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.
94
~
101
IS
S
N: 25
02
-
4752, DO
I: 10
.11
591/ijeecs
.v1
3
.i
1
.pp
94
-
101
94
Journ
al h
om
e
page
:
http:
//
ia
es
core.c
om/j
ourn
als/i
ndex.
ph
p/ij
eecs
Appl
ication of
virt
ual
wi
nd
ows
to
determi
ne the p
ath of a
un
ifor
ml
y movin
g obstacl
e
M.U. Ka
malu
ddin, Hj
. M.
A
. Hj.
M
an
s
or
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,
Sel
angor
,
Malay
s
ia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
A
ug
1
4
, 201
8
Re
vised Oct
15
, 2
018
Accepte
d Oct
29
, 201
8
Two
virt
ual
win
dows
are
used
t
o
det
ermine
the
pat
h
of
a
single
uniforml
y
m
oving
obstac
l
e
.
If
the
pat
h
of
t
he
obsta
cl
e
cro
s
ses
the
two
virt
u
al
windows
,
the
n
it
s
pat
h
c
an
be
ea
sil
y
de
te
rm
ine
d.
A
sim
ula
ti
on
is
imp
le
m
ent
ed
t
o
asc
ertain
the vi
a
bil
ity
and
a
cc
ur
a
c
y
of this
te
chn
i
que.
Ke
yw
or
ds:
Path
determ
inati
on
Un
i
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
:
M.U. Kam
al
uddin
,
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
, S
el
ango
r
, M
al
ay
sia
.
Em
a
il
:
m
oh
du833@sal
am
.u
itm
.ed
u.
m
y
1.
INTROD
U
CTION
In
r
ecent
ye
ars
,
m
any
research
ers
ha
ve
their
at
te
ntion
poin
te
d
to
the
so
l
ut
ion
of
ob
sta
cl
e
avo
i
dan
ce
in
path
pla
nn
i
ng.
This
in
par
t
is
du
e
to
the
ex
te
ns
io
n
an
d
interest
in
cru
ise
con
t
ro
l
in
la
nd
veh
ic
le
s,
un
m
ann
e
d
veh
ic
le
an
d
auto
no
m
ou
s
m
ob
il
e
r
obots
in
an
en
vir
onm
ent
cl
uttered
with
ob
sta
cl
e
s.
Path
plan
ni
ng
is
a
n
i
m
po
rtant
pro
bl
e
m
in
the
nav
i
gation
of
a
uton
om
ou
s
m
ob
il
e
rob
ots.
The
re
are
m
any
path
plann
in
g
al
gorit
hm
s
with
obsta
cl
e
avo
i
dan
ce
,
su
c
h
as
pote
ntial
fiel
d
[1
-
4],
visibil
it
y
gr
a
phs
[
5
-
6],
gr
i
d
m
et
ho
ds
[
7],
Lee
-
Al
gorithm
[8
-
9], a
nd v
irt
ual w
i
ndow
[10].
Au
t
onom
ou
s
syst
e
m
s
[1
1]
al
low
a
ve
hic
le
to
m
ov
e
without
any
need
for
hu
m
an
co
ntr
ol.
These
ve
hicle
s
are
al
so
cal
led
dr
i
ver
le
ss
ca
r
or
sel
f
-
dri
vi
ng
car.
A
dvan
c
ed
co
ntr
ol
syst
e
m
s
interpr
et
sens
or
y
inf
or
m
at
ion
to i
den
ti
fy a
ppr
opriat
e n
a
vig
at
io
n paths
as
well
as
ob
sta
cl
es a
nd r
el
e
van
t si
na
ge [1
2
-
13]
.
Po
te
ntial
fiel
d
m
et
ho
d
as
su
m
es
that
al
l
entit
ie
s
in
the
e
nv
i
r
on
m
ent
ge
ner
a
te
an
arti
fici
al
fiel
d
ar
ound
them
sel
ves
in
su
c
h
a
way
that
a
m
ob
il
e
ro
bo
t
is
at
tract
ed
to
it
s
go
al
or
ta
rg
et
,
w
hile
at
the
sa
m
e
t
i
m
e
is
repulsed
b
y
ob
sta
cl
es. Th
e
po
te
ntial
f
ie
ld approac
h
ca
n be
us
e
d
as a
g
l
ob
a
l
m
otion
plan
ni
ng alg
or
it
hm
.
