A novel interception and trajectory tracking control approach for a mobile robot
Introduction. In nature, interception is a hunting strategy where a predator moves to a point ahead of a moving prey’s trajectory to catch it, rather than directly pursuing it. Also, in transportation and manufacturing sectors, trajectory interception is carried out by the correspondence of the posi...
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National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine
2026
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Electrical Engineering & Electromechanics| _version_ | 1869562802653364224 |
|---|---|
| author | Ben Hadj Mohamed, S. Mahjoub, A. Ben Njima, C. Benamor, A. |
| author_facet | Ben Hadj Mohamed, S. Mahjoub, A. Ben Njima, C. Benamor, A. |
| author_institution_txt_mv | [
{
"author": "S. Ben Hadj Mohamed",
"institution": "National School of Engineers of Monastir"
},
{
"author": "A. Mahjoub",
"institution": "University of Kairouan"
},
{
"author": "C. Ben Njima",
"institution": "National School of Engineers of Monastir"
},
{
"author": "A. Benamor",
"institution": "National School of Engineers of Monastir"
}
] |
| author_sort | Ben Hadj Mohamed, S. |
| baseUrl_str | http://eie.khpi.edu.ua/oai |
| collection | OJS |
| datestamp_date | 2026-07-01T21:42:56Z |
| description | Introduction. In nature, interception is a hunting strategy where a predator moves to a point ahead of a moving prey’s trajectory to catch it, rather than directly pursuing it. Also, in transportation and manufacturing sectors, trajectory interception is carried out by the correspondence of the position and velocity of a target object with those of the robot interceptor. It is within this context that our research work takes place. The problem of the work consists in the development of a new intercepting and trajectory tracking strategy of a two-wheeled differential-drive mobile robot. Goal. To propose a novel intercepting and trajectory tracking technique whose principle is based on the orientation angle of the mobile robot interceptor guarantees a faster convergence with a minimum error and lower energy consumption. Methodology. The problem is solved using both a sliding mode controller and a backstepping controller to test the proposed strategy based on particle swarm optimization (PSO). Results. The results proved the effectiveness of the new approach especially in fast reaching-time and energy consumption compared to direct pursuit. In other words, the results indicate that the proposed approach achieves a noticeable reduction in convergence time (up to 82.5% faster) and significantly lowers oscillations in the control signals compared to classical methods. Scientific novelty. To get interception and accurate tracking in a reduced reaching-time, an original control technique based on PSO is implemented using two different controllers. Practical value. The proposed strategy offers satisfactory control performances such as fast interception and smooth trajectory tracking. References 24, tables 6, figures 14. |
| doi_str_mv | 10.20998/2074-272X.2026.4.01 |
| first_indexed | 2026-07-02T01:00:27Z |
| format | Article |
| fulltext |
Electrotechnical Complexes and Systems
Electrical Engineering & Electromechanics, 2026, no. 4 3
© S. Ben Hadj Mohamed, A. Mahjoub, C. Ben Njima, A. Benamor
UDC 621.865.8 https://doi.org/10.20998/2074-272X.2026.4.01
S. Ben Hadj Mohamed, A. Mahjoub, C. Ben Njima, A. Benamor
A novel interception and trajectory tracking control approach for a mobile robot
Introduction. In nature, interception is a hunting strategy where a predator moves to a point ahead of a moving prey’s trajectory to catch it,
rather than directly pursuing it. Also, in transportation and manufacturing sectors, trajectory interception is carried out by the
correspondence of the position and velocity of a target object with those of the robot interceptor. It is within this context that our research
work takes place. The problem of the work consists in the development of a new intercepting and trajectory tracking strategy of a two-
wheeled differential-drive mobile robot. Goal. To propose a novel intercepting and trajectory tracking technique whose principle is based on
the orientation angle of the mobile robot interceptor guarantees a faster convergence with a minimum error and lower energy consumption.
