The Cubli: Modeling and Nonlinear Control Utilizing Unit Complex Numbers

• Main Authors: Bobrow, Fabio, Angelico, Bruno A, da Silva, Paulo S. P
• Format: Journal Article
• Language: English
• Published: 28-09-2020
• Subjects: Computer Science - Systems and Control
• DOI: 10.48550/arxiv.2009.14625

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.