Simple Method for Tethered Space Debris Retrieval

Space debris retrieval problem utilizing a tethered system in an elliptical orbit is studied in this paper. An analytical control law specified by a tether length rate for retrieval is derived from a dumbbell model of the system. The proposed control method can suppress large swings around the local vertical position of the tethered system. Under such a control strategy, the debris retrieval behaves in asymptotic stable motion towards the expected angle. The stability of the non-autonomous system during the retrieval control is analyzed using the Floquet theory. The result demonstrates that an orbital region exists, on which the retrieval process maintains asymptotically stable. The proposed analytical control law is validated via numerical simulations.