
befor
e
sta
rtin
g
with
the
seco
nd
sca
n.
I
f
the
tim
e
p
erio
d
was
le
ss,
s
ay
0.
000000
9
second
as
in
Table
2b,
it
can
be
seen
that
th
e
scan
of
t
he
virtu
al
wind
ow
will
not
ha
ve
c
om
ple
te
d
w
hen
the
sec
ond
tim
e
per
io
d
ca
lc
ulati
on
is
st
arte
d.
Eve
n
th
ough
t
he
cal
culat
ion
c
an
be
don
e
i
n
s
i
m
ulati
on
,
in
pract
ic
e
the
first
scan
is
not
ye
t
com
plete
d
an
d
thu
s
will
p
r
oduce
a
n
il
log
ic
al
res
ul
t. Th
e s
ugge
ste
d
ti
m
e p
eriod
is t
he
m
ini
m
u
m
tim
e p
erio
d.
Fr
om
Table
2a
and
dep
ic
te
d
in
Figure
5,
the
relat
ive
pat
h
an
d
sp
ee
d
of
the
obsta
cl
e
can
the
n
b
e
cal
culat
ed.
Ta
ki
ng
the t
wo
c
oor
din
at
es,
(
98, 101
)
an
d
(
97.
9644
7,
100964
47)
, th
e
gr
a
dient
is found
to
be 1 and
the
y
-
inte
rsect
is
3.
This
gi
ve
s
the
pat
h
e
quat
ion
as
y
=
x
+
3
.
F
or
relat
ive
sp
ee
d,
the
ti
m
e
it
tak
es
f
or
the
ob
sta
cl
e
t
o
tra
vel
f
ro
m
point
(
98)
t
o
po
i
nt
(
97.96
447)
in
the
x
directi
on,
a
nd
from
po
int
(10
1)
to
po
i
nt
(10
0.964
47)
in
the
y
directi
on
is
0.
0000
0201
sec
each.
Bot
h
will
giv
e
a
sp
eed
of
176.7
66
2
m
/s.
The
res
ultant
of
the
t
wo
c
ompone
nts w
il
l
gi
ve
a
relat
ive spee
d
of
24
9.985
m
/s
at
an
an
gle
of
45°.
This
r
esult
com
par
es
ve
ry
well
w
it
h
t
he p
aram
et
ers
us
ed
in
the
sim
ulatio
n.
Table
3
an
d
Fi
gure
6
s
hows
a
second
sim
ul
at
ion
pe
rfor
m
ed
but
with
a
r
el
at
ive
sp
eed
of
5000
m
/
s
towa
rd
s
the
di
recti
on
of
the
m
ob
il
e
ro
bot.
Discusse
d
ea
rl
ie
r
that
the
m
axim
u
m
sp
e
ed
acce
ptable
in
order
to
sti
ll
be
able
to
detect
the
tw
o
inter
sect
ions
is
4975.
124
m
/s,
this
si
m
ulati
on
will
fail
in
it
s
at
tem
pt
t
o
get
a
valid
relat
ive
pa
th
an
d
s
pee
d
of
t
he
obsta
cl
e.
Eve
n
th
ough
t
he
ti
m
e
per
iod
is
m
or
e
tha
n
t
he
tim
e
ta
ken
to
sca
n
the
vi
rtual
wi
ndow,
the
re
is
only
on
e
valid
r
esult.
The
sec
ond
re
su
lt
can
not
be
ap
plied
as
it
exceeds
the
ran
ge
that was
set ear
li
er,
1 cm
.
V
i
r
t
u
a
l
w
i
n
d
o
w
S
e
c
o
n
d
i
n
t
e
r
s
e
c
t
i
o
n
:
(
9
7
.
9
6
4
4
7
,
1
0
0
.
9
6
4
4
7
)
F
i
r
s
t
i
n
t
e
r
s
e
c
t
i
o
n
:
(
9
8
,
1
0
1
)
2
5
0
m
/
s
Figure
5
.
The
two intersect
i
ons w
it
h t
he virtu
al
w
in
dow
i
n
t
he first si
m
ulatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
13
, N
o.
1
,
Ja
nu
a
ry 20
19
:
109
–
115
114
Table
3
.
A
Ta
bl
e Show
i
ng
the
Re
su
lt
s
f
r
om
Seco
nd Sim
ula
ti
on
us
in
g
Para
m
et
ers
Shown
No
t (
seco
n
d
)
T
vw
(
seco
n
d
)
x
(
c
m
)
y
(
c
m
)
1
0
.00
0
0
0
0
0
0
0
0
.00
0
0
0
1
0
1
0
9
8
.00
0
1
0
1
.000
2
0
.00
0
0
0
2
0
1
0
0
.00
0
0
0
1
0
0
0
9
8
.00
0
9
9
.99
5
3
0
.00
0
0
0
4
0
2
0
0
.00
0
0
0
0
9
9
0
9
8
.00
0
9
8
.99
0
Relativ
e
sp
eed, v (
m
/
s):
5
0
0
0
.0
0
Sp
eed o
f
ligh
t,
c (
m
/
s):
2
×
1
0
8
An
g
le,
θ (deg
rees
):
9
0
.00
Pix
el r
eso
lu
tio
n
,
R:
100
V
i
r
t
u
a
l
w
i
n
d
o
w
S
e
c
o
n
d
i
n
t
e
r
s
e
c
t
i
o
n
:
(
9
8
,
9
9
.
9
9
5
)
F
i
r
s
t
i
n
t
e
r
s
e
c
t
i
o
n
:
(
9
8
,
1
0
1
)
5
0
0
0
m
/
s
Fig
ure
6
.
The
two intersect
i
ons w
it
h t
he virtu
al
window i
n
t
he
sec
ond si
m
ulati
on
5.
CONCL
US
I
O
N
It
was
sho
wn
that
the
syst
em
was
able
to
determ
ine
the
relat
ive
sp
eed
and
path
of
the
unif
or
m
ly
m
ov
ing
obsta
c
le
wh
e
n
the
re
a
re
two
i
ntersec
ti
on
s
wit
h
the
virtu
al
window
.
W
it
h
the
sim
ulati
on
,
t
he
ch
oice
of
the
tim
e
per
io
d
has
t
o
be
a
caref
ully
sel
ect
ed
valu
e
.
I
f
the
value
c
hose
n
is
valid,
that
is,
it
ta
kes
into
consi
der
at
io
n
t
he
tim
e
need
e
d
f
or
t
he
tw
o
scan
of
the
vir
tual
window,
t
hen
t
he
res
ult
of
the
sim
ulati
on
i
s
acce
ptable.
O
ther
wise,
eve
n
thou
gh
the
resu
lt
is
pr
esent
bu
t
in
pr
act
ic
e
it
ca
nnot
be
reali
se
d
a
s
exp
la
ine
d ea
rlie
r.
ACKN
OWLE
DGME
NT
The
a
utho
rs
w
ou
l
d
li
ke
to
ac
knowle
dge
t
ha
t
this
re
searc
h
pro
j
ect
is
fun
de
d
from
a
gr
a
nt
awarde
d
by
the Mi
nistry
of H
ig
he
r
E
du
cat
ion
: FR
GS
/
1/2017/ICT
04/UI
TM/
02
/5
.
REFERE
NCE
S
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m
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i
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y
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l
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y
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