Minghan Wei

Zhengbang Yang, Md. Tasin Tazwar, Minghan Wei et al.

Robotic path planning problems are often NP-hard, and practical solutions typically rely on approximation algorithms with provable performance guarantees for general cases. While designing such algorithms is challenging, formally proving their approximation optimality is even more demanding, which requires domain-specific geometric insights and multi-step mathematical reasoning over complex operational constraints. Recent Large Language Models (LLMs) have demonstrated strong performance on mathematical reasoning benchmarks, yet their ability to assist with research-level optimality proofs in robotic path planning remains under-explored. In this work, we introduce the first benchmark for evaluating LLMs on approximation-ratio proofs of robotic path planning algorithms. The benchmark consists of 34 research-grade proof tasks spanning diverse planning problem types and complexity levels, each requiring structured reasoning over algorithm descriptions, problem constraints, and theoretical guarantees. Our evaluation of state-of-the-art proprietary and open-source LLMs reveals that even the strongest models struggle to produce fully valid proofs without external domain knowledge. However, providing LLMs with task-specific in-context lemmas substantially improves reasoning quality, a factor that is more effective than generic chain-of-thought prompting or supplying the ground-truth approximation ratio as posterior knowledge. We further provide fine-grained error analysis to characterize common logical failures and hallucinations, and demonstrate how each error type can be mitigated through targeted context augmentation.

Dylan Shim, Minghan Wei

Real-world path planning tasks typically involve multiple constraints beyond simple route optimization, such as the number of routes, maximum route length, depot locations, and task-specific requirements. Traditional approaches rely on dedicated formulations and algorithms for each problem variant, making them difficult to scale across diverse scenarios. In this work, we propose a flexible framework that leverages large language models (LLMs) to solve constrained path planning problems directly from natural language input. The core idea is to allow users to describe routing tasks conversationally, while enabling the LLM to interpret and solve the problem through solution verification and iterative refinement. The proposed method consists of two integrated components. For problem types that have been previously formulated and studied, the LLM first matches the input request to a known problem formulation in a library of pre-defined templates. For novel or unseen problem instances, the LLM autonomously infers a problem representation from the natural language description and constructs a suitable formulation in an in-context learning manner. In both cases, an iterative solution generation and verification process guides the LLM toward producing feasible and increasingly optimal solutions. Candidate solutions are compared and refined through multiple rounds of self-correction, inspired by genetic-algorithm-style refinement. We present the design, implementation, and evaluation of this LLM-based framework, demonstrating its capability to handle a variety of constrained path planning problems. This method provides a scalable and generalizable approach for solving real-world routing tasks with minimal human intervention, while enabling flexible problem specification through natural language.

Minghan Wei, Volkan Isler

As mobile robots find increasing use in outdoor applications, designing energy-efficient robot navigation algorithms is gaining importance. There are two primary approaches to energy efficient navigation: Offline approaches rely on a previously built energy map as input to a path planner. Obtaining energy maps for large environments is challenging. Alternatively, the robot can navigate in an online fashion and build the map as it navigates. Online navigation in unknown environments with only local information is still a challenging research problem. In this paper, we present a novel approach which addresses both of these challenges. Our approach starts with a segmented aerial image of the environment. We show that a coarse energy map can be built from the segmentation. However, the absolute energy value for a specific terrain type (e.g. grass) can vary across environments. Therefore, rather than using this energy map directly, we use it to build the covariance function for a Gaussian Process (GP) based representation of the environment. In the online phase, energy measurements collected during navigation are used for estimating energy profiles across the environment using GP regression. Coupled with an A*-like navigation algorithm, we show in simulations that our approach outperforms representative baseline approaches. We also present results from field experiments which demonstrate the practical applicability of our method.