Distributed tracking of a rigid formation for multi-agent systems

In this paper, two algorithms based on the rigidity matrix are proposed to control a formation of a multi-agent system. The objective is to drive all the agents to achieve a predefined formation while following a desired translational velocity under the constrains that the desired velocity is available to only a subset of the agents and the agents have only local interaction. The proposed control algorithms consist of a formation acquisition term which depends on a potential function and the rigidity matrix, and a velocity estimation term. Simulation results are provided to show the effectiveness of the proposed control algorithms.