A Fuel Optimization Method for the Pursuer in the Spacecraft Pursuit-Evasion Game

The fuel optimization of the spacecraft is significant for its service life. In this paper, a fuel optimization method is proposed to solve the fuel optimization problem of the pursuer in the spacecraft pursuit-evasion game (SPE game). This method first takes both the magnitude and direction of the pursuer's thrust as the control variables to be optimized, then models the fuel optimization problem as a two-player zero-sum differential game whose payoff function is the fuel consumption of the pursuer, and finally obtains the optimal control strategy of the pursuer by solving the saddle point of the differential game. Considering that the solving of the saddle point usually leads to the solving of a high-dimensional (12-dimensional in this paper) two-point boundary value problem (TPBVP), which is very challenging, the proposed method adopts a dimension-reduction algorithm which can simplify the TPBVP to the solving of a four-dimensional nonlinear equations and a terminal constraint, and then presents an hybrid numerical algorithm combining the particle swarm optimization algorithm and the Powell algorithm to solve the nonlinear equations and terminal constraint. The simulation results show that the proposed method can achieve the fuel optimization of the pursuer in the SPE game and is robust to the orbital altitude, the initial relative state between the pursuer and evader and the magnitude of the evader's thrust.