Indonesian
Journal
of
Electrical
Engineering
and
Computer
Science
V
ol.
2,
No
.
3,
J
une
2016,
pp
.
478
485
DOI:
10.11591/ijeecs
.v2.i3.pp478-485
478
Bac
kstepping
Appr
oac
h
f
or
A
utonomous
Mobile
Robot
T
rajector
y
T
rac
king
Ibari
Benaoumeur*
1
,
Benc
hikh
Laredj
2
,
Hanifi
Elhac
himi
Amar
Reda
3
,
and
Ahmed-f
oitih
Zoubir
4
1,3,4
Labor
ator
y
of
P
o
w
er
Systems
,
Solar
Energy
and
A
utomation
L.E.P
.E.S
.A.
Univ
ersity
of
Sci
ences
and
T
echnology
of
Or
an
UST
O/MB
.
Or
an,
Alger
ia
2
IBISC
labor
ator
y
(Inf
or
matics
,
Integ
r
ativ
e
Biology
and
Comple
x
Systems),
Univ
ersit
y
of
Evr
y
,
F
r
ance
*
Corresponding
author
,
e-mail:
benaoumeur
.ibar
i@univ-usto
.dz
Abstract
This
paper
proposes
a
bac
kstep
ping
controller
design
f
or
tr
ajector
y
tr
ac
kin
g
of
unicycle-type
mobile
robots
.
The
main
object
of
the
control
algor
ithms
de
v
eloped
is
to
design
a
rob
ust
output
tr
ac
king
controller
.
The
design
of
the
controller
is
based
on
the
ly
apuno
v
theorem,
kinematic
tr
ac
king
controller
of
an
unicycle-
lik
e
mobile
robot
is
used
to
pro
vides
t
he
desired
v
alues
of
the
linear
and
angular
v
elocities
f
or
the
giv
en
tr
ajector
y
.
A
L
y
apuno
v-based
stability
analysis
is
presented
to
guar
antee
the
robot
stability
of
the
tr
ac
king
errors
.
Sim
ulation
and
e
xper
imental
results
sho
w
the
eff
ectiv
eness
of
the
proposed
rob
ust
controller
in
ter
m
of
accur
acy
and
stability
under
diff
erent
load
conditions
.
K
e
yw
or
ds:
Non-linear
systems
,
T
r
ajector
y
tr
ac
king,
Dynamic
model,
bac
kstepping.
Cop
yright
c
2016
Institute
of
Ad
v
anced
Engineering
and
Science
1.
Intr
oduction
Diff
erential
wheeled
robot
are
becoming
more
popular
f
or
perf
or
ming
tasks
that
are
too
dangerous
or
tedious
f
or
humans
,
the
y
are
widely
used
in:
industr
y
,
science
,
education
,
enter
tain-
ment
and
militar
y
applications
[1],
f
or
this
w
a
y
,
There
are
man
y
research
ar
ticles
emphasizing
the
impor
tance
of
designing
controller
at
the
control
of
mobile
robot.
Most
of
them
ha
v
e
f
ocused
on
tr
ajector
y
tr
aking
[2,
3,
4].
In
these
algor
ithms
,
the
v
elocity
control
inputs
is
defined
to
stabiliz
e
the
closed-loop
system.
In
path
f
ollo
wing,
the
v
elocity
control
is
designed
to
stabiliz
e
a
car-lik
e
mobile
robot
[5],
this
prob
lem
of
stabilization
is
solv
ed
about
a
desired
posture
in
[6].
Most
controllers
designed
in
control
systems
are
not
based
on
dynam
ic
systems
and
control
theor
y
[7,
8,
9].
In
[10]
an
adaptiv
e
f
ollo
wing
controller
based
on
the
PID
f
or
mobile
robot
path
f
ollo
wing
is
presented,
one
adv
antage
of
their
controller
is
that
its
the
control
la
w
is
constr
ucted
on
the
basis
of
L
y
apuno
v
stability
theor
y
.
Once
more
,
just
a
model
of
the
robot
mobile
kinematics
is
used
and
no
e
xper
ime
ntal
results
w
ere
repor
ted.
Ho
w
e
v
er
,
it
is
necessar
y
to
using
the
tools
from
control
theor
y
and
dynamic
systems
in
order
to
ensure
system
stability
.
