The (unreasonable?) effectiveness of resistive force theory in granular locomotion

Daniel I. Goldman

School of Physics, Georgia Institute of Technology




Resistive force theory (RFT) has been used for over 70 years to analyze the movement of microscopic organisms swimming in fluids. In RFT, a body is partitioned into infinitesimal segments, each which generates thrust and experiences drag. Linear superposition of forces from elements over the body allows prediction of locomotion dynamics. While RFT does always not show quantitative agreement with experimental measurements in fluids [Rodenborn et al, PNAS, 2013], we show that it quantitatively models the locomotion of animals and robots that move on and within dry granular media. RFT shows excellent agreement when the medium is slightly polydisperse, in the '' frictional fluid " regime such that frictional forces dominate material inertial forces, and when locomotion can be approximated as confined to a plane. Within a given plane (horizontal or vertical) relationships that govern the force versus orientation of an elemental intruder are functionally independent of the granular medium. We use RFT to explain aspects of locomotion; some examples that I will mention include the role of body shape on sand-swimming performance, how neuromechanical phase lags emerge during swimming, optimization of leg shape for maximum running robot performance, and appendage coordination during ascent of sandy slopes. Granular RFT also facilitates use of a geometric formulation of movement first introduced by Shapere & Wilczek in 1987. This framework, improved by Hatton & Choset [Eur. Phys. J, 2015], allows understanding and visualization of the emergence of translation and rotation from patterns of arbitrary body self-deformation; as an example I will discuss our work studying sand-swimming in a 3-link "Purcell'' swimming robot. Finally, I will briefly discuss recent theoretical results from Kamrin's group at MIT which reveal that granular RFT emerges as a surprising simplicity of frictional yielding materials; this model indicates why RFT performs better in granular media than in viscous fluids.