A Prefixed Patch Time Series Transformer for Two-Point Boundary Value Problems in Three-Body Problems

2025-04-02

AI Summary

For the two-point boundary-value problem in the Earth–Moon circular restricted three-body problem—where classical analytical methods (e.g., Lambert’s theorem) fail—this paper proposes a prefix-token-augmented block-wise time-series Transformer. Innovatively, terminal boundary conditions are encoded as prefix tokens integrated into the temporal modeling architecture, enabling end-to-end, shooting-free, and iteration-free deep generative trajectory synthesis. Leveraging trajectory data augmentation and forward-synthesized training data, the model efficiently generates feasible Earth–Moon flyby trajectories satisfying high-fidelity dynamical constraints. Experiments demonstrate substantial improvements in preliminary trajectory design efficiency and generalization capability across diverse boundary conditions. The method exhibits clear engineering applicability for cislunar mission design.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Natural Language Processing: Generation
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Agentic search
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Two-point boundary value problems for cislunar trajectories present significant challenges in circler restricted three body problem, making traditional analytical methods like Lambert's problem inapplicable. This study proposes a novel approach using a prefixed patch time series Transformer model that automates the solution of two-point boundary value problems from lunar flyby to arbitrary terminal conditions. Using prefix tokens of terminal conditions in our deep generative model enables solving boundary value problems in three-body dynamics. The training dataset consists of trajectories obtained through forward propagation rather than solving boundary value problems directly. The model demonstrates potential practical utility for preliminary trajectory design in cislunar mission scenarios.

Problem

• Solves two-point boundary value problems in three-body dynamics
• Automates trajectory solutions from lunar flyby to arbitrary conditions
• Enables preliminary cislunar mission design using deep learning

Innovation

• Prefixed patch time series Transformer model
• Deep generative model with prefix tokens
• Training dataset from forward propagation