Legged locomotion on sand

To understand how and why animals modulate foot kinematics to achieve effective locomotion on granular media, we study the speed of a six-legged robot with c-shaped legs, SandBot, moving on granular media for varying volume fraction, $\phi$, limb frequency, $f$, and gait timing parameters\footnote{Li et. al, PNAS, \textbf{106}, 3029, 2009}. Speed is determined by step length which in turn depends on limb penetration. At low $f$ and high $\phi$ penetration is small, step length is large, and SandBot advances with a rotary walking gait in which c-legs rotate about their centers by slipping relative to stationary grains. In the opposite extreme, grains cannot support the robot; its underside always contacts the ground and it advances slowly via thrust generated as the c-legs translate through the grains. For varied gait parameters, high speeds are only observed in a small area of parameter space. A yield stress based model predicts the speed and reveals that performance is maximized when gait parameters minimize limb acceleration and interference, and limbs utilize the solidification properties of the media.