Constrained energy-optimal guidance in relative motion via theory of functional connections and rapidly-explored random trees

In this paper, we present a new approach to solving constrained energy-optimal guidance problems for spacecraft relative motion. The proposed methodology is developed on two fundamental blocks, i.e. solution of boundary value problems via Theory of Functional Connections and generation of dynamically feasible optimal trajectory via Rapidly-explored Random Trees. The method enables fast generation of trajectories in relative motion that drive the chaser spacecraft and to the target in an energy-optimal fashion while satisfy state constraints arising from operational constraints.