Dynamic model of a spherical robot from first principles

Abstract

A prototype of a pendulum driven spherical robot has been developed during previous research and shown to exhibit unique dynamic behavior. Starting from first principles, a mathematical model for this spherical robot rolling on flat ground was developed in order to determine if this unique behavior was inherent to spherical robots in general or simply peculiar to this prototype. The complete equations of motion were found using Lagrangian methods, and numerically integrated using computer tools. A 3D simulation program was written to animate the results of integrating the equations. The dynamics apparent in the simulations were found to closely match the observed dynamics of the physical prototype.