Convergent multiagent formation control with collision avoidance

A key problem in the formation control of homogeneous multiagent systems is the collision-free convergence of the agent positions into a desired formation. It is a typical NP-hard problem by considering the problem as optimizing the assignment of multiple destinations to the same number of agents deployed in an open space. It becomes even harder if the collision avoidance is required during the motion of agents, and thus, a suboptimal but efficient solution is adequate. The traditional methods make it by accurate preplanning of the motion trajectory of each single agent, or simply letting them reach an equilibrium as a tradeoff between the collision avoidance and the desired formation. In this article, a distributed control algorithm embedded with an assignment switch scheme is proposed to guarantee that the asymptotic convergence to the desired formation is achieved with no collisions between agents. By the proposed algorithm, the agents keep moving in straight lines toward their respective destinations until they are going to collide if they do not stop, at which moment the agents will communicate their information locally to switch their destination assignments so that they will continue to move in different directions and avoid potential collisions. Distributed control rules are also defined to confine the motion space of each agent for collision avoidance. It has been rigorously proven that the positions of all agents converge to the desired formation with no collision under random initial deployment. In addition, a detailed parameter design procedure is provided for both setting and controlling of the formation. Finally, Monte Carlo simulations and actual experiments in the outdoor environment are implemented and the results verify the effectiveness of the proposed algorithm.