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Design of low-energy transfers in cislunar space using sequences of lobe dynamics

Naoki Hiraiwa, Mai Bando, Yuzuru Sato, Shinji Hokamoto

Abstract

Dynamical structures in the circular restricted three-body problem (CR3BP) are fundamental for designing low-energy transfers, as they aid in analyzing phase space transport and designing desirable trajectories. This study focuses on lobe dynamics to exploit local chaotic transport around celestial bodies, and proposes a new method for systematically designing low-energy transfers by combining multiple lobe dynamics. A graph-based framework is constructed to explore possible transfer paths between departure and arrival orbits, reducing the complexity of the combinatorial optimization problem for designing fuel-efficient transfers. Based on this graph, low-energy transfer trajectories are constructed by connecting chaotic orbits within lobes. The resulting optimal trajectory in the Earth--Moon CR3BP is then converted into an optimal transfer in the bicircular restricted four-body problem using multiple shooting. The obtained transfer is compared with existing optimal solutions to demonstrate the effectiveness of the proposed method.

Design of low-energy transfers in cislunar space using sequences of lobe dynamics

Abstract

Dynamical structures in the circular restricted three-body problem (CR3BP) are fundamental for designing low-energy transfers, as they aid in analyzing phase space transport and designing desirable trajectories. This study focuses on lobe dynamics to exploit local chaotic transport around celestial bodies, and proposes a new method for systematically designing low-energy transfers by combining multiple lobe dynamics. A graph-based framework is constructed to explore possible transfer paths between departure and arrival orbits, reducing the complexity of the combinatorial optimization problem for designing fuel-efficient transfers. Based on this graph, low-energy transfer trajectories are constructed by connecting chaotic orbits within lobes. The resulting optimal trajectory in the Earth--Moon CR3BP is then converted into an optimal transfer in the bicircular restricted four-body problem using multiple shooting. The obtained transfer is compared with existing optimal solutions to demonstrate the effectiveness of the proposed method.
Paper Structure (22 sections, 23 equations, 48 figures, 3 tables)

This paper contains 22 sections, 23 equations, 48 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Circular restricted three-body problem (CR3BP)
  4. Resonant orbit
  5. Periapsis Poincaré map
  6. Bicircular restricted four-body problem (BCR4BP)
  7. Lobe dynamics
  8. Description of lobe dynamics for trajectory design
  9. Lobe sequences in the CR3BP
  10. Trajectory design based on lobe dynamics
  11. Overview of the design method
  12. Test problem settings
  13. Test results
  14. Application to Earth--Moon transfer in the CR3BP
  15. Earth--Moon transfer design
  16. ...and 7 more sections

Figures (48)

  • Figure 1: Coordinate system in CR3BP (Rotating frame).
  • Figure 2: In the $x$-$y$ plane.
  • Figure 3: Time history of the semi-major axis along the orbit.
  • Figure 5: In the rotating frame.
  • Figure 6: In the inertial frame.
  • ...and 43 more figures

Theorems & Definitions (7)

  • Definition 1: Heteroclinic/ homoclinic point
  • Definition 2: Primary intersection point, pip rom1990tranport
  • Definition 3: Lobe rom1990tranport
  • Definition 4: Lobe sequence hiraiwa2024designing
  • Definition 5: Radius of a lobe hiraiwa2024designing
  • Definition 6: Effective lobe hiraiwa2024designing
  • Definition 7: Effective lobe sequence hiraiwa2024designing