Optimal control of multi-vehicle systems with LTL specifications

In this paper, optimal control of multi-vehicle systems is studied. When collision avoidance between vehicles and obstacle avoidance are imposed, state discretization is effective as one of the simplified approaches. Furthermore, using state discretization, cooperative actions such as rendezvous can be easily specified by linear temporal logic (LTL) formulas. However, it is not necessary to discretize all states, and partial states (e.g., the position of vehicles) should be discretized. From this viewpoint, a new control method for multi-vehicle systems is proposed in this paper. First, the system in which partial states are discretized is formulated. Next, the optimal control problem with constraints described by LTL formulas is formulated, and its solution method is proposed. Finally, numerical simulation is shown. The proposed method provides us a useful method in control of multi-vehicle systems.