Mechanical models of sandfish locomotion reveal principles of high performance subsurface sand-swimming

Are toe fringes important for lizard burying in highly mobile sand?

Toe fringes are a key innovation for sand dwelling lizards, and the relationship between toe fringe function and substrate properties is helpful in understanding the adaptation of lizards to sand dune environments. We tested the sand burial performance of Phrynocephalus mystaceus on different sand substrates with toe fringe manipulation, with the aim of assessing whether the function of the toe fringes shifts under different substrate properties, especially in highly mobile substrates. The sand burial performance of P. mystaceus was influenced by substrate properties in relation to the toe fringe states of the lizard. After removal of the bilateral toe fringes, the sand burial ability score of P. mystaceus was significantly higher on sand substrates below 100 mesh than on native sand substrates. As the angle of stability of the substrate properties decreased, the sand burial performance of the lizard was even better after the bilateral toe fringes were removed. The results of the LASSO model and the path analysis model showed that the stability angle provided the opposite effect on sand burial performance in different toe fringe states. These results further suggest that the sand burial function of toe fringes may not be suitable for highly mobile sand substrates. It remains to be tested further whether the function of toe fringes is more important for running on sand.

Active Adaptive Strategies of Mallard Feet in Response to Changes in Wetness and Compactness of the Sand Terrain

Mallards (Anas platyrhynchos) exhibit exceptional locomotive abilities in diverse terrains, such as beaches, swamps, and tidal flats. This capability is primarily attributed to their unique webbed toe structure and cooperative locomotion posture of their feet. Therefore, this study aims to further delve into the active adaptive strategies of mallard feet in response to diverse external environmental conditions. Six adult male mallards were selected for this research. Their locomotion on sandy surfaces with differing wetness levels and varying degrees of compaction were captured using a high-speed camera, and analysis of instantaneous and continuous changes in the primary joint angles of the mallards' feet, including the toe-webbed opening and closing angles, the tarsometatarsal-phalangeal joint (TMTPJ), and the intertarsal joint (ITJ). It was found that on loose sandy surfaces, increasing wetness expanded the ground contact area of the mallards' feet. This led to greater flexion at the TMTPJ joint during mid-stance, accompanied by decreased flexion of the ITJ during touch-down and mid-stance. Conversely, on compacted sand, increasing wetness resulted in a reduced foot effect area and lessened ITJ flexion at both touch-down and mid-stance. Furthermore, on looser sand, the ground contact area of the mallards' feet decreased, with an increase in ITJ buckling at touch-down. During the swing phase, sand wetness and compactness effected minimally on the feet of the mallards. On dry and loose sand ground, mallards will contract their second and fourth toes with webbing upon ground contact, covering and compacting the sand beneath, while increasing ITJ flexion to mitigate sinking. This adaptation reduces the energy expended on sand and enhances body stability. In wet and compacted sand conditions, mallards expand their second and fourth toes upon ground contact and reduce ITJ flexion. Therefore, this coordinated foot and ITJ locomotion offers mallards a natural advantage when moving on various environmental media.

Influence of the frequency on undulatory swimming speed in granular media

Sand is a highly dissipative system, where the local spatial arrangements and densities depend strongly on the applied forces, resulting in fluid-like or solid-like behaviour. This makes sand swimming challenging and intriguing, raising questions about the nature of the motion and how to optimize the design of artificial swimmers able to swim in sand. Recent experiments suggest that lateral undulatory motion enables efficient locomotion, with a non-monotonic dependence of the swimming speed on the undulatory frequency and the height of the sediment bed. Here, we propose a 2D granular model, where the effect of the sediment height is modeled by an effective frictional force with the substrate. We show that the optimal frequency coincides with the second vibrational mode of the swimmer and explain the underlying mechanism through a characterization of the rheology of the medium. Potential implications in the design of artificial swimmers are discussed.

Geometric phase predicts locomotion performance in undulating living systems across scales

Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar traveling waves of axial body bending for movement. Delineating how self-deformation parameters lead to locomotor performance (e.g. speed, energy, turning capabilities) remains challenging. We show that a geometric framework, replacing laborious calculation with a diagrammatic scheme, is well-suited to discovery and comparison of effective patterns of wave dynamics in diverse living systems. We focus on a regime of undulatory locomotion, that of highly damped environments, which is applicable not only to small organisms in viscous fluids, but also larger animals in frictional fluids (sand) and on frictional ground. We find that the traveling wave dynamics used by mm-scale nematode worms and cm-scale desert dwelling snakes and lizards can be described by time series of weights associated with two principal modes. The approximately circular closed path trajectories of mode weights in a self-deformation space enclose near-maximal surface integral (geometric phase) for organisms spanning two decades in body length. We hypothesize that such trajectories are targets of control (which we refer to as "serpenoid templates"). Further, the geometric approach reveals how seemingly complex behaviors such as turning in worms and sidewinding snakes can be described as modulations of templates. Thus, the use of differential geometry in the locomotion of living systems generates a common description of locomotion across taxa and provides hypotheses for neuromechanical control schemes at lower levels of organization.

The environment to the rescue: can physics help predict predator-prey interactions?

Understanding the factors that determine the occurrence and strength of ecological interactions under specific abiotic and biotic conditions is fundamental since many aspects of ecological community stability and ecosystem functioning depend on patterns of interactions among species. Current approaches to mapping food webs are mostly based on traits, expert knowledge, experiments, and/or statistical inference. However, they do not offer clear mechanisms explaining how trophic interactions are affected by the interplay between organism characteristics and aspects of the physical environment, such as temperature, light intensity or viscosity. Hence, they cannot yet predict accurately how local food webs will respond to anthropogenic pressures, notably to climate change and species invasions. Herein, we propose a framework that synthesises recent developments in food-web theory, integrating body size and metabolism with the physical properties of ecosystems. We advocate for combination of the movement paradigm with a modular definition of the predation sequence, because movement is central to predator-prey interactions, and a generic, modular model is needed to describe all the possible variation in predator-prey interactions. Pending sufficient empirical and theoretical knowledge, our framework will help predict the food-web impacts of well-studied physical factors, such as temperature and oxygen availability, as well as less commonly considered variables such as wind, turbidity or electrical conductivity. An improved predictive capability will facilitate a better understanding of ecosystem responses to a changing world.

