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This paper introduces a geometry-aligned LLM fine-tuning framework for rigid-body motion planning through sequential narrow openings, a task requiring long-horizon geometric reasoning. The framework uses a bi-level training pipeline involving failure-driven LoRA supervised fine-tuning on human demonstrations, followed by Group Relative Policy Optimization (GRPO) with geometric verification. The method achieves state-of-the-art success rates in both in-distribution and out-of-distribution environments, demonstrating long-horizon geometric reasoning capabilities.
LLMs can now plan complex, sequential robotic maneuvers through narrow spaces by learning from human demos and refining with geometric rewards, outperforming traditional methods.
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.
