Formations on directed cycles with bearing-only measurements

Abstract

This paper studies a bearing-only-based formation control problem for a group of single-integrator agents with directed cycle sensing topology. In a 2-dimensional space, a necessary and sufficient condition for the set of desired bearing vectors to be feasible is derived. Then, we propose a bearing-only control law for every agent and prove that the formation asymptotically converges to a formation specified by a set of feasible desired bearing vectors. Analysis of the equilibrium formations in the plane for a 3-agent system and subsequent extension to an n-agent system is provided. We further extend the analysis on directed triangular formation into a 3-dimensional space. Finally, simulations validate the theoretical results.