Simulation and Structural Analysis of a Flexible Coupling Bionic Desorption Mechanism Based on the Engineering Discrete Element Method

Soil adhesion is one of the important factors affecting the working stability and quality of agricultural machinery. The application of bionic non-smooth surfaces provides a novel idea for soil anti-adhesion. The parameters of sandy loam with 21% moisture content were calibrated by the Engineering Discrete Element Method (EDEM). The final simulated soil repose angle was highly consistent with the measured soil repose angle, and the obtained regression equation of the soil repose angle provides a numerical reference for the parameter calibration of different soils. By simulating the sinusoidal swing of a sandfish, it was found that the contact interface shows the phenomenon of stress concentration and periodic change, which reflects the effectiveness of flexible desorption and soil anti-adhesion. The moving resistance of the wedge with different wedge angles and different serrated structures was simulated. Finally, it was found that a 40° wedge with a high-tail sparse staggered serrated structure on the surface has the best drag reduction effect, and the drag reduction is about 10.73%.

Functional diversity of snake locomotor behaviors: A review of the biological literature for bioinspiration

Organismal solutions to natural challenges can spark creative engineering applications. However, most engineers are not experts in organismal biology, creating a potential barrier to maximally effective bioinspired design. In this review, we aim to reduce that barrier with respect to a group of organisms that hold particular promise for a variety of applications: snakes. Representing >10% of tetrapod vertebrates, snakes inhabit nearly every imaginable terrestrial environment, moving with ease under many conditions that would thwart other animals. To do so, they employ over a dozen different types of locomotion (perhaps well over). Lacking limbs, they have evolved axial musculoskeletal features that enable their vast functional diversity, which can vary across species. Different species also have various skin features that provide numerous functional benefits, including frictional anisotropy or isotropy (as their locomotor habits demand), waterproofing, dirt shedding, antimicrobial properties, structural colors, and wear resistance. Snakes clearly have much to offer to the fields of robotics and materials science. We aim for this review to increase knowledge of snake functional diversity by facilitating access to the relevant literature.

DROD: bio-robotic drill/sampler for planetary subterranean exploration: experiments and challenges

Key features for space exploration equipment, and in particular drills and sampling mechanisms, are low weight, small size, and energy efficiency. These characteristics are substantially required not only in reducing the spaceship flight cost, but also in extending the exploration time on the extraterrestrial bodies. This article experimentally investigates the feasibility of a novel drill bioinspired by wood-wasp and sand-fish lizard as an integrated robotic solution for rover exploration tasks. A new penetration depth of 820 mm in terms of reciprocation drilling technique has been achieved by the proposed dual reciprocation and oscillation drill (DROD), especially with the new enhancements such as miniature sample compartment and toothed stems. Additionally, a first sampling experiment with DROD has been performed and a sample amount of 20 g and size of 30 cm3has been collected successfully. Finally, the article provides developments for integration of DROD with rovers for future exploration missions and potentials for horizontal drilling for subterranean applications.

Radial Expansion Favors the Burrowing Behavior of Urechis unicinctus

Urechis unicinctus can utilize the ability of large deformation to advance in sands by radial expansion, just using a small force. However, the large deformation of U. unicinctus skin and the discrete nature of the sands make it hard to analyze this process quantitatively. In this study, we aim to uncover the burrowing mechanism of U. unicinctus in granular sediments by combining discrete and finite elements. We observe that U. unicinctus will expand radially at the head, and then the head will shrink to move forward. The radial expansion will collapse the sands and let them flow, making it easy to advance. U. unicinctus mainly relies on the skin's large deformation and sufficient pressure to achieve radial expansion. Thus, we first establish the large deformation constitutive model of the skin. The stress-strain relationship can be expressed by the Yeoh model. Meanwhile, the pressure required for radial expansion is indirectly measured by the balloon experiment. To study the effect of radial expansion on the burrowing behavior, we use the finite element method-discrete element method (FEM-DEM) coupling model to simulate the expansion process of burrowing. The simulated pressure for radial expansion is very close to the experimental data, verifying the reliability of the simulation. The results show that the expansion can drastically reduce the pressure of sand particles on the head front face by 97.1% ± 0.6%, significantly decreasing the difficulty of burrowing. This unique underwater burrow method of U. unicinctus can provide new ideas for engineering burrowing devices in soft soil, especially for granular sediments.

Schrödinger Dynamics and Berry Phase of Undulatory Locomotion

Spectral mode representations play an essential role in various areas of physics, from quantum mechanics to fluid turbulence, but they are not yet extensively used to characterize and describe the behavioral dynamics of living systems. Here, we show that mode-based linear models inferred from experimental live-imaging data can provide an accurate low-dimensional description of undulatory locomotion in worms, centipedes, robots, and snakes. By incorporating physical symmetries and known biological constraints into the dynamical model, we find that the shape dynamics are generically governed by Schrödinger equations in mode space. The eigenstates of the effective biophysical Hamiltonians and their adiabatic variations enable the efficient classification and differentiation of locomotion behaviors in natural, simulated, and robotic organisms using Grassmann distances and Berry phases. While our analysis focuses on a widely studied class of biophysical locomotion phenomena, the underlying approach generalizes to other physical or living systems that permit a mode representation subject to geometric shape constraints.

Maneuvering on non-Newtonian fluidic terrain: a survey of animal and bio-inspired robot locomotion techniques on soft yielding grounds

Frictionally yielding media are a particular type of non-Newtonian fluids that significantly deform under stress and do not recover their original shape. For example, mud, snow, soil, leaf litters, or sand are such substrates because they flow when stress is applied but do not bounce back when released. Some robots have been designed to move on those substrates. However, compared to moving on solid ground, significantly fewer prototypes have been developed and only a few prototypes have been demonstrated outside of the research laboratory. This paper surveys the existing biology and robotics literature to analyze principles of physics facilitating motion on yielding substrates. We categorize animal and robot locomotion based on the mechanical principles and then further on the nature of the contact: discrete contact, continuous contact above the material, or through the medium. Then, we extract different hardware solutions and motion strategies enabling different robots and animals to progress. The result reveals which design principles are more widely used and which may represent research gaps for robotics. We also discuss that higher level of abstraction helps transferring the solutions to the robotics domain also when the robot is not explicitly meant to be bio-inspired. The contribution of this paper is a review of the biology and robotics literature for identifying locomotion principles that can be applied for future robot design in yielding environments, as well as a catalog of existing solutions either in nature or man-made, to enable locomotion on yielding grounds.

