General scaling relations for locomotion in granular media

TL;DR

This paper develops and validates a universal set of scaling laws for granular locomotion, enabling prediction of robot performance across different sizes, shapes, and gravity conditions using experiments and simulations.

Contribution

It introduces a general dimensionless framework for granular locomotion that unifies experimental and simulation results, applicable across various conditions and gravitational environments.

Findings

Scaling laws are confirmed experimentally with wheels of different sizes and shapes.

DEM simulations validate the scaling relations across different gravity levels.

The framework applies to diverse locomotor configurations in granular media.

Abstract

We derive a general dimensionless form for granular locomotion, which is validated in experiments and Discrete Element Method (DEM) simulations. The form instructs how to scale size, mass, and driving parameters in order to relate dynamic behaviors of different locomotors in the same granular media. The scaling can be derived by assuming intrusion forces arise from Resistive Force Theory (RFT) or equivalently by assuming the granular material behaves as a continuum obeying a frictional yield criterion. The scalings are experimentally confirmed using pairs of wheels of various shapes and sizes under many driving conditions in a common sand bed. We discuss why the two models provide such a robust set of scaling laws even though they neglect a number of the complexities of granular rheology. Motivated by potential extra-planetary applications, the dimensionless form also implies a way to predict wheel performance in one ambient gravity based on tests in a different ambient gravity. We confirm this using DEM simulations, which show that scaling relations are satisfied over an array of driving modes even when gravity differs between scaled tests.