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Al-Khwarizmi 

  Engineering  
Journal 

Al-Khwarizmi Engineering Journal,Vol. 13, No. 3, P.P. 64- 73 (2017) 

 

A Cognitive Hybrid Tuning Control Algorithm Design for Nonlinear 

Path-Tracking Controller for Wheeled Mobile Robot 
 

Ahmed S. Al-Araji*            Noor Q. Yousif** 
*,**Department of Control and Systems Engineering/  University of Technology 

*Email:ahmedalaraji76@gmail.com 

 
(Received 13 December 2016; accepted 7 March 2017)  

https://doi.org/10.22153/kej.2017.03.004 
 

 

Abstract  

This research presents a on-line cognitive tuning control algorithm for the nonlinear controller of path-tracking for 

dynamic wheeled mobile robot to stabilize and follow a continuous reference path with minimum tracking pose error. 

The goal of the proposed structure of a hybrid (Bees-PSO) algorithm is to find and tune the values of the control gains 

of the nonlinear (neural and back-stepping method) controllers as a simple on-line with fast tuning techniques in order 
to obtain the best torques actions of the wheels for the cart mobile robot from the proposed two controllers. Simulation 

results (Matlab Package 2012a) show that the nonlinear neural controller with hybrid Bees-PSO cognitive algorithm is 

more accurate in terms of fast on-line finding and tuning  parameters of the controller lead to obtaining smoothness with 

small spikes control action as well as minimizing tracking pose error of the wheeled mobile robot than the performance 

of nonlinear back-stepping technique. 

 

Keywords: Bees Algorithm, Nonlinear Controller, Matlab Package, Particle Swarm Optimization, Wheeled Mobile 

Robots. 

 

1. Introduction 
 

In general, a wheeled mobile robot system 

considers a multi-input multi-output nonlinear 
dynamic and time variant system and the one of 

fundamental problems in the control engineering 

is the motion control design to track the desired 
path [1] because the mobile robot has many 

applications in various directions life such as: 

science; education; industry; entertainment; 
security and military therefore the mobile robot is 

still active region of research [2]. 

In the recent years, different types of control 

algorithms and controllers that they are based on 
mathematical model of the wheeled mobile robot 

and they are proposed to solve the motion control 

of the robot’s wheels in order to follow the 
desired trajectory with high performance of the 

controllers in terms of generating optimal action 

that lead to minimizing tracking pose error during 
tracking reference path, such as nonlinear neural 

PID controllers [3 and 4], fuzzy logic and PID 

controllers [5 and 6], neural networks controllers 
[7 and 8],  back-stepping controllers [9 and 10], 

adaptive sliding mode controllers [11 and 12] and 

neural predictive controllers [13 and 14]. 
The motivation for this research is taken from [2, 

3, 4 and 10] which are focusing on the problems 

of the mobile robot in terms of tracking and 

stabilizing the mobile robot on the desired path as 
well as how can generate best torque control 

action without saturation state and no spike 

action? 
The main core of the contribution of this research 

is described as follows: 

• Using a different types of controllers with high 
computational accuracy that have been derived 
of the control laws in order to generate best 

torque action and lead to minimizing tracking 

pose error of the wheeled mobile robot. 

• Cognitive hybrid Bees-PSO optimization 
algorithm proposed to show the ability in the 
fast search in local (PSO) and global (Bees) 



Ahmed S. Al-Araji                             Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 64- 73 (2017) 

 

65 

 

regions in order to find and tune on-line the best 
parameters of the two types of controllers. 

• Adding a dynamic disturbance to investigate the 
robustness performance of the proposed 

controllers. 

• Changing the initial pose state to verify the 
adaptation performance of the proposed 

controllers. 

• Tracking a variable radius continuous trajectory 
to validate the capability of the proposed 

controllers. 
 

The organization of this paper can be described 

as follows: in Section two, is a description of the 
dynamic wheeled mobile robot model. Section 

three is deriving the different types of the  

proposed nonlinear controllers. In section four, 

the proposed of a cognitive hybrid Bees-PSO 
optimization algorithms is explained. Section five 

is presented the performance of the proposed 

controllers through simulation results. In section 
five, the conclusions are drawn. 

