This paper develops a feedback control solution for the automatization of a motorized skateboard, also called symmetric snakeboard in the Robotics and Automatic Control literature. Controlling this system is particularly challenging due to the association of kinematic and dynamic nonintegrable constraints to which it is subjected. The Transverse Function approach, combined with backstepping, is used to derive dynamic feedback laws that ensure practical stabilization of arbitrary reference trajectories in the Cartesian space. Simulation results illustrate the proposed approach.