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Event-Based Impulsive Control for Spacecraft Rendezvous Hovering Phases

Julio C. Sanchez, Christophe Louembet, Francisco Gavilan, Rafael Vazquez

TL;DR

This work presents an event-triggered controller for spacecraft rendezvous hovering phases that maintains the chaser within a bounded region with respect to the target.

Abstract

This work presents an event-triggered controller for spacecraft rendezvous hovering phases. The goal is to maintain the chaser within a bounded region with respect to the target. The main assumption is that the chaser vehicle has impulsive thrusters. These are assumed to be orientable at any direction and are constrained by dead-zone and saturation bounds. The event-based controller relies on trigger rules deciding when a suitable control law is applied. The local control law consists on a single impulse; therefore the trigger rules design is based on the instantaneous reachability to the admissible set. The final outcome is a very efficient algorithm from both computational burden and footprint perspectives. Because the proposed methodology is based on a single impulse control, the controller invariance is local and assessed through impulsive systems theory. Finally, numerical results are shown and discussed.

Event-Based Impulsive Control for Spacecraft Rendezvous Hovering Phases

TL;DR

This work presents an event-triggered controller for spacecraft rendezvous hovering phases that maintains the chaser within a bounded region with respect to the target.

Abstract

This work presents an event-triggered controller for spacecraft rendezvous hovering phases. The goal is to maintain the chaser within a bounded region with respect to the target. The main assumption is that the chaser vehicle has impulsive thrusters. These are assumed to be orientable at any direction and are constrained by dead-zone and saturation bounds. The event-based controller relies on trigger rules deciding when a suitable control law is applied. The local control law consists on a single impulse; therefore the trigger rules design is based on the instantaneous reachability to the admissible set. The final outcome is a very efficient algorithm from both computational burden and footprint perspectives. Because the proposed methodology is based on a single impulse control, the controller invariance is local and assessed through impulsive systems theory. Finally, numerical results are shown and discussed.
Paper Structure (36 sections, 1 theorem, 79 equations, 17 figures, 2 tables, 1 algorithm)

This paper contains 36 sections, 1 theorem, 79 equations, 17 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Relative motion and constrained orbits
  3. Relative motion
  4. Relative dynamics and state transition
  5. Parameterizing the relative motion
  6. Impulsive control
  7. Decoupling the relative motion
  8. Constrained orbits
  9. Event-based predictive controller
  10. Reachability conditions
  11. Instantaneous reachable set
  12. Out-of-plane motion
  13. In-plane motion
  14. Admissible set reachability conditions
  15. Region of attraction
  16. ...and 21 more sections

Key Result

Theorem 1

Consider the impulsive dynamical system given by eq:hybrid_system. Define the set $\mathcal{M}=\mathcal{D} \cup \mathcal{S}_{D}$. If the dead-zone set is empty, $\mathcal{D}_{\textup{dz}}=\emptyset$, then for $D(0)\in\mathcal{M}$, it holds that $D(\nu)\rightarrow\mathcal{M}$ as $\nu\rightarrow\infty

Figures (17)

  • Figure 1: Inertial Earth-centered and LVLH frames.
  • Figure 2: Constrained periodic relative orbits.
  • Figure 3: Sketch illustrating the admissible set instantaneous reachability for $\nu_1\leq\nu_2\leq\nu_3$.
  • Figure 4: Trajectory for (a): $e=0$, (b): $e=0.6$. Hovering impulses scale 10:1 with respect to approach impulses.
  • Figure 5: The variables $G_{xz}$, $G_y$, $\lVert \Delta V_{xz}\rVert_1$ and $\lVert \Delta V_y\rVert_1$ for (a): $e=0$, (b): $e=0.6$.
  • ...and 12 more figures

Theorems & Definitions (4)

  • Remark 1
  • Remark IV.1
  • Theorem 1
  • Remark IV.2