Online leader selection for collective tracking and formation control: The second-order case

In this paper, we deal with a double control task for a group of interacting agents that have second-order dynamics. Adopting the leader-follower paradigm, the given multiagent system is required to maintain a desired formation and to collectively track a velocity reference provided by an external source only to a single agent at time, called the 'leader.' We prove that it is possible to optimize the group performance by persistently selecting online the leader among the agents. To do this, we first define a suitable error metric that is able to capture the tracking performance of the multiagent group while maintaining a desired formation through a (even time-varying) communication-graph topology. Then, we show that this depends on the algebraic connectivity and on the maximum eigenvalue of the Laplacian matrix of a special directed graph depending on the selected leader. By exploiting these theoretical results, we finally design a fully distributed adaptive procedure that is able to periodically select online the optimum leader among the neighbors of the current one. The effectiveness of the proposed solution against other possible strategies is confirmed by numerical simulations.