Planar Motion Control, Coordination and Dynamic Entrainment in Chaplygin Beanies

Abstract

The Chaplygin beanie is a single-input robotic vehicle for which partial planar motion control can be achieved by exploiting a simple nonholonomic constraint. A previous paper suggested a strategy for such motion control. In the present paper, this strategy is validated experimentally and extended to the context of multi-vehicle coordination. It is then shown that when the plane on which two such vehicles operate is translationally compliant, energy transfer between the two can enable a mechanism whereby one (operating under control) may entrain the other (operating passively), partly coordinating their motion. As an extension to this result, it is further demonstrated that a pair of passive vehicles operating on a translationally compliant platform can eventually attain the same heading when released from their deformed configurations.