Stabilization of a PR planar underactuated robot

We consider the stabilization problem for an underactuated prismatic-rotational (PR) robot with the second joint passive and moving on the horizontal plane. After a controllability analysis, a nilpotent approximation of the system is derived and used for designing an open-loop polynomial command that reduces the state error in finite time. Under suitable hypotheses, the iterative application of this command, computed as a function of the state at the end of each iteration, leads to exponential convergence to the desired equilibrium configuration. Simulation results are reported, also in the presence of unmodeled viscous friction.