Low-Thrust to Solar-Sail Trajectories: A Homotopic Approach

Abstract

This paper describes a novel method to compute minimum-time solar-sail trajectories starting from a given low-thrust solution. The method is based on the use of homotopy and numerical continuation. Homotopy is used to link the low-thrust with the solar-sail optimal control problem. Numerical continuation is used to compute the optimal solar-sail solution, starting from a given low-thrust planar solution, which is normally easy to find. Planar solar-sail trajectories are computed by means of the homotopic approach. These solutions are used to compute, in a single-shooting approach, three-dimensional solar-sail trajectories, for transfer scenarios involving a small change of the orbital inclination. The proposed homotopic approach is tested against a conventional approach, based on the use of a genetic algorithm. Numerical test cases are performed both on Earth–Mars and Earth–Apophis rendezvous. The results show that the proposed method is advantageous, in terms of accuracy of the solution and computational time.