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

Predicting muscle forces of individuals with hemiparesis following stroke

<p>Abstract</p> <p>Background</p> <p>Functional electrical stimulation (FES) has been used to improve function in individuals with hemiparesis following stroke. An ideal functional electrical stimulation (FES) system needs an accurate mathematical model capable of designing subject and task-specific stimulation patterns. Such a model was previously developed in our laboratory and shown to predict the isometric forces produced by the quadriceps femoris muscles of able-bodied individuals and individuals with spinal cord injury in response to a wide range of clinically relevant stimulation frequencies and patterns. The aim of this study was to test our isometric muscle force model on the quadriceps femoris, ankle dorsiflexor, and ankle plantar-flexor muscles of individuals with post-stroke hemiparesis.</p> <p>Methods</p> <p>Subjects were seated on a force dynamometer and isometric forces were measured in response to a range of stimulation frequencies (10 to 80-Hz) and 3 different patterns. Subject-specific model parameter values were obtained by fitting the measured force responses from 2 stimulation trains. The model parameters thus obtained were then used to obtain predicted forces for a range of frequencies and patterns. Predicted and measured forces were compared using intra-class correlation coefficients, r²values, and model error relative to the physiological error (variability of measured forces).</p> <p>Results</p> <p>Results showed excellent agreement between measured and predicted force-time responses (r²>0.80), peak forces (ICCs>0.84), and force-time integrals (ICCs>0.82) for the quadriceps, dorsiflexor, and plantar-fexor muscles. The <it>model error </it>was within or below the +95% confidence interval of the <it>physiological error </it>for >88% comparisons between measured and predicted forces.</p> <p>Conclusion</p> <p>Our results show that the model has potential to be incorporated as a feed-forward controller for predicting subject-specific stimulation patterns during FES.</p

Towards a terramechanics for bio-in spired locomotion in granular environments

Granular media (GM) present locomotor challenges for terrestrial and extraterrestrial devices because they can flow and solidify in response to localized intrusion of wheels, limbs and bodies. While the development of airplanes and submarines is aided by understanding of hydrodynamics, fundamental theory does not yet exist to describe the complex interactions of locomotors with GM. In this paper, we use experimental, computational, and theoretical approaches to develop a terramechanics for bio-inspired locomotion in granular environments. We use a fluidized bed to prepare GM with a desired global packing fraction, and use empirical force measurements and the Discrete Element Method (DEM) to elucidate interaction mechanics during locomotion-relevant intrusions in GM such as vertical penetration and horizontal drag. We develop a resistive force theory (RFT) to account for more complex intrusions. We use these force models to understand the locomotor performance of two bio-inspired robots moving on and within GM. The sponsor was DARPA/SPAWAR N66001–05-C-8025. For further information, visit Kod*lab

Sand swimming lizard: sandfish

We use high-speed x-ray imaging to reveal how a small (~10cm) desert dwelling lizard, the sandfish (Scincus scincus), swims within a granular medium [1]. On the surface, the lizard uses a standard diagonal gait, but once below the surface, the organism no longer uses limbs for propulsion. Instead it propagates a large amplitude single period sinusoidal traveling wave down its body and tail to propel itself at speeds up to ~1.5 body-length/sec. Motivated by these experiments we study a numerical model of the sandfish as it swims within a validated soft sphere Molecular Dynamics granular media simulation. We use this model as a tool to understand dynamics like flow fields and forces generated as the animal swims within the granular media. [1] Maladen, R.D., Ding, Y., Li, C., and Goldman, D.I., Undulatory Swimming in Sand: Subsurface Locomotion of the Sandfish Lizard, Science, 325, 314, 2009NSF Physics of Living System

Biophysically inspired development of a sand-swimming robot

© 2011 MIT PressPresented at Robotics: Science and Systems (RSS) 2010, held at the University of Zaragoza in Spain, from June 27 to June 30, 2010.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

Predicting muscle forces of individuals with hemiparesis following stroke.

BackgroundFunctional electrical stimulation (FES) has been used to improve function in individuals with hemiparesis following stroke. An ideal functional electrical stimulation (FES) system needs an accurate mathematical model capable of designing subject and task-specific stimulation patterns. Such a model was previously developed in our laboratory and shown to predict the isometric forces produced by the quadriceps femoris muscles of able-bodied individuals and individuals with spinal cord injury in response to a wide range of clinically relevant stimulation frequencies and patterns. The aim of this study was to test our isometric muscle force model on the quadriceps femoris, ankle dorsiflexor, and ankle plantar-flexor muscles of individuals with post-stroke hemiparesis.MethodsSubjects were seated on a force dynamometer and isometric forces were measured in response to a range of stimulation frequencies (10 to 80-Hz) and 3 different patterns. Subject-specific model parameter values were obtained by fitting the measured force responses from 2 stimulation trains. The model parameters thus obtained were then used to obtain predicted forces for a range of frequencies and patterns. Predicted and measured forces were compared using intra-class correlation coefficients, r2 values, and model error relative to the physiological error (variability of measured forces).ResultsResults showed excellent agreement between measured and predicted force-time responses (r2 &gt;0.80), peak forces (ICCs&gt;0.84), and force-time integrals (ICCs&gt;0.82) for the quadriceps, dorsiflexor, and plantar-fexor muscles. The model error was within or below the +95% confidence interval of the physiological error for &gt;88% comparisons between measured and predicted forces.ConclusionOur results show that the model has potential to be incorporated as a feed-forward controller for predicting subject-specific stimulation patterns during FES