01569nas a2200181   4500008004100000022001400041245006000055210005800115300001400173490000700187520100500194653001901199653002201218653002801240100002601268700002201294856007101316       2015                        eng d  a0020-746200aMotility of a model bristle-bot: A theoretical analysis0 aMotility of a model bristlebot A theoretical analysis  a233 - 2390 v763 a<p>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.</p>10aBristle-robots10aCrawling motility10aFrictional interactions1 aCicconofri, Giancarlo1 aDeSimone, Antonio  uhttp://www.sciencedirect.com/science/article/pii/S0020746215000025