Avoidance Control with Relative Velocity Information for Lagrangian Dynamics

In this paper, a novel cooperative control strategy with relative velocity information is derived to guarantee collision-free trajectories for multi-agent systems with Lagrangian dynamics. An important feature of this method is that the avoidance control input of an agent depends not only on its proximity to other agents/obstacles but also on their relative motions. For instance, agents approaching at high speeds might be more critical than slow moving yet physically closer agents. The main advantage of using this additional velocity information is that the collision avoidance maneuvers of agents are smoother, and less conservative in the sense that the agents do not spread out as much while avoiding collisions with one another. A Lyapunov-based analysis is adopted to guarantee that the agents meet their desired objectives without colliding. Finally, simulation results on three different systems are provided to illustrate the effectiveness of the proposed control strategy.