 

 

2. Model of a  Dynamic Wheeled Mobile 
Robot 

 

Fig.1 shows the schematic diagram of the cart 

wheeled mobile robot that it consists of a two DC 

motors which is driving the two wheels with one 
an omni-directional castor wheel that will 

stabilize the platform of the mobile robot [12 and 

13]. The motion and orientation of the mobile 
robot depends on a two independent actuators 

(DC motors) for left and right wheels. r is the 
radius of the same of the two wheels and the 

distance between these wheels is  L and c is the 
center of gravity of the mobile robot.  

 

 
 
Fig. 1. Mobile robot Platform model. 

 

In general, the global coordinate frame is defined 

as [ ]YXO ,,  while the pose vector of the mobile 

robot in the surface is defined as:  
T

yxq ),,( θ=                                                       … (1) 

The position coordinates (x,y) are at point cwhile 
θ  is orientation angle that is measured with 
respect to global frame in the X-axis therefore the 

configuration of mobile robot can be described by 
these three generalized coordinates.  

To investigate the motion and orientation of the 

wheeled mobile robot, two conditions should be 
achieved; the first is pure-rolling and the second is 

without-slipping in order to make the mobile 

robot’s lateral velocity is equal to zero as equation 

(2) [3 and 4]. 

0)(cos)()(sin)( =+−
••

ttyttx θθ                            …(2) 

Then, the equations of the kinematics wheeled 
mobile robot in the world frame can be 

represented as follows [7 and 10]: 

)(cos)
2

)()((
)( t

twltwrr
tx θ

+
=&                                 …(3) 

)(sin
2

))()((
)( t

twltwrr
ty θ

−
=&                                 …(4) 

L

twltwrr
t

))()((
)(

−
=θ&

                                         …(5) 

where wr(t)  and wl(t) are the right and left 

angular velocities respectively. 

Based on Euler Lagrange formulation [9 and13], 
the dynamic model of the mobile robot can be 

described as follows: 

λθ

θ

τ

τ
θθ

θθ

τ

θ 













−

+


























−
=+



































••

••

••

0

cos

sin

22

sinsin

coscos
1

00

00

00

R

L

LLr
dy

x

I

M

M ..(6) 

where  

L
τ is the torque of the left wheel. 

R
τ  is the torque of the right wheel. 
M is the mobile robot’s mass. 

I  is the mobile robot’s inertia.  

λ is the constraint forces. 

d
τ is bounded dynamic disturbances. 
The pose equations of the mobile robot in the 

simulation can be described as follows:    

���� =
�����	�
���

�
                                         …(7) 

�
 ��� =
�.����������
����

�
                              …(8) 

��������� =
����

�
                                            …(9) 

���
�� ��� =
�����

�
                                        …(10) 

������� = ��������� × ∆!                           …(11) 
�
�� ��� = ���
�� ��� × ∆!                         …(12) 

"#��� =
�.�$%&�'(���	&�()����*

�
                      …(13)       



Ahmed S. Al-Araji                             Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 64- 73 (2017) 

 

66 

 

"+��� =
�.�$%&�'(����&�()����*

�
                      …(14) 

)1()(cos)]()([5.0)( −+∆+= kxtkkwlkwrrkx θ ...(15) 

)1()(sin)]()([5.0)( −+∆+= kytkkwlkwrrky θ ...(16) 

)1()]()([)( −+∆−= ktkwlkwr
L

r
k θθ      …(17) 

where � is total linear force; �
  is total angular 
torque;  ������ is linear acceleration; ���
��  is 
angular acceleration; ���� is linear velocity; �
��  
is angular velocity; "+ is angular velocity of the 
left wheel; "# is angular velocity of the right 
wheel; )(),(),( kkykx θ  are the pose of the mobile 

robot at each step kth of the movement and t∆ is 
the sampling time. 

 

 

3. Nonlinear Controller Methodology 
 

In general, a feedback control signal based on 

different types of the nonlinear controllers are 
very important in the structure of the proposed 

controller in terms of stabilizing and minimizing 

the tracking pose error of the wheeled mobile 
robot during the mobile robot’s pose is drifted 

from the reference path.  

