Autonomous Orbital Rendezvous Using a Coordinate-Free, Nonsingular Orbit Representation

Abstract

This paper develops a general method to execute orbital rendezvous in continuation of previous work, verifies it in simulations, and examines the effects of perturbations. The method uses a coordinate-free representation of the orbit as a basis for discrete feedback control and can be used autonomously to rendezvous to arbitrary target orbits. Rendezvous is accomplished in two distinct phases where the spacecraft state is split into a 5 degree-of-freedom orbit and an along-track position, which the algorithm matches separately in an orbit matching and phasing maneuver, respectively. The 5 DoF portion of the state is represented by the angular momentum and eccentricity vector of the orbit, along with the orbital energy. These quantities offer several qualities that make them attractive for use in closed-loop control. They do not depend on coordinate representation, are nonsingular, and are stationary in the dynamic steady-state of no applied forces. Further, their dynamics are governed by simple equations, leading to a simple transition matrix. A metric that represents the relative distance between the spacecraft and the target orbit determines when the orbit-matching phase is complete. Then a phasing maneuver slightly changes the relative orbit such that the follower catches up to or falls back to the leaders along-track position. Once within a short distance of the target position, the spacecraft enters a close-proximity mode that utilizes a previously developed state transition matrix of relative motion on elliptical orbits for higher precision. Simulation results permit a comparison of Δ$V$ to that of other techniques. The primary benefits of this method are that it can be used for arbitrary orbits, executes autonomously, and avoids limitations by either singularities or linearized dynamics. This efficient, autonomous method for executing orbital rendezvous developed in this paper improves the feasibility and robustness of small spacecraft missions because it does not require a dedicated ground station or constant communication during maneuver execution.