Feedback Control for Directional Rendezvous Using Constant-Magnitude Low Thrust

Feedback control for close-range orbital rendezvous, which permits choosing the direction of the final approach, is beneficial for numerous space missions. However, developing such a feedback controller for satellites operating with constant-magnitude low thrust without introducing chattering is nontrivial due to the underactuated nature of the dynamics. This paper develops a feedback control law for rendezvous with a target on a nearly circular orbit, assuming that the chaser satellite utilizes constant-magnitude low thrust. Based on the Clohessy–Wiltshire (CW) model, a sliding surface is chosen on which the states approach the origin. A feedback law driving given initial states to the sliding surface is developed first. Close to the origin, a bang-bang type controller is then employed, which drives the state errors to zero in finite time while allowing to choose the final approach direction along the R-, V-, or H-bar. Solutions to the state trajectories are obtained in closed form, except for the case of the R-bar approach, which is proven to be finite-time stable. It is shown that the higher-order dynamics neglected in the CW equations can be handled through dynamic inversion combined with a hopping maneuver.