The Effectiveness of Resistive Force Theory in Granular Locomotion

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Zhang, Tingnan
Goldman, Daniel I.
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Resistive force theory (RFT) is often used to analyze the movement of microscopic organisms swimming in fluids. In RFT, a body is partitioned into infinitesimal segments, each of which generates thrust and experiences drag. Linear superposition of forces from elements over the body allows prediction of swimming velocities and efficiencies. We show that RFT quantitatively describes the movement of animals and robots that move on and within dry granular media (GM), collections of particles that display solid, fluid, and gas-like features. RFT works well when the GM is slightly polydisperse, and 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 the RFT to explain features of locomotion on and within granular media including kinematic and muscle activation patterns during sand-swimming by a sandfish lizard and a shovel-nosed snake, optimal movement patterns of a Purcell 3-link sand-swimming robot revealed by a geometric mechanics approach, and legged locomotion of small robots on the surface of GM. We close by discussing situations to which granular RFT has not yet been applied (such as inclined granular surfaces), and the advances in the physics of granular media needed to apply RFT in such situations.
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