Granular lift forces predict vertical motion of a sand-swimming robot

Maladen, Ryan D.; Umbanhowar, Paul B.; Ding, Yanheng; Masse, Andrew; Goldman, Daniel I.

doi:10.1109/icra.2011.5980301

Cited by 28 publications

(27 citation statements)

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“…The prediction of locomotor performance in relation to features of body morphology (body shape, skin properties and limb number) is a topic of interest from bio/neuromechanical (Aristotle, 350 BCE; Dayton et al, 2005;Gans, 1975;Mosauer, 1932;Russell, 1917;Tytell et al, 2010;Wainwright and Reilly, 1994) and robotic perspectives (Brooks, 1992;Lauder et al, 2007;Maladen et al, 2011a;Maladen et al, 2011c;Pfeifer et al, 2007;Yim et al, 2007). From an evolutionary perspective, it is important to quantitatively address questions associated with putative selective pressures for locomotor apparatus and bauplans in different environments (Lauder, 1981;Lauder and Drucker, 2004;Walker and Westneat, 2000).…”

Section: Introductionmentioning

confidence: 99%

Locomotor benefits of being a slender and slick sand-swimmer

Sharpe

Koehler

Kuckuk

et al. 2014

Journal of Experimental Biology

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There was an error published in J. Exp. Biol. 218,[440][441][442][443][444][445][446][447][448][449][450] In Fig. 5 of this paper, there was a mistake in the theoretical calculation of the average slip angle, b s . The corrected calculations show that b s rises more sharply for low mean relative curvatures and approaches 90 deg. This change does not affect the conclusions set forth in the original paper, and shows better agreement with the experimental findings.The corrected figure is reproduced below:The authors apologise for any inconvenience this may have caused. b s ) with changing mean relative curvature (kl s ), average number of undulations along the body ( j), body length to width ratio (L/w) and effective friction. Force relationships were established from empirical drag data in loosely packed (LP) media. The color of the curves and experimental data correspond to different j (where dark blue is j=0, dark red is j=5). Solid curves are predictions for an undulatory swimmer with a L/w=7.1 and body-particle friction, m s , of 0.17. The dotted-dashed curves show the theoretical predictions with L/w=33.5 and m s =0.17. The dashed curves are the predictions for L/w=33.5 and half the tangential force (which occurs when there is a 50% decrease in body-particle friction, i.e. ABSTRACT Squamates classified as 'subarenaceous' possess the ability to move long distances within dry sand; body elongation among sand and soil burrowers has been hypothesized to enhance subsurface performance. Using X-ray imaging, we performed the first kinematic investigation of the subsurface locomotion of the long, slender shovel-nosed snake (Chionactis occipitalis) and compared its biomechanics with those of the shorter, limbed sandfish lizard (Scincus scincus). The sandfish was previously shown to maximize swimming speed and minimize the mechanical cost of transport during burial. Our measurements revealed that the snake also swims through sand by propagating traveling waves down the body, head to tail. Unlike the sandfish, the snake nearly followed its own tracks, thus swimming in an approximate tube of self-fluidized granular media. We measured deviations from tube movement by introducing a parameter, the local slip angle, β s , which measures the angle between the direction of movement of each segment and body orientation. The average β s was smaller for the snake than for the sandfish; granular resistive force theory (RFT) revealed that the curvature utilized by each animal optimized its performance. The snake benefits from its slender body shape (and increased vertebral number), which allows propagation of a higher number of optimal curvature body undulations. The snake's low skin friction also increases performance. The agreement between experiment and RFT combined with the relatively simple properties of the granular 'frictional fluid' make subarenaceous swimming an attractive system to study functional morphology and bauplan evolution.