Man
y
researchers
ha
v
e
sho
wn
interest
in
applying
controllers
designed
f
or
wheeled
robot
mobile
based
on
dynamic
model.
Diff
erent
approaches
ha
v
e
been
in
v
estigated
using
fuzzy
control
[11,
12],
sliding
mode
control
(SMC)[13,
14],
adaptiv
e
control
[15,
16,
17],
or
bac
kstepping
control
[18,
19].
In
the
presence
of
par
ametr
ic
uncer
ta
inties
and
noises
in
only
its
dynamic
model,
a
com-
bination
of
model
ref
erence
adaptiv
e
control
and
gain
scheduling
is
de
v
eloped
in
[15]
to
control
the
robot
motion
b
y
the
adaptiv
e
controller
.
In
[16]
an
adaptiv
e
controller
based
on
the
dynamic
model
pro
vides
the
torques
of
the
robot
actuators
f
or
yielding
the
required
v
elocities
is
designed
in
the
presence
of
unkno
wn
dynamics
only
in
its
dynamic
model.
An
adaptiv
e
tr
ajector
y-tr
ac
king
con-
troller
based
on
the
robot
dynamics
is
proposed
with
e
xper
imental
results
in
[17],
and
its
stability
is
pro
v
ed
using
the
L
y
apuno
v
stability
theorem,
The
dynamic
controller
is
capab
le
of
updating
the
estimated
par
ameters
,
which
are
directly
related
to
ph
ysical
par
ameters
of
the
robot.
In
order
to
o
v
ercome
tr
aj
ector
y
tr
ac
king
prob
lems
,
in
[20]
an
adaptiv
e
nonlinear
control
of
a
wheeled
mobile
Receiv
ed
F
ebr
uar
y
2,
2016;
Re
vised
Ma
y
9,
2016;
Accepted
Ma
y
20,
2016
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4752
479
robot
approach
is
proposed
in
the
presence
of
uncer
tainties
.
A
methodo
logy
based
on
linear
in-
ter
polation
is
used
in
[21]
to
design
control
algor
ithms
f
or
tr
ajector
y
tr
ac
king
of
mobile
robots
,The
proposed
control
can
be
applied
to
the
design
of
a
large
class
a
mobile
robot.
In
this
paper
,
the
tr
ajector
y
tr
ac
king
prob
lem
f
or
an
unicycle-lik
e
mobile
robot
has
been
addressed.
First,
the
dynamic
model
of
the
unicycle-lik
e
mobile
is
presented
and
the
kinematic
controller
,
which
is
based
on
the
robot
kinematics
,
is
introduced
to
gener
ate
the
desired
linear
and
angular
v
elocities
f
or
the
giv
en
tr
ajector
y
.
The
control
la
w
is
de
v
eloped
using
bac
kstepping
technique
to
gener
ate
the
commands
of
linear
and
angular
v
elocities
deliv
ered
to
the
robot
ser
v
os
,
and
its
stability
proper
ty
is
pro
v
ed
using
the
L
y
apuno
v
theor
y
.
The
rest
of
the
paper
is
organiz
ed
as
f
ollo
ws
.
Section
2
presents
the
dynamic
unicycle-lik
e
robot
model.
The
kinematic
controller
is
detailed
and
the
complete
equations
of
the
bac
kstepping
controller
design
a
re
de
v
eloped
in
section
3.
Respectiv
ely
,
in
section
4,
sim
ulations
and
e
xper
i-
mental
results
are
discussed.
Finally
,
section
5
concludes
this
paper
.
2.
Dynamic
model
In
this
w
or
k,
the
dynamic
model
of
the
unicycle-lik
e
mobile
is
considered,
this
model
is
proposed
in
[22],
The
mobile
robot
is
illustr
ated
in
Figure
1.
G
is
the
center
of
mass
of
the
robot,
C
is
the
position
of
the
castor
wheel,
E
is
the
location
of
a
tool
onboard
the
robot,
h
is
the
point
of
interest
with
coordin
ates
x
and
y
in
the
XY
plane
,
is
the
robot
or
ientation,
and
a
is
the
distance
betw
een
the
point
of
interest
and
the
centr
al
point
of
the
vir
tual
axis
linking
the
tr
action
wheels
(point
B
),
u
and
!
are
the
linear
and
angular
v
elocities
of
the
robot.
