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Active Learning-Enhanced Dual Control for Angle-Only Initial Relative Orbit Determination

Kui Xie, Giovanni Romagnoli, Giordana Bucchioni, Alberto Bemporad

TL;DR

Angle-only IROD is hampered by limited observability; this paper develops an Active Learning–enhanced dual control framework to design input sequences offline and online to improve observability without extra sensors. The method leverages Clohessy–Wiltshire dynamics and LOS measurements to estimate the initial relative state $\bm{x}_0$ while enforcing station-keeping through a dual-control input $\bm{u}_k$. Three offline AL schemes (expected-state-estimation error minimization and greedy-y) and an online AL rule are proposed, with numerical simulations showing improved accuracy and robustness to initial distance $x_0$ and observation period $\Delta t$. The approach enables reliable autonomous relative navigation for spacecraft without additional hardware, enhancing collision avoidance and mission safety.

Abstract

Accurate relative orbit determination is a key challenge in modern space operations, particularly when relying on angle-only measurements. The inherent observability limitations of this approach make initial state estimation difficult, impacting mission safety and performance. This work explores the use of active learning (AL) techniques to enhance observability by dynamically designing the input excitation signal offline and at runtime. Our approach leverages AL to design the input signal dynamically, enhancing the observability of the system without requiring additional hardware or predefined maneuvers. We incorporate a dual control technique to ensure target tracking while maintaining observability. The proposed method is validated through numerical simulations, demonstrating its effectiveness in estimating the initial relative state of the chaser and target spacecrafts and its robustness to various initial relative distances and observation periods.

Active Learning-Enhanced Dual Control for Angle-Only Initial Relative Orbit Determination

TL;DR

Angle-only IROD is hampered by limited observability; this paper develops an Active Learning–enhanced dual control framework to design input sequences offline and online to improve observability without extra sensors. The method leverages Clohessy–Wiltshire dynamics and LOS measurements to estimate the initial relative state while enforcing station-keeping through a dual-control input . Three offline AL schemes (expected-state-estimation error minimization and greedy-y) and an online AL rule are proposed, with numerical simulations showing improved accuracy and robustness to initial distance and observation period . The approach enables reliable autonomous relative navigation for spacecraft without additional hardware, enhancing collision avoidance and mission safety.

Abstract

Accurate relative orbit determination is a key challenge in modern space operations, particularly when relying on angle-only measurements. The inherent observability limitations of this approach make initial state estimation difficult, impacting mission safety and performance. This work explores the use of active learning (AL) techniques to enhance observability by dynamically designing the input excitation signal offline and at runtime. Our approach leverages AL to design the input signal dynamically, enhancing the observability of the system without requiring additional hardware or predefined maneuvers. We incorporate a dual control technique to ensure target tracking while maintaining observability. The proposed method is validated through numerical simulations, demonstrating its effectiveness in estimating the initial relative state of the chaser and target spacecrafts and its robustness to various initial relative distances and observation periods.

Paper Structure

This paper contains 14 sections, 30 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Angle-Only IROD Problem
  3. Active Learning for Input Sequence Design
  4. Offline Design of Experiments
  5. Expected state-estimation error minimization
  6. Greedy-y active learning
  7. Greedy-y active learning (One step)
  8. Online Active Learning
  9. Numerical Experiments
  10. Active Learning-Enhanced Dual Control Setting
  11. Performance Analysis for V-Bar Station-Keeping
  12. Influence of the initial distance
  13. Influence of the observation period
  14. Conclusion

Figures (6)

  • Figure 1: Active Learning-Enhanced Dual Control for Angle-Only IROD
  • Figure 2: Difference between $\bm{u}^{\text{ref}}$ and $\bm{u}$ by PD with dithering offline design (yellow circles), PD with AL offline \ref{['eq:uk-AL-offline-SUM2']} design (cyan triangles), and AL-IROD with offline AL \ref{['eq:uk-AL-offline-SUM2']} (coral squares).
  • Figure 3: Initial states estimation error with open-loop (PD with dithering offline, yellow triangles), open-loop (PD with AL offline \ref{['eq:uk-AL-offline-SUM2']} design, cyan triangles), and closed-loop (AL-IROD with offline AL \ref{['eq:uk-AL-offline-SUM2']}, coral squares).
  • Figure 4: Desired states (black dashed lines) and state trajectories of PD with dithering offline (yellow lines), PD with AL offline \ref{['eq:uk-AL-offline-SUM2']} design (cyan lines) and AL-IROD with offline AL \ref{['eq:uk-AL-offline-SUM2']} (coral dashed lines) in closed-loop (AL-IROD with offline AL \ref{['eq:uk-AL-offline-SUM2']}).
  • Figure 5: Relative MAE of PD with dithering offline design (purple lines), PD with AL offline \ref{['eq:uk-AL-offline-SUM2']} design (cyan lines) and AL-IROD with offline AL \ref{['eq:uk-AL-offline-SUM2']} (coral dashed lines) in closed-loop (AL-IROD with offline AL \ref{['eq:uk-AL-offline-SUM2']}) over different initial state $x_0$. Shaded areas represent median absolute deviation.
  • ...and 1 more figures