symmetry S S Article Development of Machine Learning Algorithms for the Determination of the Centre of Mass Danilo D’Andrea 1, * , Filippo Cucinotta 1 , Flavio Farroni 2 , Giacomo Risitano 1 , Dario Santonocito 1 and Lorenzo Scappaticci 3   Citation: D’Andrea, D.; Cucinotta, F.; Farroni, F.; Risitano, G.; Santonocito, D.; Scappaticci, L. Development of Machine Learning Algorithms for the Determination of the Centre of Mass. Symmetry 2021, 13, 401. https:// doi.org/10.3390/sym13030401 Academic Editor: Raúl Baños Navarro Received: 13 February 2021 Accepted: 24 February 2021 Published: 28 February 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Engineering, University of Messina, Contrada di Dio (S. Agata), 98166 Messina, Italy; filippo.cucinotta@unime.it (F.C.); grisitano@unime.it (G.R.); dsantonocito@unime.it (D.S.) 2 Department of Industrial Engineering, University of Naples Federico II, via Claudio 21, 80125 Napoli, Italy; flavio.farroni@unina.it 3 Sustainability Engineering Department, Guglielmo Marconi University, via Plinio 44, 00193 Rome, Italy; l.scappaticci@unimarconi.it * Correspondence: dandread@unime.it; Tel.: +39-3930209246 Abstract: The study of the human body and its movements is still a matter of great interest today. Most of these issues have as their fulcrum the study of the balance characteristics of the human body and the determination of its Centre of Mass. In sports, a lot of attention is paid to improving and analysing the athlete’s performance. Almost all the techniques for determining the Centre of Mass make use of special sensors, which allow determining the physical magnitudes related to the different movements made by athletes. In this paper, a markerless method for determining the Centre of Mass of a subject has been studied, comparing it with a direct widely validated equipment such as the Wii Balance Board, which allows determining the coordinates of the Centre of Pressure. The Motion Capture technique was applied with the OpenPose software, a Computer Vision method boosted with the use of Convolution Neural Networks. Ten quasi-static analyses have been carried out. The results have shown an error of the Centre of Mass position, compared to that obtained from the Wii Balance Board, which has been considered acceptable given the complexity of the analysis. Furthermore, this method, despite the traditional methods based on the use of balances, can be used also for prediction of the vertical position of the Centre of Mass. Keywords: 3D motion capture; Open Pose; convolution neural networks 1. Introduction The study of the human body and its movements has acquired a key role in scientific research in recent years, particularly in the biomedical fields. The technological evolution allowed significant steps forward, especially in motor rehabilitation techniques [1,2], in the study of motor problems [3] related to ageing [4], pregnancy [5], sport rehabilitation [6,7], neuromuscular diseases [8], and in the analysis of dynamic systems, in which man interacts with the surrounding environment, be it real or virtual [9,10]. Most of these issues focus on the study of the balance characteristics of the human body and the determination of its Centre of Mass (CoM) [11–16]. In sports, much attention is paid to improving and analysing the athlete’s performance [17–19]. This is done by means of advanced techniques that allow detecting, through the use of special sensors [20,21], what are the physical quantities (strength, speed, acceleration, and displacement) related to the different movements performed by the athletes [22–24]. Many biomedical studies are made through the use of tools such as the Nintendo™ Wii Balance Board™ (BB) and Wii-Fit, the playful video game that allows performing aerobic exercises and balance games using the multi-sensor platform. Following the exe- cution of each exercise, on the basis of the detections made by the sensors, it is possible to calculate the weight but also the body mass index and the shift of the Centre of Mass Symmetry 2021, 13, 401. https://doi.org/10.3390/sym13030401 https://www.mdpi.com/journal/symmetry