Methodology. The problem is solved using both a sliding mode controller and a backstepping controller to test the proposed strategy based
on particle swarm optimization (PSO). Results. The results proved the effectiveness of the new approach especially in fast reaching-time and
energy consumption compared to direct pursuit. In other words, the results indicate that the proposed approach achieves a noticeable
reduction in convergence time (up to 82.5% faster) and significantly lowers oscillations in the control signals compared to classical
methods. Scientific novelty. To get interception and accurate tracking in a reduced reaching-time, an original control technique based on
PSO is implemented using two different controllers. Practical value. The proposed strategy offers satisfactory control performances such as
fast interception and smooth trajectory tracking. References 24, tables 6, figures 14.
Key words: trajectory tracking, mobile robot, sliding mode control, backstepping control, particle swarm optimization.
Вступ. У природі перехоплення є стратегією полювання, за якої хижак рухається не безпосередньо за здобиччю, а до точки
попереду її траєкторії для забезпечення захоплення. Аналогічно у транспортній та виробничій сферах перехоплення траєкторії
здійснюється шляхом узгодження положення та швидкості цільового об’єкта з параметрами робота-перехоплювача. Саме в
цьому контексті виконано дане дослідження. Проблема. Робота присвячена розробленню нової стратегії перехоплення та
відстеження траєкторії для двоколісного мобільного робота з диференціальним приводом. Мета. Запропонувати новий метод
перехоплення та відстеження траєкторії, принцип якого ґрунтується на використанні кута орієнтації мобільного робота-
перехоплювача та забезпечує швидшу збіжність, мінімальну похибку і менше енергоспоживання. Методика. Для розв’язання
поставленої задачі використано регулятор ковзного режиму та бекстепінг-регулятор з метою перевірки запропонованої
стратегії на основі оптимізації роєм часток (PSO). Результати. Отримані результати підтвердили ефективність нового
підходу, зокрема щодо зменшення часу досягнення цілі та енергоспоживання порівняно з методом прямого переслідування.
Зокрема, запропонований підхід забезпечує суттєве скорочення часу збіжності (до 82,5 %) та значне зменшення коливань у
сигналах керування порівняно з класичними методами. Наукова новизна. Для забезпечення перехоплення та точного відстеження
траєкторії за мінімального часу збіжності реалізовано оригінальний метод керування на основі PSO із використанням двох
різних регуляторів. Практична значимість. Запропонована стратегія забезпечує високі показники якості керування, зокрема
швидке перехоплення та плавне відстеження траєкторії. Бібл. 24, табл. 6, рис. 14.
Ключові слова: відстеження траєкторії, мобільний робот, керування ковзним режимом, бекстепінг-керування,
оптимізація роєм часток.
Introduction. Nowadays, the control of mobile
robots is swiftly in continuous progress, with a principal
focus on the control of robots capable of autonomous
movement and tasks performance. Particularly, the
trajectory tracking problem represents one of the most
important challenges. The robot control study gave rise to
several different techniques which have been proposed to
get efficient control of mobiles robots.
To control the position of a simulated mobile robot,
the authors in [1] used two reinforcement learning
algorithms to control the position of a simulated robot.
The authors showed the effectiveness for position control
in environments with and without obstacles. In [2], the
authors addressed the challenge of controlling a mobile
robot to reach a target posture in a minimum time. He
used a dynamic adaptive PID controller based on genetic
algorithm optimization.
Certain studies, to ameliorate the trajectory tracking
capabilities of a mobile robot, developed a neural network
controller [3]. Also, [1, 4] proposed an artificial
intelligence control method to minimize movement time
of a mobile robot, and a control gains optimization using
genetic algorithm has been done in the first research.
These works focus exclusively on the tracking
performances and reaching time but they don’t emphasize
the minimization of the convergence error.
Many other research works used model predictive
control strategy; for example [5], focused on controlling
mobile robots, they proposed a model predictive controller
by minimizing quadratic criterion after linearizing the
nonlinear dynamic model of the differential drive mobile
robot using input-output linearization technique.
