Limit-Cycle-Based Decoupled Design of Circle Formation Control with Collision Avoidance for Anonymous Agents in a Plane

We study the circle formation problem for a group of anonymous mobile agents in a plane, in which the agents are required to converge onto a circle with a preset target as the center, as well as to maintain the desired relative positions when rotating around the target at the same speed. Each agent is modeled as a kinematic point and can merely perceive the relative positions of the target and its limited neighbors. In order to solve the circle formation problem, a limit-cycle-based decoupled-design approach is delivered. We divide the overall control objective into two subobjectives, where the first is target circling that all agents converge onto the circle around the target, and the second is spacing adjustment that each agent maintains the desired distance from its neighbors. Then, we propose to use a controller comprised of converging part and layout part to deal with these two subobjectives, respectively. The former part is based on a limit-cycle oscillator using only the relative position from the target, and the latter is designed by also perceiving the relative position from the agent's neighbors. An important feature of the controller is that it guarantees that no collision between agents ever takes place throughout the system's evolution. Another feature is that some of the parameters in the proposed controller have explicit physical meanings related to the agents' rotating motion around the target, so that they can be set more reasonable and easily in real applications. Numerical simulations are given to show the effectiveness and performance of the proposed circle formation controller.