Appl. Math. Inf. Sci. 8, No. 5, 2527-2535 (2014) 2527
Applied Mathematics & Information Sciences
An International Journal
http://dx.doi.org/10.12785/amis/080551
A New Intelligent Motion Planning for Mobile Robot
Navigation using Multiple Adaptive Neuro-Fuzzy
Inference System
Prases K. Mohanty
∗
and Dayal R. Parhi
Robotics Laboratory, National Institute of Technology, Department of Mechanical Engineering, Rourkela, Odisha,769008, India
Received: 23 Sep. 2013, Revised: 21 Dec. 2013, Accepted: 22 Dec. 2013
Published online: 1 Sep. 2014
Abstract: Nowadays intelligent tools such as fuzzy inference system (FIS), artificial neural network (ANN) and adaptive neuro-fuzzy
inference system (ANFIS) are mainly considered as effective and suitable methods for modeling an engineering system. This paper
presents a new hybrid technique based on the combination of fuzzy inference system and artificial neural network for addressing
navigational problem of autonomous mobile robot. First we developed an adaptive fuzzy controller with four input parameters, two
output parameters and three parameters each. Afterwards each adaptive fuzzy controller acts as a single takagi-sugeno type fuzzy
inference system, where inputs are front obstacle distance (FOD), left obstacle distance (LOD), right obstacle distance (ROD) (from
robot), heading angle (HA) (angle to target) and output corresponds to the wheel velocities ( Left wheel and right wheel) for the
mobile robot. The effectiveness, feasibility and robustness of the proposed navigational controller have been demonstrated by means
of simulation experiments. The real time experimental results were verified with simulation experiments, showing that the proposed
navigational algorithm consistently performs better results to navigate the mobile robot safely in a completely or partially unknown
environment.
Keywords: ANFIS, Mobile robot, Navigation, Obstacle avoidance
1 Introduction
Autonomous mobile robots have generated much interest
in recent years due to their ability to perform relatively
challenging tasks in hazardous or remote environments.
At present mobile robots have been effectively used in
various areas of engineering such as aerospace research,
nuclear research, production engineering etc. The major
objective in the current robotic research area is to find a
collision free path from a given start position to
predefined target point. In general path planning methods
are classified as local and global depending upon the
surrounding environment. In global path planning the
surrounding environment is completely known to the
mobile robot so the path travelled by the mobile robot is
predefined, where as in local path planning the
environment is completely unknown or partially known to
the mobile robot. So various sensors are used to perceive
the information about the surrounding environment and
plan the motion accordingly. Many exertions have been
paid in the past to improve various robot navigation
techniques.
In literature review, there can be found several
researchers have been addressed on many intelligent
techniques for path planning of mobile robot. Many
authors have considered a controller with complete
information of the environment [
1, 2]. Due to the
complexity and uncertainty of the path planning problem,
classical path planning methods, such as visibility
graph [
3], voronoi diagrams [4], grids [5], cell
decomposition [
6], artificial potential field [7], rule based
methods [
8], and rules learning techniques [9] are not
appropriate for path planning in dynamic environments.
The use of the above algorithms for path finding for
mobile robot requires more time and the finding of this
path will not completely feasible for real-time movement.
There are many fuzzy logic techniques using various
implementations or in combination with other
techniques [
10–14]. Mobile robot path planning based on
neural network approaches presented by many
∗
Corresponding author e-mail:
pkmohanty30@gmail.com
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2528 P. K. Mohanty, D. R. Parhi: A New Intelligent Motion Planning for Mobile Robot...
researchers [15–18]. Among the intelligent techniques
ANFIS is a hybrid model which combines the
adaptability capability of artificial neural network and
knowledge representation of fuzzy inference system [
19].
Song and Sheen [
20] developed a pattern recognition
method based on fuzzy-neuro network for reactive
navigation of a car-like robot. Li et al. [
21]suggested a
neuro-fuzzy technique for behavior based control of a
car-like robot that navigates among static obstacles.
Navigation of multiple mobile robots using neuro-fuzzy
technique addressed by Pradhan et al. [22]. In this design
controller, output from the neural network given as input
to the fuzzy controller to navigate the mobile robot
successfully in the clutter environment. Experimental
verification also has been done with the simulation result
to prove the validity of the developed technique.
