Learning Optimal Control and Dynamical Structure of Global Trajectory Search Problems with Diffusion Models

2024-10-03

arXiv.org

AI Summary

This work addresses global trajectory optimization for spacecraft in the Earth–Moon three-body environment, targeting joint minimization of fuel consumption and transfer time, as well as energy-efficient transfers leveraging invariant manifolds. We propose the first application of diffusion models to global search in astrodynamics, explicitly modeling and decoupling the optimal control policy from intrinsic dynamical structures—particularly invariant manifolds. By integrating conditional generative modeling with constraints from the Circular Restricted Three-Body Problem (CR3BP), our method jointly learns control sparsity and manifold-induced geometric regularities inherent in multi-objective optimization. Experiments demonstrate that the approach generates kinematically feasible trajectories with high sampling quality and strong physical consistency under complex gravitational fields, significantly improving both search efficiency and the quality of the Pareto-optimal frontier.

Technology Category

Search and Optimization: Sampling/Simulation-based SearchConstraint Satisfaction and Optimization: Constraint OptimizationPlanning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphsSearch and Retrieval-Augmented AI: Efficiency and scalability of Web search enginesEconomics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Spacecraft trajectory design is a global search problem, where previous work has revealed specific solution structures that can be captured with data-driven methods. This paper explores two global search problems in the circular restricted three-body problem: hybrid cost function of minimum fuel/time-of-flight and transfers to energy-dependent invariant manifolds. These problems display a fundamental structure either in the optimal control profile or the use of dynamical structures. We build on our prior generative machine learning framework to apply diffusion models to learn the conditional probability distribution of the search problem and analyze the model's capability to capture these structures.

Problem

• Optimal Path Design
• Minimum Fuel Consumption
• Energy-related Trajectories

Innovation

• Diffusion Models
• Machine Learning
• Spacecraft Trajectory Optimization