Optimal Strategies of Orbital Target-Attacker-Defender Game with a Non-maneuvering Target

This paper investigates game-theoretic strategies to protect Targets against potential unsafe approaches by Attackers within the context of the orbital TAD (Target-Attacker-Defender) game. Utilizing game theory principles, we formulate the orbital TAD game, as a differential game model, incorporating players, states, actions, payoffs, and constraints. The orbital TAD game accounts for the constrained control capabilities of the spacecrafts, and we establish three variants: the fuel-constrained TAD game, the thrust-constrained TAD game, and the thrust-fixed TAD game. These models address the specific constraints on the Defender's control capabilities during the game. By solving these models using differential game theory, we obtain Nash equilibrium solutions, representing optimal strategies for both the Defender and the Attacker. We validate the correctness and effectiveness of the solution methods through simulations. The simulation results demonstrate the efficacy of the proposed Defender strategies, where the Defender successfully intercepts the Attackers and ensures the safety of the Target at the terminal time. Moreover, we analyze the impact of dynamic effects, such as Earth's gravity, on the trajectories of both parties during the TAD game. Importantly, the Defender's initial position emerges as a critical factor in determining the game outcome, leading to distinct regions of interception success, attack success, and protection success. Furthermore, the application of differential game theory and the derivation of Nash equilibrium solutions contribute to the theoretical foundation of this research.