A Combinatorial Optimization Method for Free-Time Orbital Pursuit-Evasion Game

The orbital pursuit-evasion game has become a hotspot in space engineering research. This paper proposes a combinatorial optimization method to solve the orbital pursuit-evasion game based on the Hill-Clohessy-Wiltshire equation. First, the dynamics of the pursuer and evader are presented under HCW. Next, the game is modeled as a free-time differential game, which is transformed into a two-point boundary value problem considering necessary conditions. Subsequently, based on the necessary conditions of terminal costates for the saddle point solution, the original problem can be transformed into finding a set of a four-dimensional problem. Then, a combinatorial optimization method is proposed based on the Improved Grey Wolf Optimizer and Sequential Quadratic Programming for the free-time orbital pursuit-evasion game. Numerical simulation results demonstrate the proposed method is effective and efficient.