Many research studies have been elaborated
concerning the tracking and interception of a moving target
in the literature. In [6], the authors developed a control
strategy for the interception of a moving object by a wheeled
mobile robot. The called guidance approach allowed the
mobile robot, when it is faster, to intercept successfully the
moving target. Many research studies used sliding mode
control techniques to get robust systems with insensitivity to
external disturbances and uncertainties [7]. The work [8]
proposed a new interception algorithm for a manipulator
robot to intercept a moving object. To reach interception
objective in a prescribed time, the authors used the
combination of a robust second-order sliding mode control
with a terminal attractor based on a designed time base
generator, while [9] developed a nonlinear sliding mode
control approach to achieve trajectory tracking of 2-wheeled
mobile robot. These two works focus on the robustness in
prescribed time interception and rejecting disturbances,
respectively, but they neglect to be interested in the
minimization of the convergence error. On the other hand, in
[10], the authors addressed the problem of controlling
uncertain 4-wheeled mobile robot presenting a WSS
phenomenon (wheel slipping, skidding). The sliding mode
control [11, 12] technique has been used to achieve a fixed-
time prescribed control performance. Despite the robustness
achieved and the convergence error that the authors have
mentioned, it remains to be verified whether this strategy
works with any controller that can be used.
However, most of these research studies don’t focus
on the reaching time and the minimization of the position
and orientation angle error.
4 Electrical Engineering & Electromechanics, 2026, no. 4
The goal of the paper is to propose a novel
intercepting and trajectory tracking technique whose
principle is based on the orientation angle of the mobile
robot interceptor guarantees a faster convergence with a
minimum error and lower energy consumption.
To show the effectiveness of this technique, it will
be tested using a first-order sliding mode controller and a
backstepping controller.
Problem formulation. Consider a mobile robot
which is placed in a 2D reference mark. The mobile robot
is counterclockwise oriented with an angle relative to X-
axis. Figure 1,a shows the mobile robot, the posture errors
consisting of linear positions (x, y) and the orientation
angle θ in the global frame OXY. The robot’s kinematic
model is defined by:
uqSq )( , (1)
where q = (x, y, θ)T is the actual robot posture; a Jacobian
matrix is
11
0sin
0cos
qS ; [u] =
w
v
is the velocity
control vector; v is the linear velocity; w is the angular
velocity.
XO
a
b
Fig. 1. Mobile robot posture error (a);
closed loop of controlled system (b)
The desired posture and the desired velocity vector
are defined as:
),,( dddd yxq ; ),( ddd wvV . (2)
The posture error in the robot’s local frame is:
),,( eeee yxq , (3)
where:
,
);cos()(sin
);(sin)cos(
de
dde
dde
yyxxy
yyxxx
(4)
and the vector of posture error [qe] has the next form:
d
d
d
e yy
xx
100
0cossin
0sincos
q , (5)
we can also write:
d
d
d
e yy
xx
)(q ,
where )( is the orthogonal rotation matrix.
The nonholonomic constraints equation characterizing
the slip-free rolling of a wheel on the ground is:
0cossin yx . (6)
Using (1), (6), the derivative of (5) is:
d
ede
ede
e
e
e
e vx
vvy
y
x
t sin
cos
dd
q . (7)
To build a mobile robot simulation that is close to
reality, the robot dynamic model and a dynamic controller
are introduced in the block diagram of the control strategy:
,
2
;
12
2
2
2
2
LRcw
LRcw
TT
R
L
vdmI
R
L
I
TT
R
dmI
R
m
(8)
where (TR, TL) are the torques input of the mobile robot; L
is the half of the track width; R is the wheel radius; d is
the distance from the mass center to the middle point
between the right and left wheels; m, mc are the total mass
of the robot and the robot mass without its wheels and
actuators; Iw is the moment of inertia of each wheel; I is
the total inertia moment.
Optimal reference trajectory tracking. In this
part, we present our new interception and tracking
technique based on a proposed desired orientation angle.
Many results have been achieved based on mobile robot
control which emphasized on trajectory tracking
performances [13, 14]. All these works are differentiated
in the method to calculate the posture error and especially
in the choice of the desired orientation angle. There are
authors who note the desired angle as the orientation of
the reference mobile robot as in [12].
Others note the desired angle as the orientation
towards the reference mobile robot [15–18]:
d = r; (9)
e1 = r – ; (10)
xxyy ddTRd 1tan . (11)
The TR expression returns values in the interval
[–/2, /2] and may cause division-by-zero errors when xd = x.
