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Goldman, Daniel I.

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Simulation of compound anchor intrusion in dry sand by a hybrid FEM+SPH method

2022-09 , He, Haozhou , Karsai, Andras , Liu, Bangyuan , Hammond III, Frank L. , Goldman, Daniel I. , Arson, Chloé

The intrusion of deformable compound anchors in dry sand is simulated by coupling the Finite Element Method (FEM) with Smoothed Particle Hydrodynamics (SPH). This novel approach can calculate granular flows at lower computational cost than SPH alone. The SPH and FEM domains interact through reaction forces calculated from balance equations and are assigned the same soil constitutive model (Drucker-Prager) and the same constitutive parameters (measured or calibrated). Experimental force-displacement curves are reproduced for penetration depths of 8 mm or more (respectively, 20 mm or more) for spike-shaped (respectively, fan-shaped) anchors with 1 to 6 blades. As the number of blades increases, simulations reveal that the granular flow under the anchor deviates from the vertical and that the horizontal granular flow transitions from orthoradial to radial. We interpret the strain field distribution as the result of soil arching, i.e., the transfer of stress from a yielding mass of soil onto adjoining stationary soil masses. Arching is fully active when the radial distance between blade end points is less than a critical length. In that case, the normal stress that acts on the compound anchor at a given depth reaches the normal stress that acts on a disk-shaped anchor of same radius. A single-blade anchor produces soil deformation and failure similar to Prandtl’s foundation sliding model. Multiblade anchors produce a complex failure mechanism that combines sliding and arching.

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Robophysics: Physics Meets Robotics

2019-10-30 , Goldman, Daniel I.

Robots will soon move from the factory floor and into our lives (e.g., autonomous cars, package delivery drones, and search-and-rescue devices). However, compared to living systems, robot capabilities in complex environments are limited. I believe the mindset and tools of physics can help facilitate the creation of robust self-propelled autonomous systems. This “robophysics” approach – the systematic search for novel dynamics and principles in robotic systems – can aid the computer science and engineering approaches that have proven successful in less complex environments. The rapidly decreasing cost of constructing sophisticated robot models with easy access to significant computational power bodes well for such interactions. Drawing from examples in the work of my group and our collaborators, I will discuss how robophysical studies have inspired new physics questions in low dimensional dynamical systems (e.g., creation of analog quantum mechanics and gravity systems) and soft matter physics (e.g., emergent capabilities in ensembles of active “particles”). These studies have been useful to develop insight for biological locomotion in complex terrain (e.g., control targets via optimizing geometric phase) and have begun to aid engineers in the creation of devices that begin to achieve life-like locomotor abilities on and within complex environments (e.g., semi-soft myriapod robots).

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Tail use improves soft substrate performance in models of early vertebrate land locomotors

2016-05-27 , McInroe, Benjamin , Astley, Henry C. , Gong, Chaohui , Kawano, Sandy M. , Schiebel, Perrin E. , Rieser, Jennifer M. , Choset, Howie , Blob, Richard W. , Goldman, Daniel I.

In the evolutionary transition from an aquatic to a terrestrial environment, ancient vertebrates (e.g. early tetrapods) faced the challenges of terrestrial locomotion on flowable substrates (e.g. sand and mud) of variable stiffness and incline. While morphology and ranges of motion of appendages can be revealed in fossils, biological and robophysical studies of modern taxa demonstrate that movement on such substrates can be sensitive to small changes in appendage use. Using a biological model (the mudskipper), a physical model (a robot), granular drag measurements, and theoretical tools from geometric mechanics, we demonstrate how tail use can improve robustness to variable limb use and substrate conditions. We hypothesize that properly coordinated tail movements may have provided a substantial benefit for the earliest vertebrates to move on land.

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The Effectiveness of Resistive Force Theory in Granular Locomotion

2014 , Zhang, Tingnan , Goldman, Daniel I.

