A Light-weight Vibrational Motor Powered Recoil Robot that Hops Rapidly Across Granular Media

Abstract: A 1 cm coin vibrational motor fixed to the center of a 4 cm square foam platform moves rapidly across granular media (poppy seeds, millet, corn meal) at a speed of up to 30 cm/s, or about 5 body lengths/s. Fast speeds are achieved with dimensionless acceleration number, similar to a Froude number, up to 50, allowing the light-weight 1.4 g mechanism to remain above the substrate, levitated and propelled by its kicks off the surface. The mechanism is low cost and moves without any external moving parts. With 2 s exposures we photograph the trajectory of the mechanism using an LED blocked except for a pin-hole and fixed to the mechanism. Trajectories can exhibit period doubling phenomena similar to a ball bouncing on a vibrating table top. A two dimensional numerical model gives similar trajectories, though a vertical drag force is required to keep the mechanism height low. We attribute the vertical drag force to aerodynamic suction from air flow below the mechanism base and through the granular substrate. Our numerical model suggests that speed is maximized when the mechanism is prevented from jumping high off the surface. In this way the mechanism resembles a galloping or jumping animal whose body remains nearly at the same height above the ground during its gait.