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Equilibrium Strategy of the Pursuit-Evasion Game in Three-Dimensional Space

IEEE/CAA Journal of Automatica Sinica 2024年第2期11卷 446-458页

作者： Nuo Chen Linjing Li Wenji Mao School of Artificial Intelligence University of Chinese Academy of SciencesBeijing 100049 Institute of Automation Chinese Academy of SciencesBeijing 100190China

The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.

关键词： Differential game equilibrium strategy pursuit-evasion game threedegree-of-freedom control

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