Modeling and control of spherical ultrasonic motor based on nonholonomic mechanics

In this paper, we propose a new approach to dynamical modeling of the spherical multi d.o.f. ultrasonic motor based on nonholonomic mechanics, and a practical motion control method using periodic signals with variable phase. We point out that this system is analogous to the so called rolling sphere manipulation system as far as the kinematics is concerned, although there is also an indispensable influence of the drift term which stems from its momentum dynamics. For this system, we propose the multi-cycle phase switching (MCPS) method to suppress this influence by periodically changing the phase shift, of the piezoelectric vibration. The proposed method is free from redundancy because it uses only two vibration modes, while the conventional methods required three modes.