This paper focuses on coordinating a robot swarm orbiting a convex path without collisions among the individuals. The individual robots lack braking capabilities and can only adjust their courses while maintaining their constant but different speeds. Instead of controlling the spatial relations between the robots, our formation control algorithm aims to deploy a dense robot swarm that mimics the behavior of tornado schooling fish. To achieve this objective safely, we employ a combination of a scalable overtaking rule, a guiding vector field, and a control barrier function with an adaptive radius to facilitate smooth overtakes. The decision-making process of the robots is distributed, relying only on local information. Practical applications include defensive structures or escorting missions with the added resiliency of a swarm without a centralized command. We provide a rigorous analysis of the proposed strategy and validate its effectiveness through numerical simulations involving a high density of unicycles.

翻译：本文研究如何协调机器人群体沿凸路径绕行，同时避免个体间碰撞。由于个体机器人缺乏制动能力，只能通过调整航向维持恒定但各不相同的速度。与直接控制机器人空间关系不同，我们的编队控制算法旨在模拟龙卷风群鱼的行为模式，部署高密度机器人群体。为实现安全目标，我们综合运用可扩展超车规则、引导向量场以及具有自适应半径的控制障碍函数，确保平滑超车。机器人的决策过程采用分布式架构，仅依赖局部信息。该技术可应用于防御结构或护航任务，使群体无需集中指挥即可具备弹性。我们对该策略进行了严谨的理论分析，并通过高密度独轮车模型的数值仿真验证了其有效性。