A Terradynamics of Legged Locomotion on Granular Media

TLDR

Aero‑ and hydrodynamic theories predict animal movement in air and water, but terrestrial legged locomotion models have largely ignored flowable substrates, leaving a gap in understanding how animals move on granular media. The study aims to develop a force model—terradynamics—for arbitrarily‑shaped legs and bodies moving freely in granular media. Using terradynamics, the authors predict a small legged robot’s locomotion on granular media across various leg shapes and stride frequencies. The results show that stresses in granular media depend complexly on intruder depth, orientation, and movement direction, offering insights into how leg morphology and kinematics influence locomotion.

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.