Jamming aids jumping in granular media

Little is known about the impulsive force and flow fields generated during jumping on granular media. We use a simple robot jumping on poppy seeds to explore maneuvers that induce jammed (non-yielding) states, and find sensitive dependence of jumping performance to movement strategy. On loose packings (volume fraction $\phi = 0.57$), a preliminary hop followed by a delay (``delayed stutter jump'') improves the height of a push-off maneuver (``single jump''). Constant speed intrusion force measurements suggest that reentry of the foot during the preliminary hop reintroduces high surface resistance. An optimal delay time ($t = 50$ ms) leads to maximal jump heights, while a short delay time ($t \approx 0$ ms) produces the lowest jumps. Velocimetry of grain flow reveals that non-delay stutters induce fluid-like granular states into which the robot sinks before jamming occurs, lowering jump heights. While simulations of single and delayed stutter jumps are well described using a frictional (depth dependent) plus drag (velocity dependent) penetration resistance, this model does not capture stutter jump performance at low $\phi$. However, addition of an added mass term improves agreement, signaling the need for a more complex reactive force theory in impulsively forced granular media.