Optimal Strategies and Cooperative Teaming for 3-D Multiplayer Reach-Avoid Games

This article studies multiplayer reach-avoid games with a plane being the goal in 3-D space. Due to the difficulty that directly analyzing multipursuer multievader scenarios brings the curse of dimensionality, the whole problem is decomposed to distinct subgames. In the subgames, a single pursuer or multiple pursuers, which have different speeds, form a team to capture one evader cooperatively while the evader struggles to reach the plane. With the players' dominance region based on the definition of isochronous surfaces, the target points and value functions are obtained for the game of degree by using Apollonius spheres. Additionally, the corresponding closed-loop saddle-point strategies are shown to be Nash equilibrium. The degeneration between scenarios of different scales is also discussed. To minimize the sum of subgames' costs, the tasks of intercepting multiple evaders are assigned to individuals or teams in the form of bipartite graph matching. A hierarchical matching algorithm and a state-feedback rematching method are proposed which can be updated in real-time to improve the solution. Finally, diverse empirical experiments and comparisons with state-of-the-art methods are illustrated to demonstrate the optimality of proposed strategies and algorithms in this article.