Bearing-Only Consensus and Formation Control under Directed Topologies

We address the problems of bearing-only consensus and formation control, where each agent can only measure the relative bearings of its neighbors and relative distances are not available. We provide stability results for the Filippov solutions of two gradient-descent laws from non-smooth Lyapunov functions in the context of differential inclusion. For the consensus and formation control problems with undirected sensing topologies, we prove finite-time and asymptotic convergence of the proposed non-smooth gradient flows. For the directed consensus problem, we prove asymptotic convergence using a different non-smooth Lyapunov function given that the sensing graph has a globally reachable node. Finally, for the directed formation control problem we prove asymptotic convergence for directed cycles and directed acyclic graphs and also introduce a new notion of bearing persistence which guarantees convergence to the desired bearings.