Ball on Ball: Modeling and control of a novel experiment set-up

This paper introduces a new control application. The goal is to balance a bowling ball on top of another bowling ball which rotates in three axes. The first ball is placed on three so-called omni-wheels in a way that it can rotate in all directions. The second ball moves freely atop the first ball. This approach uses a model based controller design. The mathematical model for the system is first derived using the Lagrange equations. One aspect of this model is that the rolling of one ball on another is a nonholonomic constraint. A significant simplification of the mathematical model can be achieved with a suitable state transformation. A linear approximation of the model at the equilibrium point is presented along with the controller design. Implementation on the laboratory model demonstrate the successful application of the model based control concept.