Self-propulsion via slipping: Frictional swimming in multilegged locomotors

Locomotion is typically studied either in continuous media where bodies and legs experience forces generated by the flowing medium or on solid substrates dominated by friction. In the former, centralized whole-body coordination is believed to facilitate appropriate slipping through the medium for propulsion. In the latter, slip is often assumed minimal and thus avoided via decentralized control schemes. We find in laboratory experiments that terrestrial locomotion of a meter-scale multisegmented/legged robophysical model resembles undulatory fluid swimming. Experiments varying waves of leg stepping and body bending reveal how these parameters result in effective terrestrial locomotion despite seemingly ineffective isotropic frictional contacts. Dissipation dominates over inertial effects in this macroscopic-scaled regime, resulting in essentially geometric locomotion on land akin to microscopic-scale swimming in fluids. Theoretical analysis demonstrates that the high-dimensional multisegmented/legged dynamics can be simplified to a centralized low-dimensional model, which reveals an effective resistive force theory with an acquired viscous drag anisotropy. We extend our low-dimensional, geometric analysis to illustrate how body undulation can aid performance in non-flat obstacle-rich terrains and also use the scheme to quantitatively model how body undulation affects performance of biological centipede locomotion (the desert centipede Scolopendra polymorpha) moving at relatively high speeds (∼0.5 body lengths/sec). Our results could facilitate control of multilegged robots in complex terradynamic scenarios.

Fundamentals of burrowing in soft animals and robots

Creating burrows through natural soils and sediments is a problem that evolution has solved numerous times, yet burrowing locomotion is challenging for biomimetic robots. As for every type of locomotion, forward thrust must overcome resistance forces. In burrowing, these forces will depend on the sediment mechanical properties that can vary with grain size and packing density, water saturation, organic matter and depth. The burrower typically cannot change these environmental properties, but can employ common strategies to move through a range of sediments. Here we propose four challenges for burrowers to solve. First, the burrower has to create space in a solid substrate, overcoming resistance by e.g., excavation, fracture, compression, or fluidization. Second, the burrower needs to locomote into the confined space. A compliant body helps fit into the possibly irregular space, but reaching the new space requires non-rigid kinematics such as longitudinal extension through peristalsis, unbending, or eversion. Third, to generate the required thrust to overcome resistance, the burrower needs to anchor within the burrow. Anchoring can be achieved through anisotropic friction or radial expansion, or both. Fourth, the burrower must sense and navigate to adapt the burrow shape to avoid or access different parts of the environment. Our hope is that by breaking the complexity of burrowing into these component challenges, engineers will be better able to learn from biology, since animal performance tends to exceed that of their robotic counterparts. Since body size strongly affects space creation, scaling may be a limiting factor for burrowing robotics, which are typically built at larger scales. Small robots are becoming increasingly feasible, and larger robots with non-biologically-inspired anteriors (or that traverse pre-existing tunnels) can benefit from a deeper understanding of the breadth of biological solutions in current literature and to be explored by continued research.

Mechanistic framework for reduced-order models in soft materials: Application to three-dimensional granular intrusion

Soft materials often display complex behaviors that transition through apparent solid- and fluid-like regimes. While a growing number of microscale simulation methods exist for these materials, reduced-order models that encapsulate the macroscale physics are often desired to predict how external bodies interact with soft media. Such an approach could provide direct insights in diverse situations from impact and penetration problems to locomotion over natural terrains. This work proposes a systematic program to develop three-dimensional (3D) reduced-order models for soft materials from a fundamental basis using continuum symmetries and rheological principles. In particular, we derive a reduced-order, 3D resistive force theory (3D-RFT), which is capable of accurately and quickly predicting the resistive stress distribution on arbitrary-shaped bodies intruding through granular media. Aided by a continuum description of the granular medium, a comprehensive set of spatial symmetry constraints, and a limited amount of reference data, we develop a self-consistent and accurate 3D-RFT. We verify the model capabilities in a wide range of cases and show that it can be quickly recalibrated to different media and intruder surface types. The premises leading to 3D-RFT anticipate application to other soft materials with strongly hyperlocalized intrusion behavior.

Fabrication, control, and modeling of robots inspired by flagella and cilia

Flagella and cilia are slender structures that serve important functionalities in the microscopic world through their locomotion induced by fluid and structure interaction. With recent developments in microscopy, fabrication, biology, and modeling capability, robots inspired by the locomotion of these organelles in low Reynolds number flow have been manufactured and tested on the micro-and macro-scale, ranging from medicalin vivomicrobots, microfluidics to macro prototypes. We present a collection of modeling theories, control principles, and fabrication methods for flagellated and ciliary robots.

Lateral bending and buckling aids biological and robotic earthworm anchoring and locomotion

Earthworms (Lumbricus terrestris) are characterized by soft, highly flexible and extensible bodies, and are capable of locomoting in most terrestrial environments. Previous studies of earthworm movement focused on the use of retrograde peristaltic gaits in which controlled contraction of longitudinal and circular muscles results in waves of shortening/thickening and thinning/lengthening of the hydrostatic skeleton. These waves can propel the animal across ground as well as into soil. However, worms benefit from axial body bends during locomotion. Such lateral bending and buckling dynamics can aid locomotor function via hooking/anchoring (to provide propulsion), modify travel orientation (to avoid obstacles and generate turns) and even generate snake-like undulatory locomotion in environments where peristaltic locomotion results in poor performance. To the best of our knowledge, lateral bending and buckling of an earthworm's body has not yet been systematically investigated. In this study, we observed that within confined environments, worms use lateral bending and buckling to anchor their body to the walls of their burrows and tip (anterior end) bending to search the environment. This locomotion strategy improved the performance of our soft-bodied robophysical model of the earthworm both in a confined (in an acrylic tube) and above-ground heterogeneous environment (rigid pegs), where present peristaltic robots are relatively limited in terradynamic capabilities. In summary, lateral bending and buckling facilitates the mobility of earthworm locomotion in diverse terrain and can play an important role in the creation of low cost soft robotic devices capable of traversing a variety of environments.

