A GENETIC ALGORITHM FOR PLANNING THE TRAJECTORY OF A GROUP OF MOBILE ROBOTS IN THE PRESENCE OF STATIONARY AND MOBILE OBSTACLES

Abstract

The article discusses a trajectory planning method for a group of mobile robots that ensures safe
movement and eliminates the possibility of collisions both between the robots themselves and with external
obstacles, including moving objects. The developed mathematical model considers three main collision
scenarios: intersection of robot trajectories within the group, interaction with stationary obstacles, and the probability of collision with moving objects. Each of these scenarios is analyzed in detail to ensure
maximum safety during movement, and their consideration allows for efficient adaptation of robot routes
to changing environmental conditions. The trajectory of each robot is represented as a piecewise linear
path with intermediate points, which are optimized to ensure safe movement. Special attention is paid to
speed adaptation on different segments of the trajectory: a robot can adjust its speed based on current
conditions to minimize the risk of collisions. To evaluate distances between objects, the Euclidean norm is
used, allowing for the calculation of minimum distances between the centers of spherical representations
of robots and obstacles. The problem is solved in two stages. In the first stage, a trajectory is constructed
for the first robot, taking into account initial conditions and obstacle placement. In the second stage, trajectories
are formed for the remaining robots, considering the already planned routes. For optimizing the
coordinates of intermediate points and speeds, a genetic algorithm is applied, which minimizes travel time
while ensuring safe movement. The genetic algorithm uses crossover and mutation operators to generate
diverse solutions and performs checks to ensure compliance with safety conditions. Numerical simulations
were conducted using Python, with the Matplotlib library used for visualization of results. During the
experiments, 50 tests were performed with varying numbers of obstacles (from 5 to 10). Analysis of the
results showed that as the number of obstacles increased, both the computation time and the quality of the
generated trajectories improved. This confirms the effectiveness of the proposed method for controlling
groups of mobile robots in dynamically changing environments