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A Switching Strategy for Event-Trigger Control of Spacecraft Rendezvous

Tommaso Del Carro, Gerson Portilla, Alexandre Seuret, Rafael Vazquez

TL;DR

The paper develops a Lyapunov-based, offline-LMI design for an event-triggered switching controller in Hill-Clohessy-Wiltshire rendezvous with saturated impulsive inputs. By modeling control as $u(x)=\sigma(x)Kx$ and triggering via a state-dependent decision rule tied to $x^T M x$, it guarantees stability under bounded disturbances and reduces thruster firings compared to MPC, with all LMIs solved off-line. Key contributions include proving convergence to an attractor under $w\in\Omega_\lambda$, providing a framework to enlarge the basin of attraction and to maximize the attractor, and offering a trade-off optimization to balance firing frequency, energy, and robustness. The results demonstrate robust performance in both linear and nonlinear simulations, highlighting practical benefits for autonomous spacecraft proximity operations and real-time onboard feasibility.

Abstract

This paper presents the design of a state-feedback control law for spacecraft rendezvous, formulated using the Hill-Clohessy-Wiltshire equations. The proposed method introduces an impulsive control strategy to regulate thruster operations. Specifically, a state-dependent switching framework is developed to determine both the control input magnitudes and the precise state conditions that trigger thruster activation. The nonlinear control law is derived using principles from automatic control theory, particularly Lyapunov stability analysis and the Linear Matrix Inequality framework. The resulting closed-loop system is proven to be stable, while simultaneously minimizing the total number of actuation events. The effectiveness of the proposed method is demonstrated through a numerical case study, which includes a comparative analysis with a standard Model Predictive Control scheme, highlighting the advantages and trade-offs of the developed control structure.

A Switching Strategy for Event-Trigger Control of Spacecraft Rendezvous

TL;DR

The paper develops a Lyapunov-based, offline-LMI design for an event-triggered switching controller in Hill-Clohessy-Wiltshire rendezvous with saturated impulsive inputs. By modeling control as and triggering via a state-dependent decision rule tied to , it guarantees stability under bounded disturbances and reduces thruster firings compared to MPC, with all LMIs solved off-line. Key contributions include proving convergence to an attractor under , providing a framework to enlarge the basin of attraction and to maximize the attractor, and offering a trade-off optimization to balance firing frequency, energy, and robustness. The results demonstrate robust performance in both linear and nonlinear simulations, highlighting practical benefits for autonomous spacecraft proximity operations and real-time onboard feasibility.

Abstract

This paper presents the design of a state-feedback control law for spacecraft rendezvous, formulated using the Hill-Clohessy-Wiltshire equations. The proposed method introduces an impulsive control strategy to regulate thruster operations. Specifically, a state-dependent switching framework is developed to determine both the control input magnitudes and the precise state conditions that trigger thruster activation. The nonlinear control law is derived using principles from automatic control theory, particularly Lyapunov stability analysis and the Linear Matrix Inequality framework. The resulting closed-loop system is proven to be stable, while simultaneously minimizing the total number of actuation events. The effectiveness of the proposed method is demonstrated through a numerical case study, which includes a comparative analysis with a standard Model Predictive Control scheme, highlighting the advantages and trade-offs of the developed control structure.

Paper Structure

This paper contains 18 sections, 3 theorems, 39 equations, 10 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Problem statement
  3. HCW model with saturated impulsive actuation
  4. Formulation of the rendezvous control problem
  5. State-dependent switching model
  6. Event-triggered control design
  7. Preliminary lemmas
  8. Main result
  9. Discussion on Theorem \ref{['th:Stabb']} and optimization procedure
  10. Graphical interpretation of Theorem \ref{['th:Stabb']}
  11. Optimization of the basin of attraction
  12. Optimization of the attractor
  13. Event-triggering rule
  14. Tradeoff optimization
  15. Numerical application
  16. ...and 3 more sections

Key Result

Lemma 1

For any $x$ in $\mathbb R^{n_x}$, the following inequality holds where

Figures (10)

  • Figure 1: Inertial and LVLH reference frames. Adapted from CURTIS2014367
  • Figure 2: Chaser and target position in the LVLH frame. Adapted from CURTIS2014367
  • Figure 3: Attractor and basin of attraction (plane projection for any two generic states, $x_1$ and $x_2$)
  • Figure 4: Chaser trajectories for three different initial conditions (10 random realizations each) using the ETC - Linear simulation model with additive disturbances
  • Figure 5: Values of the $\sigma$ parameter for three different initial conditions (single random realization) using the ETC - Linear simulation model with additive disturbances
  • ...and 5 more figures

Theorems & Definitions (6)

  • Remark 1
  • Remark 2
  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Remark 3