Block diagram of the proposed structure of the 
nonlinear trajectory tracking controllers for 

wheeled mobile robot can be shown in Fig. 2.  

The first structure of the nonlinear controller 

equation is neural network that it performed as a 
nonlinear PID controller [3 and 4]. The nonlinear 

neural control structure has strong of adaptation 

performance, high dynamic characteristic and 
good robustness performance because the 

proposed structure is built on a traditional PID 

controller and employed the theory of the neural 
network technique. The structure of the proposed 

nonlinear neural controller can be shown in Fig. 3. 

The proposed control law of the nonlinear neural 

controller for the right and left torques as follows:  

yxRR
oBoBkBk

12111
)1()( ++−= ττ                       (18) 

θττ oBoBkBk yLL 141315 )1()( ++−=                  …(19) 

The outputs 
yx

oo , and θo  of the neural networks. 

Sigmoid function is used as nonlinear relationship 
as equation (20) [3 and 4]:  

1
1

2
−

+
=

− γγ nete
o                                       …(20)         

Where .,, θγ yx=
 

γnet is calculated from these equations: 

)]1()([)]([)(
32

−++= kekeBkeBknet
xxxx

)]1()([
4

−−+ kekeB
xx

                                    …(21) 

)]1()([)]([)(
65

−++= kekeBkeBknet
yyyy

)]1()([
7

−−+ kekeB
yy

                                    …(22) 

)]1()([)]([)(
98

−++= kekeBkeBknet θθθθ

)]1()([
10

−−+ kekeB θθ                                     …(23) 

where 

)(keγ  is the input error signal. 

The control parameters B1, B2, … and B15 are 

on-line updated by using  cognitive hybrid Bees-
PSO optimization algorithm. 

 
 

 

 

 
 

 

 
 

 

 
 

 

 

 
 

 

 
 

 

 
 

 

 

Fig. 2. The proposed structure of nonlinear trajectory tracking controllers for mobile robot. 

 

Nonlinear Controller 

Equations  

 

Cognitive Hybrid Bees-
PSO Algorithm 

)2(

)1(

)(

−

−

ke

ke

ke

γ

γ

γ  









)(

)(

k

k

L

R

τ

τ  
 

 

+       - 

Dynamic Disturbances 

[ ])1()1( −− kk
LR

ττ  
∆
  

)1(

)1(

)1(

+

+

+

k

ky

kx

θ

 

Rotation 
Matrix 

)1(

)1(

)1(

+

+

+

k

ky

kx

r

r

r

θ

 

Reference 

Velocities Eqs. 

Parameters 

 



Ahmed S. Al-Araji                             Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 64- 73 (2017) 

 

67 

 

 
 

 

 
 

 

 

 
 

 

 
 

 

 

 
 

 

 
 

Fig. 3. The structure of nonlinear neural controller 

[3 and 4]. 

 

The second structure of the nonlinear 
controller equation is back-stepping technique 

based on Lyapounov method [10]. The nonlinear 

back-steeping controller method structure can be 

shown in Fig. 4. 
Based on back-stepping technique in [9 and 

10], the nonlinear angular velocity control law can 

be described by Eq. (24) and applying the 
proposed hybrid Bees-PSO tuning algorithm for 

finding and tuning the best value of the 

parameters (B1, B2 and B3) then solving 

equations (7 to 14) to find the right and left 
torques control action for wheeled mobile robot. 























++−+

++++

=








r

evBevBw
L

eBev

r

evBevBw
L

eBev

w

w

ryrrxr

ryrrxr

L

R

))sin(
2

cos(

))sin(
2

cos(

321

321

θθ

θθ

 

(24)

 

 

 

 

4. Cognitive Hybrid Bees-PSO Algorithm 
 

The purpose of the on-line cognitive hybrid 

Bees-PSO algorithm is to find and tune the 

optimal gains control for the proposed controller 
to generate the best and smoothness torque signal 

that will lead to minimizing the tracking pose 

error of the wheeled mobile robot during dynamic 
disturbance has been added.  

