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

翻译：本文研究多智能体刚性编队在一般平面曲线上的稳定化问题。具体而言，我们旨在通过路径扫描后，将等边多边形编队稳定在闭合平面可微曲线上。通过采用随机多起点类牛顿算法，解决了在目标点处寻找内接正多边形的问题，该算法能够确保极小值的存在性。随后，我们设计了一种连续反馈控制律，该控制律保证系统收敛至曲线并完成充分扫描，继而收敛至期望的编队顶点，同时确保智能体间的避碰。通过对不同类型曲线及不同刚性编队的数值仿真，验证了所提方法的有效性。代码：https://github.com/mebbaid/paper-elobaid-ifacwc-2026