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### Title: Single-wheel robot modelling using natural orthogonal complement

Authors: Zhigang Chen; Xiaogang Ruan; Cheng Li; Xiaoping Zhang; Jianxian Cai; Ouattara Sie; Xiaoqing Zhu

Addresses: School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing, 100124, China ' School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing, 100124, China ' School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing, 100124, China ' School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing, 100124, China ' School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing, 100124, China ' School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing, 100124, China ' School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing, 100124, China; Center for Intelligent Machines, Department of Mechanical Engineering, McGill University, Montreal, Quebec, H3A 0C3, Canada

Abstract: The modelling on SWR is a foundation work for researchers to carry out further study, thus is very important. The early modelling on SWR are mostly done by the Euler-Lagrange equations, and the Euler angles are used to calculate the attitude of SWR. The method of Euler-Lagrange equations has to calculate a lot of quadratic terms and partial differential terms, while the Euler angles are known to be prone to singularities. This paper proposed a novel modelling on SWR by using nature orthogonal complement, which is simpler and more efficient in computation than Euler-Lagrange equations. Further, the quaternions was employed to calculate the attitude of SWR, thus free of singularity problem. Moreover, the radius of the toroidal wheel has been taken into account on the model firstly, so the mathematical model is more close to the real physical situation. The dynamic modelling results have been verified by numerous experiments.

Keywords: single-wheel robot; dynamics; NOC; natural orthogonal complement; quaternions; toroidal wheel; singularity.

International Journal of System Control and Information Processing, 2017 Vol.2 No.1, pp.31 - 50

Received: 10 Oct 2016
Accepted: 10 Oct 2016

Published online: 22 May 2017 *