A Revisit to Gradient-Descent Bearing-Only Formation Control

Abstract

This paper addresses the problem of bearing-only formation control of multi-agent systems, where each agent can merely obtain the relative bearing measurements of their neighbor neighbors whereas relative distance or position measurements are unavailable. In particular, we revisit a bearing-only formation control law proposed in [1]. Unlike many other existing ones, this control law is gradient-descent, which is favorable from the stability analysis point of view. It has the potential to be extended to handle more complex agent models and moving target formations. Up to now, this control law has not attracted sufficient attention probably because its stability analysis is based on optimization techniques and challenging to generalize. The contribution of this paper is to present a new stability analysis of this formation control law based on Lyapunov approaches. The new stability analysis reveals some new properties of the control law such as exponential convergence rate and lays a foundation for deriving new bearing-only control laws in the future.