Optimal formation control and collision avoidance in environment with multiple rectangle obstacles

This paper addresses formation control problem with collision avoidance for general linear multi-agent systems via an optimal control strategy. In the proposed optimal control strategy, a novel potential function is designed to accomplish formation of multi-agent systems (MASs) with obstacle/collision avoidance capability, which can avoid rectangle obstacles accurately. In this potential function, a novel relative velocity based self-adaptive detection region is proposed to avoid collisions with adjacent agents. Moreover, a non-quadratic avoidance performance index is constructed based on inverse optimal control approach. Then, the optimal control strategy is designed to guarantee the asymptotic stability of the closed-loop system and optimality of the proposed performance index. Finally, a simulation example is given to illustrate the efficiency of the proposed approach.