We study the general formation problem for a group of mobile agents in a plane, in which the agents are required to maintain a distribution pattern, as well as to rotate around or remain static relative to a static/moving target. The prescribed distribution pattern is a class of general formations that the distances between neighboring agents or the distances from each agent to the target do not need to be equal. Each agent is modeled as a double integrator and can merely perceive the relative information of the target and its neighbors. A distributed control law is designed using the limit-cycle based idea to solve the problem. One merit of the controller is that it can be implemented by each agent in its Frenet-Serret frame so that only local information is utilized without knowing global information. Theoretical analysis is provided of the equilibrium of the N-agent system and of the convergence of its converging part. Numerical simulations are given to show the effectiveness and performance of the proposed controller.
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