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Generative Design of Periodic Orbits in the Restricted Three-Body Problem

Alvaro Francisco Gil, Walther Litteri, Victor Rodriguez-Fernandez, David Camacho, Massimiliano Vasile

TL;DR

The paper tackles the challenge of discovering and generating periodic orbits in the circular restricted three-body problem (CR3BP) to aid space mission design. It trains a two-dimensional latent-space Variational Autoencoder on a NASA CR3BP dataset of 44,112 periodic initial conditions across 40 orbital families, generating new trajectory seeds that are refined into physical orbits via a Multiple Shooting algorithm. Key findings include that the latent space clusters orbits by family (NMI 0.78, accuracy 0.56 for 40 classes) and that 46 of 100 generated seeds converge to new, physically plausible trajectories after refinement, with period correlating to a latent axis. This work demonstrates a tangible step toward Generative Astrodynamics, offering data-driven methods for orbit discovery and potential acceleration of mission design, with future work expanding architectures and datasets across planetary systems.

Abstract

The Three-Body Problem has fascinated scientists for centuries and it has been crucial in the design of modern space missions. Recent developments in Generative Artificial Intelligence hold transformative promise for addressing this longstanding problem. This work investigates the use of Variational Autoencoder (VAE) and its internal representation to generate periodic orbits. We utilize a comprehensive dataset of periodic orbits in the Circular Restricted Three-Body Problem (CR3BP) to train deep-learning architectures that capture key orbital characteristics, and we set up physical evaluation metrics for the generated trajectories. Through this investigation, we seek to enhance the understanding of how Generative AI can improve space mission planning and astrodynamics research, leading to novel, data-driven approaches in the field.

Generative Design of Periodic Orbits in the Restricted Three-Body Problem

TL;DR

The paper tackles the challenge of discovering and generating periodic orbits in the circular restricted three-body problem (CR3BP) to aid space mission design. It trains a two-dimensional latent-space Variational Autoencoder on a NASA CR3BP dataset of 44,112 periodic initial conditions across 40 orbital families, generating new trajectory seeds that are refined into physical orbits via a Multiple Shooting algorithm. Key findings include that the latent space clusters orbits by family (NMI 0.78, accuracy 0.56 for 40 classes) and that 46 of 100 generated seeds converge to new, physically plausible trajectories after refinement, with period correlating to a latent axis. This work demonstrates a tangible step toward Generative Astrodynamics, offering data-driven methods for orbit discovery and potential acceleration of mission design, with future work expanding architectures and datasets across planetary systems.

Abstract

The Three-Body Problem has fascinated scientists for centuries and it has been crucial in the design of modern space missions. Recent developments in Generative Artificial Intelligence hold transformative promise for addressing this longstanding problem. This work investigates the use of Variational Autoencoder (VAE) and its internal representation to generate periodic orbits. We utilize a comprehensive dataset of periodic orbits in the Circular Restricted Three-Body Problem (CR3BP) to train deep-learning architectures that capture key orbital characteristics, and we set up physical evaluation metrics for the generated trajectories. Through this investigation, we seek to enhance the understanding of how Generative AI can improve space mission planning and astrodynamics research, leading to novel, data-driven approaches in the field.
Paper Structure (16 sections, 9 equations, 6 figures)

This paper contains 16 sections, 9 equations, 6 figures.

Table of Contents

  1. Introduction
  2. The Restricted Three-Body Problem
  3. Periodic Orbits
  4. Generative AI
  5. Variational Autoencoder
  6. Research Motivation
  7. Methodology
  8. Dataset
  9. Model
  10. Convergence
  11. Results
  12. Generation
  13. Latent Space
  14. Refinement
  15. Discussion
  16. ...and 1 more sections

Figures (6)

  • Figure 1: Geometry of the Circular-Restricted Three-Body Problem in a rotating reference frame.
  • Figure 2: Schematic representation of an orbit Variational Autoencoder architecture (VAE).
  • Figure 3: Example of a refined orbit. The blue trajectory is the initial output of the model, whereas the orange one is the trajectory refined.
  • Figure 4: Generation of 100 synthetic orbits.
  • Figure 5: Visualization of the latent space from the experiment colored by orbital family labels, with plots showing the average distribution of the Jacobi constant, period, and stability.
  • ...and 1 more figures