The
visibil
it
y
gr
a
ph
m
et
ho
d
const
ru
ct
s
a
grap
h
of
ver
ti
ce
s
of
poly
gons
represe
nting
obsta
cl
es.
It
m
eans
that
tw
o
ve
rtic
es
are
connecte
d
i
n
t
he
gra
ph
if
t
he
y
are
m
utu
al
l
y
visible.
Lee'
s
al
gorithm
is
a
path
fin
ding
al
gorit
hm
and
is
nor
m
al
l
y
app
li
ed
for
the
place
m
ent
of
ci
r
c
ui
ts
on
t
he
pr
in
te
d
ci
rcu
it
board.
It
gu
a
ra
ntees
to
f
ind
a
path
bet
ween
t
wo
po
i
nt
s
if
it
exists.
This
w
ork
co
nce
ntrates
on
determ
ining
the
pa
th
of
a
un
i
form
l
y
m
o
ving
obsta
cl
e
us
in
g
tw
o
virt
ual
wind
ow
s
.
On
ce
t
he
pat
h
is
determ
ined,
the
m
ob
il
e
ro
bot
can
the
n decid
es th
e n
e
xt step
in
it
s acti
on to
a
void c
olli
din
g wit
h
the
obstacl
e.
A
descr
i
ption
of
a
virtu
al
wi
ndow
is
giv
e
n
al
ong
with
it
s
i
m
ple
m
entat
io
n
within
t
he
c
on
te
xt
of
t
his
work.
T
he
n,
t
he
te
chn
i
qu
e
th
at
is
app
li
ed
usi
ng
t
wo
virt
ua
l
windows
t
o
cal
culat
e
the
path
of
the
unifo
rm
l
y
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
Ap
plicati
on o
f
Virt
ua
l Wi
ndow
s to Det
ermi
ne
the P
ath of
a Un
if
ormly
M
ov
ing
O
bs
tacle
(
M.U
.
Ka
m
alud
din
)
95
m
ov
ing
obsta
cl
e
is
pr
ese
nted.
A
sim
ulatio
n
a
pp
ly
in
g
this
te
chn
i
qu
e
is
perform
ed
to
co
rrobo
rate
the
eff
ect
ive
ness o
f
the
pro
pose
d sy
stem
.
2.
METHO
DOL
OGY
2.1
.
Discussi
on
o
f
t
he
Virt
ua
l Wi
n
do
w
A
virtu
al
wind
ow
is
basical
ly
a
rectan
gula
r
plane
t
hat
is
pro
j
ect
ed
ahea
d
of
a
m
ob
il
e
r
obot
f
or
th
e
pur
po
se
of
det
ect
ing
obsta
cl
e
s.
I
n
a
visi
on
syst
e
m
,
an
i
m
age
of
the
vie
w
f
orwa
rd
of
the
m
ob
il
e
robo
t
is
captu
red.
This
con
ta
ins
in
for
m
at
ion
of
not
on
ly
the
plane
of
interest
,
bu
t
al
so
of
anyt
hi
ng
be
fore
an
d
after
that
plane
.
Th
e
i
m
age
m
ay
be
sh
ar
p
at
the
plane
of
i
ntere
st
and
blur
in
the
vicinit
y
of
the
pla
ne
of
i
nterest
.
A
virt
ual
window
ca
ptu
re
s
i
m
age
j
us
t
of
the
plane
of
i
nterest.
I
nfo
rm
at
ion
be
fore
a
nd
a
fter
the
plane
is
disre
garde
d.
A
f
ull
an
d
c
om
ple
te
discussi
on
of
the
vir
tual
wind
ow
and
it
s
i
m
plem
entat
ion
is
in
[
14]
.
The
intersect
i
on
of
this
virt
ua
l
window
with
an
obsta
cl
e
w
il
l
pr
ov
i
de
the
m
ob
il
e
ro
bo
t
with
the
posit
ion
of
the
obsta
cl
e.