The function «atan2» is used instead of tan–1 to
return the 4-quadrant inverse tangent, so:
d = TR = atan2[(yd – y); (xd – x)]; (12)
e2 = TR – . (13)
The proposed method is to take as the desired angle
the orientation towards a virtual reference mobile robot,
d = TVR.
Figure 2 depicts the graphical the proposed strategy
where the virtual reference mobile robot is the predicted
posture of the reference mobile robot after a period ∆t, with
∆t is the minimum-time interception of the moving
reference mobile robot such that 0lim
e
tt
q
. Assumption:
the linear velocities of the actual mobile robot and the
reference mobile robot are positive. We define: d1 = vdt is
the distance between the reference mobile robot and its
predicted position; d3 = vt is the distance between the
virtual reference robot and the actual mobile robot;
22
2 )()( xxyyd dd is the distance between the
reference mobile robot and the actual mobile robot:
Electrical Engineering & Electromechanics, 2026, no. 4 5
d = TVR = TR + p, (14)
where p is the angle resulted from the prediction
So, it is readily seen that with a rotation of –TR in
Fig. 2,c we obtain the following Fig. 3.
a
b
c
Fig. 2. a – the desired angle d is the orientation
of the reference mobile robot r;
b – the desired angle d = TR is the orientation towards the
reference mobile robot; c – the proposed strategy d = TVR
Fig. 3. Rotation of Fig. 2,c of –TR
Then, we get:
)sin(sin 1
TRr
d
p v
v
, (15)
with v 0 and –1 sin(r – TR) 1.
The inverse sine «sin–1» returns one value of in the
interval [–/2, /2], however there are 2 solutions:p or
p – ; TRrp ,0 . If p 0 then TR d r; if
p 0 then r d TR; if p = 0 then r = d = TR.
According to Fig. 3, we can write:
213 coscos ddd TRrp ;
2cos)cos( dtvtV dTRrp ;
dTRrp vv
d
t
cos)cos(
2 ;
t0 leads to
0cos)cos( dTRrp vv ;
dTRrp vv cos)cos( .
The error angle e3 = TVR – :
)sin(sin)(),(2atan 1
3 TRr
d
dde v
v
xxyy .(16)
The angle error is minimized when e3> to avoid
the long path when the mobile robot rotates:
if e3 > then e3min = e3 – 2; (17)
if e3 < – then e3min = e3 + 2. (18)
So e3min [–, ].
The proposed interception strategy flowchart is
shown in Fig. 4 and illustrates how the posture error is
calculated at each step of time based on the proposed
desired angle TVR. Here, the control law block and the
error block are separated. This separation gives the
possibility to apply this approach with any control law
and with any model of mobile robot, offering flexibility
and adaptability in various control frameworks.
Fig. 4. Proposed interception strategy flowchart
Kinematic controller. In this section, 2 kinematic
controllers will be presented for the test with the 3 desired
angles d1 = r, d2 = TR, d3 = TVR. Simulink was used
for the development of the mobile robot’s control system
(Fig. 1,b), leveraging its block-based environment to
facilitate rapid prototyping, model-based simulation, and
to improve analysis and debugging.
The overall architecture of the control system is
illustrated in the Simulink model flowchart presented in
Fig. 5, which details the interconnections and data flow
between the various functional blocks.
First order sliding mode controller (FOSMC).
The trajectory tracking control law developed by [19] is
based on the FOSMC technique using a non-singular
coordinate transformation. This formulation enables
improved stability and control near the target by avoiding
singularities that occur in Cartesian coordinates.
Therefore, the control law is defined as:
*)(sat0
1
0
GAB
w
v
c
c
c
u , (19)
with
6 Electrical Engineering & Electromechanics, 2026, no. 4
ded
ed
e v
v
A
q
32
1
00 )sin(
)cos(
A ;
31
11
00 0
e
e
e x
y
B
q
B ;
))((*
*
,
32321
2
1
2
1*
eeeee
e
e
yxyx
x
tq
σ . (20)
Fig. 5. Simulink model flowchart of the control system
In [19] the «sign» function was replaced by a
saturation function to reduce the chattering phenomenon,
where sat(*) is component wise discontinuous and
defined as:
Tsatsat )()(])sat([ *
2
*
1
* ;
;if),(sign
;if,
])sat([
**
*
*
*
ii
i
i
where is the boundary layer thickness (i = 1, 2);
G = diag([g1, g2]). (21)
To ensure that B0σ is always nonsingular, the
following condition must be satisfied:
k32 with
1
1
0
ex
k .
