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Goldman, Daniel I.

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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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Mechanics of undulatory swimming in a frictional fluid

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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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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Effect of Volume Fraction on Granular Aavalanche Dynamics

2014 , Gravish, Nick , Goldman, Daniel I.

We study the evolution and failure of a granular slope as a function of prepared volume fraction, φ0. We rotated an initially horizontal layer of granular material (0.3-mm-diam glass spheres) to a 45◦ angle while we monitor the motion of grains from the side and top with high-speed video cameras. The dynamics of grain motion during the tilt process depended sensitively on φ0∈ [0.58–0.63] and differed above or below the granular critical state, φc, defined as the onset of dilation as a function of increasing volume fraction. For φ0−φc < 0, slopes experienced short, rapid, precursor compaction events prior to the onset of a sustained avalanche. Precursor compaction events began at an initial angle θ0 = 7.7 ± 1.4◦ and occurred intermittently prior to the onset of an avalanche. Avalanches occurred at the maximal slope angle θm =28.5 ± 1.0◦. Granular material at φ0 − φc > 0 did not experience precursor compaction prior to avalanche flow, and instead experienced a single dilational motion at θ0 = 32.1 ± 1.5◦ prior to the onset of an avalanche at θm = 35.9 ± 0.7◦. Both θ0 and θm increased with φ0 and approached the same value in the limit of random close packing. The angle at which avalanching grains came to rest, θR = 22 ± 2◦, was independent of φ0. From side-view high-speed video, we measured the velocity field of intermittent and avalanching flow. We found that flow direction, depth, and duration were affected by φ0, with φ0 − φc < 0 precursor flow extending deeper into the granular bed and occurring more rapidly than precursor flow at φ0 − φc > 0. Our study elucidates how initial conditions—including volume fraction—are important determinants of granular slope stability and the onset of avalanches.

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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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A terradynamics of legged locomotion on granular media

2013-03-22 , Li, Chen , Zhang, Tingnan , Goldman, Daniel I.

The theories of aero- and hydrodynamics predict animal movement and device design in air and water through the computation of lift, drag, and thrust forces. Although models of terrestrial legged locomotion have focused on interactions with solid ground, many animals move on substrates that flow in response to intrusion. However, locomotor-ground interaction models on such flowable ground are often unavailable. We developed a force model for arbitrarily-shaped legs and bodies moving freely in granular media, and used this “terradynamics" to predict a small legged robot's locomotion on granular media using various leg shapes and stride frequencies. Our study reveals a complex but generic dependence of stresses in granular media on intruder depth, orientation, and movement direction and gives insight into the effects of leg morphology and kinematics on movement

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