W
it
h
this
i
nf
orm
ation
,
t
he
m
ob
il
e
ro
bot
can
the
n
deci
de
on
t
he
a
ppropr
ia
te
ste
p
to
a
vo
i
d
colli
sion
with t
he obst
acl
e.
Con
si
der
a
sin
gle
virtu
al
window
ha
ving
a
siz
e
of
1m
×
1m
and
is
placed
1m
away
fr
om
the
m
ob
il
e
ro
bot.
As
in
a
dig
it
a
l
disp
la
y
or
c
a
m
era,
a
disp
l
ay
reso
luti
on
can
be
a
sso
ci
a
te
d
with
this
virtu
al
window.
T
his resoluti
on is
ve
r
y
m
uch
sim
il
ar
in
c
on
ce
pt t
o
t
he pixels i
n
a c
harge
-
c
ouple
d dev
ic
e c
hi
p.
The
siz
e (le
ng
t
h
an
d heig
ht o
f
the v
irt
ual w
in
dow)
a
nd p
i
xel r
esol
ution
ca
n be set to an
y
va
lue that is
re
quire
d.
I
deall
y,
the
siz
e
is
usual
ly
re
nd
e
re
d
a
li
tt
le
big
ge
r
tha
n
t
he
siz
e
of
the
m
ob
il
e
r
obot.
This
al
lo
ws
f
or
a
big
ge
r
f
orwa
rd
im
age
to
be
m
on
it
or
e
d
an
d
thu
s
a
great
e
r
am
ou
nt
of
in
form
ation
avai
la
ble
fo
r
proce
ssing.
This
will
giv
e
bette
r
protect
ion
to
t
he
m
obil
e
ro
bot
from
colli
sion
with
a
m
ov
ing
obs
ta
cl
e
co
m
par
ed
to
a
si
m
il
ar o
r
sm
aller s
iz
e v
i
rtual
window.
Let
’s
assum
ed
that
the
widt
h
of
a
n
obsta
cl
e
in
this
scena
rio
is
no
t
le
ss
than
0.1m
,
thu
s
in
order
not
t
o
m
iss
detect
ing
the
intersect
ion
with
the
vi
rtual
wind
ow,
the
reco
m
m
end
ed
l
ow
est
res
olu
ti
on
of
the
virtu
a
l
window
m
us
t
be
at
le
ast
10
×
10
pi
xels
Fig
ure
1
.
Assum
ing
the
sp
ee
d
of
li
gh
t
in
ai
r
to
be
2
×
108m
s
-
1,
then
t
he
ti
m
e
t
aken
f
or
a
si
ngle
la
ser
be
am
t
o
a
pix
el
on
t
he
virt
ual
wi
ndow
an
d
bac
k
t
o
the
se
ns
or
is
ab
ou
t
10ns
ecs
. Fo
r
a
total
p
ixel c
ou
nt of
100, the
total
tim
e is 1µsecs.
Figure
1. A
v
is
ual im
age r
ep
r
e
sentat
ion o
f
t
he virtual
wind
ow
Fo
r
sm
al
le
r
obsta
cl
e
siz
es,
hi
gh
e
r
res
olu
ti
on
is
rec
omm
end
ed,
t
hough
this
will
im
pact
the
proces
sin
g
tim
e. H
ow
e
ve
r
, for al
l p
racti
cal
p
ur
po
se
s,
c
urre
nt m
ob
il
e robo
ts
are
m
uch
bigger
tha
n 0.1
m
[
15
-
17
]
.
As
an
oth
e
r
ex
a
m
ple,
con
si
de
r
an
obsta
cl
e
hav
i
ng
a
wi
dt
h
of
0.01
m
.
The
rec
omm
e
nd
e
d
lo
west
reso
l
ution
f
or
the
virtu
al
window
is
t
hen
at
le
ast
100
×
100
pi
xel
s.
F
or
this
total
pi
xel
co
un
t
of
10,
000,
t
he
total
tim
e taken for the
sca
nning
of the
wh
ole v
irt
ual w
i
ndow is
100µsecs
or 0.1m
s.
2.2
.