Resistive force theory (RFT) is often used to analyze the movement of microscopic organisms swimming in fluids. In RFT, a body is partitioned into infinitesimal segments, each of which generates thrust and experiences drag. Linear superposition of forces from elements over the body allows prediction of swimming velocities and efficiencies. We show that RFT quantitatively describes the movement of animals and robots that move on and within dry granular media (GM), collections of particles that display solid, fluid, and gas-like features. RFT works well when the GM is slightly polydisperse, and in the “frictional fluid” regime such that frictional forces dominate material inertial forces, and when locomotion can be approximated as confined to a plane. Within a given plane (horizontal or vertical) relationships that govern the force versus orientation of an elemental intruder are functionally independent of the granular medium. We use the RFT to explain features of locomotion on and within granular media including kinematic and muscle activation patterns during sand-swimming by a sandfish lizard and a shovel-nosed snake, optimal movement patterns of a Purcell 3-link sand-swimming robot revealed by a geometric mechanics approach, and legged locomotion of small robots on the surface of GM. We close by discussing situations to which granular RFT has not yet been applied (such as inclined granular surfaces), and the advances in the physics of granular media needed to apply RFT in such situations.

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Data for 'Locomotion without force, and impulse via dissipation: Robotic swimming in curved space via geometric phase'

2022 , Li, Shengkai , Wang, Tianyu , Kojouharov, Velin H. , McInerney, James , Aydin, Enes , Aydin, Yasemin O. , Goldman, Daniel I. , Rocklin, D. Zeb

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Tracked data for Chionactis occipitalis through a post array

2019-01-25 , Schiebel, Perrin E. , Rieser, Jennifer M. , Hubbard, Alex M. , Chen, Lillian , Rocklin, D. Zeb , Goldman, Daniel I.

Limbless animals like snakes inhabit most terrestrial environments, generating thrust to overcome drag on the elongate body via contacts with heterogeneities. The complex body postures of some snakes and the unknown physics of most terrestrial materials frustrates understanding of strategies for effective locomotion. As a result, little is known about how limbless animals contend with unplanned obstacle contacts. We studied a desert snake, Chionactis occipitalis, which uses a stereotyped head-to-tail traveling wave to move quickly on homogeneous sand. In laboratory experiments, we challenged snakes to move across a uniform substrate and through a regular array of force sensitive posts. The snakes were reoriented by the array in a manner reminiscent of the matter-wave diffraction of subatomic particles. Force patterns indicated the animals did not change their self-deformation pattern to either avoid or grab the posts. A model using open-loop control incorporating previously described snake muscle activation patterns and body-buckling dynamics reproduced the observed patterns, suggesting a similar control strategy may be used by the animals. Our results reveal how passive dynamics can benefit limbless locomotors by allowing robust transit in heterogeneous environments with minimal sensing.

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Force and flow at the onset of drag in plowed granular media

2014 , Gravish, Nick , Umbanhowar, Paul B. , Goldman, Daniel I.

We study the transient drag force F[subscript D] on a localized intruder in a granular medium composed of spherical glass particles. A flat plate is translated horizontally from rest through the granular medium to observe how F[subscript D] varies as a function of the medium’s initial volume fraction, φ. The force response of the granular material differs above and below the granular critical state, φ[subscript c], the volume fraction which corresponds to the onset of grain dilatancy. For φ<φ[subscript c] F[subscript D] increases monotonically with displacement and is independent of drag velocity for the range of velocities examined (<10 cm/s). For φ>φ[subscript c], F[subscript D] rapidly rises to a maximum and then decreases over further displacement. The maximum force for φ>φ[subscript c] increases with increasing drag velocity. In quasi-two-dimensional drag experiments, we use granular particle image velocimetry (PIV) to measure time resolved strain fields associated with the horizontal motion of a plate started from rest. PIV experiments show that the maxima in F[subscript D] for φ>φ[subscript c] are associated with maxima in the spatially averaged shear strain field. For φ>φ[subscript c] the shear strain occurs in a narrow region in front of the plate, a shear band. For φ<φ[subscript c] the shear strain is not localized, the shear band fluctuates in space and time, and the average shear increases monotonically with displacement. Laser speckle measurements made at the granular surface ahead of the plate reveal that for φ<φ[subscript c] particles are in motion far from the intruder and shearing region. For φ>φ[subscript c], surface particles move only during the formation of the shear band, coincident with the maxima in F[subscript D], after which the particles remain immobile until the sheared region reaches the measurement region.

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Comparative study of snake lateral undulation kinematics in model heterogeneous terrain dataset

2020-09-24 , Schiebel, Perrin E. , Hubbard, Alex M. , Goldman, Daniel I.

