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arXiv · 2512.10700

On the Stabilization of Rigid Formations on Regular Curves

Mohamed Elobaid·Shinkyu Park·Eric Feron
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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

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Mohamed Elobaid, Shinkyu Park, Eric Feron. 2025-12-11. On the Stabilization of Rigid Formations on Regular Curves. https://arxiv.org/abs/2512.10700

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