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.