Revisiting Scaling Laws for Robotic Mobility in Granular Media

Abstract

The development, building, and testing of robotic vehicles for applications in deformable media can be costly. Typical approaches rely on full-sized builds empirically evaluating performance metrics such as drawbar pull and slip. Recently developed granular scaling laws offer a new opportunity for terramechanics as a field. Using non-dimensional analysis on the wheel characteristics and treating the terrain as a deformable continuum, the performance of a larger, more massive wheel may be predicted from a smaller one. This allows for new wheel design approaches. However, robot-soil interaction and specific characteristics of the soil or robot dynamics may create discrepancies in prediction. In particular, we find that for a lightweight rover (2-5 kg), the scaling laws significantly overpredicted mechanical power requirements. To further explore the limitations of the current granular scaling laws, a pair of differently sized grousered wheels were tested at three masses and a pair of differently sized sandpaper wheels were tested at two masses across five speeds. Analysis indicates similar error for both designs, a mass dependency for all five pairs that explains the laws' overprediction, and a speed dependency for both of the heaviest sets. The findings create insights for using the laws with lightweight robots in granular media and generalizing granular scaling laws.