Backstepping controller. In [21, 22], the tracking
error xe is replaced by Vx in the backstepping model so
that we obtain a new backstepping controller based on
biologically-inspired shunting neural model, the control
law is defined as follows:
ededd
edx
c
c
c vkyvk
vVk
w
v
sin
cos
][
32
1u , (22)
where k1 – k3 are the given positive constants;
)()()()( exexxx xgVDxfVBAVV . (23)
where Vx is the biological model control output voltage,
so that f(xe) = max(xe, 0) and g(xe) = max(–xe, 0); xe is the
biological model control input; A, B, D are the positive
constants such as B = D.
PSO optimization. In this part, we developed a
MATLAB code based on the predefined function
«particleswarm» to optimize controllers’ gains in a
Simulink model. The gains in the controllers of sliding
mode and backstepping directly influence the performance
of the control technique for interception and trajectory
tracking. Correctly adjusted gains ensure fast convergence
and enhanced robustness of the control system. To achieve
optimal controller performance, gain tuning, which can be
a time-consuming and complicated phase, is a primordial
task. To optimize the parameters of the controllers, we
adopt the particle swarm optimization (PSO) algorithm
[23]. The PSO algorithm is applied within the trajectory
tracking control framework to get right control gains by
optimizing a predefined objective function.
An integral time square error (ITSE) based on the
posture error vector is selected as the objective function:
tqtJ eITSE d2 . (24)
In the PSO algorithm, iterative computation is
performed with the objective of minimizing the cost
function JITSE. Each particle in the swarm represents a
candidate solution, where its position corresponds to a
specific set of control gains to be optimized. During the
optimization process, particles move through the solution
space with a certain velocity, updating their positions
iteratively. Through this process, the swarm converges
toward the global optimal solution.
Inspired from the problem-based approach to
optimize a function using particle swarm, a custom
objective function file was developed. To overcome the
limitations of converting the function file to an
optimization expression, the Simulink model is executed,
and the resulting ITSE value is returned to
«particleswarm» as a «black-box» cost function.
Figure 6 shows the interaction between MATLAB
and Simulink during the optimization process and the
PSO algorithm can be described in the next main steps.
Initialization: particles are randomly initialized
within the parameter bounds. The objective function is
evaluated for each particle. Each particle’s best position pi
and the global best position g are recorded.
Velocity update: the velocity of each particle is
updated using the following equation:
)()( 22111 iiiiii xguyxpuyWvv , (25)
where W is the inertia weight; y1, y2 are the acceleration
coefficients (self and social adjustment); u1, u2 are the
random numbers uniformly distributed in (0, 1).
Position update: each particle’s position is updated by:
11 iii vxx . (26)
Boundary constraints are applied to ensure all
parameters remain within their valid ranges.
Evaluation and update: The new position is
evaluated using the cost function. If it yields a better
result, the particle’s personal best is updated. The global
best is also updated if a better solution is found across all
particles.
Electrical Engineering & Electromechanics, 2026, no. 4 7
Adaptation: the neighborhood size and inertia
weight W are adapted based on the improvement of the
global best solution to enhance convergence behavior.
Termination: the algorithm repeats until a stopping
condition is met, such as a maximum number of iterations
or a convergence threshold.
Fig. 6. Proposed optimization flowchart
By optimizing the controller gains through PSO in
offline mode, the control system achieves better
performance in terms of tracking accuracy and faster
convergence, all while maintaining low computational
complexity during robot simulation.
Simulation results and discussion. To highlight the
advantages and the effectiveness of the proposed control
approach, a simulation is carried out on the trajectory
tracking of a circle to verify the effectiveness of the
strategy used.
