Finite-time formation control for linear multi-agent systems: A motion planning approach

This paper investigates the problem of finite-time formation control for multi-agent systems with general linear dynamics. First of all, the considered formation problem is converted into the motion planning problem, where the systems are steered from initial positions to the desired terminal configurations. Then, by using Pontryagin maximum principle, an optimal formation control law is developed for multi-agent systems based on some invertible conditions. With the designed control law, the multi-agent systems can achieve the desired formation in finite time, where the formation configurations and the settling time can be specified in advance according to task requirements. Meanwhile, a performance index is guaranteed to be optimal. Further, it is proved that the formation problem concerned is solved if and only if the linear systems are controllable. Finally, a possible application of the proposed control law to spacecraft formation flying with circular and near-circular reference orbit is illustrated.