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

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

Track: long paper (up to 10 pages)

Keywords: Large Language Model, Retrieval-Augmented Generation, Unmanned Aerial Vehicle, UAV-Math-Bench

TL;DR: In this work, we explore how RAG enhances the mathematical reasoning of LLMs for UAV applications. We use state-of-the-art models and augment them with a vector-based retrieval mechanism to supply external info during problem-solving.

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) of-
fer 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 assess-
ment, we introduce the UAV-Math-Bench (a 20-question pilot problem set) of
UAV-centric mathematical problems across four difficulty levels. Our experiments
suggest that incorporating retrieval substantially increases exact answer accuracy
(achieving up to 75% with o1), reduces instances of incorrect formulation selec-
tion (from 25% without RAG to 5% with RAG in a limited setting), 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 data are available.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Funding: No, the presenting author of this submission does *not* fall under ICLR’s funding aims, or has sufficient alternate funding.

Submission Number: 6