Multiple-Pursuer Single-Evader Reach-Avoid Games in Constant Flow Fields

This article considers a planar multiple-pursuer single-evader reach-avoid game played in a constant flow field. Such a game problem arises in practical applications, such as maritime escort, aircraft confrontation in airflow fields, and defense of moving targets. The dominance boundary, which serves as an analogy to the Apollonius circle and the Cartesian oval, is investigated. The existence of semipermeable surfaces in the game is shown. Under reasonable assumptions, there exists a semipermeable surface, which is part of the barrier surface separating the winning regions for the evader and pursuers. The winning strategies are designed for both sides of players in their corresponding winning regions. It is also shown that at most two pursuers are necessary for successful protection, as in the situation where there is no flow field. Finally, numerical results are given to illustrate the conclusions.