Time Optimal Consensus Tracking for Kinematic Points in a Plane

This paper addresses the issue of time optimality in consensus tracking problems for a group of agents with bounded inputs, moving in a plane. A special agent called "leader" autonomously generates a trajectory and all the agents are required to converge onto this leader trajectory in minimum possible time. Any two agents can communicate with each other only if they are within a fixed distance of each other. Time optimal pursuit evasion policies are used to derive local feedback laws for each agent. The local feedback laws achieve global min-max time consensus tracking when the information graph is a spanning tree. Further, given any initial communication graph, we propose a decentralized algorithm to find a spanning tree, which gives the least min-max time to consensus.