Biological, simulation, and robotic studies to discover principles of swimming within granular media

The locomotion of organisms whether by running, flying, or swimming is the result of multiple degree-of-freedom nervous and musculoskeletal systems interacting with an environment that often flows and deforms in response to movement. A major challenge in biology is to understand the locomotion of organisms that crawl or burrow within terrestrial substrates like sand, soil, and muddy sediments that display both solid and fluid-like behavior. In such materials, validated theories such as the Navier-Stokes equations for fluids do not exist, and visualization techniques (such as particle image velocimetry in fluids) are nearly nonexistent. In this dissertation we integrated biological experiment, numerical simulation, and a physical robot model to reveal principles of undulatory locomotion in granular media. First, we used high speed x-ray imaging techniques to reveal how a desert dwelling lizard, the sandfish, swims within dry granular media without limb use by propagating a single period sinusoidal traveling wave along its body, resulting in a wave efficiency, the ratio of its average forward speed to wave speed, of approximately 0.5. The wave efficiency was independent of the media preparation (loosely and tightly packed). We compared this observation against two complementary modeling approaches: a numerical model of the sandfish coupled to a discrete particle simulation of the granular medium, and an undulatory robot which was designed to swim within granular media. We used these mechanical models to vary the ratio of undulation amplitude (A) to wavelength (λ) and demonstrated that an optimal condition for sand-swimming exists which results from competition between A and λ. The animal simulation and robot model, predicted that for a single period sinusoidal wave, maximal speed occurs for A/ λ = 0.2, the same kinematics used by the sandfish. Inspired by the tapered head shape of the sandfish lizard, we showed that the lift forces and hence vertical position of the robot as it moves forward within granular media can be varied by designing an appropriate head shape and controlling its angle of attack, in a similar way to flaps or wings moving in fluids. These results support the biological hypotheses which propose that morphological adaptations of desert dwelling organisms aid in their subsurface locomotion. This work also demonstrates that the discovery of biological principles of high performance locomotion within sand can help create the next generation of biophysically inspired robots that could explore potentially hazardous complex flowing environments.PhDCommittee Chair: Daniel I. Goldman; Committee Member: Hang Lu; Committee Member: Jeanette Yen; Committee Member: Shella Keilholz; Committee Member: Young-Hui Chan