# From Semantic Decisions to Feasible Trajectories: Self-Evolving LLM-Guided Optimal Control for Narrow-Space Parking

arXiv: https://arxiv.org/abs/2609.24631 · HTML: https://mlsanity.com/paper/2609.24631/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Self-evolving LLM agents, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-evolving LLM agents](https://mlsanity.com/synth/self-evolving-llm-agents/)

## Builds on (most cited first, 17 of 17)

- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Code as Policies: Language Model Programs for Embodied Control](https://mlsanity.com/paper/2209.07753/) (2022)
- [Inner Monologue: Embodied Reasoning through Planning with Language Models](https://mlsanity.com/paper/2207.05608/) (2022)
- [Language Models as Zero-Shot Planners: Extracting Actionable Knowledge for Embodied Agents](https://mlsanity.com/paper/2201.07207/) (2022)
- [VoxPoser: Composable 3D Value Maps for Robotic Manipulation with Language Models](https://mlsanity.com/paper/2307.05973/) (2023)
- [DriveVLM: The Convergence of Autonomous Driving and Large Vision-Language Models](https://mlsanity.com/paper/2402.12289/) (2024)
- [GPT-Driver: Learning to Drive with GPT](https://mlsanity.com/paper/2310.01415/) (2023)
- [SayPlan: Grounding Large Language Models using 3D Scene Graphs for Scalable Robot Task Planning](https://mlsanity.com/paper/2307.06135/) (2023)
- [DiLu: A Knowledge-Driven Approach to Autonomous Driving with Large Language Models](https://mlsanity.com/paper/2309.16292/) (2023)
- [AutoTAMP: Autoregressive Task and Motion Planning with LLMs as Translators and Checkers](https://mlsanity.com/paper/2306.06531/) (2023)
- [Optimization-Based Collision Avoidance](https://mlsanity.com/paper/1711.03449/) (2017)
- [ParkingE2E: Camera-based End-to-end Parking Network, from Images to Planning](https://mlsanity.com/paper/2408.02061/) (2024)
- [RDA: An Accelerated Collision Free Motion Planner for Autonomous Navigation in Cluttered Environments](https://mlsanity.com/paper/2210.00192/) (2022)
- [An Efficient Spatial-Temporal Trajectory Planner for Autonomous Vehicles in Unstructured Environments](https://mlsanity.com/paper/2208.13160/) (2022)
- [MultiPark: Multimodal Parking Transformer with Next-Segment Prediction](https://mlsanity.com/paper/2508.11537/) (2025)
- [Bridging Large-Model Reasoning and Real-Time Control via Agentic Fast-Slow Planning](https://mlsanity.com/paper/2604.01681/) (2026)

## Abstract (arXiv)

Autonomous parking in nonconvex and narrow environments remains challenging. Although optimal-control methods can explicitly enforce vehicle dynamics and collision constraints, nonconvexity compromises solver robustness and can cause failures. Large language models (LLMs) exhibit strong semantic reasoning capabilities, but directly generating dense trajectories makes it difficult to guarantee physical feasibility. We introduce SE-LLM-OCP, a unified framework in which LLMs make high-level discrete maneuver decisions, while an optimal-control module enforces low-level vehicle dynamics and collision constraints. Online, the LLM proposes sparse maneuver plans, decomposing the parking task into a sequence of short-horizon trajectory-optimization problems. A low-level solver then sequentially solves optimal-control problems. If the solver fails, the LLM aggregates failure evidence from the solver and validation stages to guide replanning. Offline, SE-LLM-OCP automatically evolves a structured decision-making knowledge base from scratch, driven by accumulated online failures. We validate our proposed framework in simulation on a car-like vehicle model and on a differential-drive robot. Our experimental results show that SE-LLM-OCP enables safer autonomous parking in narrow scenarios and demonstrates transfer of the same maneuver representation to a different kinematic platform.