Finite-time Stabilization of Circular Formations using Bearing-only Measurements

TL;DR

This paper introduces a decentralized control method for stabilizing circular formations of vehicles using only bearing measurements, achieving finite-time stability without distance information.

Contribution

It proposes a novel discontinuous control law based on angle errors and nonsmooth analysis to ensure local finite-time stability of formations.

Findings

Formation is locally finite-time stable.

Collision avoidance is guaranteed.

The vehicle positions' evolution is characterized.

Abstract

This paper studies decentralized formation control of multiple vehicles when each vehicle can only measure the local bearings of their neighbors 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 circular formation, where each vehicle has exactly two neighbors and the angle at each vehicle subtended by its two neighbors is pre-specified. To stabilize 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 analyzed 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. The evolution of the vehicle positions in the plane is also characterized.