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Section: Introductionmentioning

confidence: 99%

Locomotor benefits of being a slender and slick sand-swimmer

Sharpe

Koehler

Kuckuk

et al. 2014

Journal of Experimental Biology

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“…Changes in muscle activation pattern do not always reflect internal force changes and such models can be used to estimate forces during sand-swimming. In addition, our sandfishinspired robotic model can be used to test neuromechanical control strategies in real-world granular environments (Maladen et al, 2011c). For example, we can change morphology and passive stiffness to test how they would affect neuromechanical phase lags.…”

Section: Discussionmentioning

confidence: 99%

“…Also, control systems that modify the robotic model's motor output based on the resistive force can be implemented to optimally change gait with varying conditions. These biologically inspired activation strategies can also give insight into challenges associated with the movement of robots through complex terrain (Choset et al, 2005;Maladen et al, 2011b;Maladen et al, 2011c). average forward speed η wave efficiency -the ratio of the average forward speed of the animal to the speed of the kinematic traveling wave θ d angle of descent -angle between horizontal and the best linear fit to the positions of all tracked dorsal markers during the subsurface descent λ wavelength of the sinusoidal wave ϕ volume fraction -the ratio of the solid volume of the grains to the total occupied volume…”

Section: Discussionmentioning

confidence: 99%

“…Korta and colleagues found that mechanosensory input may act to regulate this temporal frequency and allow gait adaptation in response to different surroundings (Korta et al, 2007). Studies of our sandfish models (Maladen et al, 2011a;Maladen et al, 2011b;Maladen et al, 2011c) could be used to determine the extent of muscle power reduction as a result of decreasing frequency with depth for a sandswimmer.…”

Section: Depth Dependencementioning

confidence: 99%

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Environmental interaction influences muscle activation strategy during sand-swimming in the sandfish lizard Scincus scincus

Sharpe

Ding

Goldman

2013

Journal of Experimental Biology

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SUMMARYAnimals like the sandfish lizard (Scincus scincus) that live in desert sand locomote on and within a granular medium whose resistance to intrusion is dominated by frictional forces. Recent kinematic studies revealed that the sandfish utilizes a wave of body undulation during swimming. Models predict that a particular combination of wave amplitude and wavelength yields maximum speed for a given frequency, and experiments have suggested that the sandfish targets this kinematic waveform. To investigate the neuromechanical strategy of the sandfish during walking, burial and swimming, here we use high-speed X-ray and visible light imaging with synchronized electromyogram (EMG) recordings of epaxial muscle activity. While moving on the surface, body undulation was not observed and EMG showed no muscle activation. During subsurface sand-swimming, EMG revealed an anterior-to-posterior traveling wave of muscle activation which traveled faster than the kinematic wave. Muscle activation intensity increased as the animal swam deeper into the material but was insensitive to undulation frequency. These findings were in accord with empirical force measurements, which showed that resistance force increased with depth but was independent of speed. The change in EMG intensity with depth indicates that the sandfish targets a kinematic waveform (a template) that models predict maximizes swimming speed and minimizes the mechanical cost of transport as the animal descends into granular media. The differences in the EMG pattern compared with EMG of undulatory swimmers in fluids can be attributed to the friction-dominated intrusion forces of granular media. Supplementary material available online at

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“…The reason we use this dynamic friction coefficient is that the flow induced by the inclined plate is not quasi-static. In references [14][15] , they showed that the effective friction coefficient depends on the inertial number, ( )…”

Section: Resultsmentioning

confidence: 99%

A Continuum Model of Drag and Lift Forces for Inclined Planes Dragged Through Granular Beds

Guo¹,

Fu²,

Guo³

et al. 2019

Preprint

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Both drag and lift forces impact an inclined plane when it is dragged through a granular bed. In this paper, the following results have been obtained: the drag and lift forces grow with the velocity of motion; when the immersion depth is constant, the inclination angle has no effect on drag force, however, the lift force increases linearly with this inclination angle; the ratio of drag and lift forces is exactly equal to the tangent value of the inclined angle. In order to describe this physical process macroscopically, a continuum wedge model based on the Coulomb model is established to predict drag and lift forces. Particularly，the dynamic friction angle in the assumed shear band is predicted as a function of both inclined angle and moving velocity.

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Granular lift forces predict vertical motion of a sand-swimming robot

Cited by 28 publications

References 28 publications

Locomotor benefits of being a slender and slick sand-swimmer

Locomotor benefits of being a slender and slick sand-swimmer

Environmental interaction influences muscle activation strategy during sand-swimming in the sandfish lizard Scincus scincus

A Continuum Model of Drag and Lift Forces for Inclined Planes Dragged Through Granular Beds

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