Page 256 - 2024-Vol20-Issue2

252 |
Fig. 4. Repulsive field method for a mobile robot.
for controlling the robot’s motion. By adjusting the angular
velocities of the left and right wheels (dfL/dt, dfR/dt), the
mobile robot can be controlled to move forward or turn.
2) The Repulsive Field Method
The Repulsive Field Method [40] is a form of potential field-
based path planning in robotics. In this method, the envi-
ronment is represented as a field of repulsive forces, which
push the robot away from obstacles. As shown in Fig. 4, each
obstacle in the environment generates a repulsive field, and
the overall repulsive force experienced by the robot is the sum
of these fields. The robot navigates by moving in the direction
of the resultant force, attempting to minimize the potential
energy associated with the repulsive fields. This approach
allows the robot to avoid obstacles while reaching its destina-
tion. The repulsive field method usually consists of essential
elements, which encompass settings to regulate repulsion in-
tensity, methods for identifying and pinpointing obstacles in
the surroundings, and forces or fields with an attractive nature
employed to direct the robot towards a desired destination.
However, it is important to note that although the repulsive
field method can prove successful in specific situations, it
does have constraints. These limitations include challenges in
dealing with intricate environments characterized by narrow
pathways and the possibility of the robot becoming trapped in
localized low-performance states.
3) Obstacle Avoidance Model
A repulsive potential field method is used to avoid obstacles.
For a circular obstacle located at (ox, oy) with a radius robs,
the potential field is given by equation (4) [41]:
Uobs = kobs 2 (4) 5) Optimal Trajectory
1 -1
(x - ox)2 + (y - oy)2 robs
Where:
Uobs: The potential energy associated with obstacle avoidance.
kobs: Gain parameter for obstacle avoidance.
Sabeeh & Al-Furati
(x, y): Robot coordinates.
(ox, oy): Obstacle coordinates.
This potential field creates a repulsive force that pushes
the robot away from the obstacle. In equation (4), the first
part calculates the inverse of the distance between the robot’s
current position (x, y) and the center of the circular obsta-
cle (ox, oy). It represents the strength of the repulsive force;
shorter distances lead to higher repulsion. Finally, the square
of the difference is taken to enhance the repulsive effect and
ensure it is always positive.
Fundamentally, equation (4) calculates a repulsive poten-
tial field, Uobs , that increases, as the robot gets closer to
the circular obstacle. The gain parameter, kobs, controls the
strength of this repulsion, and the distance-based terms deter-
mine the shape of the repulsive force field. This potential field
is commonly used in robotics for obstacle avoidance, where
robots move away from obstacles by following the gradient
of this field.
4) Dynamic Obstacle Model
When dealing with a moving obstacle, its position can be dy-
namically described as a function of time, denoted as T . This
dynamic position is calculated using equations (5) and (6):
oxdynamic(T ) = oxinitial + vobstacle cos(?obstacle)T (5)
oydynamic(T ) = oyinitial + vobstacle sin(?obstacle)T (6)
Where:
(oxinitial, oyinitial): These represent the initial coordinates of
the moving obstacle, specifying where the obstacle is located
at the start of its movement.
vobstacle: This parameter signifies the velocity of the moving
obstacle. It defines how fast the obstacle is moving through
space.
?obstacle: The initial orientation of the moving obstacle is
represented by this angle. It indicates the direction in which
the obstacle is initially facing.
Equations (5) and (6) enable to track the dynamic position
of a moving obstacle over time, allowing for effective collision
avoidance and path planning in dynamic environments.
An optimal trajectory in mobile robot path planning is the
most efficient and effective path the robot can take to reach its
destination while meeting specific criteria. “Optimal” implies
that this path is the best choice based on defined metrics. The
key aspects of optimal trajectories include efficiency, obstacle
avoidance, smoothness, consideration of dynamic constraints,
task-specific objectives, global vs. local optimization, and
real-time adaptation [42].