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

TL;DR

This paper introduces RAG-UAV, a retrieval-augmented framework that enhances large language models' mathematical reasoning for UAV tasks, significantly improving accuracy and reducing errors in UAV-specific mathematical problems.

Contribution

The paper presents RAG-UAV, a novel retrieval-augmented approach that improves LLMs' mathematical reasoning capabilities specifically for UAV applications, validated on a new UAV-Math-Bench dataset.

Findings

Retrieval augmentation increases answer accuracy up to 75%.

It reduces incorrect formulation selection from 25% to 5%.

Numerical errors decrease significantly with RAG.

Abstract

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.