General scaling relations for locomotion in granular media

Slonaker, James; Motley, D. Carrington; Zhang, Qiong; Townsend, Stephen; Senatore, Carmine; Iagnemma, Karl; Kamrin, Ken

doi:10.1103/physreve.95.052901

Cited by 37 publications

(25 citation statements)

References 30 publications

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“…The motion of objects through wet granular materials consisting of athermal solids sedimented in a fluid medium is encountered in a range of chemical and food processing industries, besides the muddy bottoms of ponds and rivers [1,2]. In the quasi-static limit, the drag experienced by objects of various shapes, and their interactions, have been investigated in granular media to study fundamental granular physics and biolocomotion [3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Micromechanics of intruder motion in wet granular medium

2018

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We investigate the effective friction encountered by an intruder moving through a sedimented medium which consists of transparent granular hydrogels immersed in water, and the resulting motion of the medium. We show that the effective friction µ e on a spherical intruder is captured by the inertial number I given by the ratio of the time scale over which the intruder moves and the inertial time scale of the granular medium set by the overburden pressure. Further, µ e is described by the function µ e (I) = µ s + αI β , where µ s is the static friction, and α and β are material dependent constants which are independent of intruder depth and size. By measuring the mean flow of the granular component around the intruder, we find significant slip between the intruder and the granular medium. The motion of the medium is strongly confined near the intruder compared with a viscous Newtonian fluid and is of the order of the intruder size. The return flow of the medium occurs closer to the intruder as its depth is increased. Further, we study the reversible and irreversible displacement of the medium by not only following the medium as the intruder moves down but also while returning the intruder back up to its original depth. We find that the flow remains largely reversible in the quasi-static regime, as well as when µ e increases rapidly over the range of I probed. * akudrolli@clarku.edu 1 arXiv:1807.07833v1 [physics.flu-dyn] 20 Jul 2018Recently, it was demonstrated [21] that a sphere dragged through granular hydrogels immersed in water can be described by an effective friction which scales with inertial number I [22], and increases non-linearly from a non-zero static value. The form was found to be similar to that derived from the Herschel and Bulkley model [23], which is used to describe non-Newtonian fluids and muds [24]. Building on that study, we probe the dynamics of an intruder settling through granular hydrogels immersed in water as a model of wet granular medium or mud consisting of soft granular medium immersed in water. This is a much

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Section: Introductionmentioning

confidence: 99%

Micromechanics of intruder motion in wet granular medium

2018

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“…There is generally good agreement, but it is necessary to identify what granular media qualities are essential for a particular comparison. For example, there is very close experimental validation for recent developments in granular scaling laws for locomotion. This also serves to show another DEM strength not easily replicated: testing gravity variation, as it effects granular compaction in locomotion.…”

Section: Introductionmentioning

confidence: 87%

“…Recently, advancements have been made using continuum modeling, which treats granular media as a continuum uniform body . Evidence suggests that RFT and continuum approaches can be explained by plasticity theories and both have also been experimentally validated . In contrast, discrete element method (DEM) is a computational approach widely used for studying granular media.…”

Section: Introductionmentioning

confidence: 99%

Screw‐generated forces in granular media: Experimental, computational, and analytical comparison

2019

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This study presents an experimental, computational, and analytical comparison of a submerged, double‐helix Archimedes screw generating propulsive force against a bed of glass beads. Three screws of different pitch lengths were studied. Each screw was tested at six speeds in approximately 10 trials for a total of 180 experimental trials. These experiments were then replicated in EDEM, a discrete element method (DEM) software program. DEM simulation results for thrust forces in the 30–120 rpm regime had a 5%–20% inflation of forces compared to experimental results. These simulations were then compared with resistive force theory (RFT) plate approximation of the screw geometries. We analyze a superposition‐based partition approach to the full‐length screws as well as force generation in shortened, one‐ and two‐blade screws. We find that the force generation is dependent on the flow patterns and cannot be reduced to partitioned approximations as with simple intruders. © 2018 American Institute of Chemical Engineers AIChE J, 65: 894–903, 2019

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“…Bulk-behavior models of granular media developed for the purposes of modeling animal and robot locomotion characterize ground reaction forces in response to intrusion by a limb [9], [10]. In general, bulk-behavior models of the plastic flows of granular media are accurate when the size of the intruder far exceeds the size of the grains [11], and the results scale well with different sizes and masses of intruders [12]. Bulk-behavior models can now predict the terrain response with sufficient accuracy to allow optimal control methods to generate robot motion trajectories that result in jumps to a desired height [13], [14].…”

Section: B Previous Research Has Produced Bulk-behavior Models With mentioning

confidence: 99%

Reactive velocity control reduces energetic cost of jumping with a virtual leg spring on simulated granular media

Roberts

Koditschek²

2018

2018 IEEE International Conference on Robotics and Biomimetics (ROBIO)

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Robots capable of dynamic locomotion behaviors and high-bandwidth sensing with their limbs have a high cost of transport, especially when locomoting over highly dissipative substrates such as sand. We formulate the problem of reducing the energetic cost of locomotion by a Minitaur robot on sand, reacting to robot state variables in the inertial world frame without modeling the ground online. Using a bulkbehavior model of high-velocity intrusions into dry granular media, we simulated single jumps by a onelegged hopper using a Raibert-style compression-extension virtual leg spring. We compose this controller with a controller that added damping to the leg spring in proportion to the intrusion velocity of the robot's foot into the simulated sand while the robot is pushing off in the second half of stance. This has the effect of both reducing the torque exerted by the motors because the added virtual "active damping" force acts in opposition to the virtual leg spring force, and reducing the transfer of energy from the robot to the sand by slowing the intrusion velocity of the foot. Varying the simulated robot's initial conditions and the simulated ground parameters, we gained a consistent 20% energy savings by adding active damping with no cost in apex height. For more information, see the Kod*lab website: kodlab.seas.upenn.edu

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General scaling relations for locomotion in granular media

Cited by 37 publications

References 30 publications

Micromechanics of intruder motion in wet granular medium

Micromechanics of intruder motion in wet granular medium

Screw‐generated forces in granular media: Experimental, computational, and analytical comparison

Reactive velocity control reduces energetic cost of jumping with a virtual leg spring on simulated granular media

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