Discussi
on
Of
The Im
plem
ent
at
i
on
Of
Tw
o Vir
tual Wi
nd
ows
The
ai
m
of
thi
s
resea
rc
h
wor
k
is
t
o
determ
i
ne
t
he
path
of
the
un
if
orm
l
y
m
ov
ing
obsta
cl
e.
F
or
any
path
to
be
det
erm
ined
there
m
us
t
be
at
le
a
st
two
points
of
inte
rsecti
on.
Since
the
obs
ta
cl
e
is
a
un
if
or
m
l
y
m
ov
ing
obje
ct
(h
a
ving
a
strai
gh
t
pat
h
with
co
ns
ta
nt
spe
ed),
then
obviously
there
m
us
t
be
two
virtu
a
l
windows
place
d
forw
a
r
d
of
e
ach
oth
e
r
in
or
der
f
or
the
t
wo
intersect
io
ns
t
o
occur
Fig
ure
2
.
I
ntersecti
on
s
wit
h
the
two
virt
ua
l
windows
will
giv
e
s
uffici
ent
inf
or
m
at
ion
to
cal
culat
e
the
pat
h
of
the
un
i
form
l
y
m
ov
i
ng
ob
sta
cl
e.
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
:
94
–
101
96
Figure
2. To
p view
showi
ng t
he
tw
o virt
ual
windows
w
it
h
resp
ect
t
o
th
e
m
ob
il
e ro
bot
Table
1
s
hows
the
relat
ion
s
hi
p
bet
ween
th
e
m
axi
m
u
m
theor
et
ic
al
sp
eed
of
the
m
ov
ing
obsta
cl
e
that
can
sti
ll
be
det
ect
ed
with
respec
t
to
the
pix
el
reso
l
ution
a
nd
gap
betwee
n
t
he
tw
o
virt
ual
windows.
For
a
gap
of
2c
m
and
wi
th
a
pix
el
reso
l
ution
of
10
×
10,
the
m
axi
mu
m
theor
et
ic
al
sp
ee
d
that
the
m
ov
ing
obsta
c
le
can
m
ov
e
wh
il
e
sti
ll
being
detect
ed
by
the
vir
tual
windows
is
abo
ut
10,
00
0m
s
-
1
(equiva
le
nt
to
36
,
000kph
,
or
22,37
0m
ph
)
. Th
is d
oes no
t
m
ean th
at
the system
can
no
t st
il
l deter
m
ine
the p
at
h
at
a h
i
gh
e
r
spe
ed
, but ther
e
will
be
an
ass
oc
ia
te
d
offset
er
ror
with
s
pee
d
gr
eat
er
t
han
t
he
theoret
ic
al
m
axim
u
m
sp
eed.
This
will
be
s
how
n
la
te
r
in
a
sim
ul
at
ion
.
For
a
m
or
e
ty
pical
s
pe
ed
of
a
n
e
xp
e
rim
ental
m
ob
il
e
rob
ot
[18],
the
syst
e
m
is
ver
y
m
uch
able to
detect
t
he
inte
rsecti
on
s w
it
h t
he
t
wo
virtu
al
wind
ows w
it
h am
ple tim
e fo
r
pr
ocess
ing
.
Si
m
il
arly
,
the
m
axi
m
u
m
theor
et
ic
al
sp
eed
f
or
a
ga
p
of
2c
m
and
pix
el
re
so
luti
on
of
10
0
×
100
is
a
m
or
e
reali
sti
c
10m
s
-
1.
Ma
xim
u
m
theor
et
ic
al
s
pee
ds
f
or
oth
e
r
values
of
t
he
tw
o
pa
ram
et
ers
are
sho
w
n
in Ta
ble 1.
Table
1.
Rel
at
ion
s
hi
p
Be
twee
n
Ma
xim
u
m
S
peed
of
O
bs
ta
cl
e to the
Pixel
Re
so
luti
on
and
Ga
p
Be
t
w
een
the
Vi
rtual
W
i
nd
ows
Gap
bet. virtu
al
wi
n
d
o
ws
(c
m
)
Pix
el r
eso
lu
tio
n
10
×
10
100
×
100
2
1
0
,00
0
m
s
-
1
(
≈ 36
,00
0
k
p
h
)
1
0
m
s
-
1
(≈
36
k
p
h
)
5
2
5
,00
0
m
s
-
1
2
5
0
m
s
-
1
10
5
0
,00
0
m
s
-
1
5
0
0
m
s
-
1
3.
