Forming Circle Formations of Anonymous Mobile Agents With Order Preservation

We propose distributed control laws for a group of anonymous mobile agents to form desired circle formations when the agents move in the one-dimensional space of a circle. The agents are modeled by kinematic points. They share the common knowledge of the orientation of the circle, but are oblivious and anonymous. Moreover, each agent can only sense the relative positions of its neighboring two agents that are immediately in front of or behind itself. Distributed control strategies are designed for the agents using only the information of the relative positions of their two neighbors and also the given desired distances to its neighboring two agents. To make the control strategies more practical, we discuss the corresponding sampled-data control laws, and utilizing the technique of adopting time-varying gains, we obtain control laws that are able to guide the agents to form the desired circle formation within any given finite time. One feature of the proposed control laws is that they guarantee that the spatial ordering of the agents are preserved throughout the system´s evolution, and thus no collision may take place during the process of forming circle formations. Both theoretical analysis and numerical simulations are given to show the effectiveness of the proposed formation control strategies.