A State Feedback Control Approach to Optimal Low-Thrust Earth-Moon Trajectories

Abstract

A state feedback control method based on orbit elements is proposed for low-thrust earth-moon transfer tasks. Firstly, the dynamic models of earth escape trajectory and lunar capture trajectory are established by using classical orbit elements, and the dynamic model of cislunar coast trajectory is established by using the circular restricted three-body model. Then, the libration point L1 of the Earth-Moon system is taken as the crossing point from Earth gravitation region to Moon gravitation region, and cislunar coast trajectory is designed by adjusting the velocity vector of spacecraft in this point. Finally, a state feedback analytic control law based on the classical orbit elements is derived, the Earth escape trajectory is obtained by backward orbit propagation and the moon capture trajectory is obtained by forward orbit propagation. The simulation results show that the state feedback method needs no initial value estimation and is not affected by the multi-revolution orbit, the optimal-fuel low-thrust Earth-Moon trajectories can be solved rapidly. The results in the fuel consumption and flight time are similar to the SMART-1 trajectory, and the calculation time is 4 orders of magnitude less than that of the direct method in solving SMART-1 trajectory.