Rapid Determination of Low-Thrust Spacecraft Reachable Sets Subject to Eclipse Constraints
Ehsan Taheri
Abstract
Accurate and rapid determination of reachable sets is invaluable for enabling autonomy of controlled dynamical systems. The reachable set of dynamical systems, by definition, consists of all states that can be achieved from an initial state over a specified time horizon. In space flight and astrodynamics applications, accurate and rapid determination of reachable sets has many utilities for trajectory planning, collision avoidance, and safe and optimal operation. In this paper, we leverage the connection between minimum-time trajectories and the boundary of reachable sets and present Precise Reachability via Indirect Solution Method (PRISM). PRISM is a rapid and efficient method for accurate determination of solar-powered low-thrust spacecraft reachable sets that takes into account operational constraints such as eclipses during which the spacecraft cannot operate its thrusters. We show that it is possible to use indirect formalism of optimal control theory with an appropriate choice of coordinates and/or elements to significantly speed up the algorithm. We use PRISM to compute the reachable sets of low-thrust spacecraft at a medium-altitude Earth orbit subject to J2 perturbations. Additionally, we analyze and compare the reachable sets with and without the inclusion of eclipse effects. The results highlight the utility of PRISM for precise and rapid determination of low-thrust spacecraft reachable sets.