Design of Spacecraft Formation Orbits Relative to a Stabilized Trajectory

The design of spacecraft formation orbits traveling relative to an unstable trajectory is investigated. We implement the designs with position and velocity feedback control laws, so that the entire constellation is forced to follow a similar path relative to a nominal trajectory. We find sufficient conditions under which the relative motion of the spacecraft constellation is stable and a controller can be designed. We consider the problem of specifying the orientation of the formation orbit, which is equivalent to eigenvector placement, and show how these modes can be combined to force a formation to fly in a range of orientations. Applications of our approach to relative motion in rotating and nonrotating systems are given.