This paper presents an approach to modeling the movement of a multi-agent system in a two-dimensional space using a modified Particle Swarm Optimization (PSO) algorithm, adapted to account for the physical properties of the agents. The standard PSO, originally designed for solving optimization problems through swarm behavior, has been extended to simulate the motion of physical objects with defined mass, velocity, and inter-agent interactions. To ensure physically plausible motion and prevent collisions between agents, hybrid methods have been proposed that combine classical PSO with inter-particle potential functions. Trajectory planning and control over the direction and speed of agent movement have been governed by the modified PSOs, while collision avoidance is achieved through the influence of repulsive potential fields. Numerical simulations have been conducted to analyze the collective behavior of the swarm.
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