用大模型自动求解深空低推力轨道优化问题，无需人工编程。
HELIOS: An LLM-Driven Autonomous Indirect Trajectory Optimization Agent
- 基于大语言模型自动完成庞特里亚金原理符号推导与代码生成
- 11个测试场景全部成功求解，变量数最多达48个，编译成功率100%
- 支持多种动力学模型和约束类型，适合航天任务设计人员使用
低推力轨道优化是深空任务设计的核心技术。基于庞特里亚金最小值原理（PMP）的间接方法虽有严格最优性保证，但实际应用面临三大瓶颈：(1) 每类约束需手动推导横截条件；(2) 不同动力学模型需重复编写代码；(3) 射击方程对初值高度敏感。本文提出HELIOS（Heuristic Engine for Low-thrust Interplanetary Optimization System），一个以大语言模型（LLM）为核心的自主轨迹优化代理。给定自然语言描述的物理问题，系统可自动完成PMP符号推导、SymPy验证、C++射击代码生成与数值求解，全程无需人工干预。关键创新包括：(1) 约束自适应推导框架，将任意约束统一为psi(x,p)=0形式，并自动生成自由参数（如引力辅助转向角）的平稳条件；(2) 动力学自适应四模块代码生成，支持非标准动力学（太阳帆、J2摄动）而无需修改模板；(3) 覆盖PMP推导中关键易错点的通用推导规则集。在11个渐进式测试场景中，HELIOS成功求解从简单交会（8变量）到多航段停留转移（48变量）、引力辅助轨迹（17变量）及太阳帆最短时间转移（8变量）等问题。最佳编译成功率100%（11/11）。多模型对比（8个开源LLM后端，总分250–905）验证了架构的模型无关性，并揭示模型规模与推导能力呈正相关。
原文摘要 · Abstract (English)
Low-thrust trajectory optimization is a core technology in deep-space mission design. Indirect methods based on Pontryagin's Minimum Principle (PMP) offer rigorous optimality guarantees, yet their practical application faces three bottlenecks: (1) transversality conditions must be derived case by case for each constraint type; (2) different dynamics models require repeated code rewrites; and (3) shooting equations are highly sensitive to initial guesses. This paper presents HELIOS (Heuristic Engine for Low-thrust Interplanetary Optimization System), a trajectory optimization agent built around a large language model (LLM). Given a physical problem described in natural language, the system autonomously performs PMP symbolic derivation, SymPy verification, C++ shooting-code generation, and numerical solution without human intervention. Key innovations include: (1) a constraint-adaptive derivation framework that unifies arbitrary constraints into psi(x,p)=0 form and automatically generates stationarity conditions for free parameters (e.g., gravity-assist turning angle); (2) dynamics-adaptive four-module code generation supporting non-standard dynamics (solar sail, J2 perturbation) without modifying the underlying template; and (3) a general derivation rule set covering critical error-prone points in PMP derivation. Experiments on 11 progressive test scenarios show that HELIOS correctly derives and solves problems from simple rendezvous (8 variables) to multi-leg stay transfers (48 variables), gravity-assist trajectories (17 variables), and solar-sail minimum-time transfers (8 variables). The best compilation success rate reaches 100% (11/11). A multi-model comparison (8 open-source LLM backends, total scores 250-905) verifies the model-agnostic architecture and reveals a positive correlation between model scale and derivation capability.
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