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Space exploitation will require efficient techniques for manipulating passive objects on orbit. This work presents a manipulation concept that utilizes both the on-off thrusters and manipulator proportional forces to manipulate passive objects on orbit more efficiently. The system dynamics arising from the unilateral constraints and the on-off thrusting are discussed. The manipulation concept is illustrated using a simplified one-dimensional model. A novel controller based on backstepping and Lyapunov stability is presented and its performance, stability and robustness are discussed. The performance of this system is compared to that of a standard using on-off thrusters only, and is shown to use less fuel.