论文标题
Cubli：使用单元复台建模和非线性控制
The Cubli: Modeling and Nonlinear Control Utilizing Unit Complex Numbers
论文作者
论文摘要
本文涵盖了Cubli的建模和非线性控制，这是一个位于正交面上的三个反应车轮的立方体，当位于其边缘之一（1D）或顶点（3D）中时，它变成了反应轮的1D/3D反倒摆。单位复数用作1D配置的控制状态，而不是角度。这种方法不仅可以摆脱三角函数，而且主要是因为它是3D配置的特定情况，它将单位超复杂数字（四元组）作为系统状态，因此可以促进其理解。派生的非线性控制定律等效于线性，并且仅以三个直接调谐参数为特征。提出了实验结果以验证建模和对照。
This paper covers the modeling and nonlinear control of the Cubli, a cube with three reaction wheels mounted on orthogonal faces that becomes a reaction wheel-based 1D/3D inverted pendulum when positioned in one of its edges (1D) or vertices (3D). Instead of angles, unit complex numbers are used as control states for the 1D configuration. This approach is useful not only to get rid of trigonometric functions, but mainly because it is a specific case of the 3D configuration, that utilizes unit ultra-complex numbers (quaternions) as system states, and therefore facilitates its understanding. The derived nonlinear control law is equivalent to a linear one and is characterized by only three straightforward tuning parameters. Experiment results are presented to validate modeling and control.
