🤖 AI Summary
This work addresses key limitations of indirect methods in low-thrust trajectory optimization—namely, the manual derivation of transversality conditions, code reimplementation upon dynamical model changes, and the sensitivity of shooting methods to initial guesses. The authors propose an autonomous optimization agent powered by large language models that accepts natural-language mission descriptions and automatically performs symbolic derivations based on Pontryagin’s Minimum Principle (PMP), validates them via SymPy, and generates high-performance C++ solvers. Central innovations include a constraint-adaptive derivation framework that uniformly handles arbitrary terminal constraints and auto-generates smoothness conditions for free parameters, a dynamics-adaptive four-module architecture accommodating non-standard dynamics, and a comprehensive rule set covering common PMP derivation pitfalls. The approach successfully solves 11 progressively complex scenarios—including rendezvous, multi-phase hovering, gravity assists, and minimum-time solar sail transfers—with 8–48 variables, demonstrating model-agnosticism and scalability.
📝 Abstract
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.