Biological, robotic, and physics studies to discover principles of legged locomotion on granular media
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Terrestrial animals encounter natural surfaces which comprise materials that can yield and flow such as sand, rubble, and debris, yet appear to nimbly walk, run, crawl, or climb across them with great ease. In contrast, man-made devices on wheels and treads suffer large performance loss on these surfaces. Legged locomotion thus provides an excellent source of inspiration for creating devices of increased locomotor capabilities on natural surfaces. While principles of legged locomotion on solid ground have been discovered, the mechanisms by which legged animals move on yielding/flowing surfaces remain poorly understood, largely due to the lack of fundamental understanding of the complex interactions of body/limbs with these substrates on the level of the Navier-Stokes Equations for fluids. Granular media (e.g., sand) provide a promising model substrate for discovering the principles of legged locomotion on yielding/flowing surfaces, because they can display solid- and fluid-like behaviors, are directly relevant for many desert-dwelling animals, can be repeatably and precisely controlled, and the intrusion force laws can be determined empirically. In this dissertation, we created laboratory devices to prepare granular media in well-controlled states, and integrated biological, robotic, and physics studies to discover principles of legged locomotion on granular media. For both animals and bio-inspired robots, legged locomotion on granular surfaces must be achieved by limb intrusion to generate sufficient vertical ground reaction force (lift) to balance body weight and inertial force. When limb intrusion was slow (speed < 0.5 m/s), granular forces were independent of intrusion speed (dominated by grain-grain and grain-intruder friction) and generally increased with intrusion depth (due to granular hydrostatic pressure). Locomotor performance (speed) depended sensitively on limb kinematics, limb morphology, and the strength of the granular media, which together determined vertical force balance (or lack thereof). Based on these findings, we developed a granular resistive force theory in the sagittal plane as a general model for calculating forces during low-speed intrusions relevant to legged locomotion.