The initial robot state x, y and θ are respectively 6m,
2m and π. The initial states of the reference robot are
xd = m, yd = 0, r = /2.
The expected trajectory of circle can be concluded as:
,
);sin(
);cos(
t
tvy
tvx
rr
ddr
ddr
(27)
where vd = 4 m/s, ωd = 1 rad/s.
We consider that the mass center of the mobile robot
is at the middle point between the right and left wheels
(d=0), and the moment of inertia of each wheel is neglected
(Iw = 0). The robot parameters are listed in Table 1.
Table 1
Robot parameters
L, m R, m m, kg I, kgm2
0.15 0.03 4.5 3
The parameters of kinematic controllers in Table 2
remain constant throughout the simulation experiments.
While gains g1, g2 of the FOSMC controller and A,
B, D of the backstepping controller are optimized by the
PSO each time the desired angle is selected. The
optimization process is executed offline six times for the
two kinematic controllers and the three desired angles.
Tables 3, 4 show the optimal controllers’ gains and the
total simulation errors reflected by the cost function JITSE.
Table 2
Constant parameters of the controllers
FOSMC controller Backstepping controller
ϕ 0.5 k1 2
1 1 k2 6
2 6 k3 6
3 1
Table 3
Optimal gains of the FOSMC controller
Desired angle g1 g2 JITSE
d1 = r 32.5166 44.9584 0.1152
d2 = TR 0.9444 82.9444 0.4175
Proposed d3 = TVR 13.1741 32.7398 0.0588
Table 4
Optimal gains of the backstepping controller
Controller
Optimal FOSMC
controller
Optimal
backstepping
controller
Classical strategies d1 = r d2 = TR d1 = r d2 = TR
Time reduction using our
strategy d3 = TVR
30 % 82.5 % 8.33 % 81.66 %
The minimal error obtained by the cost function
while d3 = TVR indicates the high accuracy of the
proposed strategy. The responses of both controllers in
Fig. 7, 8 show a fast and smooth tracking trajectory in the
X-Y plane using the proposed desired angle TVR.
x, m
y, m
Fig. 7. Circular trajectory tracking – optimal FOSMC controller
x, m
y, m
Fig. 8. Circular trajectory tracking – optimal backstepping controller
The convergence time values of posture error
qe = (xe, ye, e)
T to the steady-stable value can be extracted
from Fig. 9–12 and all listed in Table 5. During the
transient phase, as it is clear in Fig. 11, the optimal
FOSMC controller exhibits less oscillations around the
reference trajectory while trajectory while d3 = TVR.
8 Electrical Engineering & Electromechanics, 2026, no. 4
Table 5
Reduction in convergence time, s
Desired angle
Optimal FOSMC
controller
Optimal backstepping
controller
d1 = r 1 1.2
d2 = TR 4 6
d3 = TVR 0.7 1.1
Optimal FOSMC controller + desired angle: d1
Optimal FOSMC controller + desired angle: d2
Optimal FOSMC controller + desired angle: d3
Fig. 9. Posture error – optimal FOSMC controller
Optimal backstepping controller + desired angle: d1
Optimal backstepping controller + desired angle: d2
Optimal backstepping controller + desired angle: d3
Fig. 10. Posture error – optimal backstepping controller
To evaluate the convergence speed of the proposed
strategy, the Table 6 summarizes, for each kinematic
controller and each desired angle, the reduction in
convergence time of the posture error using the
interception strategy.
Optimal FOSMC controller + desired angle: d1
Optimal FOSMC controller + desired angle: d2
Optimal FOSMC controller + desired angle: d3
Fig. 11. Zoom in posture error – optimal FOSMC controller
Table 6
Reduction in convergence time, s
Desired angle A B = D JITSE
d1 = r 37.2667 100 0.1099
d2 = TR 94.2135 18.2315 0.4476
Proposed d3 = TVR 55.1726 100 0.0418
Optimal backstepping controller + desired angle: d1
Optimal backstepping controller + desired angle: d2
Optimal backstepping controller + desired angle: d3
Fig. 12. Zoom in posture error – optimal backstepping controller
As shown in Fig. 13, 14, the kinematic controllers
significantly reduce the chattering phenomenon during the
transient phase, resulting in a smoother and less
oscillatory control signal compared to the conventional
approach. This strategy is crucial to our energy-saving
strategy, as it effectively reduces transient oscillations,
which are known to increase heat losses and decrease the
efficiency of a robotic system’s actuators [24].
