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Ohta Kuramoto, Jorge Ruben Casir Ricano, and Kenji Nagaoka
Grouser wheels are effective for robotic mobility in soft, loose terrain. So far, particle image velocimetry (PIV) has been widely used to observe sand flow beneath a traveling wheel. Although the PIV-based spatial velocity field at a moment in time has been discussed, but few studies have discussed its time evolution, or spatio-temporal dynamics. This could be due to the fact that the sand flow vector field is complex high-dimensional dynamics and a mixture of spatial and temporal information. Thus, we apply dynamic mode decomposition (DMD) to the sand flow data obtained by the PIV method to reduce its dimension and decompose it into major modes. A mode is a characteristic pattern or correlation. The DMD can extract temporal and spatial information separately, allowing the dynamics to be analyzed by the major modes. We first conducted PIV experiments using the traveling wheel on sand at high-slip (slip ratio is approximately 70%) and low-slip (slip ratio is approximately 20%) conditions. Then, the DMD was applied to decompose the PIV-based sand velocity data into major modes. As a result, the obtained modes were mainly divided into two dynamics, one representing the inter-grouser sand flow trapped in the grouser motion and the other representing soil compaction and failure, affecting deeper soil. It was found that the low-slip condition included both modes, whereas the high-slip one did only inter-grouser sand flow. The DMD analysis confirmed that two major modes can explain wheel-soil interaction.
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