Distance-based Control of K4 Formation with Almost Global Convergence

TL;DR

This paper introduces a distance-based control method for four agents to achieve a formation with almost global convergence, improving upon existing local stability results by leveraging properties from 3D formation control.

Contribution

It proposes a modified gradient-based control law that guarantees almost global convergence for 2D four-agent formations, extending stability analysis beyond local results.

Findings

Achieves almost global convergence in formation control

Validates the control law with simulation results

Builds on properties from 3D formation control

Abstract

In this paper, we propose a distance-based formation control strategy that can enable four mobile agents, which are modelled by a group of single-integrators, to achieve the desired formation shape specified by using six consistent inter-agent distances in a 2-dimensional space. The control law is closely related to a gradient-based control law formed from a potential function reflecting the error between the actual inter-agent distances and the desired inter-agent distances. There are already control strategies achieving the same objective in a distance-based control manner in the literature, but the results do not yet include a global as opposed to local stability analysis. We propose a control strategy modified from the existing gradient-based control law so that we can achieve almost global convergence to the desired formation shape, and the control law uses known properties for an associated formation shape control problem involving a four-agent tetrahedron formation in 3-dimensional space. Simulation results verifying our analysis are also presented.