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Single-wheel robot modelling using natural orthogonal complement

机译:使用自然正交补充的单轮机器人建模

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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.
机译:SWR的建模是研究人员进行进一步研究的基础工作,因此非常重要。 SWR上的早期建模主要由Euler-Lagrange方程式完成,欧拉角用于计算SWR的态度。 Euler-Lagrange方程的方法必须计算大量的二次术语和部分差异术语,而众所周知欧拉角度易于奇点。 本文提出了通过使用自然正交的补品对SWR进行了新颖的建模,这在比Euler-Lagrange方程中更简单和更有效。 此外,使用四季度来计算SWR的态度,从而无奇点问题。 此外,首先在模型上考虑了环形轮的半径,因此数学模型更接近真实的物理情况。 动态建模结果已经通过许多实验验证。

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