Multi-objective low-thrust spacecraft trajectory design using reachability analysis

One of the fundamental problems in spacecraft trajectory design is finding the optimal transfer trajectory that minimizes the propellant consumption and transfer time simultaneously. We formulate this as a multi-objective optimal control (MOC) problem that involves optimizing over the initial or final state, subject to state constraints. Drawing on recent developments in reachability analysis subject to state constraints, we show that the proposed MOC problem can be stated as an optimization problem subject to a constraint that involves the sub-level set of the viscosity solution of a quasi-variational inequality. We then generalize this approach to account for more general optimal control problems in Bolza form. We relate these problems to the Pareto front of the developed multi-objective programs. The proposed approach is demonstrated on two low-thrust orbital transfer problems around a rotating asteroid.