Energy-Based Trajectory Tracking for Underactuated Mechanical Systems: Velocity-Free and Disturbance Rejection Methods

This work investigates three energy-shaping control approaches to address the trajectory-tracking problem for specific classes of underactuated mechanical systems. In particular, the notions of contractive systems and dynamic extensions are utilized to solve the trajectory-tracking problem while addressing implementation issues such as the lack of velocity sensors and the presence of constant disturbances. To this end, a first tracking controller is developed without the need for velocity measurements. A second controller is introduced, solving the trajectory-tracking problem while rejecting matched constant disturbances. Then, a third approach establishes conditions to combine both mentioned controllers. It is shown that the proposed design methods guarantee exponential convergence of closed-loop systems for specific classes of underactuated mechanical systems. The third method is illustrated with an example.