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：本文聚焦于协调机器人蜂群沿凸曲线轨道运行，同时避免个体间碰撞。各机器人不具备制动能力，仅能调整运动方向，并保持各自恒定但不同的速度。不同于控制机器人之间的空间关系，我们的编队控制算法旨在部署密集机器人蜂群，模拟龙卷风式鱼群行为。为安全实现该目标，我们结合了可扩展的超车规则、引导向量场以及具有自适应半径的控制障碍函数，以实现平稳超车。机器人的决策过程是分布式的，仅依赖局部信息。实际应用包括防御结构或护航任务，使蜂群具有无需集中指挥的额外韧性。我们对所提策略进行了严谨分析，并通过涉及高密度独轮车模型的数值模拟验证了其有效性。