Figure
1.
The
unicycle-lik
e
mobile
robot.
The
model
of
the
mobile
robot
can
be
obtained
as
f
ollo
ws
[22]:
0
B
B
B
B
@
_
x
_
y
_
_
u
_
!
1
C
C
C
C
A
=
0
B
B
B
B
@
u
cos(
)
aw
sin(
)
u
sin(
)
+
aw
cos(
)
!
3
1
!
2
4
1
u
5
2
u!
6
2
!
1
C
C
C
C
A
+
0
B
B
B
B
@
0
0
0
0
0
0
1
1
0
0
1
2
1
C
C
C
C
A
u
r
ef
!
r
ef
(1)
The
par
ameters
of
the
dynamic
model
are:
i
;
i
=
1
::::;
6
and
defined
as
f
ollo
ws:
Bac
kstepping
Approach
f
or
A
utonomous
Mobile
Robot
T
r
ajector
y
T
r
ac
king
(Ibar
i
Benaoumeur)
Evaluation Warning : The document was created with Spire.PDF for Python.
480
ISSN:
2502-4752
8
>
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
>
:
1
=
R
a
k
a
(
mR
t
r
+2
I
e
)+2
r
k
D
T
(2
r
k
P
T
)
2
=
R
a
k
a
(
I
e
d
2
+2
R
t
r
(
I
z
+
mb
2
))+2
r
dk
D
R
(2
r
dk
P
R
)
3
=
R
a
k
a
mbR
t
2
k
P
T
4
=
R
a
k
a
(
k
a
k
b
R
a
+
B
e
)
(
r
k
P
T
)
+
1
5
=
R
a
k
a
mbR
t
2
k
P
R
6
=
R
a
k
a
(
k
a
k
b
R
a
+
B
e
)
d
(
r
k
P
R
)
+
1
(2)
where
m
is
the
robot
mass
,
I
z
is
the
r
obot
moment
of
iner
tia
at
G,
r
is
the
r
ight
and
left
wheel
r
adius
,
I
e
and
B
e
are
the
moment
of
iner
tia
and
the
viscous
fr
iction
coefficient
of
th
e
combined
motor
rotor
,
gearbo
x,
and
wheel,
and
R
t
is
the
nominal
r
adius
of
the
tire
,
k
b
is
electromotiv
e
constant
of
motors
,
k
a
is
the
constant
of
torque
.
R
a
is
the
electr
ical
resistance
of
the
motors
,
b
and
d
are
the
distances
.
The
robot
ha
v
e
PD
controllers
to
control
the
v
elocities
of
each
motor
,
with
propor
tional
gains
k
P
T
and
k
P
R
,
and
der
iv
ativ
e
gains
k
D
T
and
k
D
R
.
3.
Rob
ust
contr
oller
design
In
this
w
or
k,
tw
o
diff
erent
types
of
controllers
are
considered
:
kinematic
controller
f
or
e
xter
nal
loop
and
a
bac
kstepping
controller
f
or
an
inter
nal
loop
as
see
in
figure
2.
3.1.
Kinematic
contr
oller
F
or
the
giv
en
tr
ajector
y
,
the
desired
v
alues
of
the
linear
and
angular
v
elocities
are
gener-
ated
b
y
the
kinematic
controller
,
it
is
based
on
the
kinematic
model
of
the
robot.
The
kinematic
equations
of
mobile
robot
in
Figure
1
are
descr
ibed
b
y:
_
x
_
y
=
A
u
r
ef
!
r
ef
(3)
with
A
=
cos
(
)
asin
(
)
sin
(
)
acos
(
)
(4)
whose
respectiv
ely
u
r
ef
;
!
r
ef
are
the
desired
v
alues
of
the
linear
and
angular
v
elocities
and
h
(
x;
y
)
is
the
point
of
interest.
whose
in
v
erse
is
A
1
=
cos
(
)
sin
(
)
1
a
sin
(
)
1
a
cos
(
)
(5)
Thus
,
choosing
the
control
la
w
u
k
r
ef
!
k
r
ef
=
cos
sin
1
a
sin
1
a
cos
_
x
d
+
x
_
y
d
+
y
(6)
where
x
=
x
d
x
,
y
=
y
d
y
are
the
current
position
errors
,
h
(
x;
y
)
and
h
d
(
x
d
,
y
d
)
are
the
current
and
the
desired
coordinates
.
