AI summaryⓘ
The authors developed HELIOS, a system that uses a large language model to automatically solve low-thrust space mission trajectory problems, which usually require complicated math and coding. HELIOS takes a natural language description of the mission, derives the necessary equations, generates code, and finds solutions without human help. It handles various constraints and different spacecraft dynamics, such as solar sails or gravity assists, and works well across multiple test cases. Their experiments show that HELIOS can successfully manage complex trajectory optimization tasks with high accuracy and adaptability. They also found that bigger language models generally perform better at these derivations.
Low-thrust trajectory optimizationPontryagin's Minimum PrincipleTransversality conditionsShooting methodSymPySolar sail dynamicsGravity assistLarge language model (LLM)Symbolic derivationNumerical solution
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.