Online Leader Selection forMulti-Agent Collective Tracking and FormationMaintenance?

In this paper we propose an extension of the popular leader-follower framework for multi-agent collective tracking and formation maintenance. We introduce a new paradigm, the online leader selection, which allows the agent group to persistently select the identity of the current leader in order to maximize the tracking performance of an exogenous velocity command while maintaining a given formation and across a (possibly time-varying) communication-graph topology. By employing two of the most widely used fully-decentralized multi-agent coordination schemes (a first-order and second-order ones), we theoretically analyze the effects of a leader change and propose two corresponding error metrics able to adequately characterize the tracking performance of the multi-agent group. Both the group performance and the choice of the right metrics are found to depend upon the spectral properties of a special directed graph induced by the identity of the chosen leader. By exploiting the proposed analysis and distributed estimation techniques, we then detail two fully-decentralized adaptive controllers able to periodically select the best leader among the neighbors of the current leader. Numerical simulations show that the application of the proposed technique results in an clear improvement of the overall performance of the group behavior