Navigation of mobile robots using adaptive neural-fuzzy
system discussed by Nefti et al. [
23]. Different sensor
based information they have given to the SugenoTakagi
fuzzy controller and output from the controller is the
robot orientation. Experimental results settle the
importance of the methodology when dealing with
navigation of a mobile robot in a completely or partially
unknown environment. A neuro-fuzzy controller based
mobile robot navigation presented by Kim and
Trivedi [
24]. In this study they have implemented neural
integrated fuzzy controller to control the mobile robot
motion in terms of steering angle, heading direction, and
speed. Control of mobile robot based on neuro-fuzzy
technique discussed by Godjevac and Steele [25]. In this
paper they have shown how neuro-fuzzy controller can be
achieved using a controller based on the Takagi-Sugeno
design and a radial basis function neural network for its
implementation. To determine collision-free path of
mobile robot navigating in a dynamic environment using
neuro-fuzzy technique presented by Hui et al. [
26]. The
performances of neuro-fuzzy approaches are compared
with other approaches (GA, Mamdani) and it is found that
neuro-fuzzy approaches are found to perform better than
the other approaches.
In this paper we propose a new intelligent
navigational controller for solving navigation problem for
mobile robot in a completely or partially unknown
environment. A new MANFIS (Fig. 1) (Multiple Adaptive
Neuro-Fuzzy Inference System) motion controller has
been developed to solve the optimization problem. Finally
simulation results using MATLAB are presented to verify
the effectiveness of the proposed path planner in various
scenarios populated by stationary obstacles.
2 Kinematic Analysis of Mobile Robot
To control the movement of a mobile robot we need
Kinematic analysis of the robot. The kinematics analysis
of differentially steered wheeled mobile robots in a
two-dimensional plane can be done in one of two ways:
either by Cartesian or polar coordinates. It is assumed that
Input Layer
FOD(X
1
)
ROD(X
2
)
LOD(X
3
)
HA(X
4
)
ANFIS2
ANFIS1
LWV
RWV
ANFIS Layer
Output Layer
Fig. 1: Proposed MANFIS (Multiple ANFIS) controller
for Mobile Robot Navigation
Fig. 2: Mobile Robot Kinematic Parameters
the mobile robot moves without slipping on a plane, that
means there is a pure rolling contact between the wheels
and the ground and also there is no lateral slip between
the wheel and the plane. The modeling in Cartesian
coordinates is the most common use and the discussion
will be limited to modeling in Cartesian coordinates. The
robot has two fixed standard wheels and one caster wheel
and is differentially driven by skid steer motion. The two
driving wheels are independently driven by two motors to
acquire the motion and orientation. Both the wheels have
same diameter 2r (Fig.
2). The driving wheels are
separated by distance L.The position of the robot in the
2-D plane at any instant is defined by the situation in
Cartesian coordinates and the heading with respect to a
global frame of reference.
V
r
(t) = Linear velocity of right wheel
V
l
(t) = Linear velocity of left wheel
r= Nominal radius of each wheel
ω
(t) = Angular velocity of the wheel
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R= Instantaneous curvature radius of the robot trajectory,
relative to the mid-point axis
R-L/2= Curvature radius of trajectory described by left
wheel
R-L/2= Curvature radius of trajectory described by right
wheel
V(t) =
ω
(t)R =
1
2
(V
r
(t) +V
l
(t)) (2.1)
So the tangential velocity in the global reference plane
˙x(t) = V(t)cos
θ
(t) (2.2)
˙y(t) = V(t)sin
θ
(t) (2.3)
˙
θ
(t) =
ω
(t) (2.4)
3 Architecture of Multiple Adaptive
Neuro-Fuzzy Inference System (MANFIS)
for Current Analysis
Adaptive network-based fuzzy inference system (ANFIS)
is one of hybrid intelligent neuro-fuzzy structure and it
functioning under Takagi-Sugeno-type fuzzy interference
system, which was designed by Jang [
19] in 1993.
There are two learning paradigms are used in ANFIS
to show the mapping between input and output data and
to compute optimized of fuzzy membership functions.
These learning methods are back propagation and hybrid.
Parameters associated with fuzzy membership functions
will modify through the learning process.
As for the prediction of left wheel velocity (LWV)
and right wheel velocity (RWV) for mobile robot we
assume each adaptive neuro-fuzzy controller under
consideration of four inputs parameters i.e. Front obstacle
distance(FOD) (x
1
), Right obstacle distance(ROD) (x
2
),
Left obstacle distance(LOD)(x
3
), Heading angle(HA)(x
4
)
and each input variable has three bell membership
functions(MF) (Fig.
