Diffusion Models for Generating Ballistic Spacecraft Trajectories

TL;DR

The paper tackles the challenge of generating feasible ballistic spacecraft trajectories using diffusion models. It introduces a score-based diffusion framework trained on Earth–Mars transfers solved by Lambert’s problem, enabling the generation of new, physically plausible trajectories without conditioning inputs. A key contribution is the Defect RMS Number (DRN) and its equivalent (EDRN) for evaluating trajectory feasibility across time resolutions, along with ablation studies on model size and temporal resolution. Empirical results show diffusion-generated trajectories closely resemble the training data and respect two-body dynamics, with initial/final velocity errors around $100\ \mathrm{m/s}$ and DRN on the order of $10^{-3}$, suggesting diffusion models can provide valuable initial guesses for traditional optimization pipelines. The work lays the groundwork for conditional extensions and integration with more complex dynamics, positioning diffusion-based trajectory design as a scalable, rapid tool for preliminary mission design and exploration.

Abstract

Generative modeling has drawn much attention in creative and scientific data generation tasks. Score-based Diffusion Models, a type of generative model that iteratively learns to denoise data, have shown state-of-the-art results on tasks such as image generation, multivariate time series forecasting, and robotic trajectory planning. Using score-based diffusion models, this work implements a novel generative framework to generate ballistic transfers from Earth to Mars. We further analyze the model's ability to learn the characteristics of the original dataset and its ability to produce transfers that follow the underlying dynamics. Ablation studies were conducted to determine how model performance varies with model size and trajectory temporal resolution. In addition, a performance benchmark is designed to assess the generative model's usefulness for trajectory design, conduct model performance comparisons, and lay the groundwork for evaluating different generative models for trajectory design beyond diffusion. The results of this analysis showcase several useful properties of diffusion models that, when taken together, can enable a future system for generative trajectory design powered by diffusion models.

Figures (8)

• Figure 1: 5000 randomly sampled trajectories from the Earth-Mars ballistic transfer training dataset.
• Figure 2: Example model input image and the corresponding state elements for each row in the image. Note, red boxes are added to differentiate between rows in the image.
• Figure 3: Forward-backward midpoint propagations for a 16-node trajectory. Defects computed at the midpoints are used to compute a trajectory's DRN. Note: the inset plot shows a zoomed-in view of three forward-backed propagations from the displayed trajectory, with transparency added to highlight overlapping sections.
• Figure 4: Condensation of a sixty-four node trajectory into sixteen nodes for computing the EDRN. Note that only a portion of the trajectory is shown.
• Figure 5: Trajectory generation process through iterative denoinsing shown for $x$ and $y$ state components. Note that $\tau$ here refers to the denoising step number.