No
w
,
consider
the
position
error
_
x
+
x
_
y
+
y
=
0
0
(7)
Thus
,
choosing
the
L
y
apuno
v
candidate
function
V
=
1
2
T
)
_
V
=
T
_
<
0
(8)
IJEECS
V
ol.
2,
No
.
3,
J
une
2016
:
478
485
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4752
481
where
=
_
x
+
x
_
y
+
y
T
,theref
ore
,
from
(7)
and
(8)
it
results
that:
_
V
=
T
x
_
x
=
T
x
x
<
0
T
y
_
y
=
T
y
y
<
0
(9)
is
negativ
e
definite
.
Clear
ly
,
if
goes
to
z
ero
then
h
con
v
erges
to
h
d
and
the
tr
ac
king
error
is
asymptotically
stab
le
,
which
means
that
!
0
as
t
!
1
Theref
ore
,
(6)
is
a
satisf
actor
y
tr
ac
king
controller
f
or
system
(3).
3.2.
Bac
kstepping
Contr
oller
design
and
stability
anal
ysis
The
controlle
r
receiv
es
from
the
kinematic
controller
the
ref
erences
f
or
linear
and
angular
v
elocities
,
and
gener
ates
another
pair
of
linear
and
angular
v
elocities
to
be
deliv
ered
to
the
robot
ser
v
os
,
as
sho
wn
in
Figure
2.
The
bac
kstepping
control
is
used
to
design
the
controller
which
is
making
the
error
dynamics
Figure
2.
Control
str
ucture
.
stab
le
[23,
24].
The
design
of
the
bac
kstepping
controller
is
ba
s
e
d
on
the
ly
apuno
v
theorem,
the
objectiv
e
of
this
technique
is
to
deter
mine
a
control
la
w
that
pro
vides
the
system
stability
.
The
dynamic
par
t
of
equation
(1)
is:
(
_
u
=
3
1
!
2
4
1
u
+
u
r
ef
1
_
!
=
5
2
u!
6
2
!
+
!
r
ef
2
(10)
In
the
first
step
,
the
output
error
betw
een
the
ref
erence
and
actual
controls
is
giv
en
b
y:
1
u
=
u
r
ef
u
=
)
_
1
u
=
_
u
r
ef
_
u
(11)
1
!
=
!
r
ef
!
=
)
_
1
!
=
_
!
r
ef
_
!
(12)
Choose
a
L
y
apuno
v
functions
candidate
as
V
(
1
u
)
=
1
2
2
1
u
;
V
(
1
!
)
=
1
2
2
1
!
(13)
The
time
der
iv
ativ
e
of
the
L
y
apuno
v
candidate
functions
can
be
wr
itten
as
_
V
(
1
u
)
=
1
u
_
1
u
;
_
V
(
1
!
)
=
1
!
_
1
!
(14)
Bac
kstepping
Approach
f
or
A
utonomous
Mobile
Robot
T
r
ajector
y
T
r
ac
king
(Ibar
i
Benaoumeur)
Evaluation Warning : The document was created with Spire.PDF for Python.
482
ISSN:
2502-4752
The
stability
of
the
equilibr
ium
at
the
or
igin
of
the
errors
system
can
be
obtained
b
y:
_
u
r
ef
_
u
=
K
1
u
1
u
_
!
r
ef
_
!
=
K
1
!
1
!
(15)
where
K
1
u
>
0
;
K
1
!
>
0
are
design
par
ameters
.
and
a
vir
tual
controls
la
w
is
defined
b
y:
u
u
0
=
_
u
r
ef
+
K
1
u
1
u
u
!
0
=
_
!
r
ef
+
K
1
!
1
!
(16)
F
rom
(14)
and
(15)
it
f
ollo
ws
that
(
_
V
(
1
u
)
=
K
1
u
2
1
u
<
0
_
V
(
1
!
)
=
K
1
!
2
1
!
<
0
(17)
At
the
second
step
the
ne
w
errors
giv
en
b
y:
2
u
=
_
u
u
u
0
=
)
_
2
u
=
•
u
_
u
u
0
2
!
=
_
!
u
!
0
=
)
_
2
!
