Modeling and Control of a Three-Dimensional Inverted Pendulum - A project based on Cubli featuring Kane’s method and Model Predictive Control

Abstract

Abstract The two dimensional inverted pendulum has long served as a typical classroom and textbook example when teaching classical mechanics or control theory. Then variants of the spinning top and gyroscopes have fascinated the general public, engineers and scientists for centuries. The Cubli platform developed by ETH in Switzerland takes the latter two a step further by combining them into a threedimensional inverted pendulum. Three reaction wheels mounted inside a cube shaped frame enables the platform to among other things rise up to and balance on a corner. As an advanced mechatronics system, it serves well for evaluating various aspects related to control methods and sensors. Here, a platform called Cubex, being similar to Cubli, was used. A recently presented novel approach to Model Predictive control was evaluated and deployed. Furthermore a new approach for finding an offset of the mass center of this system and a complete general procedure for correcting misaligned Inertial Measurement Units (IMU’s) have been developed and successfully implemented. Also, while ETH has released short form conference papers regarding the analytical modeling of the Cubli platform, this work aims to explain the modeling process in more detail using Kane’s method. Most relevant artifacts from the project such as source code and modeling files are released in open source repositories.