Motility of a Model Bristle-Bot: a Theoretical Analysis

TL;DR

This paper offers a comprehensive analytical study of a simplified bristle-bot model, explaining its propulsion mechanism, direction switching, and velocity formulas through rigorous mathematical methods.

Contribution

It provides the first fully analytical treatment of bristle-bot motility, including formulas for velocity and switching frequency, with proven convergence of the expansion method.

Findings

Derived formulas for average velocity and switching frequency.

Proved convergence of the analytical expansion.

Quantitative description of friction modulation mechanism.

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.