MODELING AND CONTROL DESIGN USING THE BOLTZMANN-HAMEL EQUATIONS: A ROLLER-RACER EXAMPLE

The paper presents a dynamic modeling and control design for a wheeled vehicle with idle wheels. An example we detail is a roller-racer. For this system, we cannot determine its global motion by just the shape variation, since it does not posses a sufficient number of nonholonomic constraint equations. Kinematics must be complemented with the system dynamics. Using the Boltzmann-Hamel equations we develop a control oriented dynamic model for the roller-racer. Based on this model we design a modified computed torque controller to track its desired motion. We demonstrate that the Boltzmann-Hamel equations offer a competitive tool to develop dynamic control models for constrained systems and they may facilitate a subsequent controller design.