  The paper deals with the design of an improved model predictive control
scheme for achieving station-keeping in a quasi Halo orbit around the $L_2$
point in the Earth-Moon system. The improvement is obtained thanks to a
multi-rate sampled-data trajectory planner that allows for simplifying the
optimization problem of the model predictive controller while guaranteeing
feasibility and convergence to the desired orbit. The multi-rate planner is
designed based on a simplified model of the dynamics under a preliminary
nonlinear regulation feedback. The proposed control scheme is shown to
outperform recent station-keeping nonlinear model predictive control designs
both in terms of tracking error and energy expenditures in different
situations. Finally, a brief study of aspects pertaining to computational time
are carried out so highlighting the possibility for real time implementation on
modern hardware.
