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Geometry-Aligned LLM Fine-Tuning for Sequential Narrow-Opening Planning

Al Jaber Mahmud, Xuan Wang

Abstract

We study rigid-body motion planning through multiple sequential narrow openings, which requires long-horizon geometric reasoning because the configuration used to traverse an early opening constrains the set of reachable configurations for subsequent ones. To achieve this, we propose a geometry-aligned large language model (LLM) fine-tuning framework that generates fixed-length, machine-readable waypoint sequences that are both geometrically feasible and coordinated across openings. Our approach uses a bi-level training pipeline. First, we perform failure-driven LoRA supervised fine-tuning (SFT) on human demonstrations, which incorporates structured failure feedback to teach the model common failure modes and enforce the output format. Second, we refine the same LoRA adapters using Group Relative Policy Optimization (GRPO) with geometric verification: each sampled waypoint sequence is densified by a model-based planner and scored with a deterministic geometry-derived reward to achieve continuous-motion feasibility. To validate the effectiveness of our proposed method, we provide both quantitative and qualitative results from simulations. Our method achieves the highest success rate in both in-distribution and out-of-distribution environments and qualitatively exhibits long-horizon geometric reasoning by selecting exit poses that facilitate entry into subsequent openings.

Geometry-Aligned LLM Fine-Tuning for Sequential Narrow-Opening Planning

Abstract

We study rigid-body motion planning through multiple sequential narrow openings, which requires long-horizon geometric reasoning because the configuration used to traverse an early opening constrains the set of reachable configurations for subsequent ones. To achieve this, we propose a geometry-aligned large language model (LLM) fine-tuning framework that generates fixed-length, machine-readable waypoint sequences that are both geometrically feasible and coordinated across openings. Our approach uses a bi-level training pipeline. First, we perform failure-driven LoRA supervised fine-tuning (SFT) on human demonstrations, which incorporates structured failure feedback to teach the model common failure modes and enforce the output format. Second, we refine the same LoRA adapters using Group Relative Policy Optimization (GRPO) with geometric verification: each sampled waypoint sequence is densified by a model-based planner and scored with a deterministic geometry-derived reward to achieve continuous-motion feasibility. To validate the effectiveness of our proposed method, we provide both quantitative and qualitative results from simulations. Our method achieves the highest success rate in both in-distribution and out-of-distribution environments and qualitatively exhibits long-horizon geometric reasoning by selecting exit poses that facilitate entry into subsequent openings.
Paper Structure (16 sections, 15 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 16 sections, 15 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Model-Based Motion Planning
  4. Learning-Based Planning
  5. Large Language Model Based Planners
  6. Reinforcement Learning with Large Language Models
  7. Problem Statement
  8. Main Approach
  9. Human Demonstrations Collection
  10. Prompt Construction
  11. Failure-driven LoRA Supervised Fine-Tuning (SFT)
  12. Group Relative Policy Optimization (GRPO) with Geometric Verification
  13. Experiments and Results
  14. Quantitative Evaluation
  15. Qualitative Evaluation
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Geometry-aligned LLM for Sequential Narrow-Opening Planning and a Motivating Example.
  • Figure 2: Bi-level fine-tuning stage. Level-1: Failure-driven LoRA SFT with human-demonstrated waypoints. Level-2: Refinement of LoRA adapters using GRPO with geometric verification.
  • Figure 3: Qualitative comparison of methods in terms of Geometric Correctness. Gray rectangles are obstacles forming sequential openings. (i-A and ii-A)Failure-driven LoRA SFT + GRPO with geometric verification: produces exit poses that are already oriented toward the heading needed for the next opening (red). (i-B and ii-B)sub-goal decomposed PRM: plans each opening independently using subgoal (SG, shaded) regions that yield locally feasible waypoints but leave insufficient space to align for the next opening in low-gap scenes. (iii-A, iii-B)A failure example: Failure-driven LoRA SFT alone can sometimes produce infeasible waypoints (iii-B), while adding GRPO yields feasible waypoints for the same scene (iii-A).