SIMULATI
O
N RESULTS
AND A
NA
L
Y
SIS
3.1
.
Det
ermi
ning
t
he
Path
of t
he
Ob
st
acle With
R
es
pec
t
t
o the
St
e
p T
im
e
of the
Sim
ulat
i
on
Fo
r
this
sim
ulati
on
us
in
g
Mi
c
ro
s
of
t
Excel
™,
the
near
est
vir
tual
wind
ow
(
f
irst
virt
ual
wi
ndow)
to
t
he
m
ob
il
e
ro
bot
is
set
at
1
m
(o
r
100cm
),
wh
il
e
the
seco
nd
vi
rtual
wind
ow
is
locat
ed
a
f
urt
her
0.0
2m
(o
r
2cm
)
from
the
first
virtu
al
window
Fig
ure
3
.
T
he
sta
rt
posit
io
n
of
the
obsta
cl
e
is
(1
10,
1
12)
an
d
the
e
nd
po
i
nt
is
(2,
4).
The
ob
sta
cl
e
m
ov
es
in
a
strai
gh
t
li
ne
as
s
how
n
by
the
red
da
sh
es.
The
res
ol
ution
of
the
virtu
al
windows
is
100
×
100
pi
xe
ls
an
d
it
is
l
ocated
10
0cm
from
the
m
ob
il
e
r
obot,
t
hus
the
ti
m
e
it
t
akes
t
o
com
plete
ly
sca
n
the
tw
o
v
irt
ual
wi
ndows
i
s
ab
out
0.2m
s
(
0.000
2s
)
.
T
he
relat
ive
s
pee
d
of
the
obsta
cl
e
is
assum
ed
to
be 5m
s
-
1
(
or 50
0c
m
s
-
1).
It is ob
vious
from
Fig
ure
3 t
ha
t t
he
strai
gh
t
-
l
ine equat
io
n of t
he path
of the
obstacl
e is:
y = x
+
2
(1)
This
e
qu
at
io
n
will
be
use
d
to
ver
i
fy
the
resul
t
fr
om
the
sim
ulati
on
.
T
he
pa
th
of
the
m
ov
ing
obsta
cl
e
will
b
e cal
c
ulate
d usin
g
t
he poi
nts of in
te
rsec
ti
on
with th
e t
wo v
i
rtual
windows.
The
sim
ulati
on
is
basical
ly
the
cal
culat
ion
of
t
he
posit
io
n
of
the
m
ov
i
ng
obsta
cl
e
ev
ery
0.0
002s
.
A
sam
ple
of
the
cal
culat
io
ns
for
the
posit
ion
s
of
the
obs
ta
cl
e
ever
y
0.0
002s
is
s
how
n
in
Fig
ur
e
4.
F
or
t
his
cal
culat
ion
,
t
he
sp
ee
d
of
th
e
obsta
cl
e
is
giv
e
n
as
500c
m
s
-
1
(o
r
5m
s
-
1,
wh
ic
h
is
ha
lf
of
t
he
the
or
et
ic
al
m
axi
m
u
m
sp
eed
as
sho
wn
in
Table
1),
thu
s
ha
v
in
g
co
m
po
nen
t
sp
e
e
ds
f
or
both
and
directi
on
as
353.5
534cm
s
-
1.
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Ap
plicati
on o
f
Virt
ua
l Wi
ndow
s to Det
ermi
ne
the P
ath of
a Un
if
ormly
M
ov
ing
O
bs
tacle
(
M.U
.
Ka
m
alud
din
)
97
Figure
3. To
p view
showi
ng
relat
ive posit
io
n of t
he
m
ob
il
e r
obot a
nd the
ob
sta
cl
e,
alo
ng
with
oth
e
r rel
e
van
t
par
am
et
ers
Fr
om
Table
2,
for
the
seco
nd
virtu
al
wind
ow,
the
intersect
ion
is
only
detect
ed
wh
e
n
the
locat
ion
of
the
obsta
cl
e
is
at
(9
9.4
,
101.4
).
