Control of 2D minimally persistent formations with three co-leaders in a cycle

This paper mainly solves the problem of 2D minimally persistent formation control in which three coleaders are in a cycle, which raises a great challenge in the area of persistent formation control. First, a novel control law is proposed for this problem. The fundamental moving principles of the agents are well-designed based on the property of persistence, and the non-square rigidity matrix is converted into the square one for the design of the control law. Then, the method of leading principal minor is utilized to prove that the formation with the above control law can be stabilized. Finally, simulation results show that the proposed controllers are able to stabilize the group formation to a rigid shape, while keeping the distances between the agents to the desired value.