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.