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Chance-constrained Model Predictive Control for Near Rectilinear Halo Orbit spacecraft rendezvous

Julio C. Sanchez, Francisco Gavilan, Rafael Vazquez

TL;DR

The paper tackles close spacecraft rendezvous in the restricted three-body problem near Near Rectilinear Halo Orbits by formulating a robust chance-constrained MPC that accounts for disturbances in a probabilistic sense. It supports both chemical impulsive and electric thrust, the latter via B-spline parameterization, and uses online disturbance estimation to bound constraint violations with high probability. The method discretizes the linearized relative dynamics using a state-transition matrix and enforces LOS and boundary constraints within a quadratic program, achieving improved constraint satisfaction over a non-robust controller in Monte Carlo tests. The results demonstrate practical feasibility for cislunar docking scenarios, while identifying numerical integration of time-varying matrices as a current limitation and potential area for future comparison with alternative robust techniques. Overall, the approach offers a flexible, implementable pathway to safe, fuel-efficient close rendezvous in complex multi-body environments.

Abstract

This work presents a robust Model Predictive Controller (MPC) to solve the problem of spacecraft rendezvous in the context of the restricted three-body problem (R3BP) as will be required to dock with space stations in cislunar space. The employed methodology is both valid for chemical and electric thrusters. By exploiting the state transition matrix and using a chance-constrained approach, the robust MPC assures constraints satisfaction under the presence of disturbances in a probabilistic sense. The perturbations parameters are computed on-line using a disturbance estimator. The robust controller is tested for a rendezvous scenario with a target placed in an Earth-Moon Near-Rectilinear Halo Orbit. Numerical results are shown and discussed.

Chance-constrained Model Predictive Control for Near Rectilinear Halo Orbit spacecraft rendezvous

TL;DR

The paper tackles close spacecraft rendezvous in the restricted three-body problem near Near Rectilinear Halo Orbits by formulating a robust chance-constrained MPC that accounts for disturbances in a probabilistic sense. It supports both chemical impulsive and electric thrust, the latter via B-spline parameterization, and uses online disturbance estimation to bound constraint violations with high probability. The method discretizes the linearized relative dynamics using a state-transition matrix and enforces LOS and boundary constraints within a quadratic program, achieving improved constraint satisfaction over a non-robust controller in Monte Carlo tests. The results demonstrate practical feasibility for cislunar docking scenarios, while identifying numerical integration of time-varying matrices as a current limitation and potential area for future comparison with alternative robust techniques. Overall, the approach offers a flexible, implementable pathway to safe, fuel-efficient close rendezvous in complex multi-body environments.

Abstract

This work presents a robust Model Predictive Controller (MPC) to solve the problem of spacecraft rendezvous in the context of the restricted three-body problem (R3BP) as will be required to dock with space stations in cislunar space. The employed methodology is both valid for chemical and electric thrusters. By exploiting the state transition matrix and using a chance-constrained approach, the robust MPC assures constraints satisfaction under the presence of disturbances in a probabilistic sense. The perturbations parameters are computed on-line using a disturbance estimator. The robust controller is tested for a rendezvous scenario with a target placed in an Earth-Moon Near-Rectilinear Halo Orbit. Numerical results are shown and discussed.
Paper Structure (24 sections, 44 equations, 13 figures, 3 tables)

This paper contains 24 sections, 44 equations, 13 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Relative motion in the restricted three body problem
  3. Restricted three body problem and NRHOs
  4. Relative motion in the R3BP
  5. Linearized relative motion in the R3BP
  6. Rendezvous planning problem
  7. Control input
  8. Objective function
  9. Constraints
  10. Path constraints
  11. Control bounds
  12. Boundary constraints
  13. Rendezvous problem
  14. Robust MPC formulation
  15. Discretized prediction of the state
  16. ...and 9 more sections

Figures (13)

  • Figure 1: Inertial, synodic and LVLH frames of reference for the Earth-Moon system.
  • Figure 2: Green: Southern $L_2$ Halo family; blue: Southern $L_2$ NRHOs; black: Sec.V NRHO. Parameter $a$ is the Earth-Moon semimajor axis.
  • Figure 3: Stability indexes and periods for Southern $L_2$ NRHOs
  • Figure 4: LOS region
  • Figure 5: Chaser 3D trajectory for the first random realization using the robust controller.
  • ...and 8 more figures