Applications of Adaptive Terminal Sliding Mode Control to Rendezvous with Malfunctioning Clients

This study investigates the finite-time relative position control problem which enables an inspection satellite to safely approach a malfunctioning client vehicle whose ability to communicate has been hindered, rendering it unable to communicate at all during the rendezvous maneuver. Malfunctioning clients present unique challenges, namely that the state of the client is considered unknown a priori and the inspector may not benefit from accurate and continuous information provided by the client vehicle; the client vehicle may also be subject to maneuvering and disturbances, unknown to the inspector a priori. A line-of-sight based relative motion model is introduced which uses the navigation information directly, being formulated in a coordinate frame attached to the inspector, not client. As the client's orbital state could be partially or completely unknown, it is more convenient to formulate the dynamic model in a frame attached to the inspection vehicle. Next, a robust control framework is developed in the form of an adaptive non-singular terminal sliding mode controller to ensure the closed loop system is stable and to guarantee finite-time convergence to the desired states. As the proposed control design consists of an adaptive control gain, adaptation laws are then introduced to prevent gain overestimation and mitigate the detrimental chattering phenomenon to ensure that sliding mode is established in finite time, even when unknown, but bounded, external disturbances and uncertainties are present. The proposed non-singular terminal sliding mode control framework works in tandem with the designed adaptive laws to ensure the sliding manifold is reached in finite time. The proposed controller is then proven stable in the Lyapunov regime, achieving convergence when the upper bounds of the bounded uncertainties are unknown a priori. Finally, several numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive non-singular terminal sliding mode controller and its application to future on-orbit inspection missions with malfunctioning clients.