Optimal low-thrust lunar orbit transfers with shadowing effect using a multiple-arc formulation

This research addresses the problem of finding minimum-time low-thrust lunar orbit transfers, in the presence of eclipsing constraints on the available thrust. The problem at hand is formulated as a multiple-arc space trajectory optimization problem. Unlike former studies, no regularization or averaging is employed in the numerical solution process. Instead, the multiple-arc formulation leads to identifying a set of intermediate necessary conditions for optimality, at transitions from light to eclipse (and vice versa). This work proves that a closed-form sequential solution of the intermediate conditions exists, through the use of two different representations for the state, in conjunction with costate transformation. As a result, the parameter set for an indirect algorithm retains the size of the typical set associated with a single-arc optimization problem. The indirect heuristic technique, based on the joint use of the necessary conditions and a heuristic algorithm (i.e., differential evolution) is proposed as the numerical solution method. Two low-thrust lunar orbit transfers are considered as the mission scenarios. They are particularly challenging because the space vehicle is shadowed by both Earth and Moon. The numerical results unequivocally prove that the approach proposed in this research is effective for determining minimum-time low-thrust lunar orbit transfers, even in the presence of shadowing by multiple celestial bodies.