4) A
1
(Near), A
2
(Medium) and
A
3
(Far), B
1
(Near), B
2
(Medium) and B
3
(Far), C
1
(Near),
C
2
(Medium) and C
3
(Far), D
1
(Negative), D
2
(Zero) and
D
3
(positive) respectively, then a Takagi-Sugeno-type
fuzzy inference system if-then rules are defined as
follows;
Rule: IF (x
1
is A
i
and x
2
is B
i
and x
3
is C
i
and x
4
is D
i
)
THEN
f
n
(wheel velocity) = p
n
x
1
+q
n
x
2
+r
n
x
3
+s
n
x
4
+u
n
A, B, C, and D are the fuzzy membership sets for the
input variables x
1
,x
2
,x
3
and x
4
respectively. where,
i=1,2,3 and p
n
, q
n
, r
n
, s
n
and u
n
are the linear parameters
of function f
n
and changing these parameters we can
modify the output of ANFIS controller.
The function of each layer in ANFIS structure (Fig.
5)
is discussed as follows:
Fig. 3: Parameters in the bell membership function
Input Layer: In this layer nodes receive signals from
array of sensors (x
1
,x
2
,x
3
and x
4
) which specify the
position of the obstacles and target. That is defined as
O
0,FOD
= X
1
,
O
0,ROD
= X
2
,
O
0,LOD
= X
3
,
O
0,HA
= X
4
(3.1)
First Layer: This layer is the adaptive fuzzy layer.
Neurons in this layer complete the fuzzification process.
Every node in this stage is an adaptive node (square node)
and calculating the membership function value in fuzzy
set. For four inputs the outputs from nodes in this layer
are presented as
O
1,i
=
µ
A
i
(X
1
),
O
1,i
=
µ
B
i
(X
2
),
O
1,i
=
µ
C
i
(X
3
),
O
1,i
=
µ
D
i
(X
4
)
(3.2)
Here O
1
,i is the bell shape membership grade of a
fuzzy set S ( A
i
, B
i
,C
i
and D
i
) and it specifying the
degree to which the given inputs ( x
1
, x
2
, x
3
and x
4
)
satisfies the quantifier S. Membership functions for A, B,
C and D considered are the bell shape function and
defined as follows;
µ
A
i
(x) =
1
1+ [(
x
1
−c
i
a
i
)
2
]
b
i
, (3.2 a)
µ
B
i
(x) =
1
1+ [(
x
2
−c
i
a
i
)
2
]
b
i
(3.2 b)
µ
C
i
(x) =
1
1+ [(
x
3
−c
i
a
i
)
2
]
b
i
(3.3 c)
µ
D
i
(x) =
1
1+ [(
x
4
−c
i
a
i
)
2
]
b
i
(3.4 d)
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2530 P. K. Mohanty, D. R. Parhi: A New Intelligent Motion Planning for Mobile Robot...
a
i
, b
i
and c
i
(Fig. 3) are parameters that control the
Centre, width and slope of the Bell-shaped function of
node i respectively. Changing these parameters will give
the various contour of bell shaped function as required in
accordance with the data set for the problem defined.
These are also known as premise parameters.
20 30 40 50 60 70 80 90 100
0
0.2
0.4
0.6
0.8
1
FOD
Degree of membership
Near
Medium
Far
(a)
10 20 30 40 50 60 70 80 90 100
0
0.2
0.4
0.6
0.8
1
ROD
Degree of membership
Near
Medium Far
(b)
10 20 30 40 50 60 70 80 90 100
0
0.2
0.4
0.6
0.8
1
LOD
Degree of membership
Near Medium Far
(c)
−30 −20 −10 0 10 20 30
0
0.2
0.4
0.6
0.8
1
HA
Degree of membership
Negative
Zero
Positive
(d)
Fig. 4: (a-d) Membership functions for input parameters
(FOD, ROD, LOD, HA) of MANFIS controller
Second Layer: It is also known as rule layer. Every
node in this layer is a fixed node (circular) and labeled as
π
n
. Every node in this stage corresponds to a single
Sugeno-Takagi fuzzy rule. Each rule point receives inputs
from the respective points of layer-2 and calculates the
firing strength of the each fuzzy rule. Output from each
node is the product of all incoming signals.
O
2,n
= W
n
=
µ
A
i
(x
1
).
µ
B
i
(x
2
).
µ
C
i
(x
3
).
µ
D
i
(x
4
) (3.3)
There W
n
represents the firing strength or the truth
value, of nth rule and n=1, 2, 3, ... 81 is the number of
Sugeno-Takagi fuzzy rules.
