Nash equilibrium calculation for spacecraft pursuit-evasion game with impulsive maneuver

In the multi-satellite orbital game mission, each spacecraft obtains the current situation through observation, and then formulates maneuver strategies according to observation results and plans the working time of the thrusters based on the characteristics of the actuator to generate the desired velocity impulses. This process can be described by an integrated Observation-Decision-Actuation (ODA) system. The closed-loop time of the system is crucial to the orbital mission. Making efficient decisions under the time constraints of the integrated system is the key to improving the game efficiency. This paper focuses on the three-satellite pursuit-evasion game, which composes of a pursuer, an evader, and a defender. A fast-solving method for the Nash equilibrium is proposed and then an adaptive pursuing strategy is proposed such that the pursuer can track the evader while avoiding the defender. Firstly, in order to efficiently solve the Nash equilibrium under impulsive thrust, an analytical model of the relative reachable region of the spacecraft is established. Then, the fast-solving method for the Nash equilibrium of the two participants is proposed based on the reachable region and the distribution of the Nash equilibrium for the three participants is analyzed. This method can reduce the optimization range and the calculation complexity of numerical optimization. Besides, in order to improve the tracking ability of the pursuer against different opponents, a parameter-adaptive mechanism is established to dynamically adjust the optimization index parameters such that the the distribution of the Nash equilibrium can be changed accordingly. Finally, the correctness and efficiency of the Nash equilibrium strategy proposed in this paper is verified through numerical simulation.