Orbital three-player differential game using semi-direct collocation with nonlinear programming

An orbital three-player differential game among Target spacecraft, Pursuer spacecraft and Evader spacecraft is studied in this work. It is assumed that Target spacecraft runs in its orbit without the ability of maneuver, while Pursuer spacecraft and Evader spacecraft have continuous maneuverability. There are opposing objectives between Pursuer spacecraft and Evader spacecraft. The objective of Pursuer spacecraft is to keep Evader spacecraft far away from Target spacecraft while Evader spacecraft tries its best to shorten the distance from it to Target spacecraft prior to being intercepted. The orbital three-player differential game terminates when Evader spacecraft performs successful interception of Target spacecraft or it is intercepted by Pursuer spacecraft. The semi-direct collocation with nonlinear programming incorporated with NSGA-II algorithm which provides the initial guess is employed to solve the current three-player differential game. Numerical simulation was provided to verify the availability of the algorithm in finding the optimal solution of the orbital three-player differential game presented in this paper, and the results show that this work will be useful to some practical applications.