Realization and Control of a Mobile Robot based on a Dynamic Model
with the Implementation of Artificial Intelligence
ABDELGHAFOUR SLIMANE TICH TICH
Mechanical Engineering Department LGMM Laboratory
University of Skikda
ALGERIA
FOUED INEL
Mechanical Engineering Department, Automatic Laboratory,
ALGERIA
MOHAMMED KHADEM
Mechanical Engineering Department LGMM Laboratory
ALGERIA
Abstract: - In this paper, a mobile robot (tricycle robot) and its kinematic and dynamic model are presented.
Moreover, its simulation and model control are derived. For a mobile robot to be autonomous, it must perform
command tasks and perceive the environment. In this context, navigation plays an important role in the
interaction of the robot with its environment. It consists in the determination of possible trajectories by the
robot to follow a predefined trajectory. To accomplish this task, our approach relies on the dynamic motion of
the robot to generate admissible trajectories. The reference trajectory is first constructed based on a predefined
trajectory. To eliminate the navigation problem, an optimization problem with constraints, it is necessary to
reduce the difference between the predicted trajectory of the robot and the desired trajectory. Moreover, it is
possible to control the behaviour of the robot by using a trajectory parameterized with the dynamic model and
its control. Finally, the display of experimental results up to the implementation of the object detection..
Key-Words: - Non-holonomic, mobile robot, sliding mode, fuzzy control, recognition of objects.
Received: April 12, 2022. Revised: November 22, 2022. Accepted: December 17, 2022. Published: December 31, 2022.
1 Introduction
A mobile robot can be considered synonymous with
a vehicle, as it consists of the physical and
mechanical structure that allows the robot to move,
[1]. Other disciplines, such as automation
engineering, are involved and may shed a different
light on the matter, but do not change the problems
to be solved, [2].
The interest in the determination of mobile robots is
to perform certain tasks for humans, in different
environments, with boundaries and uneven terrain,
even in places inaccessible to humans [3], [4].
Important research work has been devoted to motion
planning. The purpose of which is to transition a
system from a certain initial state to a certain final
state when the motion command is to solve basic
navigation problems, [5]; follow a reference path,
stability to a desired position, [6]. It is not easy to
take control of a non-holonomic system from a start
to a finish configuration. This problem has attracted
the attention of robotics automation engineers,
hence the possibility of applying robust control [7],
[8]. The aim of the project was to develop a non-
holonomic mobile robot. The presentation of the
obtained simulation results and the experimental
part show the realization of the prototype with the
application of object recognition.
2 Non-holonomic Mobile Robot
Model
A characteristic illustration of a non-holonomic
mobile robot can be seen in Fig.1.
WSEAS TRANSACTIONS on SYSTEMS
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Abdelghafour Slimane Tich Tich, Foued Inel, Mohammed Khadem
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Y
y x
vL v
o’ vR
2b r
O X
Fig. 1: Representation of the mobile robot
The wheeled mobile robot has two rear wheel drives
and a self-supporting passive support wheel. To
enable translational and rotational motion, the rear
wheels are controlled independently. The resulting
linear velocity at the point midway along the axis
between the two rear wheels is given by:
and the angular velocity of the moving robot is
given by:
. Two wheels have the same
radius as at and two driving wheels are separated by
2b, the ground center of the mobile robot is at point
o’, [9].
The mobile robot is parameterized by the vector.
(1)
The location of the Cartesian coordinates of the
points (x, y) and the orientation of the robot. The
linear velocity of the point o’ and the angular
velocity of the robot respectively represent the
reference quantities v and , [10].
2.1 Kinematics
By deriving equation (1), we obtain the following
transformation which describes the kinematic model
of the robot, [11], [12].
(2)
With:
(3)
2.2 Dynamics
The dynamic model of a mobile robot with electric
rotor inertia and torque-based steering can be
described as follows [11], [12]:
The inertia matrix of the system is given by:
(4)
With:
m: the total mass of the vehicle.
: moment of inertia of the vehicle.
: moment of inertia of the wheel.
(5)
(6)
The forces that produce the torque and are:
(7)
With:
: the external disturbances
: The coefficient of the wheel viscous friction.
(8)
The system matrix is:
(9)
With the transformation matrix:
(10)
2.3 Control System Architecture
The vector below gives the tracking error.
(11)
A PID sliding surface is chosen to improve the
performance and flexibility of the robot, [13].
(12)
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To avoid tending to zero, we should contribute
the damping of that results:
(12)
qd(t)
+ e(t)
-
(13)
Fuzzification is the process of converting net values
into degrees of agreement with the linguistic terms
of fuzzy sets [14].
In order to match the direction of the robot, the delta
error and the error values are used as input
parameters.
These rules specify the relationship between the
error sensor and the delta error sensor in terms of
linguistic values. In the present work, a Mamdanian
participation method is used. After the inputs are
fuzzified, FLC determines the degree to which the
prior rule is satisfied. The equation of the
Mamdanian method to check the fuzzy implication,
[15].
