High order dynamical systems approaches for low-thrust station-keeping of libration point orbits

We derive two families of low-thrust station-keeping control procedures based on the dynamical properties of the phase space near libration point orbits. The first family is obtained as the limit of impulsive maneuvers, and the second one by means of dynamically reshaping Floquet modes. Despite following different approaches, the geometrical analysis shows that all these strategies can reshape the dynamical structures about the libration point orbits and stabilize the motion. The numerical results prove their robustness in front of measurement uncertainties and large initial orbit injection errors. Moreover, the long-term behavior is analyzed by means of Poincaré maps, and the results are compared with the Hamiltonian-structure preserving control strategy. Not just restricted to the particular problem considered, the new methodology provides a general framework to analyze the geometric behavior of any low-thrust station-keeping control law and opens the possibility of compact on-board techniques.