Fuel-Optimal Maneuvers for Constrained Relative Satellite Orbits

Abstract

This research investigates strategies to enable a deputy satellite to hover within a defined volume fixed in the vicinity of a chief satellite in a circular orbit for an extended period of time. Previous research developed initial methodologies for maintaining restricted teardrop hover orbits that exist in a plane fixed within the chief's local reference frame. These methods use the natural drift of the deputy satellite in the relative frame and impulsive thrust to keep the deputy in a bounded volume relative to the chief, but do not address fuel optimality. This research extends and enhances that work by finding the optimal trajectories produced with discrete thrusts that minimize fuel spent per unit time and stay within the user-defined volume, thus providing a practical hover capability in the vicinity of the chief. The work assumes that the Clohessy―Wiltshire closeness assumption between the deputy and chief is valid. Using the new methodology developed in this work, feasible closed- and nonclosed-relative orbits are found and evaluated based on a fuel criterion and are compared with an easily calculated continuous-thrust baseline. It is shown that in certain scenarios (generally corresponding to a smaller total time of flight) a discrete-thrust solution provides a lower overall fuel cost than a continuous-thrust solution. A simple check is proposed that enables the mission planner to make the correct strategy choice.