Revisiting Scaling Laws for Robotic Mobility in Granular Media

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.