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

The article discusses a trajectory planning method for a group of mobile robots that ensures safemovement and eliminates the possibility of collisions both between the robots themselves and with externalobstacles, including moving objects. The developed mathematical model considers three main collisionscenarios: 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 ensuremaximum safety during movement, and their consideration allows for efficient adaptation of robot routesto changing environmental conditions. The trajectory of each robot is represented as a piecewise linearpath with intermediate points, which are optimized to ensure safe movement. Special attention is paid tospeed adaptation on different segments of the trajectory: a robot can adjust its speed based on currentconditions to minimize the risk of collisions. To evaluate distances between objects, the Euclidean norm isused, allowing for the calculation of minimum distances between the centers of spherical representationsof robots and obstacles. The problem is solved in two stages. In the first stage, a trajectory is constructedfor the first robot, taking into account initial conditions and obstacle placement. In the second stage, trajectoriesare formed for the remaining robots, considering the already planned routes. For optimizing thecoordinates of intermediate points and speeds, a genetic algorithm is applied, which minimizes travel timewhile ensuring safe movement. The genetic algorithm uses crossover and mutation operators to generatediverse solutions and performs checks to ensure compliance with safety conditions. Numerical simulationswere conducted using Python, with the Matplotlib library used for visualization of results. During theexperiments, 50 tests were performed with varying numbers of obstacles (from 5 to 10). Analysis of theresults showed that as the number of obstacles increased, both the computation time and the quality of thegenerated trajectories improved. This confirms the effectiveness of the proposed method for controllinggroups of mobile robots in dynamically changing environments