Optimization of Low-Thrust Transfers Using Homotopic Method in the Restricted Three-Body Problem

A method for optimization of low-thrust transfers in the restricted three-body problem is proposed. First，the optimal control laws of different performance index in trajectory optimization are deduced based on the optimal control theory. Then，a new parameter is used to construct a modified performance index. The genetic algorithm and single shooting method are used to obtain the solution of energy optimal transfer，and arc-length method is adopted to track the homotopic pathtill the fuel optimal transfer is obtained. Finally，the numerical example about transfers from GEO to Lyapunov orbit of L1 point in the Earth-Moon system is studied. Simulation results show that the initial guess can be obtained by genetic algorithm，and single shooting method can be used to obtain the fuel-optimal transfer trajectory.