A Terradynamics of Legged Locomotion on Granular Media

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Abstract

The theories of aero- and hydrodynamics predict animal movement and device design in air and water through the computation of lift, drag, and thrust forces. Although models of terrestrial legged locomotion have focused on interactions with solid ground, many animals move on substrates that flow in response to intrusion. However, locomotor-ground interaction models on such flowable ground are often unavailable. We developed a force model for arbitrarily-shaped legs and bodies moving freely in granular media, and used this "terradynamics" to predict a small legged robot's locomotion on granular media using various leg shapes and stride frequencies. Our study reveals a complex but generic dependence of stresses in granular media on intruder depth, orientation, and movement direction and gives insight into the effects of leg morphology and kinematics on movement.

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Undulatory swimming in sand: subsurface locomotion of the sandfish lizard.

Yang Ding, Chen Li, Ryan D Maladen … (2009)

The desert-dwelling sandfish (Scincus scincus) moves within dry sand, a material that displays solid and fluidlike behavior. High-speed x-ray imaging shows that below the surface, the lizard no longer uses limbs for propulsion but generates thrust to overcome drag by propagating an undulatory traveling wave down the body. Although viscous hydrodynamics can predict swimming speed in fluids such as water, an equivalent theory for granular drag is not available. To predict sandfish swimming speed, we developed an empirical model by measuring granular drag force on a small cylinder oriented at different angles relative to the displacement direction and summing these forces over the animal movement profile. The agreement between model and experiment implies that the noninertial swimming occurs in a frictional fluid.