Feasibility Study and Fuel Optimal Control Techniques for Constrained Relative Satellite Orbit Geometries

The majority of recent work in relative satellite motion has concentrated on closed or drifting orbits of a deputy satellite about a chief satellite, assumed to be located at the center of a local reference frame. A problem of interest to mission planners is the ability to “hover” in a prescribed vicinity of a chief satellite for an extended period of time. Recent papers have developed initial methodologies for maintaining restricted tear drop shaped hover orbits that exist in a plane fixed within the chief’s local reference frame. These papers develop a method to utilize the natural drift of the deputy satellite in the relative frame and non-continuous thrust to keep the deputy in a bounded area relative to the chief but do not address fuel-optimality. The research described herein explores fuel optimal trajectories such that the deputy stays within a user-defined area/volume, thus providing a “hover” capability in the vicinity of the chief. The work assumes the linear Clohessy-Wiltshire equations of motion are valid.