Constrained tension control of a tethered space-tug system with only length measurement

The paper presents a tension control law to stabilize the motions of a Tethered Space-Tug system during its deorbiting process by regulating the tension in the tether. The tension control law is designed on a basis of two straightforward ideas, i.e., the potential energy shaping and the damping injection. The law is expressed in an analytical feedback form in terms of only the tether length without the need of the feedback of full state information. Meanwhile, the requirements of measuring velocities are removed with the aid of a dynamic extension technique based on the feedback interconnection of Euler-Lagrange systems. The positive and bounded tension constraint is taken into consideration explicitly by including a pair of special saturation terms in the feedback control law. The relative motions of the space-tug and the debris are described with respect to a local non-inertial orbital frame of reference, whereas the orbital motion equations of the system are formulated in terms of the modified equinoctial elements of the orbit. Finally, the effectiveness of the proposed scheme is demonstrated via numerical case studies.