Bearing-only formation control under persistence of excitation

TL;DR

This paper develops bearing-only formation control laws in multi-dimensional spaces that leverage persistence of excitation to achieve exponential stabilization, relaxing graph topology constraints and removing scale ambiguity.

Contribution

It introduces a novel bearing PE condition for formation control, enabling exponential stabilization with relaxed graph requirements and eliminating scale ambiguity.

Findings

Proposed distributed bearing-only control laws guarantee exponential formation stabilization.

Utilized bearing PE to relax graph topology conditions compared to bearing rigidity.

Simulation results demonstrate effective formation control under the proposed method.

Abstract

This paper addresses the problem of bearing-only formation control in $d~(d\geq 2)$-dimensional space by exploring persistence of excitation (PE) of the desired bearing reference. By defining a desired formation that is bearing PE, distributed bearing-only control laws are proposed, which guarantee exponential stabilization of the desired formation only up to a translation vector. The key outcome of this approach relies in exploiting the bearing PE to significantly relax the conditions imposed on the graph topology to ensure exponential stabilization, when compared to the bearing rigidity conditions, and to remove the scale ambiguity introduced by bearing vectors. Simulation results are provided to illustrate the performance of the proposed control method.