(14)
Table.1. Rule base interface for relationship
between error and derror
Error
Derror
NB
NS
ZE
PS
PB
NB
NB
NB
NS
NS
ZE
NS
NB
NS
ZE
ZE
PS
ZE
NS
ZE
ZE
ZE
PS
PS
NS
ZE
ZE
PS
PB
PB
ZE
PS
PS
PB
PB
Fig. 3: Membership fuzzification
3 Results and Experiments
The goal of the control system is to track the exact
references of the trajectories desired by the robot by
applying the resolved equations of the kinematic
and dynamic models in combination with the fuzzy
sliding control. The simulations show the
performance of the robot in tracking a predefined
Sliding
Function
ʃ
ʃ
Mobile
Robot
Fuzzy
Controller
Fig. 2: Architecture of the control system
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trajectory. The characteristics of the robots are listed
in Table 2.
Table.2. Parametric values
Parameter Symbol Unit
Value
Mass of mobile robot kg 4
Moment of inertia of mobile robot kg m2
0.0945
Radius of wheel m
0.05
Length of platform m
0.25
Breadth of platform m
0.38
Motor coefficient N/V
0.087
Motor coefficient kg/s
11.4
Simulation results illustrating tracking performance
are shown in the figures below.
Fig. 4: Trajectory followed by the robot
Fig. 5: Displacement in X and Y
Fig. 6: Following errors
Fig. 7: control errors and derrors
The difference between the control effort without
disturbance and the control effort with disturbance
that results from solving a forward dynamic
problem is shown graphically in Figures 8 and 9.
Fig. 8: Comparison between control efforts without
interference
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Fig. 9: Comparison between control efforts with
disturbance
Fig. 10: Second derivative of the sliding function
Fig. 11: Desired inputs and control inputs
Fig. 12: Comparison between displacement,
desired orientation and actual position
The results obtained show that the tracking is almost
perfect, although certain factors were not taken into
account in the calculation of the command.
The posture error of the robot converges to almost
zero, and the actual robot velocities converge with
the selected reference velocities. According to the
simulation results, the dynamics of the system
requires special attention, with the relative velocity
errors requiring minimal movement.
3.2 Implementation of Object Detection
The goal of this study is to distinguish three robots
(humanoid robot, drone, wheeled robot) by first
using a small database (60 images per class).
Then, finally, we will study the performance of our
model by varying the size of our database without
changing the parameters, and thus be able to infer an
average size.
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Fig. 13: Organizational chart
If we keep the same parameters and vary the size of
the database, we can see that the number of
correctly classified images increases when the
database is larger. We find that the classification
rate is highest for a database of 700 images/class.
Fig. 14: Performance of the model based on the
dataset.
In this test, however, we have fixed the values of the
hyperparameters, which play an extremely
important role in the performance of the model; we
have correctly adjusted the hyperparameters for
each model. It is possible that we have a powerful
model with a database much less than 700
images/class.
The following figures show the results of
classification between wheeled robots, humanoid
robots, and drones without increasing the amount of
data.
Fig. 15: Training loss and accuracy
And the table represents the model parameters that
result after running our algorithm.
Table.3.Model parameters
Parameters
precision
recall
F1-score
support
Drone
0.75
1.00
0.86
18
Humanoid robot
1.00
0.50
0.67
19
Mobile robot
0.75
1.00
0.86
20
Accuracy
0.88
57
Macro avg
0.83
0.83
0.79
57
Weighted avg
0.85
0.80
0.78
57
Figure 14 shows the evolution of our metrics as a
function of the evolution of the epochs; we are
interested in the accuracy of validation, which is an
indicator of the progress of our model. Indeed, the
accuracy indicates the percentage of correct
predictions.
The following figures show the results of the
classification between wheeled robots, humanoid
robots, and drones as the amount of data increases.
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Fig. 16: training loss and accuracy
And the table presents the model parameters that
result after running our algorithm.
Table 4. Model parameters
Parameters
precision
Recall
F1-score
support
Drone
1.00
1.00
1.00
18
Humanoid robot
1.00
1.00
1.00
19
Mobile robot
1.00
1.00
1.00
20
Accuracy
1.00
57
Macro avg
1.00
0.92
1.00
57
Weighted avg
1.00
0.90
1.00
57
Figures 17, 18 and 19 show the image processing
for our three classes in real time.
Fig. 17: Image classification of a mobile robot
Fig. 18: Image classification of the humanoid robot
Microsofot
Fig. 19: Image classification of a drone
The prototype mobile robot used in this part is the
same as in Figure 20.
Fig. 20: Image of the physical prototype of a mobile
robot.
4 Conclusion
In this paper, path tracking by a combination of two
controllers for non-holonomic mobile robots is
presented. The proposed controller is tested for
different trajectories. Simulation and experimental
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results show that it is very capable of following any
trajectory. In addition, a new implementation of a
computer vision solution using deep learning
algorithms to detect and identify different objects on
the omnidirectional robot has been developed. We
adapted a variant of the MobileNetv2 neural
network architecture to quickly recognise and
classify images of objects. Our visual system
provides a reliable solution for recognising images
even when the object is partially occluded. We
expect to use the data computed by this system to
integrate advanced tracking into the robot in the
future.
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DOI: 10.37394/23202.2022.21.39
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