  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.
