Dynamic Modeling of Stick-Slip Motion in a Legged, Piezoelectric Driven Microrobot

Abstract

The motion of a stick-slip microrobot propelled by its piezoelectric unimorph legs is mathematically modeled. Using a continuously distributed mass model for the robot's body, the working equation of the mechanism is derived based on the assumption of linear Euler-Bernoulli beam theory and linear piezoelectric behavior. Moreover, the required condition for generating net motion is calculated in terms of physical characteristics of the microrobot. It is demonstrated that the higher the friction constant, then a lower average speed is obtained. Also, it is shown that a microrobot with heavier legs can move in a rougher environment. Regardless of the mass proportion between robot's main body and its legs, a certain level of speed can, always, be achieved. The proposed results will be well suited to design, construct, and control the microrobots moving with piezoelectric benders, as their feet.