Electrical Engineering & Electromechanics, 2026, no. 4 9
Optimal FOSMC controller + desired angle: d1
Optimal FOSMC controller + desired angle: d2
Optimal FOSMC controller + desired angle: d3
Fig. 13. Output of the optimal FOSMC controller
Optimal backstepping controller + desired angle: d1
Optimal backstepping controller + desired angle: d2
Optimal backstepping controller + desired angle: d3
Fig. 14. Output of the optimal backstepping controller
Conclusions. This paper introduced a novel
interception-based trajectory tracking control strategy for
differential-drive mobile robots, and a new approach for
optimizing controller gains was introduced, which
effectively combines the global optimization capabilities of
MATLAB’s «particleswarm» function with the block-based
modeling environment of Simulink. The results indicate that
the proposed approach achieves a noticeable reduction in
convergence time (up to 82.5 % faster) and significantly
lowers oscillations in the control signals compared to
existing classical methods from the literature. These
enhancements are directly linked to the newly designed
reference orientation and the systematic gain optimization
that form the core contributions of this work. The simulation
results show the effectiveness of the proposed interception
and trajectory tracking strategy, regardless of the controller
used. Future efforts will focus on performing real-time
experiments on an embedded control platform to further
validate robustness against physical disturbances and
unmodeled dynamics. Additionally, expanding the
framework through adaptive or learning-based mechanisms
is expected to support broader operational conditions while
maintaining strong tracking performance.
Conflict of interest. The authors declare that they
have no conflicts of interest.
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Received 12.12.2025
Accepted 13.02.2026
Published 03.07.2026
S. Ben Hadj Mohamed 1, PhD Student,
A. Mahjoub2, Associate Professor,
C. Ben Njima1, Professor,
A. Benamor1, Professor,
1 Electrical Department, National School of Engineers of Monastir,
Monastir 5000, Tunisia.
2 Higher Institute of Applied Sciences and Technologies of Kairoun,
University of Kairouan, 3064, Tunisia,
e-mail: adel.mahjoub@isigk.rnu.tn (Corresponding Author)
How to cite this article:
Ben Hadj Mohamed S., Mahjoub A., Ben Njima C., Benamor A. A novel interception and trajectory tracking control approach for a
mobile robot. Electrical Engineering & Electromechanics, 2026, no. 4, pp. 3-10. doi: https://doi.org/10.20998/2074-272X.2026.4.01
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| id | eiekhpieduua-article-344442 |
| institution | Electrical Engineering & Electromechanics |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-02T01:00:27Z |
| publishDate | 2026 |
| publisher | National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | eiekhpieduua/82/4c05c8cd994737be2aec41b381f99882.pdf |
| spelling | eiekhpieduua-article-3444422026-07-01T21:42:56Z A novel interception and trajectory tracking control approach for a mobile robot A novel interception and trajectory tracking control approach for a mobile robot Ben Hadj Mohamed, S. Mahjoub, A. Ben Njima, C. Benamor, A. відстеження траєкторії мобільний робот керування ковзним режимом бекстепінг-керування оптимізація роєм часток trajectory tracking mobile robot sliding mode control backstepping control particle swarm optimization Introduction. In nature, interception is a hunting strategy where a predator moves to a point ahead of a moving prey’s trajectory to catch it, rather than directly pursuing it. Also, in transportation and manufacturing sectors, trajectory interception is carried out by the correspondence of the position and velocity of a target object with those of the robot interceptor. It is within this context that our research work takes place. The problem of the work consists in the development of a new intercepting and trajectory tracking strategy of a two-wheeled differential-drive mobile robot. Goal. To propose a novel intercepting and trajectory tracking technique whose principle is based on the orientation angle of the mobile robot interceptor guarantees a faster convergence with a minimum error and lower energy consumption. Methodology. The problem is solved using both a sliding mode controller and a backstepping controller to test the proposed strategy based on particle swarm