Energy shaping for position and speed control of a wheeled inverted pendulum in reduced space

The paper deals with the energy-based stabilization and speed control of a wheeled inverted pendulum, which is an underactuated, unstable mechanical system subject to nonholonomic constraints. We use the method of Controlled Lagrangians for the stabilization of an equilibrium characterized by the length of the driven path, the orientation, and the pitch angle. The approach is systematic and very intuitive, for it is physically motivated. Based on the stabilization results, we design a speed control law. After the presentation of the model under nonholonomic constraints in Lagrangian representation, we provide an elegant solution to the matching equations for kinetic and potential energy shaping for the considered system. Simulations show the applicability of the method, and the comparison with a linear controller emphasizes its performance.