On the Stabilization of Rigid Formations on Regular Curves

TL;DR

This paper presents a novel method for stabilizing multi-agent rigid formations on general planar curves using a combination of a randomized Newton-Like algorithm and continuous feedback control, validated through simulations.

Contribution

It introduces a new approach for formation stabilization on arbitrary curves, combining geometric algorithms with control laws for convergence and obstacle avoidance.

Findings

Successful stabilization on various curves

Effective formation convergence demonstrated

Robustness to different rigid formations

Abstract

This work deals with the problem of stabilizing a multi-agent rigid formation on a general class of planar curves. Namely, we seek to stabilize an equilateral polygonal formation on closed planar differentiable curves after a path sweep. The task of finding an inscribed regular polygon centered at the point of interest is solved via a randomized multi-start Newton-Like algorithm for which one is able to ascertain the existence of a minimizer. Then we design a continuous feedback law that guarantees convergence to, and sufficient sweeping of the curve, followed by convergence to the desired formation vertices while ensuring inter-agent avoidance. The proposed approach is validated through numerical simulations for different classes of curves and different rigid formations. Code: https://github.com/mebbaid/paper-elobaid-ifacwc-2026