=
•
!
_
u
!
0
(18)
F
rom
(16)
and
(18)
it
f
ollo
ws
that:
_
2
u
=
•
u
•
u
r
ef
K
1
u
_
1
u
_
2
!
=
•
!
•
!
r
ef
K
1
!
_
1
!
(19)
The
augmented
L
y
apuno
v
functions
are
giv
en
b
y:
(
V
(
1
u
;
2
u
)
=
(
2
1
u
+
2
2
u
)
2
V
(
1
!
;
2
!
)
=
(
2
1
!
+
2
2
!
)
2
(20)
Its
time
der
iv
ativ
e
is
then:
_
V
(
1
u
;
2
u
)
=
1
u
_
1
u
+
2
u
_
2
u
_
V
(
1
!
;
2
!
)
=
1
!
_
1
!
+
2
!
_
2
!
(21)
No
w
,
after
substituting
(11),(12)
and
(18)
in
(21)
it
results
that:
_
V
(
1
u
;
2
u
)
=
1
u
2
u
K
1
u
2
1
u
+
2
u
(
•
u
•
u
r
ef
K
1
u
(
K
1
u
1
u
2
u
))
_
V
(
1
!
;
2
!
)
=
1
!
2
!
K
1
!
2
1
!
+
2
!
(
•
!
•
!
r
ef
K
1
!
(
K
1
!
1
!
2
!
))
(22)
In
order
to
satisfy
the
L
y
apuno
v
Condition
_
V
(
1
u
;
2
u
)
<
0
and
_
V
(
1
!
;
2
!
)
<
0
,
the
controls
la
w
is
defined
b
y
:
u
u
=
1
(
•
u
r
ef
(
K
1
u
+
K
2
u
)
2
u
(1
K
2
1
u
)
1
u
)
2
3
!
_
!
+
4
_
u
u
!
=
2
(
•
!
r
ef
(
K
1
!
+
K
2
!
)
2
!
(1
K
2
1
!
)
1
!
)
+
5
(
_
u!
+
u
_
!
)
+
6
_
!
(23)
In
such
a
w
a
y
that:
_
V
(
1
u
;
2
u
)
=
K
1
u
2
1
u
K
2
u
2
2
u
<
0
_
V
(
1
!
;
2
!
)
=
K
1
!
2
1
!
K
2
!
2
2
!
<
0
(24)
V
along
the
tr
ajector
ies
is
negativ
e
definite
.
This
pro
v
es
the
asymptotic
stability
of
the
r
ac
king
tr
ajector
y
of
the
wheeled
mobile
robot,
which
allo
ws
v
er
ifying
the
stability
of
the
equilibr
ium
at
the
or
igin
of
the
error
system.
IJEECS
V
ol.
2,
No
.
3,
J
une
2016
:
478
485
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4752
483
Figure
3.
Arduino
robot
mobile
.
−1
−0.5
0
0.5
1
−1.5
−1
−0.5
0
0.5
1
1.5
x [m]
y [m]
Reference
Actual
(a)
Robot
T
r
ajector
y
0
20
40
60
80
100
−0.1
0
0.1
0.2
0.3
u [m/s]
Reference
Actual
0
20
40
60
80
100
0
0.5
1
1.5
time [s]
ω
[rad/s]
Reference
Actual
(b)
The
Linear
V
elocity
and
Angular
V
elocity
.
0
20
40
60
80
100
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
time [s]
error [m]
(c)
Distance
errors
f
or
e
xper
iments
.
0
20
40
60
80
100
−1
−0.5
0
0.5
1
x [m]
0
20
40
60
80
100
−2
−1
0
1
2
time [s]
y [m]
Reference
Actual
(d)
Time
e
v
olution
of
current
and
the
desired
coordinates
.
.
Figure
4.
Exper
imental
results
4.
Result
and
Anal
ysis
In
this
section,
e
xper
iments
and
sim
ulations
w
ere
carr
ied
out
at
Labor
ator
y
of
P
o
w
er
Sys-
tems
,
Solar
Energy
and
A
utomation
L.E.P
.E.S
.A,
Univ
ersity
of
sciences
and
technology
of
Or
an,
Bac
kstepping
Approach
f
or
A
utonomous
Mobile
Robot
T
r
ajector
y
T
r
ac
king
(Ibar
i
Benaoumeur)
Evaluation Warning : The document was created with Spire.PDF for Python.
