# Semantic Constraint Synthesis for Adaptive Trajectory Optimization via Large Language Models

arXiv: https://arxiv.org/abs/2606.04123 · HTML: https://mlsanity.com/paper/2606.04123/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Foundation Models in Robotics: Applications, Challenges, and the Future](https://mlsanity.com/paper/2312.07843/) (2023)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [Plug in the Safety Chip: Enforcing Constraints for LLM-driven Robot Agents](https://mlsanity.com/paper/2309.09919/) (2023)
- [NL2TL: Transforming Natural Languages to Temporal Logics using Large Language Models](https://mlsanity.com/paper/2305.07766/) (2023)
- [Transformers for Trajectory Optimization with Application to Spacecraft Rendezvous](https://mlsanity.com/paper/2310.13831/) (2023)
- [Space-LLaVA: a Vision-Language Model Adapted to Extraterrestrial Applications](https://mlsanity.com/paper/2408.05924/) (2024)
- [Towards Robust Spacecraft Trajectory Optimization via Transformers](https://mlsanity.com/paper/2410.05585/) (2024)
- [Bridging Natural Language and Formal Specification--Automated Translation of Software Requirements to LTL via Hierarchical Semantics Decomposition Using LLMs](https://mlsanity.com/paper/2512.17334/) (2025)
- [Fast Homotopy for Spacecraft Rendezvous Trajectory Optimization with Discrete Logic](https://mlsanity.com/paper/2107.07001/) (2021)
- [VernaCopter: Disambiguated Natural-Language-Driven Robot via Formal Specifications](https://mlsanity.com/paper/2409.09536/) (2024)
- [Autonomous Reasoning for Spacecraft Control: A Large Language Model Framework with Group Relative Policy Optimization](https://mlsanity.com/paper/2601.04334/) (2026)
- [Language-Conditioned Safe Trajectory Generation for Spacecraft Rendezvous](https://mlsanity.com/paper/2512.09111/) (2025)
- [NC2C: Automated Convexification of Generic Non-Convex Optimization Problems](https://mlsanity.com/paper/2601.04789/) (2026)
- [Canonical Intermediate Representation for LLM-based optimization problem formulation and code generation](https://mlsanity.com/paper/2602.02029/) (2026)

## Built on by (most cited first, 1 of 1)

- [OrbitTAMP: Grounding Language Models for Task and Motion Planning in Spacecraft Rendezvous](https://mlsanity.com/paper/2610.01093/) (2026)

## Abstract (arXiv)

Trajectory optimization is a critical component for enabling safe and reliable autonomous operations in space exploration. As space missions increase in frequency, complexity, and scope, there is a growing need to rapidly formulate mathematically sound trajectory optimization problems that accurately reflect mission objectives and operational constraints. However, translating mission intent into tractable analytical formulations for trajectory optimization requires substantial domain expertise. This paper presents a framework that leverages large language models (LLMs) to translate natural language descriptions of mission requirements and constraints into executable trajectory optimization code and corresponding mathematical formulations. Experiments in spacecraft rendezvous scenarios demonstrate a high success rate in reconditioning a convex trajectory optimization problem from semantic mission requirements. Ultimately, this work highlights the potential of LLMs to bridge high-level intent and formal optimization models, enabling more flexible and efficient trajectory design of spacecraft.