让多智能体在曲线路径上稳定形成等边多边形，避免碰撞。
On the Stabilization of Rigid Formations on Regular Curves
- 用随机多起点牛顿类算法求解曲线内接正多边形位置。
- 设计连续反馈控制律，确保轨迹覆盖与形态收敛。
- 适用于各类平面闭合曲线，适合群体机器人编队控制。
本文研究在一类平面闭合可微曲线上的多智能体刚性构型稳定问题。目标是在完成路径扫掠后，使智能体形成等边多边形构型。通过一种随机多起点牛顿类算法求解以关注点为中心的内接正多边形，可保证极小值存在。随后设计连续反馈控制律，确保对曲线的充分扫掠，并实现向期望构型顶点的收敛，同时保证智能体间避碰。该方法在多种曲线类型和不同刚性构型下通过数值仿真验证有效。代码已公开于 https://github.com/mebbaid/paper-elobaid-ifacwc-2026。
原文摘要 · Abstract (English)
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
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。