The
inte
rsect
ion
co
ordi
nates
with
the
first
virtu
al
wi
ndow
is
at
(9
8,
100)
.
The
coor
din
at
e (
10
0.1, 1
02.1) is
not vali
d be
caus
e the
obsta
cl
e h
as
not i
nterse
ct
the sec
ond v
irtual
w
i
ndow
ye
t.
Using
1
f
or
the
path
of
the
m
ov
in
g
ob
sta
cl
e, co
nve
ntion
al
c
al
culat
ion
g
ive
s
the
inte
rsecti
on
s
as (
10
0,
102)
with
t
he
s
econd
virtu
al
window,
a
nd
(
98,
10
0)
with
t
he
fir
st
virtu
al
window.
The
offset
per
ce
ntag
e
error
for
the
co
ordi
na
te
s
at
the
second
vi
r
tual
wi
ndow
is
arou
nd
0.0
4%,
wh
il
e
the
per
ce
nta
ge
er
ror
at
the
first
is
arou
nd 0.02%.
(a)
(b)
Figure
4. (a
) A
sam
ple o
f
th
e
cal
culat
ion
s a
s
an
im
age cap
tu
red f
ro
m
Mi
cro
soft E
xcel™
at
a tim
e step of
0.000
2s
, (
b) A
sam
ple o
f
the
re
su
lt
s w
it
h t
he
two
i
ntersecti
ons
highli
ghte
d and hi
gh preci
s
ion
sim
ulate
d
values
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m
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Sci,
Vo
l.
13
, N
o.
1
,
Ja
nu
a
ry 20
19
:
94
–
101
98
Table
2.
T
he
P
os
it
ion C
oor
di
nates
of
t
he
M
ov
i
ng Obstac
le
in the
Vici
nity
of
First
(y=1
00cm
)
and
Sec
ond
(y
=102cm
)
Virtu
al
W
in
dows
Virtual win
d
o
w
Co
o
rdin
ates (c
m
)
x
y
Seco
n
d
1
0
0
.03
1
0
2
.03
9
9
.96
1
0
1
.96
First
9
8
.05
1
0
0
.05
9
7
.98
9
9
.98
Fr
om
the
c
oord
i
nates
of
i
ntersecti
on
in
T
able
2,
t
he
e
qu
at
io
n
of
th
e
path
of
t
he
ob
sta
cl
e
i
s
fou
nd to be:
y = x
+
2
(2)
The
pat
h
of
th
e
ob
sta
cl
e
obta
ined
th
rou
gh
t
he
sim
ulatio
n
is
exactl
y
the
sa
m
e
a
s
the
set
path
of
the
ob
sta
cl
e
1
.
Fig
ur
e 5
show
s
th
e
path
of
the
obsta
cl
e
achieve
d
thr
ough
sim
ulati
on
an
d
co
nventio
nal
cal
cu
la
ti
on
.
The
reas
on
f
or
the
offset
is
that
the
syst
e
m
is
assum
ed
to
detect
the
i
ntersecti
on
with
the
seco
nd
virtu
al
window
at
y
=
101.9
6,
i
ns
te
a
d
of
10
2.
T
hi
s
is
beca
us
e
the
cal
culat
io
n
was
done
in
ste
ps
of
0.
0002s,
corres
pondin
g
to
the
tim
e
ta
ken
f
or
t
he
syst
e
m
to
scan
the
two
virtu
al
wi
ndows.
T
he
er
r
or
as
s
how
n
a
bove
is
ver
y sm
al
l, less t
ha
n 0.05%
.
Figure
5. Com
par
is
on of t
he
s
i
m
ulate
d
path
against t
he
cal
culat
ed path
of
the m
ov
in
g obst
acl
e for
a ti
m
e step
of 0.0
002s
Alte
rn
at
ively
,
t
he
co
ordinates
for
the
tw
o
int
ersecti
ons
with
bo
t
h
virt
ual
w
indows
ca
n
be
consi
der
e
d
to
be
(97.9
8,
100)
i
ns
te
ad
of
(97.9
8,
99.
98)
for
t
he
first
vir
tual
wi
ndow,
a
nd
(
99.
