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ItemMechanics of undulatory swimming in a frictional fluid(Georgia Institute of Technology, 2012-12) Ding, Yang ; Sharpe, Sarah S. ; Masse, Andrew ; Goldman, Daniel I.The sandfish lizard (Scincus scincus) swims within granular media (sand) using axial body undulations to propel itself without the use of limbs. In previous work we predicted average swimming speed by developing a numerical simulation that incorporated experimentally measured biological kinematics into a multibody sandfish model. The model was coupled to an experimentally validated soft sphere discrete element method simulation of the granular medium. In this paper, we use the simulation to study the detailed mechanics of undulatory swimming in a ‘‘granular frictional fluid’’ and compare the predictions to our previously developed resistive force theory (RFT) which models sand-swimming using empirically determined granular drag laws. The simulation reveals that the forward speed of the center of mass (CoM) oscillates about its average speed in antiphase with head drag. The coupling between overall body motion and body deformation results in a non-trivial pattern in the magnitude of lateral displacement of the segments along the body. The actuator torque and segment power are maximal near the center of the body and decrease to zero toward the head and the tail. Approximately 30% of the net swimming power is dissipated in head drag. The power consumption is proportional to the frequency in the biologically relevant range, which confirms that frictional forces dominate during sand-swimming by the sandfish. Comparison of the segmental forces measured in simulation with the force on a laterally oscillating rod reveals that a granular hysteresis effect causes the overestimation of the body thrust forces in the RFT. Our models provide detailed testable predictions for biological locomotion in a granular environment.
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ItemSimulation and theoretical study of swimming and resistive forces within granular media(Georgia Institute of Technology, 2011-11-14) Ding, YangUnderstanding animal locomotion requires modeling the interaction of the organism with its environment. Locomotion within granular media like sand, soil, and debris that display both solid and fluid-like behavior in response to stress is less studied than locomotion within fluids or on solid ground. To begin to reveal the secrets of movement in sand, I developed models to explain the subsurface locomotion of the sand-swimming sandfish lizard. I developed a resistive force theory (RFT) with empirical force laws to explain the swimming speed observed in animal experiments. By varying the amplitude of the undulation in the RFT, I found that the range of amplitude used by the animal predicted the optimal swimming speed. I developed a numerical model of the sandfish coupled to a discrete element method simulation of the granular medium to test assumptions in the RFT and to study more detailed mechanics of sand-swimming. Inspired by the shovel-shaped head of the sandfish lizard, I used the simulation to study lift forces in granular media: I found that when a submerged intruder moved at a constant speed within a granular medium it experienced a lift force whose sign and magnitude depended on the intruder shape. The principles learned from the models guided the development of a biologically inspired robot that swam within granular media with similar performance to the lizard.
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ItemDrag induced lift in granular media(Georgia Institute of Technology, 2011-01-14) Ding, Yang ; Gravish, Nick ; Goldman, Daniel I.Laboratory experiments and numerical simulation reveal that a submerged intruder dragged horizontally at a constant velocity within a granular medium experiences a lift force whose sign and magnitude depend on the intruder shape. Comparing the stress on a flat plate at varied inclination angle with the local surface stress on the intruders at regions with the same orientation demonstrates that intruder lift forces are well approximated as the sum of contributions from flat-plate elements. The plate stress is deduced from the force balance on the flowing media near the plate.
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ItemBiophysically inspired development of a sand-swimming robot(Georgia Institute of Technology, 2011) Maladen, Ryan D. ; Ding, Yang ; Umbanhowar, Paul B. ; Kamor, Adam ; Goldman, Daniel I.Previous study of a sand-swimming lizard, the sandfish, Scincus scincus, revealed that the animal swims within granular media at speeds up to 0:4 body-lengths/cycle using body undulation (approximately a single period sinusoidal traveling wave) without limb use [1]. Inspired by this biological experiment and challenged by the absence of robotic devices with comparable subterranean locomotor abilities, we developed a numerical simulation of a robot swimming in a granular medium (modeled using a multi-particle discrete element method simulation) to guide the design of a physical sand-swimming device built with off-the-shelf servo motors. Both in simulation and experiment the robot swims limblessly subsurface and, like the animal, increases its speed by increasing its oscillation frequency. It was able to achieve speeds of up to 0:3 body-lengths/cycle. The performance of the robot measured in terms of its wave efficiency, the ratio of its forward speed to wave speed, was 0:34 0:02, within 8 % of the simulation prediction. Our work provides a validated simulation tool and a functional initial design for the development of robots that can move within yielding terrestrial substrates.
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ItemComparative studies reveal principles of movement on and within granular media(Georgia Institute of Technology, 2010-06) Ding, Yang ; Gravish, Nick ; Li, Chen ; Maladen, Ryan D. ; Mazouchova, Nicole ; Sharpe, Sarah S. ; Umbanhowar, Paul B. ; Goldman, Daniel I.Terrestrial locomotion can take place on complex substrates such as leaf litter, debris, and soil that flow or solidify in response to stress. While principles of movement in air and water are revealed through study of the hydrodynamic equations of fluid motion, discovery of principles of movement in complex terrestrial environments is less advanced in part because describing the physics of limb and body interaction with such environments remains challenging. We report progress our group has made in discovering principles of movement of organisms and models of organisms (robots) on and within granular materials (GM) like sand. We review current understanding of localized intrusion in GM relevant to foot and body interactions. We discuss the limb-ground interactions of a desert lizard, a hatchling sea turtle, and various robots and reveal that control of granular solidification can generate effective movement. We describe the sensitivity of movement on GM to gait parameters and discuss how changes in material state can strongly affect locomotor performance. We examine subsurface movement, common in desert animals like the sandfish lizard. High speed x-ray imaging resolves subsurface kinematics, while electromyography (EMG) allows muscle activation patterns to be studied. Our resistive force theory, numerical, and robotic models of sand-swimming reveal that subsurface swimming occurs in a “frictional fluid” whose properties differ from Newtonian fluids.
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ItemIntegrating a Hierarchy of Simulation Tools for Legged Robot Locomotion(Georgia Institute of Technology, 2008-09) Slatton, Andrew ; Cohen, Daniel ; Ding, Yang ; Umbanhowar, Paul B. ; Goldman, Daniel I. ; Haynes, G. Clark ; Komsuoglu, Haldun ; Koditschek, Daniel E.We are interested in the development of a variety of legged robot platforms intended for operation in unstructured outdoor terrain. In such settings, the traditions of rational engineering design, driven by analytically informed and computationally assisted studies of robot-environment models, remain ineffective due to the complexity of both the robot designs and the terrain in which they must operate. Instead, empirical trial and error often drives the necessary incremental and iterative design process, hence the development of such robots remains expensive both in time and cost, and is often closely dependent upon the substrate properties of the locomotion terrain. This paper describes a series of concurrent but increasingly coordinated software development efforts that aim to diminish the gap between easily interfaced and physically sound computational models of a real robot’s operation in a complex natural environment. We describe a robot simulation environment in which simple robot modifications can be easily prototyped along and “played” into phenomenological models of contact mechanics. We particularly focus on the daunting but practically compelling example of robot feet interacting granular media, such as gravel or sand, offering a brief report of our progress in deriving and importing physically accurate but computationally tractable phenomenological substrate models into the robot execution simulation environment. With a goal of integration for future robot prototyping simulations, we review the prospects for diminishing the gap between the integrated computational models and the needs of physical platform development.