Abstract
This technical note proves analytically how the exact equivalence of the Newton-Euler and Euler-Lagrange modeling formulations as applied to multirotor UAVs is achieved. This is done by deriving a correct Euler-Lagrange multirotor attitude dynamics model. A review of the published literature reveals that the commonly adopted Euler-Lagrange multirotor dynamics model is equivalent to the Newton-Euler model only when it comes to the position dynamics, but not in the attitude dynamics. Step-by-step derivations and calculations are provided to show how modeling equivalence to the Newton-Euler formulation is proven. The modeling equivalence is then verified by obtaining identical results in numerical simulation studies. Simulation results also illustrate that when using the correct model for feedback linearization, controller stability at high gains is improved.
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Acknowledgements
This work is part of the Ph.D. research of Simone Martini conducted at the University of Denver Unmanned Systems Research Institute (\(\text {DU}^{2}\text {SRI}\)) in collaboration with Politecnico di Torino. Dr. Rizzo is supported by the MOST - Sustainable Mobility National Research Center and received funding from the European Union Next-GenerationEU (PIANO NAZIONALE DI RIPRESA E RESILIENZA (PNRR) - MISSIONE 4 COMPONENTE 2, INVESTIMENTO 1.4 - D.D. 1033 17/06/2022, CN00000023). A pre print version of this technical note has been uploaded to https://doi.org/10.48550/arXiv.2310.09306.
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Simone Martini contributed to the study conception. The study was designed by Simone Martini, Dr. Kimon Valavavanis, and Dr. Alessandro Rizzo. Literature Review was written by Simone Martini and Dr. Kimon Valavanis. Mathemathical proof was written by Simone Martini under supervision of Dr. Kimon Valavanis and Dr. Margareta Stefanovic. Data analysis was performed by all authors. The first draft of the manuscript was written by Simone Martini and all authors commented on previous versions of the manuscript.
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Martini, S., Valavanis, K.P., Stefanovic, M. et al. Correction to the Euler Lagrange Multirotor Model with Euler Angles Generalized Coordinates. J Intell Robot Syst 110, 17 (2024). https://doi.org/10.1007/s10846-023-02040-9
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DOI: https://doi.org/10.1007/s10846-023-02040-9