Single-wheel robot modelling using natural orthogonal complement. (2017) - Chen, Zhigang; Ruan, Xiaogang; Li, Cheng; Zhang, Xiaoping; Cai, Jianxian; Sie, Ouattara; Zhu, Xiaoqing
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.