In general, Bees algorithm mimics the food 

foraging behavior of swarms of honey bees and 
this algorithm carries out by using local 

(neighborhood) search that has two types of Bees 

(Selected and Recruit Bees) and global (random) 

search that has also two types of Bess (Scout and 
Fittest Bees) [15 and 16] while the particle swarm 

optimization (PSO) is considered one of the 

algorithms types that has a capability to search for 
the optimal solution by simulating the movement 

and flocking of birds. In PSO algorithm, the 

particles that have a position and velocity are a 

population of individual in order to move around 
the search space to find best or optimal solution 

through evaluation each particle by using a fitness 

function [3 and 4]. 
  

 

4.1. Hybrid Bee-PSO (HBPSO) Algorithm 
 

In this work, the proposed on-line optimization 

algorithm is a hybrid tuning control algorithm 

which consists of Bees algorithm [15 and 16] and 
PSO algorithm [3 and 4].  

The main advantages for this proposed 

optimization algorithm are to solve the problem of 
local search of the Bees algorithm using PSO 

algorithm which has the high ability for local 

search through generating population (Recruit 

Bees) as particles and this will speed up the 
process of optimization while the problem of the 

global search in the PSO algorithm is solved by 

using Bees algorithm which has the capability of 
combining the (Fittest Bees) and a new population 

of (Scout Bees) generating in the global search. 

The proposed on-line HBPSO algorithm is 
applied as a powerful optimization algorithm to 

H 

)(ke
x

 

+ 

)(kRτ  

)1( −k
R

τ

Ox 

 
+ 

 
+ 

+1 

+1 

 
+ 

+1 

)1( −ke
x

 

B1 

H 

)(ke
y

 
Oy 

 
+ 

 
+ 

+1 

+1 

+1 

-1 

 
+ 

+1 

)1( −ke
y

 

H 

)(keθ
 

+ 

)(kLτ  

)1( −k
L

τ  

O

 
+ 

 
+ -1 

+1 

+1 

+1 
 
+ 

+1 

-1 

)1( −ke
θ

 

-1 

+1 

B15 

B11 

B12 

B13 

B14 

B2 

B3 

B4 

B5 

B6 

B7 

B8 

B9 

B10 

Fig. 4. The nonlinear back stepping controller structure [10]. 

 

),,,,,(
3,2,1

BLrwvqfv
rrecc

=

 















θe

ey

ex

 

[ ]
321

BBB  [ ]rr wv  










L

R

w

w  
t

velocity

∂

∂  

[ ]Lr  










ang

lin

Acc

Acc
 ( )IM  









L

R

τ

τ  



Ahmed S. Al-Araji                             Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 64- 73 (2017) 

 

68 

 

find and tune the optimal stable parameters of the 
nonlinear neural controller in order to enhance the 

performance characteristics of the system by 

reducing the processing time as well as improve 
the response accuracy through minimizing the 

tracking error for mobile robot. 

The proposed HBPSO algorithm’s steps can be 

described as follows: 
1. Scout Bees (n) are generated in the global 

(random) search as the initial population with 

randomly fifteen values of the controller’s 
parameters in the nonlinear neural controller 

while only three control parameters in the 

nonlinear back-stepping controller.  

2. Calculated the fitness of the (n) Scout Bees by 
using the fitness equation (25) [3] based cost 

function. 

  -.!/011 =
2

3	4567  �8�97�5�
                           ...(25) 

Where: 

: > 0  to avoid division by zero. 
The proposed cost function is a mean square error 

as equation (26). 

=>? =
2

@
∑ ��B�CD − B�

%+�G�CD − G�
%�H�CD − H�

%@
�I2                         

 + ��+./�CD − �+./�
% + �J�CD − J�

%�              …(26)  
K: is the number of iteration. 
3. In the local search, chosen the number of 

particles depends on the number of the highest 
fitness for the Scout Bees (population) as (m) 

Selected Bees. 

4. The size of (patch size) of the local search is 
determined by applying the proposed 
equations (27).  

∆L̅ = 0.025 × L̅5PQ × #R/STU�0,1�           …(27) 
  L̅�CX = L̅5PQ + ∆L̅                                      …(28) 
  Where 

  L̅ : is the vector of the fifteen parameters of the 
proposed controller. 

