A discontinuous controller for a class of mechanical systems with second-order non-holonomic constraints
A discontinuous controller for tracking feasible trajectories in a class of underactuated mechanical systems with second-order non-holonomic constraints is proposed. The controller is designed as an extension to the underactuated case of the inverse dynamic control approach (originally designed for completely-actuated systems) plus a class of PD controllers. The proposal ensures stability of the closed-loop system, and allows to track, simultaneously for all the system variables, feasible trajectories to reach static or non-static configurations under large drifts in initial conditions. Numerical simulations for tracking inverted periodic motions in the Acrobot are provided to show the effectiveness of the proposed control scheme.