Quadrotor Dynamics Modeling by Fuzzy Machine Learning Approaches

Abstract

Solving the problem in precise control and simulation of unmanned aerial vehicles remains relevant. It helps to achieve the accuracy and performance increase in many applied areas of human activity. The most successful method for quadrotor control is a data-driven approach. Besides the physical properties analysis, the data-driven control allows for planning considering the most probable scenario. A conventional multilayer perceptron lacks interpretability and suffers from spectral bias. Unlike standard 'black-box' models, the more recent Kolmogorov-Arnold network with Chebyshev polynomials has a more interpretable structure. The Kolmogorov-Arnold architecture replaces fixed activation functions and weights with learnable Chebyshev polynomials on edges. It significantly enhances parameter efficiency and approximation power. However, it is not a fully interpretable model and depends on backpropagation. In this paper, we propose a novel fuzzy neural network based on Frank t- and s- norms. Such a machine learning model does not have such limitations in interpretability and backpropagation. In the experimental part, we integrate the proposed and known data-driven control models in the governing quadrotor dynamics equations directly into the loss function, ensuring physical consistency. The fuzzy neural network uses learnable Frank norms to process flexible logical reasoning, improving robustness against noisy sensor data. Experimental validation on quadrotor flight trajectories demonstrates that the proposed fuzzy model outperforms standard multilayer perceptron and Kolmogorov-Arnold network in convergence rate and predictive accuracy. The results indicate that these interpretable models offer a superior framework for real-time UAV dynamics modeling and control.