The ocellate river stingray (Potamotrygon motoro) exploits vortices of sediment to bury into the substrate

Particle image velocimetry and video analysis were employed to determine the pectoral-fin mechanism used by the stingray Potamotrygon motoro to bury into sand. Rapid oscillations of the body and folding motions of the posterior portion of the pectoral fin suspended sediment beneath the pectoral disc and directed vortices of sediment onto the dorsal surface, where they dissipated and the sediment settled. Body coverage was increased by increased fin displacement and speed and also by the occasional collision of vortices that redirected sediment flow towards the head and tail.

Pivot burrowing of scarab beetle (Trypoxylus dichotomus) larva

Many organisms live in the soil but only a little is known about their ecology especially movement style. Scarab beetle larvae do not have appendages to shovel soil and their trunk is thick compared to their body length. Hence, their movement through the soil is perplexing. Here, we established the observation and analysis system of larval movement and found that the last larval instars of Trypoxylus dichotomus burrow in two different ways, depending on the hardness of the soil. If the soil is soft, the larvae keep their body in a straight line and use longitudinal expansion and contraction; if the soil is hard, they flex and rotate their body. It is thought that the larvae adapt to diverse soil conditions using two different excavation methods. These results are important for understanding the soil ecology and pose a challenge to engineer of newer excavation technology.

Controlling subterranean forces enables a fast, steerable, burrowing soft robot

Robotic navigation on land, through air, and in water is well researched; numerous robots have successfully demonstrated motion in these environments. However, one frontier for robotic locomotion remains largely unexplored-below ground. Subterranean navigation is simply hard to do, in part because the interaction forces of underground motion are higher than in air or water by orders of magnitude and because we lack for these interactions a robust fundamental physics understanding. We present and test three hypotheses, derived from biological observation and the physics of granular intrusion, and use the results to inform the design of our burrowing robot. These results reveal that (i) tip extension reduces total drag by an amount equal to the skin drag of the body, (ii) granular aeration via tip-based airflow reduces drag with a nonlinear dependence on depth and flow angle, and (iii) variation of the angle of the tip-based flow has a nonmonotonic effect on lift in granular media. Informed by these results, we realize a steerable, root-like soft robot that controls subterranean lift and drag forces to burrow faster than previous approaches by over an order of magnitude and does so through real sand. We also demonstrate that the robot can modulate its pullout force by an order of magnitude and control its direction of motion in both the horizontal and vertical planes to navigate around subterranean obstacles. Our results advance the understanding and capabilities of robotic subterranean locomotion.

Burrowing soft robots break new ground

A bioinspired soft robot burrows through shallow dry sand with remarkable speed and maneuverability.

How head shape and substrate particle size affect fossorial locomotion in lizards

Granular substrates ranging from silt to gravel cover much of the Earth's land area, providing an important habitat for fossorial animals. Many of these animals use their heads to penetrate the substrate. Although there is considerable variation in head shape, how head shape affects fossorial locomotor performance in different granular substrates is poorly understood. Here, head shape variation for 152 species of fossorial lizards was quantified for head diameter, slope and pointiness of the snout. The force needed to penetrate different substrates was measured using 28 physical models spanning this evolved variation. Ten substrates were considered, ranging in particle size from 0.025 to 4 mm in diameter and consisting of spherical or angular particles. Head shape evolved in a weakly correlated manner, with snouts that were gently sloped being blunter. There were also significant clade differences in head shape among fossorial lizards. Experiments with physical models showed that as head diameter increased, absolute penetration force increased but force normalized by cross-sectional area decreased. Penetration force decreased for snouts that tapered more gradually and were pointier. Larger and angular particles required higher penetration forces, although intermediate size spherical particles, consistent with coarse sand, required the lowest force. Particle size and head diameter effect were largest, indicating that fossorial burrowers should evolve narrow heads and bodies, and select relatively fine particles. However, variation in evolved head shapes and recorded penetration forces suggests that kinematics of fossorial movement are likely an important factor in explaining evolved diversity.

Comparing the turn performance of different motor control schemes in multilink fish-inspired robots

Fish robots have many possible applications in exploration, industry, research, and continue to increase in design complexity, control, and the behaviors they can complete. Maneuverability is an important metric of fish robot performance, with several strategies being implemented. By far the most common control scheme for fish robot maneuvers is an offset control scheme, wherein the robot's steady swimming is controlled by sinusoidal function and turns are generated biasing bending to one side or another. An early bio-inspired turn control scheme is based on the C-start escape response observed in live fish. We developed a control scheme that is based on the kinematics of routine maneuvers in live fish that we call the 'pulse', which is a pattern of increasing and decreasing curvature that propagates down the body. This pattern of curvature is consistent across a wide range of turn types and can be described with a limited number of variables. We compared the performance of turns using each of these three control schemes across a range of durations and bending amplitudes. We found that C-start and offset turns had the highest heading changes for a given set of inputs, whereas the bio-inspired pulse turns had the highest linear accelerations for a given set of inputs. However, pulses shift the conceptualization of swimming away from it being a continuous behavior towards it being an intermittent behavior that is built by combining individual bending events. Our bio-inspired pulse control scheme has the potential to increase the behavioral flexibility of bio-inspired robotic fish and solve some of the problems associated with integrating different swimming behaviors, despite lower maximal turning performance.

Complex fluids in animal survival strategies

Animals have evolved distinctive survival strategies in response to constant selective pressure. In this review, we highlight how animals exploit flow phenomena by manipulating their habitat (exogenous) or by secreting (endogenous) complex fluids. Ubiquitous endogenous complex fluids such as mucus demonstrate rheological versatility and are therefore involved in many animal behavioral traits ranging from sexual reproduction to protection against predators. Exogenous complex fluids such as sand can be used either for movement or for predation. In all cases, time-dependent rheological properties of complex fluids are decisive for the fate of the biological behavior and vice versa. To exploit these rheological properties, it is essential that the animal is able to sense the rheology of their surrounding complex fluids in a timely fashion. As timing is key in nature, such rheological materials often have clearly defined action windows matching the time frame of their direct biological behavior. As many rheological properties of these biological materials remain poorly studied, we demonstrate with this review that rheology and material science might provide an interesting quantitative approach to study these biological materials in particular in context towards ethology and bio-mimicking material design.

