Modeling and control of spherical ultrasonic motor based on nonholonomic mechanics

In this paper, we propose a new dynamical model of a spherical multi-degree-of-freedom (DOF) ultrasonic motor (USM) and its fundamental control method based on nonholonomic mechanics. This system is analogous to the so-called rolling sphere manipulation system as far as the kinematics is concerned, but there is also an indispensable influence of the momentum dynamics. We propose multi-cycle phase switching (MCPS) method to keep this influence under control, using only two pieces of piezoelectric oscillators for bending vibrations rather than three including a longitudinal vibration as required in the conventional methods.