Indirect Optimization of Low-thrust Earth-Moon Transfers in the Sun-Earth-Moon System

摘要

This paper investigates the numerical computation of low-energy low-thrust Earth-Moon transfers in the Planar Bicircular Restricted Four-Body Problem via indirect optimal control theory. First, a minimum-fuel optimal control problem is formulated and the standard numerical difficulties related to its solution by means of indirect shooting methods are recalled. Then, for the problem under consideration, additional specific difficulties arising from the huge sensitivity of the state and costate equations are detailed. To overcome these difficulties, continuation techniques are implemented. Then, a new robust indirect approach is developed in this work. Instead of using a standard shooting method, based on a Newton-like scheme, a derivative-free algorithm is used to find the zeros of the shooting function. Numerical results arc provided demonstrating the efficiency of the developed approach. Different families of locally optimal medium-duration trajectories are presented. Finally, long-duration trajectories are shown. Some of them exploit the counterparts in the Planar Bicircular Restricted Four-Body Problem of manifolds defined in both Sun-Earth and Earth-Moon Circular Restricted Three-Body Problems. Other ones, use the practical stability regions around the Lagrange points L_4 and L_5 of the Earth-Moon problem.