Hamiltonian formulation and energy-based control for space tethered system deployment and retrieval

Usually, the dynamic equations of tethered systems are derived using Lagrangian formulation. However, Hamiltonian formulation is also widely used for mechanical systems because of its well-known symplectic structure property. In this paper, the dynamic equations of the tethered system are deduced using Hamiltonian formulation. The goodness of the Hamiltonian formulation is intuitive to reveal the energy balance property that corresponds to the passive property. Furthermore, the Hamiltonian function of the tethered system is employed to facilitate the design of the controller. The energy-based control is to achieve the tether deployment/retrieval with suppressing the tether liberation. Numerical simulations are used to demonstrate the effectiveness of the designed controller.