Nash-equilibrium strategies of orbital Target-Attacker-Defender game with a non-maneuvering target

This study investigates the orbital Target-Attacker-Defender (TAD) game problem in the context of space missions. In this game, the Attacker and the Defender compete for a Target that is unable to maneuver due to its original mission constraints. This paper establishes three TAD game models based on the thrust output capabilities: unconstrained thrust output, thrust constrained by an upper bound, and fixed thrust magnitude. These models are then solved using differential game theory to obtain Nash equilibrium solutions for the game problems, and the correctness and effectiveness of the solution methods are verified through simulations. Furthermore, an analysis of the winning mechanisms of the game is conducted, identifying key factors that influence the game's outcomes, including weight coefficients in payoffs, the maximum thrust acceleration limit, and the initial game state. Considering the unique characteristics of space missions, a specific focus is given to the analysis of the Defender's initial states in the hovering formation and in-plane circling formation, revealing overall success patterns for defense strategies from these two formations. In summary, this study provides valuable insights into the control strategies and winning mechanisms of orbital TAD games, deepening our understanding of these games and offering practical guidance to improve success rates in real-world scenarios.