Optimal pursuit/evasion spacecraft trajectories in the hill reference frame

The pursuit/evasion game for two spacecraft is significantly simplified by being described with a linearized system of equations of motion. A pursuit/evasion game is also known as a “minimax” problem, because the objective of the pursuer is to minimize the time to capture, while the evader's goal is to maximize the time to capture. In this work, the minimax problem is solved in the Hill-Clohessy-Wiltshire (HCW) reference frame with Earth as the central body and each spacecraft uses continuous low-thrust propulsion. The thrust-pointing direction is the control for each spacecraft. Each vehicle has a finite specific impulse and therefore the mass of each vehicle decreases as propellant is consumed. Optimal closed-loop controllers were also sought, but due to the nature of the minimax problem, creating a traditional closed-loop feedback control is difficult. A closed-loop controller has been developed using a method called kriging. Results for both open and closed-loop trajectories are reported for a significant range of initial conditions and for different thrust accelerations of the two spacecraft