Flying near the libration points by impulse control

Formation flying along a halo orbit near the L₁ point in the Sun-Earth circular restricted three-body system with impulse control is considered. The reference orbit is a periodic perturbation of the halo orbit generated by an exosystem, and the output regulation theory for discrete system is employed for the transition and maintenance. The minimum impulse number and the total velocity change required for the maintenance of the halo orbit are shown. Then the total velocity change for the maintenance of the perturbed reference orbits is shown. Finally, formation flying near the L₁ point is considered, where the reference orbit is a periodic orbit whose frequency is equal to that of the linearized equations of motion at the L ₁ point.