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

arXiv: https://arxiv.org/abs/2506.04998 · HTML: https://mlsanity.com/paper/2506.04998/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 6 of its 16 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 6 of 6)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [UAVs Meet LLMs: Overviews and Perspectives Toward Agentic Low-Altitude Mobility](https://mlsanity.com/paper/2501.02341/) (2025)
- [REAL: Resilience and Adaptation using Large Language Models on Autonomous Aerial Robots](https://mlsanity.com/paper/2311.01403/) (2023)
- [GSCE: A Prompt Framework with Enhanced Reasoning for Reliable LLM-driven Drone Control](https://mlsanity.com/paper/2502.12531/) (2025)
- [Backhaul-aware Drone Base Station Placement and Resource Management for FSO-based Drone-assisted Mobile Networks](https://mlsanity.com/paper/2112.12883/) (2021)

## Abstract (arXiv)

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.