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

5 Jun 2025arXiv:2506.04998archive 2025-07-28

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

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.

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Arithmetic Reasoning Math Mathematical Reasoning RAG Retrieval Retrieval-augmented Generation Trajectory Planning

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Methods

Attention Attention Dropout BART BERT BPE Cosine Annealing Dense Connections Discriminative Fine-Tuning Dropout GPT Layer Normalization Linear Layer Linear Warmup With Cosine Annealing Linear Warmup With Linear Decay Multi-Head Attention RAG SET Softmax WordPiece

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