Station-keeping of $L_2$ halo orbits under sampled-data model predictive control

TL;DR

This paper presents a multi-rate sampled-data model predictive control scheme for station-keeping in $L_2$ halo orbits around the Earth-Moon system's L2 point, improving tracking accuracy and energy efficiency.

Contribution

It introduces a multi-rate trajectory planner that simplifies the MPC optimization while ensuring feasibility and convergence, outperforming existing nonlinear MPC methods.

Findings

Outperforms recent nonlinear MPC in tracking error

Reduces energy expenditure during station-keeping

Potential for real-time implementation on modern hardware

Abstract

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.