Distributed coordinated tracking via a variable structure approach - part I: Consensus tracking

This is the first part of a two-part paper on distributed coordinated tracking for a group of autonomous vehicles via a variable structure approach. Here, the term coordinated tracking is used to refer to both consensus tracking and swarm tracking. In the first part of this paper, we focus on the consensus tracking problem where a group of autonomous vehicles can track a (time-varying) virtual leader when the state of the virtual leader is available to only a subset of the group of vehicles. In the case of first-order kinematics, we propose a distributed consensus tracking algorithm without velocity measurements under both fixed and switching network topologies. In particular, we show that distributed consensus tracking can be achieved in finite time. In the case of second-order dynamics, we propose two distributed consensus tracking algorithms without acceleration measurements under, respectively, a fixed and switching network topology. In particular, we show that the proposed algorithms guarantee at least global exponential tracking. For distributed consensus tracking in the case of both first-order kinematics and second-order dynamics, a mild connectivity requirement is proposed by adopting a connectivity maintenance mechanism in which the adjacency matrix is defined in a proper way.