This paper focuses on the tethered satellite deployment control issue via tether tension control in a propellant-free manner. The tether deployment is a typical underactuated control problem when only the tension control was employed by actively accommodate tether length by mechanical device. Firstly, unlike most existing control methods, the energy-based view of feedback approaches are proposed in an analytical form with tension constraint. To regulate the dynamic behavior of tether deployment, an artificial potential energy function is introduced and combined with the system's Hamiltonian to construct the Lyapunov function. The asymptotic stability is shown by invoking the Lyapunov technique and LaSalle's invariance principle. Secondly, the proposed control approach is extended into an output feedback form without velocity measurement. Because the relative position can be easily measured rather than velocity from the practical perspective. In the controller, the term of tether length velocity is replaced by an approximate differentiation. Finally, numerical simulations are carried on to verify the effectiveness of the proposed control approaches. Performance of these proposed control approaches is investigated according to their dependency on control gains.
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