Collision-Free Stable Polygon Formation of Multi-Agent Robots

Abstract

This paper presents a control design of multi-agent robot dynamic systems that drives multiple robots to move in a polygon formation while also avoiding collision with each other and possible obstacles. By placing the equilibrium of the system in a polygon formation configuration, the system succeeds to converge the robots’ individual configuration at surrounding of the center point of the polygon formation. To obtain a collective goal objective, a state of the center point as a target point is defined in which its dynamic is stable and converges to the goal point. By using a smooth repulsive potential function, the robots are guaranteed to be safe from collisions with other robots in the formation and with obstacles. When a robot is at far from obstacle edges, the multi-agent robots form a polygon formation. The proof of multi-agent robots forming a polygon formation is shown by using the Lyapunov method. Simulations are carried out to show that the multi-agent robots develop a polygon formation and avoids collisions with each other and a static obstacle. Another advantage of the proposed algorithm is when one robot cannot continue to follow the group formation, the multi-robot system is able to re-coordinate with the remaining number of agents.