Collision-free consensus in second-order multi-agent dynamical systems

A collision-free consensus algorithm with leader tracking for multi-agent systems is presented. Virtual force is introduced for avoiding agents' inner collisions, and a method for choosing virtual force function is proposed. It is supposed that this kind of force is only effective when the distance between two agents is beyond a safe region. It performs repulsion function when the distances among agents get shorter, to separate agents from each other. With the presented consensus algorithm, agents match the leader's speed, operate following the leader, and keep a certain distance from each other. Lyapunov stability theorem is applied to prove the stability of the dynamic system. Simulation results verify the effectiveness of the proposed algorithm.