Morphological study of the integument and corporal skeletal muscles of two psammophilous members of Scincidae (Scincus scincus and Eumeces schneideri)

Sand deserts are common biotopes on the earth's surface. Numerous morphological and physiological adaptations have appeared to cope with the peculiar conditions imposed by sandy substrates, such as abrasion, mechanical resistance and the potential low oxygen levels. The psammophilous scincids (Lepidosauria) Scincus scincus and Eumeces schneideri are among those. S. scincus is a species frequently used to study displacement inside a sandy substrate. E. schneideri is a species phylogenetically closely related to S. scincus with a similar lifestyle. The aims of this study focus on the morphology of the integument and the muscular system. Briefly, we describe interspecific differences at the superficial architecture of the scales pattern and the thickness of the integument. We highlight a high cellular turnover rate at the level of the basal germinal layer of the epidermis, which, we suggest, corresponds to an adaptation to cutaneous wear caused by abrasion. We demonstrate the presence of numerous cutaneous holocrine glands whose secretion probably plays a role in the flow of sand along the integument. Several strata of osteoderms strengthen the skin. We characterize the corporal (M. longissimus dorsi and M. rectus abdominus) and caudal muscular fibers using immunohistochemistry, and quantify them using morphometry. The musculature exhibits a high proportion of glycolytic fast fibers that allow rapid burying and are well adapted to this mechanically resistant and oxygen‐poor substrate. Oxidative slow fibers are low in abundance, less than 10% in S. scincus, but a little higher in E. schneideri.

Granular scaling laws for helically driven dynamics

Exploration of granular physics for three-dimensional geometries interacting with deformable media is crucial for further understanding of granular mechanics and vehicle-terrain dynamics. A modular screw propelled vehicle is, therefore, designed for testing the accuracy of a novel helical granular scaling law in predicting vehicle translational velocity and power. A dimensional analysis is performed on the vehicle and screw pontoons. Two additional pontoon pairs of increased size and mass are determined from dimensional scalars. The power and velocity of these larger pairs are predicted by the smaller pair using the scaling relationships. All three sets are subjected to ten trials of five angular velocities ranging from 13.7 to 75.0 revolutions per minute in a high interlock lunar regolith analog derived from mining tailings. Experimental agreement for prediction of power (3-9% error) and translational velocity (2-12% error) are observed. A similar set of geometries is subjected to multibody dynamics and discrete element method cosimulations of Earth and lunar gravity to verify a gravity-dependent subset of the scaling laws. These simulations show agreement (under 5% error for all sets) and support law validity for gravity between Earth and lunar magnitude. These results support further expansion of granular scaling models to enable prediction for vehicle-terrain dynamics for a variety of environments and geometries.

Randomness in appendage coordination facilitates strenuous ground self-righting

Randomness is common in biological and artificial systems, resulting either from stochasticity of the environment or noise in organisms or devices themselves. In locomotor control, randomness is typically considered a nuisance. For example, during dynamic walking, randomness in stochastic terrain leads to metastable dynamics, which must be mitigated to stabilize the system around limit cycles. Here, we studied whether randomness in motion is beneficial for strenuous locomotor tasks. Our study used robotic simulation modeling of strenuous, leg-assisted, winged ground self-righting observed in cockroaches, in which unusually large randomness in wing and leg motions is present. We developed a simplified simulation robot capable of generating similar self-righting behavior and varied the randomness level in wing-leg coordination. During each wing opening attempt, the more randomness added to the time delay between wing opening and leg swinging, the more likely it was for the naive robot (which did not know what coordination is best) to self-right within a finite time. Wing-leg coordination, measured by the phase between wing and leg oscillations, had a crucial impact on self-righting outcome. Without randomness, periodic wing and leg oscillations often limited the system to visit a few bad phases, leading to failure to escape from the metastable state. With randomness, the system explored phases thoroughly and had a better chance of encountering good phases to self-right. Our study complements previous work by demonstrating that randomness helps destabilize locomotor systems from being trapped in undesired metastable states, a situation common in strenuous locomotion.

Leg Joint Stiffness Affects Dynamics of Backward Falling From Standing Height: A Simulation Work

Falling backward can lead to injuries including hip fracture, back injury, and traumatic brain impact among older adults. A loss of consciousness is associated with falling backward and accounts for about 13% of all falls among older adults. Little is known about the dynamics of backward falls, such as the falling duration, the impact severity, and how the fall dynamics are affected by the biomechanical properties of the lower limb joints, particularly the rotational stiffness. The purpose of this study was to investigate the influence of the stiffness of individual leg joints on the dynamics of backward falls after losing consciousness in terms of the falling duration and impact velocities. Based on a 15-segment human model, we simulated the process of falling backward by sweeping the parameter space of ankle, knee, and hip's stiffnesses varying from 0 to 8.73 N·m·deg-1 (or 500 N·m·rad-1). The results revealed that the falling duration and impact speeds of the head and hip ranged from 0.27 to 0.63 s, 2.65 to 7.88 m·s-1, and 0.35 to 3.36 m·s-1, respectively, when the stiffness of the leg joints changed within their limits. Overall, the influence of the joint stiffness on the falling dynamics (falling duration and impact speed) is comparable between hip and knee joints, whereas ankle stiffness showed little influence on the backward falling dynamics. Our findings could provide references for designing protective devices to prevent impact-induced injuries after a backward fall.

Towards bio-inspired robots for underground and surface exploration in planetary environments: An overview and novel developments inspired in sand-swimmers

Dessert organisms like sandfish lizards (SLs) bend and generate thrust in granular mediums to scape heat and hunt for prey [1]. Further, SLs seems to have striking capabilities to swim in undulatory form keeping the same wavelength even in terrains with different volumetric densities, hence behaving as rigid bodies. This paper tries to recommend new research directions for planetary robotics, adapting principles of sand swimmers for improving robustness of surface exploration robots. First, we summarize previous efforts on bio-inspired hardware developed for granular terrains and accessing complex geological features. Later, a rigid wheel design has been proposed to imitate SLs locomotion capabilities. In order to derive the force models to predict performance of such bio-inspired mobility system, different approaches as RFT (Resistive Force Theory) and analytical terramechanics are introduced. Even in typical wheeled robots the slip and sinkage increase with time, the new design intends to imitate traversability capabilities of SLs, that seem to keep the same slip while displacing at subsurface levels.