 

5. Particles are generated by using equations (28) 
to search and find the best controller’s 
parameters. 

6. Evaluated the proposed cost function of each 
particle using the mean square error equation 
(26). 

7. Set to pbest for each particle in the current 
searching point. When the search is finding the 
best value of pbest then sets the pbest to gbest 

and store the number of the particle with the 

best value.  

8. The pbest value is replaced by the current 
value if the value is better than the current 

pbest of the particle and if the best value of 

pbest is better than the current gbest, gbest is 
replaced by the best value and the particle 

number with the best value is stored. 

9. Each particle is update by using Eqs. (29 and 
30).  

)()(
)(

)(

22

)(
)(

11

)()1( k

m
k

k

m
k

m

k

m

k

m BgbestrcBpbestrcBB −+−+Ω∆=∆
+

 
…

(29)

)1()()1( ++
∆+=

k

m

k

m

k

m BBB                      …(30) 

where  

popm ,.....3,2,1= ;

)(k

mB is the particle’s weight m at 

kth iteration; Ω : is the inertia weight factor;   c1 and 

c2 are the positive values ;  r1 and r2 are random 

numbers between 0 and 1; 
m

pbest is best previous 

weight of m
th
 ;Particle and gbest is best particle 

among all the particle in the population. 

10. Return to step six if the current iteration 
number did not reach to the predefined 
maximum iteration number otherwise pick out 

the highest fitness for the particles as Fittest 

Bees (m). 
11. Return to global search by assign the (n-m) 

remaining Bees to random search and 

generating a new population of Scout Bees. 
 

In general, the steps of the on-line cognitive 

hybrid Bees-PSO optimization algorithm for 

finding and tuning control parameters are repeated 
at 0.1 second (sampling time) for each k

th
 sample 

based on Shannon theorem. 

 

 

5. Simulation Results 
 

MATLAB package used to verify the proposed 

nonlinear controllers of the trajectory tracking for 

the dynamic model of the wheeled mobile robot. 

The Eddie mobile robot platform specifications 
are picked from [17]: M=12kg is the mobile 

robot’s mass; I=1.536kg.m
2
 is the mobile robot’s 

inertia; r=0.075m is the radius of wheel and 
L=0.39m is the distance between wheels. 

The MATLAB simulation is carried out on-

line cognitive tuning control algorithm with 
proposed controllers as shown in Figure (2) to 

track a reference pose with continuous variable 

radius path and 0.1 sec is sampling time. In this 

paper, two types of the nonlinear controllers are 
used (neural network and back-stepping 

technique) with hybrid Bees-PSO tuning control 

parameters to show which of them is batter in 
term of generating optimal and smoothness torque 

control action and minimizing the tracking error 

with minimum number of iteration. The 

parameters of the optimization hybrid Bees-PSO 
algorithm that will define as follows: 

The Scout Bees (n) is equal to 10 at the global 

search; the Selected Bees is equal to 5; the particle 
is equal to 40 in the local search; the Fittest Bees 



Ahmed S. Al-Araji                             Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 64- 73 (2017) 

 

69 

 

is equal to 5; the iteration number (N) in the 
global search is equal to 3and the iteration number 

(P) in the local search is equal to 3. 

 
 

Case Study 
 

The reference pose trajectory for wheeled 
mobile robot can be described in below equations 

(31, 32 and 33):  

)
20

2
sin()(

t
tx

r

π
=                                                

…(31) 

)
40

2
sin()(

t
ty

r

π
=                                             …(32) 

)
)())(())((

)(
(tan2)(

22

1

txtytx

ty
t

rrr

r
r

∆+∆−∆

∆
=

−θ

…

(33) 

