General scaling relations for locomotion in granular media

Area of Science:

• Physics of granular materials
• Robotics and locomotion
• Planetary exploration engineering

Background:

• Locomotion in granular media, such as sand, presents unique challenges due to the material's complex rheology.
• Understanding how to scale locomotion parameters is crucial for designing effective robots and vehicles for terrestrial and extraterrestrial environments.
• Existing models often struggle to capture the full range of behaviors in granular systems.

Purpose of the Study:

• To derive a general dimensionless form for granular locomotion based on principles of dynamic similarity.
• To validate this dimensionless form through experimental testing and discrete element method (DEM) simulations.
• To explore the applicability of the derived scaling laws for predicting performance under varying gravitational conditions.

Main Methods:

• Derivation of dimensionless scaling laws by applying resistive force theory or continuum mechanics with a frictional yield criterion.
• Experimental validation using scaled wheels of various shapes and sizes driven under diverse conditions in a sand bed.
• Numerical validation using discrete element method (DEM) simulations across different driving modes and gravitational accelerations.

Main Results:

• A general dimensionless form for granular locomotion was successfully derived and validated.
• Experimental results confirmed the predicted scaling laws for size, mass, and driving parameters.
• DEM simulations demonstrated the robustness of the scaling relations, even when gravity varied.

Conclusions:

• The derived dimensionless form provides a powerful tool for understanding and predicting granular locomotion dynamics.
• The scaling laws are effective despite simplifications in the underlying physical models, highlighting their practical utility.
• The findings have significant implications for designing extraterrestrial exploration rovers and other granular locomotion systems.