Mitigating memory effects during undulatory locomotion on hysteretic materials

While terrestrial locomotors often contend with permanently deformable substrates like sand, soil, and mud, principles of motion on such materials are lacking. We study the desert-specialist shovel-nosed snake traversing a model sand and find body inertia is negligible despite rapid transit and speed dependent granular reaction forces. New surface resistive force theory (RFT) calculation reveals how wave shape in these snakes minimizes material memory effects and optimizes escape performance given physiological power limitations. RFT explains the morphology and waveform-dependent performance of a diversity of non-sand-specialist snakes but overestimates the capability of those snakes which suffer high lateral slipping of the body. Robophysical experiments recapitulate aspects of these failure-prone snakes and elucidate how re-encountering previously deformed material hinders performance. This study reveals how memory effects stymied the locomotion of a diversity of snakes in our previous studies (Marvi et al., 2014) and indicates avenues to improve all-terrain robots.

Surprising simplicities and syntheses in limbless self-propulsion in sand

Animals moving on and in fluids and solids move their bodies in diverse ways to generate propulsion and lift forces. In fluids, animals can wiggle, stroke, paddle or slap, whereas on hard frictional terrain, animals largely engage their appendages with the substrate to avoid slip. Granular substrates, such as desert sand, can display complex responses to animal interactions. This complexity has led to locomotor strategies that make use of fluid-like or solid-like features of this substrate, or combinations of the two. Here, we use examples from our work to demonstrate the diverse array of methods used and insights gained in the study of both surface and subsurface limbless locomotion in these habitats. Counterintuitively, these seemingly complex granular environments offer certain experimental, theoretical, robotic and computational advantages for studying terrestrial movement, with the potential for providing broad insights into morphology and locomotor control in fluids and solids, including neuromechanical control templates and morphological and behavioral evolution. In particular, granular media provide an excellent testbed for a locomotion framework called geometric mechanics, which was introduced by particle physicists and control engineers in the last century, and which allows quantitative analysis of alternative locomotor patterns and morphology to test for control templates, optimality and evolutionary alternatives. Thus, we posit that insights gained from movement in granular environments can be translated into principles that have broader applications across taxa, habitats and movement patterns, including those at microscopic scales.

Tunnel-tube and Fourier methods for measuring three-dimensional medium reaction force in burrowing animals

Subterranean digging behaviors provide opportunities for protection, access to prey, and predator avoidance for a diverse array of vertebrates, yet studies of the biomechanics of burrowing have been limited by the technical challenges of measuring kinetics and kinematics of animals moving within a medium. We describe a new system for measuring 3D reaction forces during burrowing, called a 'tunnel-tube', which is composed of two, separately instrumented plastic tubes: an 'entry tube' with no medium, in series with a 'digging tube' filled with medium. Mean reaction forces are measured for a digging bout and Fourier analysis is used to quantify the amplitude of oscillatory digging force as a function of frequency. In sample data from pocket gophers digging in artificial and natural media, the mean ground reaction force is constant, whereas Fourier analysis resolves a reduced amplitude of oscillatory force in the artificial medium with lower compaction strength.

Granular segregation induced by a moving subsurface blade

Size-driven particle segregation can occur when an object such as a blade moves through an otherwise static bed of granular material. Here we use discrete element method (DEM) simulations to study segregation resulting from a subsurface blade moving through a bed of size-bidisperse spherical particles. Segregation increases with each pass of the blade until a surface layer of mostly large particles forms above a small-particle layer adjacent to the bottom wall. The rate of segregation decreases with each pass so that the degree of segregation asymptotically approaches its maximum value, and the number of passes to reach a steady segregation state increases as the bed depth is increased or the blade height decreased. In shallow beds, the characteristic number of passes for segregation, τ, scales with the inverse of the granular inertial number, I. In deep beds with small blade heights, the effect of the blade is more localized to its immediate vicinity, resulting in many more passes of the blade to reach a steady segregation state, and a corresponding deviation from the shallow bed scaling of τ with I^{-1}.

A robot made of robots: Emergent transport and control of a smarticle ensemble

Robot locomotion is typically generated by coordinated integration of single-purpose components, like actuators, sensors, body segments, and limbs. We posit that certain future robots could self-propel using systems in which a delineation of components and their interactions is not so clear, becoming robust and flexible entities composed of functional components that are redundant and generic and can interact stochastically. Control of such a collective becomes a challenge because synthesis techniques typically assume known input-output relationships. To discover principles by which such future robots can be built and controlled, we study a model robophysical system: planar ensembles of periodically deforming smart, active particles—smarticles. When enclosed, these individually immotile robots could collectively diffuse via stochastic mechanical interactions. We show experimentally and theoretically that directed drift of such a supersmarticle could be achieved via inactivation of individual smarticles and used this phenomenon to generate endogenous phototaxis. By numerically modeling the relationship between smarticle activity and transport, we elucidated the role of smarticle deactivation on supersmarticle dynamics from little data—a single experimental trial. From this mapping, we demonstrate that the supersmarticle could be exogenously steered anywhere in the plane, expanding supersmarticle capabilities while simultaneously enabling decentralized closed-loop control. We suggest that the smarticle model system may aid discovery of principles by which a class of future “stochastic” robots can rely on collective internal mechanical interactions to perform tasks.

Helically-driven granular mobility and gravity-variant scaling relations

This study discusses the role and function of helical design as it relates to slippage during translation of a vehicle in glass bead media. We show discrete element method (DEM) and multi-body dynamics (MBD) simulations and experiments of a double-helix Archimedes screw propelled vehicle traveling in a bed of soda-lime glass beads. Utilizing granular parameters from the literature and a reduced Young's modulus, we validate the set of granular parameters against experiments. The results suggest that MBD-DEM provides reliable dynamic velocity estimates. We provide the glass, ABS, and glass-ABS simulation parameters used to obtain these results. We also examine recently developed granular scaling laws for wheels applied to these shear-driven vehicles under three different simulated gravities. The results indicate that the system obeys gravity granular scaling laws for constant slip conditions but is limited in each gravity regime when slip begins to increase.

