  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.
