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Segment-Based Two-Loop Adaptive Iterative Learning Control for Spacecraft Position and Attitude Tracking

Fan Zhang, Deyuan Meng, Ying Tan

TL;DR

This work tackles the problem of simultaneous, high-precision 6-DOF tracking for spacecraft proximity operations under unknown but repeatable disturbances. It introduces a segment-based, dual-number based two-loop adaptive ILC that unifies position and attitude errors using unit dual quaternions, enabling coordinated learning between translational and rotational dynamics. A segment-based dynamic projection mechanism guarantees bounded control inputs and parameter estimates in the presence of uncertainties, and a rigorous convergence analysis yields perfect tracking or boundedness under the proposed framework. Simulations on a rigid satellite demonstrate substantial improvements in both position and attitude tracking with all signals remaining bounded, highlighting the method's practical potential for autonomous rendezvous, docking, and formation maneuvers.

Abstract

Proximity operations of rigid bodies, such as spacecraft rendezvous and docking, require precise tracking of both position and attitude over finite time intervals. These operations are often repeated under uncertain conditions, with unknown but repeatable parameters and disturbances. Adaptive iterative learning control (ILC) is well suited to such tasks, as it can track desired trajectories while learning unknown, iteration-invariant signals or parameters. However, conventional adaptive ILC faces two challenges: (i) the coupling between rotational and translational dynamics complicates the design of the two coordinated learning loops for position and attitude, and (ii) standard adaptive ILC designs cannot guarantee bounded control inputs. To address these issues, we propose a dual-number-based, segment-based two-loop adaptive ILC framework for simultaneous high-precision position and attitude tracking. The framework employs two learning loops that interact through a dual-number representation of tracking errors, combining position and attitude errors into a single mathematical object for unified control design. A segment-based dynamic projection mechanism ensures that both parameter estimates and control inputs remain bounded without prior knowledge of uncertainties. Mathematical analysis and numerical simulations demonstrate that the proposed framework significantly enhances tracking performance under unknown but repeatable uncertainties and strong rotational-translational coupling.

Segment-Based Two-Loop Adaptive Iterative Learning Control for Spacecraft Position and Attitude Tracking

TL;DR

This work tackles the problem of simultaneous, high-precision 6-DOF tracking for spacecraft proximity operations under unknown but repeatable disturbances. It introduces a segment-based, dual-number based two-loop adaptive ILC that unifies position and attitude errors using unit dual quaternions, enabling coordinated learning between translational and rotational dynamics. A segment-based dynamic projection mechanism guarantees bounded control inputs and parameter estimates in the presence of uncertainties, and a rigorous convergence analysis yields perfect tracking or boundedness under the proposed framework. Simulations on a rigid satellite demonstrate substantial improvements in both position and attitude tracking with all signals remaining bounded, highlighting the method's practical potential for autonomous rendezvous, docking, and formation maneuvers.

Abstract

Proximity operations of rigid bodies, such as spacecraft rendezvous and docking, require precise tracking of both position and attitude over finite time intervals. These operations are often repeated under uncertain conditions, with unknown but repeatable parameters and disturbances. Adaptive iterative learning control (ILC) is well suited to such tasks, as it can track desired trajectories while learning unknown, iteration-invariant signals or parameters. However, conventional adaptive ILC faces two challenges: (i) the coupling between rotational and translational dynamics complicates the design of the two coordinated learning loops for position and attitude, and (ii) standard adaptive ILC designs cannot guarantee bounded control inputs. To address these issues, we propose a dual-number-based, segment-based two-loop adaptive ILC framework for simultaneous high-precision position and attitude tracking. The framework employs two learning loops that interact through a dual-number representation of tracking errors, combining position and attitude errors into a single mathematical object for unified control design. A segment-based dynamic projection mechanism ensures that both parameter estimates and control inputs remain bounded without prior knowledge of uncertainties. Mathematical analysis and numerical simulations demonstrate that the proposed framework significantly enhances tracking performance under unknown but repeatable uncertainties and strong rotational-translational coupling.
Paper Structure (20 sections, 7 theorems, 99 equations, 7 figures)

This paper contains 20 sections, 7 theorems, 99 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Quaternions and Dual Quaternions
  3. Quaternions and Unit Quaternions
  4. Dual Quaternions and Unit Dual Quaternions
  5. Motion Kinematics and Dynamics
  6. Coordinate Frames
  7. Actual Attitude-Position Kinematics and Dynamics
  8. Error Attitude-Position Kinematics and Dynamics
  9. Control Objectives
  10. Controller Design and Analysis
  11. Two-Loop ILC Design
  12. Convergence and Boundedness Analysis
  13. Simulation Verification
  14. Conclusions
  15. Proof of Lemma \ref{['lem1']}
  16. ...and 5 more sections

Key Result

Lemma 1

Let $\mathring{\boldsymbol{Q}}_1$ and $\mathring{\boldsymbol{Q}}_2$ be unit dual quaternions, i.e., $\mathring{\boldsymbol{Q}}_1, \mathring{\boldsymbol{Q}}_2 \in \mathbb{DS}^3$. Then, Moreover, and

Figures (7)

  • Figure 1: Demonstration of the couple position-attitude tracking in the rigid body proximity operation.
  • Figure 2: Position errors along the time axis for $k=0$.
  • Figure 3: Position errors along the time axis for $k=30$.
  • Figure 4: Attitude errors along the time axis for $k=0$.
  • Figure 5: Attitude errors along the time axis for $k=30$.
  • ...and 2 more figures

Theorems & Definitions (30)

  • Lemma 1
  • proof
  • Remark 1
  • Lemma 2
  • proof
  • Remark 2
  • Remark 3
  • Lemma 3
  • proof
  • Remark 4
  • ...and 20 more