Potential Shaping and the Method of Controlled Lagrangians

We extend the method of controlled Lagrangians to include potential shaping for complete state-space stabilization of mechanical systems. The method of controlled Lagrangians deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline.