On the Stabilization of Rigid Formations on Regular Curves

• URL: http://arxiv.org/abs/2512.10700v1
• Date: Thu, 11 Dec 2025 14:41:19 GMT
• Title: On the Stabilization of Rigid Formations on Regular Curves
• Abstract summary: This work deals with the problem of stabilizing a multi-agent rigid formation on a general class of planar curves.<n> Namely, we seek to stabilize an equilateral polygonal formation on closed planar differentiable curves after a path sweep.
• Score: 6.646268876373452
• License: http://creativecommons.org/licenses/by/4.0/
• 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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