Formation Shape Control Based on Distance Measurements Using Lie Bracket Approximations

TL;DR

This paper introduces a distributed control law for multi-agent formation shape control using only distance measurements, leveraging Lie bracket approximations and sinusoidal perturbations for stability.

Contribution

It presents a novel distance-only control method that does not require synchronization or data storage, applicable to agents in any Euclidean dimension.

Findings

Achieves local uniform asymptotic stability of formations

Uses sinusoidal perturbations to extract gradient information

Employs Lie bracket approximations for control design

Abstract

We study the problem of distance-based formation control in autonomous multi-agent systems in which only distance measurements are available. This means that the target formations as well as the sensed variables are both determined by distances. We propose a fully distributed distance-only control law, which requires neither a time synchronization of the agents nor storage of measured data. The approach is applicable to point agents in the Euclidean space of arbitrary dimension. Under the assumption of infinitesimal rigidity of the target formations, we show that the proposed control law induces local uniform asymptotic stability. Our approach involves sinusoidal perturbations in order to extract information about the negative gradient direction of each agent's local potential function. An averaging analysis reveals that the gradient information originates from an approximation of Lie brackets of certain vector fields. The method is based on a recently introduced approach to the problem of extremum seeking control. We discuss the relation in the paper.