Dynamics and control of tethered multi-satellites in elliptic orbits

This paper studies the dynamics and libration suppression of tethered multi-satellites in elliptic orbits, where the tethered system is subject to periodic excitation resulting from the change of gravity gradient. The tethered system is modeled as a multiple dumbbell model and the relationship between periodical libration and tether length rate is studied. The outcome of study leads to a new tension control law to suppress the libration of tethered multi-satellites in a desired periodic motion by regulating tether length without thrust. The simulation results show that the libration motion of tethered multi-satellites is successfully stabilized to the desired periodic motion with the proposed tension control law. When the orbital eccentricity is small, the analytical solution of time-dependent tether lengths is derived to minimize the magnitudes of tether length rate. Furthermore, the tension control law is modified by including a sliding mode control to suppress initial external perturbations to increase the robustness of control law.