Artificial Potential-Based Formation Control with Collision and Obstacle Avoidance for Second-order Multi-Agent Systems

A formation control strategy with collision avoidance and obstacle avoidance mechanisms is proposed for second-order continuous multi-agent systems (MAS) under a directed topology. The control objectives can be achieved by introducing artificial potential field (APF) methods and the leader-follower formation methods. The leader-follower formation methods are employed to assist follower agents to obtain the coordination of positions and consensus of velocities with the leader-agent, the control objectives of formation generation and formation maintenance can be achieved. In the APF methods, obstacles and agents are regarded as high potential fields. The repulsive forces provided by the potential fields can solve the problems of avoiding collisions among agents and avoiding the extern-obstacles. By using Lyapunov stability theory and graph theory, the fact, the stability of the closed-loop MAS can be guaranteed, is proven. In the end, the simulation results verified the effectiveness of the proposed formation control strategy.