Applications of Sliding Mode Control to Orbital Rendezvous with Tumbling or Maneuvering Clients

The capabilities of autonomous inspection vehicles that operate near malfunctioning clients have developed significantly over the last decade due to their rapidly evolving mission set. On-orbit inspection serves as a necessary catalyst to gain vital information of a prospective client vehicle prior to executing a servicing operation. The associated challenges are augmented when the client is deemed inoperable or malfunctioning, such that the inspector is incapable of actively assisting in a coordinated rendezvous maneuver. The nature of a client, deemed either inoperable or malfunctioning, suggest that the client could be uncontrollably tumbling, or translationally maneuvering, due to a damaged propulsion system. Therefore, the focus of this study is to investigate the satellite relative position control problem, which enables an autonomous inspection vehicle to approach, and operate around, a malfunctioning client capable of producing uncertain maneuvering. The line-of-sight based relative motion model is first introduced, being formulated in a coordinate frame attached to the inspector, not client, which leverages the navigation information directly. The state of the client could be partially or completely unknown, and therefore, its more convenient to formulate the dynamic model in a frame attached to the inspecting vehicle. This investigation then synthesizes adaptive and robust control into a single, continuous framework without bounding knowledge of unknown perturbation and uncertainties in the form of an adaptive second-order fast non-singular terminal sliding mode control law. The proposed control scheme is designed to deliver an inspection vehicle into proximity of a freely tumbling, or maneuvering client, while ensuring finite-time convergence of the sliding variables to the design manifold, in spite of these system uncertainties and perturbations.