New dynamic model for a Ballbot system

A Ballbot is a self-balanced mobile robot designed for omnidirectional mobility. The structure self-balanced on a ball giving to the system only one contact point with the ground. In this paper the dynamical model of a Ballbot system is investigated in order to find a linearized model which is able to describe the three-dimensional dynamics of the mechatronic system by a simpler set of equations. Due to the system's complexity, the equations of motion are often obtained by the energy method of Lagrange, they consist of a vast nonlinear ordinary differential equations (ODE), which are often numerically linearized for small perturbations. The present paper proposes to model the whole 3D dynamics of the Ballbot with the Newton-Euler formalism and Tait-Bryan angles in order to describe the model in terms of the system's physical parameters without resorting to numeric solution. This physical modelling is introduced to allow the simplification of the dynamic motion control of the ballbot.