Attitude Parameter Inspired Relative Motion Descriptions for Relative Orbital Motion Control

Abstract

This paper describes the development of novel relative orbital motion descriptions for a two craft formation, defined by a separation distance and relative orientation parameter set. These descriptions allow for the use of separation distance as a state parameter for the relative motion, while avoiding singularity issues that plague spherical coordinate descriptions. Instead, Euler parameterlike or modified Rodrigues parameterlike coordinates are employed to describe the relative orientation. Equations of motion are developed that allow propagation of these new descriptions for the case of a circular reference orbit and small separation distances between the craft. These equations of motion are derived from the Clohessy–Wiltshire equations. Feedback control laws are developed to stabilize the relative motion between the craft. Numerical simulation is used to compare the newly developed relative motion descriptions with inertial equations of motion. The results validate these new descriptions as a practical method for describing relative motion.