Constructing barriers for arbitrary velocity players in mutual attack-defense games

Abstract

In this paper, a novel two-player mutual attack-defense game is proposed and addressed where each player protects its own static target and performs both intrusion and defense tasks without distinguishing between their respective roles. In particular, each player has its own territory, meaning that each player has a capture advantage in its own territory, independent of velocity. The game can be solved by dividing it into active and passive goals. To address the positive goals, a method of combining barriers is proposed, where geometric methods are employed to construct barriers for arbitrary velocity conditions. And the time advantage needs to be further validated for passive goals. Through the combinatorial barriers, the entire state space is partitioned into different subspaces, corresponding to various terminal sets. The successive analysis builds upon this foundation by numerically analyzing each subspace, which yields detailed results on strategies for both players in the proposed novel game scenario. Finally, the simulation validates the effectiveness of the proposed strategies.