484
ISSN:
2502-4752
Or
an,
Alger
ia.
The
proposed
bac
kstepping
controller
is
tested
on
a
Arduino
Robot
Mobile
(Radius
of
185
mm,
height
of
85
mm
and
w
eight
of
0.150
kg),
see
Figure
3,
Arduino
Robot
has
tw
o
pro-
cessors
based
on
the
A
Tmega32u4,
which
admits
linear
and
angular
v
elocities
as
input
ref
erence
signals
and
it
uses
tw
o
DC
motor
dr
iv
en
wheels
.
The
robot
is
wirelessly
connected
to
computer
with
Arduino
Y
un,
these
modules
can
comm
unicate
point
to
point,
from
one
point
to
a
PC
,
or
in
a
mesh
netw
or
k.
Card
arduino
Y
un
mounted
on
the
robot
that
is
used
to
tr
ansmit
data
from
matlab
to
the
robot
using
the
Wireless
netw
or
k
protocol.
4.1.
Discussion
Exper
imental
results
f
or
the
bac
kstepping
controller
proposed
in
sectio
n
3
are
sho
wn
in
figure
4.
The
task
f
or
a
mobile
robot
is
to
f
ollo
w
a
circular
tr
ajector
y
,
the
mobile
robot
star
ts
from
the
initial
p
osture
P
0
(
x;
y
;
)
=
(1
;
0
:
5
;
0
)
,
it
can
be
seen
that
the
robot
f
ollo
ws
the
ref
erence
tr
a-
jector
y
with
small
e
rror
as
see
in
figure
4a.
At
t=20
s
,
it
can
be
seen
in
figure
4c
that
the
distance
error
begins
to
increase
with
time
,
and
tends
to
z
ero
.
The
robot
v
elocities
v
and
!
are
plotted
in
Figure
4b,
and
asymptotically
tr
ac
ks
their
desired
ref
erence
,
there
are
used
to
obtain
the
r
ight
and
left
v
elociities
(
!
l
;
!
r
).
F
rom
Figure
4d,
it
can
be
seen
that
robo
t
arr
iv
es
at
the
end
of
the
ref
erence
tr
ajector
y
and
catches
up
to
the
desired
coordinates
.
Unlik
e
the
af
orementioned
w
or
ks
,
especially
in
compar
ison
with
[17,
20],
in
this
method,
the
tr
ac
k-
ing
errors
are
v
er
y
lo
w
and
the
system
is
guar
anteed
to
be
stab
le
.
5.
Conc
lusion
In
this
w
or
k,
a
re
vie
w
of
the
kinematics
and
dynamics
of
a
dierential
dr
iv
e
wheeled
mobile
robot
w
as
giv
en
and
a
bac
kstep
ping
controller
f
or
a
unicycle-lik
e
mobile
robot
w
as
also
studied
and
tested.
The
control
la
w
w
as
created
b
y
giving
the
robot
f
orw
ard
and
angular
ref
erence
v
eloc-
ities
,
collecting
the
actual
v
elocities
.
The
stability
analysis
based
on
L
y
apuno
v
theor
y
sho
ws
the
eff
ectiv
eness
of
the
control
la
w
which
are
the
tr
ajector
y
tr
ac
king
and
the
stability
maintaining
of
the
closed
loop
dynamics
of
the
mobile
robot.
The
analysis
of
results
sho
ws
the
good
perf
or
mance
of
the
proposed
controller
f
or
tr
ajector
y
tr
ac
king
when
applied
to
an
e
xper
imental
mobile
robot
in
ter
m
of
accur
acy
,
stability
and
con
v
ergence
.
The
tr
ac
king
errors
are
v
er
y
lo
w
with
respect
to
the
mobile
robot
dimensions
.
The
proposed
controller
allo
w
ed
f
or
use
on
diff
erent
robotic
platf
or
ms
and
it
can
be
tested
in
an
en
vironment
with
obstacles
.
In
future
w
or
k,
w
e
intend
to
impro
v
e
the
mobile
robot
b
y
using
the
augmented
reality
[25],
This
w
or
k
can
be
applied
also
to
remote
control
using
the
vir
tual
reality
[26].
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ISSN:
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