arXiv 2506.049982025-06-30cs.AI

无人机数学推理：基于检索增强生成的方法用于复杂算术推理

Mathematical Reasoning for Unmanned Aerial Vehicles: A RAG-Based Approach for Complex Arithmetic Reasoning

Department of Computer Science（计算机科学系）；Institute For Artificial Intelligence（人工智能研究所）；Hamm-Lippstadt University of Applied Sciences（哈姆-利普施塔特应用科学大学）；University of Stuttgart（斯图加特大学）

Mehdi Azarafza, Mojtaba Nayyeri, Faezeh Pasandideh, Steffen Staab, Achim Rettberg

备注：: 15 pages, 7 figures, 4 appendix subsections
发表信息：: ICLR 2026 Workshop on Logical Reasoning of Large Language Models

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AI总结：

本文提出RAG-UAV框架，通过引入领域文献提升LLM在无人机任务中的数学推理能力，实验表明检索显著提高准确率并减少错误选择。

摘要：

自主无人机操作需要可靠的数学推理能力以完成轨迹规划和功率管理等任务。尽管传统飞行控制依赖硬编码方程，但近年来大型语言模型（LLMs）在灵活性方面具有潜力，但难以可靠选择和应用正确的数学公式并执行精确的多步算术。我们提出了RAG-UAV，一种检索增强生成框架，旨在通过提供相关领域文献来改进几种LLM（包括GPT o1/Turbo、Llama-3.2/3.3、Mistral和DeepSeek R1）在无人机特定情境中的数学推理能力。为了进行初步评估，我们引入了UAV-Math-Bench，一个包含20个问题的无人机中心数学问题集，涵盖四个难度级别。我们的实验表明，结合检索显著提高了精确答案的准确性（使用o1达到75%），减少了错误公式选择的实例（从无RAG时的25%降至有RAG时的5%），并减少了数值误差，使最佳性能模型的均方误差（MSE）降低多个数量级。这项初步研究表明，RAG可以使得通用LLM成为更可靠的工程分析工具，尽管直接实时飞行控制仍需进一步调查和在更大规模上的验证。所有基准数据、问题和答案均已公开。

英文摘要：

Autonomous UAV operation necessitates reliable mathematical reasoning for tasks such as trajectory planning and power management. While traditional flight control relies on hardcoded equations, recent Large Language Models (LLMs) offer potential for more flexible problem-solving but struggle with reliably selecting and applying correct mathematical formulations and executing precise multi-step arithmetic. We propose RAG-UAV, a retrieval-augmented generation framework designed to improve the mathematical reasoning of several LLMs (including GPT o1/Turbo, Llama-3.2/3.3, Mistral, and DeepSeek R1) in UAV-specific contexts by providing access to relevant domain literature. To conduct an initial assessment, we introduce the UAV-Math-Bench, a 20-question problem set of UAV-centric mathematical problems across four difficulty levels. Our experiments demonstrate that incorporating retrieval substantially increases exact answer accuracy (achieving up to 75% with o1), reduces instances of incorrect formulation selection (from 25% without RAG to 5\% with RAG), and decreases numerical errors, reducing Mean Squared Error (MSE) by orders of magnitude for the best-performing models. This pilot study indicates that RAG can enable general-purpose LLMs to function as more reliable tools for engineering analysis, although direct real-time flight control requires further investigation and validation on a larger scale. All benchmark data, questions, and answers are publicly available.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。