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

ABSTRACT 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.