Dynamics of a magnetically rotated micro swimmer inspired by paramecium metachronal wave

In the past few years, a significant body of research has been devoted to designing magnetic micron scale robotic systems for minimally invasive medicine. The motion of different microorganisms is the nature's solution for efficient propulsion of these swimmers. So far, there has been a considerable effort in designing micro swimmers based on the propulsion of bacteria while the motion of numerous other microorganisms has not been a source of inspiration for designing micro swimmers yet. Inspired by propulsion of Paramecium which is a ciliate microorganism, a novel micro swimmer is proposed in this article which is capable of cargo transport. This novel swimmer is composed of multiple equally spaced rigid loxodromic rods spanning the surface of a sphere which can carry a cargo placed inside it. The propulsion of this swimmer is influenced by the geometry of the swimmer (diameter, number of rods, cargo size), therefore, CFD simulations have been performed to investigate it. Finally, the dynamics of this swimmer is investigated analytically which sheds light into the complex dynamics of a swimmer with this geometry.

Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions

Interest in the design of bioinspired robotic microswimmers is growing rapidly, motivated by the spectacular capabilities of their unicellular biological templates. Predicting the swimming speed and efficiency of such devices in a reliable way is essential for their rational design, and to optimize their performance. The hydrodynamic simulations needed for this purpose are demanding and simplified models that neglect nonlocal hydrodynamic interactions (e.g., resistive force theory for slender, filament-like objects that are the typical propulsive apparatus for unicellular swimmers) are commonly used. We show through a detailed case study of a model robotic system consisting of a spherical head powered by a rotating helical flagellum that (a) the errors one makes in the prediction of swimming speed and efficiency by neglecting hydrodynamic interactions are never quite acceptable and (b) there are simple ways to correct the predictions of the simplified theories to make them more accurate. We also formulate optimal design problems for the length of the helical flagellum giving maximal energetic efficiency, maximal distance traveled per motor turn, or maximal distance traveled per unit of work expended, and exhibit optimal solutions.

Transition and formation of the torque pattern of undulatory locomotion in resistive force dominated media

In undulatory locomotion, torques along the body are required to overcome external forces from the environment and bend the body. These torques are usually generated by muscles in animals and closely related to muscle activations. In previous studies, researchers observed a single traveling wave pattern of the torque or muscle activation, but the formation of the torque pattern is still not well understood. To elucidate the formation of the torque pattern required by external resistive forces and the transition as kinematic parameters vary, we use simplistic resistive force theory models of self-propelled, steady undulatory locomotors and examine the spatio-temporal variation of the internal torque. We find that the internal torque has a traveling wave pattern with a decreasing speed normalized by the curvature speed as the wave number (the number of wavelengths on the locomotor's body) increases from 0.5 to 1.8. As the wave number increases to 2 and greater values, the torque transitions into a two-wave-like pattern and complex patterns. Using phasor diagram analysis, we reveal that the formation and transitions of the pattern are consequences of the integration and cancellation of force phasors.

Serpentine locomotion through elastic energy release

A model for serpentine locomotion is derived from a novel perspective based on concepts from configurational mechanics. The motion is realized through the release of the elastic energy of a deformable rod, sliding inside a frictionless channel, which represents a snake moving against lateral restraints. A new formulation is presented, correcting previous results and including situations never analysed so far, as in the cases when the serpent's body lies only partially inside the restraining channel or when the body has a muscle relaxation localized in a small zone. Micromechanical considerations show that propulsion is the result of reactions tangential to the frictionless constraint and acting on the snake's body, a counter-intuitive feature in mechanics. It is also experimentally demonstrated that the propulsive force driving serpentine motion can be directly measured on a designed apparatus in which flexible bars sweep a frictionless channel. Experiments fully confirm the theoretical modelling, so that the presented results open the way to exploration of effects, such as variability in the bending stiffness or channel geometry or friction, on the propulsive force of snake models made up of elastic rods.

Kinematics of burrowing by peristalsis in granular sands

Peristaltic burrowing in muds applies normal forces to burrow walls, which extend by fracture, but the kinematics and mechanics of peristaltic burrowing in sands has not been explored. The opheliid polychaete, Thoracophelia mucronata, uses direct peristalsis to burrow in beach sands, using kinematics consistent with the “dual anchor system” of burrowing used by diverse organisms. In addition to expansions associated with a constrictive direct peristaltic wave, worms alternately expand the head region, which is separated by septa from the open body cavity, and expansible lateral ridges that protrude from the 10th setiger. Tracking of fluorescent-dyed chaetae showed that the body wall advances while segments are thin, then stationary segments expand, applying normal forces to burrow walls. These normal forces likely compact burrow walls and serve as anchors. Perhaps more importantly, peristaltic movements minimize friction with the burrow wall, which would expand dilatant sands. Considerable slipping of worms burrowing in a lower-density sand analog suggests that this dual-anchor peristaltic burrowing may be limited to a narrow range of mechanical properties of substrata, consistent with the limited habitat of T. mucronata in a narrow swash zone on dissipative beaches.

Energy efficiency of mobile soft robots

The performance of mobile soft robots is usually characterized by their locomotion/velocity efficiency, whereas the energy efficiency is a more intrinsic and fundamental criterion for the performance evaluation of independent or integrated soft robots. In this work, a general framework is established to evaluate the energy efficiency of mobile soft robots by considering the efficiency of the energy source, actuator and locomotion, and some insights for improving the efficiency of soft robotic systems are presented. Proposed as the ratio of the desired locomotion kinetic energy to the input mechanical energy, the energy efficiency of locomotion is found to play a critical role in determining the overall energy efficiency of soft robots. Four key factors related to the locomotion energy efficiency are identified, that is, the locomotion modes, material properties, geometric sizes, and actuation states. It is found that the energy efficiency of most mobile soft robots reported in the literature is surprisingly low (mostly below 0.1%), due to the inefficient mechanical energy that essentially does not contribute to the desired locomotion. A comparison of the locomotion energy efficiency for several representative locomotion modes in the literature is presented, showing a descending ranking as: jumping ≫ fish-like swimming > snake-like slithering > rolling > rising/turning over > inchworm-like inching > quadruped gait > earthworm-like squirming. Besides, considering the same locomotion mode, soft robots with lower stiffness, higher density and larger size tend to have higher locomotion energy efficiency. Moreover, a periodic pulse actuation instead of a continuous actuation mode may significantly reduce the input mechanical energy, thus improving the locomotion energy efficiency, especially when the pulse actuation matches the resonant states of the soft robots. The results presented herein indicate a large and necessary space for improving the locomotion energy efficiency, which is of practical significance for the future development and application of soft robots.

