Abstract:
Bristle-bots are legged robots that can be easily made out of a toothbrush head
and a small vibrating engine. Despite their simple appearance, the mechanism enabling
them to propel themselves by exploiting friction with the substrate is far
from trivial. Numerical experiments on a model bristle-bot have been able to reproduce
such a mechanism revealing, in addition, the ability to switch direction
of motion by varying the vibration frequency. This paper provides a detailed account
of these phenomena through a fully analytical treatment of the model. The
equations of motion are solved through an expansion in terms of a properly chosen
small parameter. The convergence of the expansion is rigorously proven. In
addition, the analysis delivers formulas for the average velocity of the robot and
for the frequency at which the direction switch takes place. A quantitative description
of the mechanism for the friction modulation underlying the motility of the
bristle-bot is also provided.
