Relaxed bearing rigidity and bearing formation control under persistence of excitation

TL;DR

This paper introduces a novel approach to bearing formation control in multi-agent systems by leveraging Persistence of Excitation, relaxing classical rigidity conditions, and ensuring exponential stabilization using distributed control laws.

Contribution

It develops the concept of Bearing Persistently Exciting formations and extends bearing rigidity conditions through PE, enabling robust formation control under more general conditions.

Findings

Guaranteed exponential stabilization of formations.

Relaxed rigidity conditions compared to classical methods.

Validated effectiveness through simulations.

Abstract

This paper addresses the problem of time-varying bearing formation control in $d$ $(d\ge 2)$-dimensional Euclidean space by exploring Persistence of Excitation (PE) of the desired bearing reference. A general concept of Bearing Persistently Exciting (BPE) formation defined in $d$-dimensional space is here fully developed. By providing a desired formation that is BPE, distributed control laws for multi-agent systems under both single- and double-integrator dynamics are proposed using bearing measurements (along with velocity measurements when the agents are described by double-integrator dynamics), which guarantee uniform exponential stabilization of the desired formation in terms of shape and scale. A key contribution of this work is to show that the classical bearing rigidity condition on the graph topology, required for achieving the stabilization of a formation up to a scaling factor, is relaxed and extended in a natural manner by exploring PE conditions imposed either on a specific set of desired bearing vectors or on the whole desired formation. Simulation results are provided to illustrate the performance of the proposed control method.