Terrestrial organisms that use traveling waves to locomote must leverage heterogeneities to overcome drag on the elongate body. While previous studies illuminated how habitat generalist snakes self-deform to use rigid obstacles in the surroundings, control strategies for multi-component terrain are largely unknown. We compared the sand-specialist Chionactis occipitalis to a habitat generalist, Pantherophis guttatus, navigating a model terrestrial terrain-rigid post arrays on a low-friction substrate. We found the waveshapes used by the generalist were more variable than the specialist. Principal component analysis revealed that while the specialized sand-swimming waveform was always present on C. occipitalis, the generalist did not have a similarly pervasive low-dimensional waveshape. We expected the generalist to thus outperform the specialist in the arrays, but body slip of both species was comparable on level ground and in all trials the snakes successfully traversed the arena. When we further challenged the snakes to ascend an inclined lattice, the sand-specialist had difficulty maintaining contact with the obstacles and was unable to progress up the steepest inclines in the largest lattice spacings. Our results suggest that species adapted to different habitats use different control modalities-the specialist is primarily controlling its kinematics to achieve a target shape while, consistent with previous research, the generalist is using force control and self-deforms in response to terrain contacts. While both strategies allowed progress on the uninclined low-friction terrain with posts, the more variable waveshapes of the generalist may be necessary when faced with more challenging locomotor tasks like climbing inclines.

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Mitigating memory effects during undulatory locomotion on hysteretic materials dataset

2019 , Schiebel, Perrin E. , Rieser, Jennifer M. , Astley, Henry C. , Agarwall, S. , Hubicki, C. , Hubbard, Alex M. , Cruz, K. , Mendelson, J. , Kamrin, K. , Goldman, Daniel I.

Undulatory swimming in flowing media like water is well studied, but little is known about locomotion in environments that are permanently deformed by body-substrate interactions like snakes in sand, eels in mud, and nematode worms in rotting fruit. We study the desert-specialist snake Chionactis occipitalis traversing granular matter and find body inertia is negligible despite rapid transit. New surface resistive force theory (RFT) calculation reveals this snake's waveform minimizes material memory effects and optimizes speed given anatomical limitations (power). RFT explains the morphology and waveform dependent performance of a diversity of non-sand-specialists, but over-predicts the capability of snakes with high slip. Robophysical experiments recapitulate aspects of these failure-prone snakes, elucidating how reencountering previously remodeled material hinders performance. This study reveals how memory effects stymied the locomotion of snakes in our previous study [Marvi et al, Science, 2014] and suggests the existence of a predictive model for history-dependent locomotion.

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Colloquium: Biophysical principles of undulatory self-propulsion in granular media

2014 , Goldman, Daniel I.

Biological locomotion, movement within environments through self-deformation, encompasses a range of time and length scales in an organism. These include the electrophysiology of the nervous system, the dynamics of muscle activation, the mechanics of the skeletal system, and the interaction mechanics of such structures within natural environments like water, air, sand, and mud. Unlike the many studies of cellular and molecular scale biophysical processes, movement of entire organisms (like flies, lizards, and snakes) is less explored. Further, while movement in fluids like air and water is also well studied, little is known in detail of the mechanics that organisms use to move on and within flowable terrestrial materials such as granular media, ensembles of small particles that collectively display solid, fluid, and gaslike behaviors. This Colloquium reviews recent progress to understand principles of biomechanics and granular physics responsible for locomotion of the sandfish, a small desert-dwelling lizard that “ swims” within sand using undulation of its body. Kinematic and muscle activity measurements of sand swimming using high speed x-ray imaging and electromyography are discussed. This locomotion problem poses an interesting challenge: namely, that equations that govern the interaction of the lizard with its environment do not yet exist. Therefore, complementary modeling approaches are also described: resistive force theory for granular media, multiparticle simulation modeling, and robotic physical modeling. The models reproduce biomechanical and neuromechanical aspects of sand swimming and give insight into how effective locomotion arises from the coupling of the body movement and flow of the granular medium. The argument is given that biophysical study of movement provides exciting opportunities to investigate emergent aspects of living systems that might not depend sensitively on biological details.

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