Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Revolution-Spaced Output-Feedback Model Predictive Control for Station Keeping on Near-Rectilinear Halo Orbits

Yuri Shimane, Stefano Di Cairano, Koki Ho, Avishai Weiss

TL;DR

This work develops an economic MPC (SKMPC) for station-keeping on Near-Rectilinear Halo Orbits by enforcing full-state tracking over a horizon containing multiple maneuvers spaced one revolution apart. The method uses sequential linearization and SOCP to minimize propellant consumption while meeting a time-varying terminal constraint near the NRHO baseline, and it operates under output feedback via an EKF that accounts for realistic disturbances and impulse events. Compared with the XAC approach, SKMPC reduces phase dispersion and achieves tighter tracking with similar or lower cumulative maneuver costs, validated through Monte Carlo simulations spanning multi-year missions. The results indicate that SKMPC provides robust, fuel-efficient SK performance suitable for operational NRHO missions like the Gateway, without relying on ad-hoc phase-correction heuristics. Overall, the paper demonstrates the practicality and advantages of multi-maneuver economic MPC in handling NRHO instability and mission-ops constraints.

Abstract

We develop a model predictive control (MPC) policy for station keeping on a Near-Rectilinear Halo Orbit (NRHO). The proposed policy achieves full-state tracking of a reference NRHO via a multiple-maneuver control horizon, each spaced one revolution apart to abide by typical mission operation requirements. We prove that the proposed policy is recursively feasible, and perform numerical evaluation in an output-feedback setting by incorporating a navigation filter and realistic operational uncertainties, where the proposed MPC is compared against the state-of-the-art station-keeping algorithm adopted for the Gateway. Our approach successfully maintains the spacecraft in the vicinity of the reference NRHO at a similar cumulative cost as existing station-keeping methods without encountering phase deviation issues, a common drawback of existing methods with one maneuver per revolution.

Revolution-Spaced Output-Feedback Model Predictive Control for Station Keeping on Near-Rectilinear Halo Orbits

TL;DR

This work develops an economic MPC (SKMPC) for station-keeping on Near-Rectilinear Halo Orbits by enforcing full-state tracking over a horizon containing multiple maneuvers spaced one revolution apart. The method uses sequential linearization and SOCP to minimize propellant consumption while meeting a time-varying terminal constraint near the NRHO baseline, and it operates under output feedback via an EKF that accounts for realistic disturbances and impulse events. Compared with the XAC approach, SKMPC reduces phase dispersion and achieves tighter tracking with similar or lower cumulative maneuver costs, validated through Monte Carlo simulations spanning multi-year missions. The results indicate that SKMPC provides robust, fuel-efficient SK performance suitable for operational NRHO missions like the Gateway, without relying on ad-hoc phase-correction heuristics. Overall, the paper demonstrates the practicality and advantages of multi-maneuver economic MPC in handling NRHO instability and mission-ops constraints.

Abstract

We develop a model predictive control (MPC) policy for station keeping on a Near-Rectilinear Halo Orbit (NRHO). The proposed policy achieves full-state tracking of a reference NRHO via a multiple-maneuver control horizon, each spaced one revolution apart to abide by typical mission operation requirements. We prove that the proposed policy is recursively feasible, and perform numerical evaluation in an output-feedback setting by incorporating a navigation filter and realistic operational uncertainties, where the proposed MPC is compared against the state-of-the-art station-keeping algorithm adopted for the Gateway. Our approach successfully maintains the spacecraft in the vicinity of the reference NRHO at a similar cumulative cost as existing station-keeping methods without encountering phase deviation issues, a common drawback of existing methods with one maneuver per revolution.

Paper Structure

This paper contains 25 sections, 1 theorem, 28 equations, 6 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Spacecraft Dynamics Model
  4. Earth-Moon Rotating Frame
  5. Stability on Near Rectilinear Halo Orbit
  6. Navigation Filter
  7. Prediction
  8. Update
  9. Measurements
  10. Impulse Events
  11. $x$-Axis Crossing Control
  12. Full-State Targeting Economic MPC for Station-Keeping on NRHO
  13. Problem Formulation
  14. Definition of Terminal Constraint Set
  15. Recursive Feasibility
  16. ...and 10 more sections

Key Result

Proposition 1

Let $2 \leq K \leq N$ correspond to the number of maneuvers such that For a large enough $u_{\rm max}$, if eq:optim_socp_general is feasible at time $t_{k-1}$ then it is feasible at $t_{k}$. Furthermore, the trajectory remains bounded in a set $\mathcal{X}_{\rm bnd}$ at the apolune times $t_k$.

Figures (6)

  • Figure 1: NRHO in Earth-Moon rotating frame
  • Figure 2: Control horizon with $N=9$ and $\theta_{\rm man} = 200^{\circ}$
  • Figure 3: Estimation error in $\mathcal{F}_{\rm Inr}$ with 3 desaturation events
  • Figure 4: Cumulative cost history with 3 desaturation events
  • Figure 5: Epoch deviation at perilune passes
  • ...and 1 more figures

Theorems & Definitions (1)

  • Proposition 1