The mobile robot has initial pose as

]4/,0,1.0[)0( π−=q . After applying the structure 
of the cognitive hybrid Bees-PSO tuning control 

algorithm with two different types of the 

nonlinear controllers and adding small values of 
the dynamic disturbances as the term that taken 

from [14] [ ]Tttd )2sin(01.0)2sin(01.0=τ to show 
the controller ability of robustness through the on-

line adaptation the parameters of these controllers. 
The trajectory tracking for mobile robot model 

can be shown in Fig. 5 which it is clearly, the 

excellent tracking performance depends on MSE 

of the mobile robot pose when was applying the 
nonlinear neural controller than nonlinear back-

stepping controller because the cognitive hybrid 

Bees-PSO tuning control algorithm was found and 
tuned fifteen parameters of the nonlinear neural 

controller that covered the nonlinear operation 

regions while in the nonlinear back-stepping 

controller has three parameters only and could not 
cover  these regions especially when adding a 

bounded dynamic disturbances. This proposed 

control algorithm has a capability of perfect 
search in two search space (local and global) with 

minimum number of iteration in both search 

space. 
 

 

 
 
Fig. 5. The desired and actual trajectory for mobile 

robot. 

 

 

In Fig. 6 demonstrates the orientation tracking 

performance of the mobile robot with two types of 

controllers. 
 

 
 

Fig. 6. The desired and actual orientation for mobile 

robot. 

 

 

In this on-line tuning control algorithm, the 
proposed Mean Square Error (MSE) clearly 

improved the performance of these controllers by 

showing the pose error convergence for the 
mobile robot motion at 200 steps, as shown in 

Figs. 7 and 8. 

 

 

 

 

-1.2 -1 -0.5 0 0.5 1 1.2
-1.2

-0.5

0

0.5

1.2

X-axis (meter)

Y
-a

x
is

 (
m

e
te

r
)

 

 

Actual Path based Back Stepping

Actual Path based Neural 

Desired Path

20 40 60 80 100 120 140 160 180 200
-4

-3

-2

-1

0

1

2

3

4

Samples (Sampling Time 0.1 Sec)

O
r

ie
n

ta
ti

o
n

 (
r

a
d

)

 

 

Orientation based Back -Stepping

Orientation based Neural

Desried Orientation



Ahmed S. Al-Araji                             Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 64- 73 (2017) 

 

70 

 

 

Fig. 7. On-line performance index for nonlinear 

neural controller. 

 

 

Fig. 8. On-line performance index for nonlinear 

back-stepping controller. 

 
 

Fig. 9 shows the effectiveness of the nonlinear 

neural controller response through generating best 
torque control action without saturation control 

action state to track the desired path in minimum 

time while the torque control action for the 
nonlinear back-stepping controller can be shown 

in Fig. 10 which has non smoothens and not high 

spikes and reach to the maximum saturation 

torque action value in data sheet of motor [17] is 3 
N.m only at starting and for very short time. 

 

 

Fig. 9. Torque control action for nonlinear neural 

controller. 

 

Fig. 10. Torque control action for nonlinear back-

stepping controller. 

 

 

The response of angular velocity of the left and 

right wheels of the platform Eddie wheeled 

mobile robot can be shown in Fig. 11 have 
smoothness response which are generated from 

nonlinear neural controller while the angular 

velocities of the left and right as shown in Fig. 12 
have small spikes response that are generated 

from the nonlinear back-stepping controller. 

It is clear, that the response between (60 to 80) 
samples and between (120 to 140) samples of the 

torque and angular velocity as shown in Figs. 9 

and 11 respectively are non-smooth and have 

spikes because in this region the orientation in 
Fig. 6 is changing between -180

o
 to 180

o
 that 

needs to add 2pi for correcting the orientation and 

this big change will lead to small spikes and non-
smooth response in this region.  

Figs. 13-a,b,c show the robustness and 

adaptation performance of the proposed controller 

in terms of keeping on minimum tracking pose 
error for the wheeled mobile robot and stabilizing 

the pose of the mobile robot when the mobile 

robot tries to drift from the desired path because 
the effect of the bounded dynamic disturbances to 

the system.  
  
 

 

 

 

 

 
 

Fig. 11. Angular Velocities of the left and right 

wheels for nonlinear neural controller. 

 

20 40 60 80 100 120 140 160 180 200
0

0.005

0.01

0.015

0.02

0.025

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Ahmed S. Al-Araji                             Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 64- 73 (2017) 

 

71 

 

 
 

Fig. 12.  Angular Velocities of the left and right 

wheels for nonlinear back-stepping controller. 

