Many animals move within granular media such as desert sand. Models of an undulatory sand-swimmer, the sandfish lizard, reveal that the grains around the organism form a frictional fluid in which inertial effects are small and kinematics dominate. To understand the fundamental mechanics of swimming in granular media (GM), we examine a reduced system that has been well-studied in Newtonian fluids: the three-link swimmer. We model this system on several levels: a physical instantiation driven by servo-motors, a high-fidelity computational model using discrete-element methods (DEM) to represent the GM, and a resistive-force theory (RFT) approximation empirically derived from the DEM results.
By combining the RFT model with recent geometric mechanics theory, we construct intuitive visualizations of the system dynamics -- connection vector fields for differential motion, and constraint curvature functions that illustrate net motion over cycles. These visualizations allow us to directly predict optimal gaits for forward, lateral and rotational motion. Experiment and simulation are in accord with the theoretical predictions; thus geometric tools can be used to study locomotion in GM.