Nonlinear Control of Tether Retrieval in an Elliptical Orbit

Tether retrieval is an important stage in many projects using space tether systems. It is known that uniform retrieval is an unstable process that leads to the winding of the tether on a satellite at the final stage of retraction. This is a serious obstacle to the practical application of space tethers in the tasks of climbing payloads to a satellite and docking the spacecraft with a tethered satellite after its capture. The paper investigates the plane motion of a space tether system with a massless tether of variable length in an elliptical orbit. A new control law that ensures the retrieval of the tether without increasing the amplitude of oscillations at the final stage is proposed. The asymptotic stability of the space tether system’s controlled motion in an elliptical orbit is proved. A numerical analysis of tether retrieval is carried out. The influence of the eccentricity of the orbit on the retrieval process is investigated. The results of the work can be useful in preparing missions of the active space debris removal and in performing operations involving tether retrieval.