 

 
 

Fig. 13. Pose error of the mobile robot: a) error in 

X-axis; b) error in Y-axis; c) orientation error. 

 

 

6. Conclusions 
 

The simulation results on the on-line cognitive 
hybrid Bees-PSO tuning algorithm of different 

types of nonlinear controllers are presented in this 

paper for the dynamic wheeled mobile robot 

model which shows preciously and that the 

proposed hybrid Bees-PSO tuning control 
algorithm was better than the results in [3 and 4] 

in terms of the following capabilities: 

• Fast and stable on-line finding and tuning the 
parameters of the controller with minimum 
number of iteration in the local and global 

search. 

• Obtaining best torque control action, with small 
spikes as well as no saturation torque action 

state for the nonlinear neural controller. 

• Minimizing the pose error and no oscillation 
output for the wheeled mobile robot during 

motion in the reference path. 

• Strong adaptability and robustness performance 
when dynamic disturbances have been added to 
the mobile robot. 

 

 

7. References 
 
[1] Leenaa N. and  Sajub K.K., Modelling and 

Trajectory Tracking of Wheeled Mobile 

Robots.  International Conference on 

Emerging Trends in Engineering, Science and 
Technology (ICETEST - 2015), vol. 24, 

Pages 538–545. 2016. 

[2] Asif M., Khan M. J., Rehan M. and Safwan, 
M., Feedforward and Feedback Kinematics 

Controller for Wheeled Mobile Robot 

Trajectory Tracking. Journal of Automation 

and Control Engineering, vol. 3, no.3, 
pp.178–182. 2015. 

[3] Ahmed  Al-Araji, Comparative Study of 

Various Intelligent Algorithms Based 
Nonlinear PID Neural Trajectory Tracking 

Controller for the Differential Wheeled 

Mobile Robot Model. Journal of Engineering 

vol. 20, no. 5, pp. 44-60. 2014 

[4] Khulood E. Dagher and Ahmed Al-Araji, 
Design of a Nonlinear PID Neural Trajectory 

Tracking Controller for Mobile Robot based 

on Optimization Algorithm. Engineering & 
Technology Journal. Vol. 32, no. 4, pp 973-

986. 2014.   

[5]  Safwan M., Uddin V. and Asif M., 

Nonholonomic Mobile Robot Trajectory 

Tracking using Hybrid Controller, Mehran 
University Research Journal of Engineering 

and Technology, vol. 35, no. 2, 2016. 

[6]  Martinez-Soto R., Castillo  O., Aguilar  L. 

and Baruch, I, Bio-Inspired Optimization of 

Fuzzy Logic Controllers for Autonomous 
Mobile Robots, Fuzzy Information Processing 

Society (NAFIPS-2012),  Annual Meeting of 

the North American, pp. 1–6, 2012.  

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The Angular Velocity of Left Whe el

The Angular Velocity of Right Wheel

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0

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Ahmed S. Al-Araji                             Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 64- 73 (2017) 

 

72 

 

[7]  Abdallan TY and Hamzah MI, Trajectory 
Tracking Control for Mobile Robot using 

Wavelet Network, International Journal of 

Computer Applications, vol. 74, no. 3, pp. 32-

7, 2013. 

[8] Ye J., Tracking Control for Nonholonomic 
Mobile Robots: Integrating the Analog Neural 

Network into the Backstepping Technique, 

Neurocomputing, vol. 71, no. 16–18, pp. 
3373–3378, 2008. 

[9] Hou Z.-G, Zou A.-M., Cheng L. and Tan M., 

Adaptive Control of an Electrically Driven 

Nonholonomic Mobile Robot via 
Backstepping and Fuzzy Approach, IEEE 

Transactions on Control Systems Technology, 

vol.17, no.4,pp. 803–815, 2009. 
[10] Ahmed Al-Araji, Development of kinematic 

path-tracking controller design for real mobile 

robot via back-stepping slice genetic robust 
algorithm technique. Arabian Journal for 

Science and Engineering 39 (12), 8825-8835, 

2014. 

