Out-of-plane chaotic motion and suppression for tethered tug-debris systems with thrust perturbation

Abstract

This paper investigates the characterization and suppression of chaotic motion in an out-of-plane tethered tug-debris system that is towed by a constant thrust with time-varying micro-perturbations at a fixed non-zero in-plane libration angle. These perturbations arise due to imperfections in the thruster’s mechanical system on the tug. Static equilibrium solutions and homoclinic orbits of the corresponding Hamiltonian system are derived, and a subcritical fork bifurcation is identified and presented. By the Melnikov method, it is found that the micro-fluctuation in the thrust could induce chaos in the system near unstable saddle points. Then, a chaotic parameter region is produced to identify chaos efficiently. The pure out-of-plane chaotic motion would appear, provided system parameters are in the region. A sliding mode controller is designed to suppress the chaotic oscillation by deploying and retrieving the tether. Finally, the impact of the system parameters on the chaotic region is estimated numerically. Simulation results demonstrate that chaotic motions exist and can be identified efficiently by the chaotic parameter region and that the control method is effective in suppressing the chaotic motion.