A three-phase vibration-driven system´s locomotion on an isotropic rough surface

Inspired by earthworm´s terrestrial locomotion, a vibration-driven system is studied. The system moves on an isotropic rough surface, which provides isotropic Coulomb dry friction force. A three-phase control mode is used to actuate the vibration-driven system. Due to the existence of the Coulomb dry friction, stick-slip effect may play a role in the motion of the system. According to the present study, when moving forward, the stick-slip motions of the system can be classified into 6 different types. Based on the classification, an optimal motion, which has both high velocity and energy efficiency, can be derived. Benefiting from the classification, one may calculate average velocity of the optimal motion analytically. At last, a numerical example of the optimal motion is given to verify the theoretical analysis. Results derived analytically and numerically turn out to be in good agreement with each other.