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Contingency-Aware Station-Keeping Control of Halo Orbits

Fausto Vega, Zachary Manchester, Martin Lo, Ricardo Restrepo

TL;DR

This work tackles fuel-efficient stationkeeping for spacecraft on unstable halo orbits within the CR3BP while guaranteeing a safe contingency exit if propulsion is lost. It introduces a convex, two-horizon trajectory-optimization framework that linearizes around a reference halo orbit and minimizes the $||u_k||_1$ fuel proxy, with two convex state-constraint variants (Euclidean-ball and ellipsoidal cost-to-go) and a novel contingency half-space constraint aligned with the unstable manifold. A receding-horizon scheme re-solves the problem to mitigate modeling and state-estimation errors, and an autonomous exit strategy is embedded to bias trajectories toward the unstable manifold. Validation in Earth–Moon and Saturn–Enceladus simulations demonstrates reduced delta-v and reliable safe exits, suggesting practical viability for autonomous halo-orbit missions with safety guarantees.

Abstract

We present an algorithm to perform fuel-optimal stationkeeping for spacecraft in unstable halo orbits with additional constraints to ensure safety in the event of a control failure. We formulate a convex trajectory-optimization problem to generate impulsive spacecraft maneuvers to loosely track a halo orbit using a receding-horizon controller. Our solution also provides a safe exit strategy in the event that propulsion is lost at any point in the mission. We validate our algorithm in simulations of the three-body Earth-Moon and Saturn-Enceladus systems, demonstrating both low total delta-v and a safe contingency plan throughout the mission.

Contingency-Aware Station-Keeping Control of Halo Orbits

TL;DR

This work tackles fuel-efficient stationkeeping for spacecraft on unstable halo orbits within the CR3BP while guaranteeing a safe contingency exit if propulsion is lost. It introduces a convex, two-horizon trajectory-optimization framework that linearizes around a reference halo orbit and minimizes the fuel proxy, with two convex state-constraint variants (Euclidean-ball and ellipsoidal cost-to-go) and a novel contingency half-space constraint aligned with the unstable manifold. A receding-horizon scheme re-solves the problem to mitigate modeling and state-estimation errors, and an autonomous exit strategy is embedded to bias trajectories toward the unstable manifold. Validation in Earth–Moon and Saturn–Enceladus simulations demonstrates reduced delta-v and reliable safe exits, suggesting practical viability for autonomous halo-orbit missions with safety guarantees.

Abstract

We present an algorithm to perform fuel-optimal stationkeeping for spacecraft in unstable halo orbits with additional constraints to ensure safety in the event of a control failure. We formulate a convex trajectory-optimization problem to generate impulsive spacecraft maneuvers to loosely track a halo orbit using a receding-horizon controller. Our solution also provides a safe exit strategy in the event that propulsion is lost at any point in the mission. We validate our algorithm in simulations of the three-body Earth-Moon and Saturn-Enceladus systems, demonstrating both low total delta-v and a safe contingency plan throughout the mission.
Paper Structure (13 sections, 14 equations, 6 figures, 2 tables)

This paper contains 13 sections, 14 equations, 6 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. BACKGROUND
  3. The Circular Restricted Three-Body Problem
  4. Lagrange Points, Periodic Orbits, and Invariant Manifolds
  5. Optimization-Based Stationkeeping
  6. Linearized Dynamics
  7. Trajectory Optimization
  8. Contingency Constraint
  9. SIMULATION EXPERIMENTS
  10. Earth-Moon Simulation
  11. Saturn-Enceladus Simulation
  12. CONCLUSIONS
  13. ACKNOWLEDGMENTS

Figures (6)

  • Figure 1: Reference halo orbits in the Earth-Moon and Saturn-Enceladus system along with their unstable invariant manifolds that we use for a safe exit.
  • Figure 2: 2D projection of the state constraints along the orbit $x_k$. The feasible set is the area intersected with green lines.
  • Figure 3: Comparison of two control strategies for revolutions 10-20 of an L2 halo orbit in the Earth-Moon system. The z control is zero for both strategies.
  • Figure 4: Burn locations for the L2 halo orbit in the Earth Moon system using the Euclidean ball state constraint
  • Figure 5: Comparison of two control strategies for revolutions 10-20 of an L2 halo orbit in the Saturn-Enceladus system.
  • ...and 1 more figures