The bearing-based multi-agent rendezvous problem on a circle

This paper studies a multi-agent rendezvous problem where the agents' positions are restricted in a circle and each can sense a bearing vector with regard to the center and communicate with its neighbor on the sensed bearing. A bearing-only control law is proposed and is proved to drive the n-agent system to a set of equilibria which contains the rendezvous space (desired equilibrium set). Depending on the interaction graph between n agents, the set of equilibria may also contain some subsets of undesired equilibria. For some specific cases (n-agent system with line graphs and three-agent system with complete graph), we show that the sets of undesired equilibria are repulsive, and thus any trajectory of the n-agent system starting outside the undesired equilibrium set approaches the rendezvous space. Simulations are also provided to validate the analysis.