Energy-limited formation design for second-order multi-agent systems

The problem of energy-limited formation for second multi-agent systems in leaderless case is investigated in this paper. First, considering that the energy is given in advance and is limited, an energy-limited formation protocol is proposed by local relative velocities and positions of each agent and its neighbors. Second, according to a special property of the Laplace matrix, the formation consensus problem is converted into a stabilization problem. Then, by the Lyapunov theory, sufficient conditions for second multi-agent systems in the form of analytic solutions of control gains are presented to achieve the energy-limited formation. Besides, the formation center function is determined, which is to show the macroscopic motion of formations. Finally, an example is given to demonstrate the validity of the the proposed theoretical results.