96,
102)
instea
d
of
(99.9
6,
101.9
6)
f
or
th
e
second.
Th
e
se
coord
i
nates
can
be
acce
pt
ed
if
the
syste
m
pr
esum
ed
that
the
intersect
ion
s
happe
ned
at
y=
100
for
the
first
virt
ual
window,
a
nd
y=
10
2
f
or
t
he
sec
ond
vi
rtual
wi
ndow
e
ve
n
th
ough
it
w
a
s
detect
ed
a
li
tt
le
bit f
ur
t
her tha
n
the
actual
po
sit
ion
of
t
he vir
tual win
dow
s.
Figure
6
s
how
s
the
sim
ulate
d
an
d
cal
culat
ed
path
of
the
m
ov
in
g
ob
sta
cl
e.
As
ca
n
be
see
n,
the
sl
op
e
s
are
al
m
os
t
si
m
il
ar.
T
he
sl
op
e
f
or
the
sim
ula
ti
on
is
f
ound
t
o
be
1.0
1,
t
hus
gi
ving
a
pe
r
centage
er
ror
of
1%
.
The
y
-
inte
rcept
,
howe
ver
,
is
fou
nd
to
be
1.04
a
nd
this
gi
ves
a
pe
rce
ntage
er
ror
of
ab
ou
t
48
%
.
E
ven
thou
gh
the
er
ror
of
the
y
-
interce
pt
is
la
rg
e
,
this
ca
n
be
disre
garde
d
because
it
de
pe
nds
on
the
po
sit
ion
in
g
of
the
axe
s
.
If
the
a
xes
we
re
place
d
nea
r
er
to
the
ce
ntr
e
of
the
m
ob
il
e
robo
t,
t
hen
t
he
er
ror
is
ex
pe
ct
ed
to
be
sm
al
le
r,
i.e.
the
y
-
inter
cept
will
be
near
er
to
the
cal
culat
ed
y
-
interc
ept
of
2.
In
thi
s
stud
y,
the
slo
pe
is
m
or
e
relevan
t
than
t
he
y
-
i
nter
cept. T
he pe
rc
e
ntage
e
rro
r
f
or
the slo
pe
is
jus
t 1%.
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Sci
IS
S
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02
-
4752
Ap
plicati
on o
f
Virt
ua
l Wi
ndow
s to Det
ermi
ne
the P
ath of
a Un
if
ormly
M
ov
ing
O
bs
tacle
(
M.U
.
Ka
m
alud
din
)
99
Figure
6. Com
par
is
on of t
he
s
i
m
ulate
d
path
against t
he
cal
culat
ed path
of
the m
ov
in
g obst
acl
e for
a ti
m
e step
of 0.0
002s an
d t
akin
g
the
y in
te
rsecti
on
s
as
be
ing
102 an
d 1
00 for t
he se
co
nd and
fi
rst
vir
tual win
dow
resp
ect
ively
Figure
7
s
hows
a
no
t
her
gr
aph
with
t
he
m
ov
ing
ob
sta
c
le
hav
i
ng
a
hi
gh
e
r
s
peed
at
1000cm
s
-
1
(10m
s
-
1)
.
T
his
is
twic
e
the
sp
eed
of
t
he
pr
evio
us
exe
rcis
e
and
at
the
li
m
it
of
this
virtu
al
wind
ow
(T
able
1).
The
pe
rce
ntage
err
ors for
t
he
slop
e an
d
the y
-
intercept are th
e sa
m
e as the p
rev
i
ou
s e
xer
ci
s
e. Th
is can
be
see
n
from
the g
ra
ph
where
the i
ntersecti
ons ar
e
th
e sam
e as in
th
e previ
ou
s
ex
e
r
ci
se.
Figure
7. Com
par
is
on of t
he
s
i
m
ulate
d
path
against t
he
cal
culat
ed path
of
the m
ov
in
g obst
acl
e for
a ti
m
e step
of 0.0
002s an
d wit
h o
bs
ta
cl
e
sp
ee
d of
10m
s
-
1
a
nd takin
g
t
he
y intersect
io
ns as
bein
g 102 a
nd 10
0 for the
seco
nd and
fi
rs
t virtual
wind
ow re
sp
ect
ively
Anothe
r
e
xam
ple
is
pe
rfor
m
ed
with
a
hi
gh
e
r
sp
ee
d
of
10
m
s
-
1
(10
00
cm
s
-
1).
