Optimal Pursuit/Evasion Spacecraft Trajectories in the Hill Reference Frame

Abstract

The pursuit/evasion game for two spacecraft is signicantly simplied by being described with a linearized system of equations of motion. A pursuit/evasion game is also known as a \minimax problem, because the object 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. The thrust-pointing direction is the control for each spacecraft. Each vehicle has a nite specic impulse and therefore the mass of each vehicle decreases as propellant is consumed. Each spacecraft uses continuous low-thrust propulsion. Due to the nature of the minimax problem, creating a traditional closed-loop feedback control is dicult. A closed-loop controller has been developed using a method called kriging. Results for both open and closed-loop trajectories are reported for a signicant range of initial conditions and for dierent thrust accelerations of the two spacecraft.