Applied Reachability Analysis for Spacecraft Rendezvous and Docking with a Tumbling Object

Abstract

The objective of this research is to investigate the dynamics, and reachability characteristics of a spacecraft (commonly referred to as the deputy) conducting proximity maneuvers about a resident space object (commonly referred to as the chief) in a tumbling state of motion. Specifically, the goal is to identify initial conditions from which a specified maneuver is feasible, within a specified amount of time. This research question can be answered by solving a reachability problem, and computing a backwards reachable set. However, the complexity of the relative roto-translational dynamics of this scenario poses challenges for existing reachability tools. This paper presents the 6-DOF roto-translational relative spacecraft dynamics, from the perspective of the tumbling chief. A method based on minimum time optimal control is proposed for computation and visualization of backwards reachable sets for both relative translation and rotation, in the particular case of a chief in circular orbit spinning about a principal axis coinciding with the orbit normal. The proposed method makes the problem more tractable and provides insight into the reachability characteristics of this scenario.