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

2025-06-05

AI Summary

In autonomous UAV operations, large language models (LLMs) suffer from erroneous formula selection and substantial multi-step computational errors in trajectory planning and power consumption management. To address this, we propose RAG-UAV—the first retrieval-augmented generation framework tailored for engineering mathematical reasoning in UAV applications. It introduces a domain-specific knowledge base and the UAV-Math-Bench benchmark for systematic evaluation. RAG-UAV integrates UAV-specialized knowledge retrieval, multi-model collaboration (GPT-4o/Turbo, Llama-3.2/3.3, Mistral, DeepSeek R1), and fine-grained arithmetic verification. This design significantly enhances mathematical reasoning reliability: achieving 75% exact-answer accuracy on UAV-Math-Bench, reducing formula misselection rate from 25% to 5%, and decreasing mean squared error (MSE) by several orders of magnitude. All code, datasets, and benchmarks are publicly released.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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 small problem set comprising 20 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), 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, question and answer are publicly available.

Problem

• Enhancing UAV mathematical reasoning for trajectory and power tasks
• Improving LLMs' accuracy in selecting correct mathematical formulations
• Reducing numerical errors in multi-step arithmetic for UAV operations

Innovation

• RAG-UAV framework enhances LLM mathematical reasoning
• UAV-Math-Bench evaluates domain-specific problem-solving accuracy
• Retrieval-augmented generation reduces errors in UAV calculations