[11] Koubaa Y., Boukattaya M. and Dammak T., 
Adaptive Sliding-Mode Dynamic Control for 

Path Tracking of Nonholonomic Wheeled 

Mobile Robot. Journal of Automation and 
Systems Engineering vol. 9,no. 2, pp. 119-

131, 2015. 

[12] Aicha B.,  Atallah B.1 and Farès B., Integral 
Sliding Mode Control for Trajectory Tracking 

of Wheeled Mobile Robot in Presence of 

Uncertainties, Journal of Control Science and 

Engineering,  
vol.2016, article ID 7915375, 2016. 

[13] Ahmed Al-Araji, Maysam Abbod, and Hamed 
Al-Raweshidy, Neural autopilot predictive 

controller for nonholonomic wheeled mobile 

robot based on a pre-assigned posture 
identifier in the presence of disturbances. 2nd 

International Conference on Control, 

Instrumentation and Automation (ICCIA),pp. 

326-331, 2011.  

[14] Ahmed S. Al-Araji, Maysam F. Abbod and 
Hamed S. Al-Raweshidy,    Design of a neural 

predictive controller for nonholonomic mobile 

robot based on posture identifier, Proceedings 

of the IASTED International Conference 
Intelligent Systems and Control (ISC). 

Cambridge, United Kingdom, July 11 - 13, 

2011, pp. 198-207, 2011. 

[15] D.T. Pham, A. Ghanbarzadeh, E. Koc, S. Otri, 
S. Rahim and M . Zaidi, The Bees Algorithm. 

Technical Note, Manufacturing Engineering 

Centre, Cardiff University, UK, 2005.   

[16] D.T. Pham, E. Kog, A. Ghanbarzadeh, S. Otri, 

S. Rahim, M. Zaidi, The Bees Algorithm – A 
Novel Tool for Complex Optimisation 

Problems, IPROMS 2006 Proceeding 2nd 

International Virtual Conference on 

Intelligent Production Machines and Systems, 

Oxford, Elsevier, 2006. 

[17] Internet websitehttp://parallax.com/. Robotics 

with the Eddie Mobile Robot text manual. 

Accessed Sept. 2016. 

 

 
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



 )2017( 64-73، صفحة 3د، العد13دجلة الخوارزمي الهندسية المجلم                                     احمد صباح االعرجي                   

73 

 

 

 

  خوارزمية هجينة مدركة لتنغيم مسيطر الخطي لتتابع مسار لعجلة اإلنسان آلي متنقل  تصميم 
 

  **نور قاسم يوسف           *أحمد صباح االعرجي
 الجامعة التكنولوجية /قسم هندسة السيطرة والنظم**،*

ahmedalaraji76@gmail.com:البريد االلكتروني*   

 

 
  

  الخالصة
  

بشكل حي ومتصل للمسيطر الالخطي لتتابع مسار عجلة اإلنسان اآللي الحركي لتباع المسار   ان هذا البحث يقدم خوارزمية تنغيم المسيطر المدركة
يطر (العصبي  المستمر المرغوب.ان الهيكلية المقترحة لخوارزمية االمثلية هي الهجينة (النحل مع حشد الجسيمات االمثلية) اليجاد وتنغم قيم كسب المس

  وبساطة تقنية التنغيم وبشكل حي ومتصل.وطريقة الخطوة الراجعة) وتتميز بسرعة 
لقد تم إثبات من  ان افضل عزم مسيطر لعجلة اليمين واليسار لعربة اإلنسان اآللي تم توليدها بشكل حي ومتصل من خالل المسيطرين المقترحين.

ر دقة من حيث ايجاد وتنغيم عناصر المسيطر بشكل خالل نتائج المحاكاة أن المسيطر العصبي الالخطي المقترح مع الخوارزمية الهجينة المدركة هي اكث
تقليل الخطأ ألتتابعي لعجلة اإلنسان اآللي مقارنة مع أداء المسيطرة ذات تقنية الخطوة  فضالعنحي ومتصل ويؤدي الى الحصول على فعل سيطرة ناعم 

   الراجعة.