Minimum-Time Trajectory Optimization of Low-Thrust Earth-Orbit Transfers with Eclipsing

The problem of determining high-accuracy minimum-time Earth-orbit transfers using low-thrust propulsion with eclipsing is considered. The orbit transfer problem is posed as a multiple-phase optimal control problem where the spacecraft can thrust only during phases where it has line of sight to the sun. Event constraints, based on the geometry of a penumbra shadow region, are enforced between the phases and determine the amount of time spent in an eclipse. An initial guess generation method is developed that constructs a useful guess by solving a series of single-phase optimal control problems and analyzing the resulting trajectory to approximate where the spacecraft enters and exits the Earth’s shadow. The single-phase and multiple-phase optimal control problems are solved using an hp adaptive Legendre–Gauss–Radau orthogonal collocation method. To demonstrate the effectiveness of the approach developed in this research, optimal transfer trajectories are computed for two Earth-orbit transfers found in the literature. In addition to the two comparison cases studied, a separate Earth-orbit transfer is examined, and solutions are presented for four different departures dates.