Optimal control of retrieval of a tethered subsatellite

The most important and complicated operations during a tethered satellite system mission are deployment and retrieval of a subsatellite from or to a space ship. The deployment process has been treated in [15]. In this paper retrieval is considered. We restrict to the practically important case that the system is moving on a circular Keplerian orbit around the Earth. The main problem during retrieval is that it results in an unstable motion concerning the radial relative equilibrium which is stable for a tether of constant length. The uncontrolled retrieval results in a strong oscillatory motion. Hence for the practically useful retrieval of a subsatellite this process must be controlled. We propose an optimal control strategy using the Maximum Principle to achieve a force controlled retrieval of the tethered subsatellite from the radial relative equilibrium position far away from the space ship to the radial relative equilibrium position close to the space ship.