Low-Thrust End-to-End trajectory with patched hyperbolic excess velocity

This paper presents a low-thrust end-to-end trajectory optimization method based on hyperbolic excess velocity patching. The entire trajectory, including both heliocentric transfer and planetary capture phases, is optimized as a whole. The hyperbolic excess velocity when the spacecraft enters the planet’s influence sphere is required to match the velocity relative to planet at the end of the heliocentric phase. The piecewise optimization solutions for both phases are firstly analyzed under different boundary conditions. Then the results of the two separate optimizations serve as initial guess for the joint optimization, yielding the overall optimal transfer trajectory. In addition, the maximum allowable hyperbolic excess velocity when the spacecraft enters the planet’s influence sphere is analyzed, and an analytical estimation formula applicable for any central body is given by curve fitting. The effectiveness of the proposed method is demonstrated through numerical simulation of a low-thrust Earth-to-Mars transfer.