optimization (PSO). Results. The results proved the effectiveness of the new approach especially in fast reaching-time and energy consumption compared to direct pursuit. In other words, the results indicate that the proposed approach achieves a noticeable reduction in convergence time (up to 82.5% faster) and significantly lowers oscillations in the control signals compared to classical methods. Scientific novelty. To get interception and accurate tracking in a reduced reaching-time, an original control technique based on PSO is implemented using two different controllers. Practical value. The proposed strategy offers satisfactory control performances such as fast interception and smooth trajectory tracking. References 24, tables 6, figures 14. Вступ. У природі перехоплення є стратегією полювання, за якої хижак рухається не безпосередньо за здобиччю, а до точки попереду її траєкторії для забезпечення захоплення. Аналогічно у транспортній та виробничій сферах перехоплення траєкторії здійснюється шляхом узгодження положення та швидкості цільового об’єкта з параметрами робота-перехоплювача. Саме в цьому контексті виконано дане дослідження. Проблема. Робота присвячена розробленню нової стратегії перехоплення та відстеження траєкторії для двоколісного мобільного робота з диференціальним приводом. Мета. Запропонувати новий метод перехоплення та відстеження траєкторії, принцип якого ґрунтується на використанні кута орієнтації мобільного робота-перехоплювача та забезпечує швидшу збіжність, мінімальну похибку і менше енергоспоживання. Методика. Для розв’язання поставленої задачі використано регулятор ковзного режиму та бекстепінг-регулятор з метою перевірки запропонованої стратегії на основі оптимізації роєм часток (PSO). Результати. Отримані результати підтвердили ефективність нового підходу, зокрема щодо зменшення часу досягнення цілі та енергоспоживання порівняно з методом прямого переслідування. Зокрема, запропонований підхід забезпечує суттєве скорочення часу збіжності (до 82,5 %) та значне зменшення коливань у сигналах керування порівняно з класичними методами. Наукова новизна. Для забезпечення перехоплення та точного відстеження траєкторії за мінімального часу збіжності реалізовано оригінальний метод керування на основі PSO із використанням двох різних регуляторів. Практична значимість. Запропонована стратегія забезпечує високі показники якості керування, зокрема швидке перехоплення та плавне відстеження траєкторії. Бібл. 24, табл. 6, рис. 14. National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine 2026-07-02 Article Article application/pdf https://eie.khpi.edu.ua/article/view/344442 10.20998/2074-272X.2026.4.01 Electrical Engineering & Electromechanics; No. 4 (2026); 3-10 Электротехника и Электромеханика; № 4 (2026); 3-10 Електротехніка і Електромеханіка; № 4 (2026); 3-10 2309-3404 2074-272X en https://eie.khpi.edu.ua/article/view/344442/351592 Copyright (c) 2026 S. Ben Hadj Mohamed, A. Mahjoub, C. Ben Njima, A. Benamor http://creativecommons.org/licenses/by-nc/4.0 |
| spellingShingle | trajectory tracking mobile robot sliding mode control backstepping control particle swarm optimization Ben Hadj Mohamed, S. Mahjoub, A. Ben Njima, C. Benamor, A. A novel interception and trajectory tracking control approach for a mobile robot |
| title | A novel interception and trajectory tracking control approach for a mobile robot |
| title_alt | A novel interception and trajectory tracking control approach for a mobile robot |
| title_full | A novel interception and trajectory tracking control approach for a mobile robot |
| title_fullStr | A novel interception and trajectory tracking control approach for a mobile robot |
| title_full_unstemmed | A novel interception and trajectory tracking control approach for a mobile robot |
| title_short | A novel interception and trajectory tracking control approach for a mobile robot |
| title_sort | novel interception and trajectory tracking control approach for a mobile robot |
| topic | trajectory tracking mobile robot sliding mode control backstepping control particle swarm optimization |
| topic_facet | відстеження траєкторії мобільний робот керування ковзним режимом бекстепінг-керування оптимізація роєм часток trajectory tracking mobile robot sliding mode control backstepping control particle swarm optimization |
| url | https://eie.khpi.edu.ua/article/view/344442 |
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