Fast solution of minimum-time low-thrust transfer with eclipses

Abstract

Optimizing low-thrust orbital transfers with eclipses by indirect methods raises several issues, namely the costate discontinuities at the eclipse entrance and exit, the initial costate guess sensitivity and the numerical accuracy required by the shooting method. The discontinuity issue is overcome by detecting the eclipse within the simulation and applying the costate jump derived analytically from the shadow constraint function. By fixing completely the targeted final position and velocity, the transversality conditions are removed and the shooting problem is recast as an unconstrained nonlinear programming problem. The numerical sensitivity issues are alleviated by using a derivative-free algorithm. The search space is reduced to four angles taking near zero values. This procedure yields a quasi-optimal solution from scratch in few minutes without requiring any specific user’s guess or tuning. The method is applicable whatever the thrust level and the eclipse configuration, as illustrated on transfers towards the geostationary orbit.