Ta
ble
3
s
ho
ws
the
po
int
of
inte
rsecti
on
s.
It
is
the
sam
e
as
the
obsta
cl
e
with
a
sp
ee
d
of
500c
m
s
-
1,
an
d
thus
the
per
ce
ntage
e
rror
s
a
re
si
m
il
ar
too
.
O
n
the
oth
e
r
ha
nd
,
if
the
s
peed
is
increase
d
to
1200cm
s
-
1,
the
slop
e
per
ce
nta
ge
er
ror
inc
rea
sed
to
2%,
w
hile
sim
il
arly
the
y
-
int
e
rcep
t
pe
rcen
t
age
e
rror
is
ca
lc
ulate
d
to
be
100%
.
T
his
c
orr
oborat
es
the
lim
its
that was
calc
ul
at
ed
an
d sh
ow
n
in
Ta
ble 1.
Table
3.
T
he
P
os
it
ion C
oor
di
nates
of
t
he
M
ov
i
ng Obstac
le
in the
Vici
nity
of
First
(y=1
00cm
)
and
Sec
ond
(y
=102cm
)
Virtu
al
W
in
dows
Havi
ng
a
Sp
ee
d
of
10
00
cm
s
-
1
Virtual win
d
o
w
Co
o
rdin
ates (c
m
)
x
y
Seco
n
d
9
9
.96
1
0
1
.96
(10
2
.0)
First
9
7
.98
9
9
.98
(10
0
.0)
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:
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Ind
on
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n
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E
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c Eng &
Co
m
p
Sci,
Vo
l.
13
, N
o.
1
,
Ja
nu
a
ry 20
19
:
94
–
101
100
Fo
r
c
om
par
iso
n,
a
no
t
her
e
xa
m
ple
is
giv
en
with
a
tim
e
step
of
0.0
05s.
Fi
gure
8
s
how
a
sam
ple
of
the
out
pu
t
from
the sim
ulatio
n
a
nd Fi
g
ure
9
t
he path
plo
tt
e
d
as
a grap
h.
Figure
8. A
sa
m
ple o
f
the cal
culat
ion
s
as a
n im
age cap
tu
red from
Mi
cro
sof
t
Excel™
at a t
i
m
e step o
f
0.005s
The
sl
op
e
was
fou
nd
to
be
1.14
gi
ving
a
per
ce
ntage
er
r
or
of
14%
.
T
he
y
-
interce
pt
is
at
-
11.
31.
This
giv
es
a
pe
rcen
ta
ge
e
rror
of 66
5.4%. Th
ese val
ues
c
orr
oborat
es the li
m
it
s that was
gi
ven
i
n
Ta
ble
1.
Figure
9. Com
par
is
on of t
he
s
i
m
ulate
d
path
against t
he
cal
culat
ed path
of
the m
ov
in
g obs
ta
cl
e for
a ti
m
e step
of 0.0
05s
4.
CONCL
US
I
O
N
It
was
s
how
n
t
hat
the
syst
em
was
a
ble
to
det
erm
ine
the
path
of
the
m
ov
in
g
obsta
cl
e
s
o
long
as
t
here
is
an
intersect
ion
eac
h
with
t
he
tw
o
virt
ual
windows.
For
the
exer
ci
ses
di
d,
the
pe
rce
ntage
offset
er
r
or
was
fou
nd to be les
s tha
n 0.1%.
This
bo
des
ve
r
y
well
fo
r
the
syst
e
m
as
th
e
offset
erro
r
do
es
no
t
af
fect
th
e
correct
deter
m
inati
on
of
the p
at
h of t
he un
i
form
l
y
m
ov
ing
obsta
cl
e.
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
.
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
Ap
plicati
on o
f
Virt
ua
l Wi
ndow
s to Det
ermi
ne
the P
ath of
a Un
if
ormly
M
ov
ing
O
bs
tacle
(
M.U
.
Ka
m
alud
din
)
101
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Evaluation Warning : The document was created with Spire.PDF for Python.