Finite-time stabilisation of cyclic formations using bearing-only measurements

Abstract

This paper studies decentralised formation control of multiple vehicles in the plane when each vehicle can only measure the local bearings of their neighbours by using bearing-only sensors. Since the inter-vehicle distance cannot be measured, the target formation involves no distance constraints. More specifically, the target formation considered in this paper is an angle-constrained cyclic formation, where each vehicle has exactly two neighbours and the angle at each vehicle subtended by its two neighbours is pre-specified. To stabilise the target formation, we propose a discontinuous control law that only requires the sign information of the angle errors. Due to the discontinuity of the proposed control law, the stability of the closed-loop system is analysed by employing a locally Lipschitz Lyapunov function and nonsmooth analysis tools. We prove that the target formation is locally finite-time stable with collision avoidance guaranteed.

Keywords:

• formation control
• bearing-only measurement
• discontinuous dynamic system
• finite-time stability

Notes

1. In some literature such as Godsil and Royle (2001), the rows of an incidence matrix are indexed by vertices and the columns are indexed by edges.