It's just sand between the toes: how particle size and shape variation affect running performance and kinematics in a generalist lizard

Animals must cope with and be able to move effectively on a variety of substrates. Substrates composed of granular media, such as sand and gravel, are extremely common in nature, and vary tremendously in particle size and shape. Despite many studies of the properties of granular media and comparisons of locomotion between granular and solid substrates, the effects of systematically manipulating these media on locomotion is poorly understood. We studied granular media ranging over four orders of magnitude in particle size, and differing in the amount of particle shape variation, to determine how these factors affected substrate physical properties and sprinting in the generalist lizard Eremias arguta. We found that media with intermediate particle sizes had high bulk densities, low angles of stability and low load-bearing capacities. Rock substrates with high shape variation had higher values for all three properties than glass bead substrates with low shape variation. We found that E. arguta had the highest maximum velocities and accelerations on intermediate size particles, and higher velocities on rock than glass beads. Lizards had higher stride frequencies and lower duty factors on intermediate particle size substrates, but their stride lengths did not change with substrate. Our findings suggest that sand and gravel may represent different locomotor challenges for animals. Sand substrates provide animals with an even surface for running, but particles shift underfoot. In contrast, gravel particles are heavy, so move far less underfoot, yet provide the animal with an uneven substrate.

Helical Locomotion in a Granular Medium

The physical mechanisms that bring about the propulsion of a rotating helix in a granular medium are considered. A propulsive motion along the axis of the rotating helix is induced by both symmetry breaking due to the helical shape, and the anisotropic frictional forces undergone by all segments of the helix in the medium. Helix dynamics is studied as a function of helix rotation speed and its geometrical parameters. The effect of the granular pressure and the applied external load were also investigated. A theoretical model is developed based on the anisotropic frictional force experienced by a slender body moving in a granular material, to account for the translation speed of the helix. A good agreement with experimental data is obtained, which allows for predicting the helix design to propel optimally within granular media. These results pave the way for the development of an efficient sand robot operating according to this mode of locomotion.

Adaptation to life in aeolian sand: how the sandfish lizard, Scincus scincus, prevents sand particles from entering its lungs

The sandfish lizard, Scincus scincus (Squamata: Scincidae), spends nearly its whole life in aeolian sand and only comes to the surface for foraging, defecating and mating. It is not yet understood how the animal can respire without sand particles entering its respiratory organs when buried under thick layers of sand. In this work, we integrated biological studies, computational calculations and physical experiments to understand this phenomenon. We present a 3D model of the upper respiratory system based on a detailed histological analysis. A 3D-printed version of this model was used in combination with characteristic ventilation patterns for computational calculations and fluid mechanics experiments. By calculating the velocity field, we identified a sharp decrease in velocity in the anterior part of the nasal cavity where mucus and cilia are present. The experiments with the 3D-printed model validate the calculations: particles, if present, were found only in the same area as suggested by the calculations. We postulate that the sandfish has an aerodynamic filtering system; more specifically, that the characteristic morphology of the respiratory channel coupled with specific ventilation patterns prevent particles from entering the lungs.

Highlighted Article: The sandfish S. scincus spends nearly its whole life in fine desert sand. We discovered that it has an aerodynamic filtering system to prevent sand particles from entering the lungs.

Magnetic resonance imaging of granular materials

Magnetic Resonance Imaging (MRI) has become one of the most important tools to screen humans in medicine; virtually every modern hospital is equipped with a Nuclear Magnetic Resonance (NMR) tomograph. The potential of NMR in 3D imaging tasks is by far greater, but there is only "a handful" of MRI studies of particulate matter. The method is expensive, time-consuming, and requires a deep understanding of pulse sequences, signal acquisition, and processing. We give a short introduction into the physical principles of this imaging technique, describe its advantages and limitations for the screening of granular matter, and present a number of examples of different application purposes, from the exploration of granular packing, via the detection of flow and particle diffusion, to real dynamic measurements. Probably, X-ray computed tomography is preferable in most applications, but fast imaging of single slices with modern MRI techniques is unmatched, and the additional opportunity to retrieve spatially resolved flow and diffusion profiles without particle tracking is a unique feature.

Vertical dynamics of a horizontally oscillating active object in a two-dimensional granular medium

We use a discrete-element method simulation and analytical considerations to study the dynamics of a self-energized object, modeled as a disk, oscillating horizontally within a two-dimensional bed of denser and smaller particles. We find that, for given material parameters, the immersed object (IO) may rise, sink, or not change depth, depending on the oscillation amplitude and frequency, as well as on the initial depth. With time, the IO settles at a specific depth that depends on the oscillation parameters. We construct a phase diagram of this behavior in the oscillation frequency and velocity amplitude variable space. We explain the observed rich behavior by two competing effects: climbing on particles, which fill voids opening under the disk, and sinking due to bed fluidization. We present a cavity model that allows us to derive analytically general results, which agree very well with the observations and explain quantitatively the phase diagram. Our specific analytical results are the following. (i) Derivation of a critical frequency, f_{c}, above which the IO cannot float up against gravity. We show that this frequency depends only on the gravitational acceleration and the IO size. (ii) Derivation of a minimal amplitude, A_{min}, below which the IO cannot rise even if the frequency is below f_{c}. We show that this amplitude also depends only on the gravitational acceleration and the IO size. (iii) Derivation of a critical value, g_{c}, of the IO's acceleration amplitude, below which the IO cannot sink. We show that the value of g_{c} depends on the characteristics of both the IO and the granular bed, as well as on the initial IO's depth.