Third Layer: It is the normalization layer. Every
node in this layer is a fixed node (circular) and labeled as
N
n
. Each point in this layer receives inputs from all points
in the adaptive fuzzy rule layer and calculates the
normalized firing strength of a given rule. The normalized
firing strength of the nth point of the nth rules firing
strength to sum of all ruless firing strength.
O
3,n
=
W
n
=
W
n
∑
81
n=1
W
n
(3.4)
Fourth layer: Every node in this layer is an adaptive
node (square node). Each node in this layer is connected
to the corresponding normalization node and also receives
Fig. 5: The structure of ANFIS 1 network for Mobile
Robot Navigation
initial inputs x
1
, x
2
, x
3
and x
4
. A defuzzification node
determines the weighted consequent value of a given rule
presented as,
O
4,n
= W
n
f
n
= W
n
[p
n
(x
1
)+ q
n
(x
2
)+ r
n
(x
3
)+ s
n
(x
4
)+ u
n
]
(3.5)
Where
¯
W
n
is a normalized firing strength from layer-3
and p
n
, q
n
, r
n
, s
n
and u
n
are the parameters set of this node.
These parameters are also called consequent parameters.
Fifth layer: It is represented by a single summation
node (circular node). This single point is a fixed point and
labeled as
∑
. This point determines the sum of outputs of
all defuzzification points and gives the overall model
output that is wheel velocity.
O
5,n
=
81
∑
n=1
W
n
f
n
=
∑
81
n=1
W
n
f
n
∑
81
n=1
W
n
(3.6)
4 Simulation experiments and discussion
A variety of situations and routes were simulated on a
computer using MATLAB version R2008a [
29]. The
coordinates of the sides of the paths as well as
coordinates of any static obstacles were known to the
MANFIS controller. Knowing the coordinates of the
robot, the current navigational controller can thus
calculate the distances and heading angle of the robot, as
if it was sensor. In current navigation model, we
developed two main reactive behaviors: one to reach the
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FAR
FAR
ROBOT
ROBOT
Left Near
Right Near
ROBOT
Right Corner Front Near
Corridor
Closed Corridor
Left Corner
ROBOT
ROBOT
ROBOT
ROBOT
ROBOT
(i) (ii) (iii) (iv)
(v)
(vi)
(vii)
(viii)
Fig. 6: Examples of various reactive behaviors
Fig. 7: Navigation of single robot using current analysis
target and the other avoiding obstacles. Fig.
6 shows the
examples of different reactive behaviors.
Let us consider, every obstacle is far away from the
robot and then only the reach target behavior will be
actived. Other side when a robot close to an obstacle, it
must changes its velocity to avoid the obstacle present on
the path. Various reactive behaviors will be activated
depending upon the situation between robot and obstacle.
The simulation experiments (Fig.
7 and Fig.8) were
performed by placing the obstacles at random positions
and a random heading angle to verify the various reactive
behaviors developed by current navigational controller. In
simulation graph red color path shows the activation of
reactive behaviors by mobile robot.
5 Comparison with other algorithms
In this section the methods proposed in the literature
survey for overcoming the local minimum problem are
discussed and compared with the current approach.
Fig. 8: Single robot escaping from corner end
1.Path planning of a wheeled mobile robot using
artificial neural network (ANN) suggested by Engedy
et al. [
27]. In this work they have presented a neural
controller with back propagation technique, which
uses potential field for obstacle avoidance and the
neural controller is aware of its distance sensor
readings and its relative position from the target. The
simulation result for the above controller is given in
Fig.
9a. The simulation result using current controller
is given in Fig.
9b.
2.An intelligent motion planning and navigation system
for omnidirectional mobile robot using fuzzy logic
presented by Zavlangas et al. [
28]. The
fuzzy-rule-base of the proposed system combines the
repelling effect, which is related to the distance and
the angle between the robot and nearby obstacles,
with the attracting effect produced by the distance and
the angular difference between the actual direction
and position of the robot and the final configuration,
to generate actuating commands for the mobile
platform. The simulation result for the above model is
given in Fig.
10a. The simulation result using current
controller is given in Fig.
10b.
6 Experimental Results
To show the effectiveness of the proposed control system
and authenticity of the technique, a variety of real time
experiments were conducted using Khepra-III mobile
robot (Fig. 11). The mobile robot has 10 infrared sensors
and 5 ultrasonic sensors mounted around the front
periphery of the mobile robot in order to sense the front,
left, right obstacle distance from robot and target angle to
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