Feedback control for retrieving an electro-dynamic tethered sub-satellite

This paper presents a model predictive control (MPC) scheme for the retrieval of an electrodynamic tethered sub-satellite in an inclined orbit. The scheme accounts for in-plane as well as out-of-plane motions. The control action is realized by adjusting only the tensional and electro-dynamic forces in the tether. Even though the proposed feedback law is not analytically explicit, it is easy to determine it by using a rapid re-computation of open-loop optimal control online and updating the control command at a fixed sampling interval. For each online step, the open-loop optimal control problem is solved by discretizing the continuous control problem first and then numerically solving the resulting large-scale optimization problem via nonlinear programming. The design of the feedback controller is based on a simple model which enjoys the advantage of low computational effort required for optimization, whereas the effectiveness and robustness of the proposed strategy are demonstrated by using a multi-body dynamics model of much higher fidelity.