Locomotor benefits of being a slender and slick sand swimmer

Grand challenges for burrowing soft robots

Robotic burrowing holds promise for applications in agriculture, resource extraction, and infrastructure development, but current approaches are ineffective, inefficient, or cause significant environmental disruption. In contrast, natural burrowers penetrate substrates with minimal disturbance, providing biomechanical principles that could inspire more efficient and sustainable mechanisms. A notable feature of many natural burrowers is their reliance on soft body compositions, raising the question of whether softness contributes to their burrowing success. This review explores the role of soft materials in biological burrowing and their implications for robotic design. We examine the mechanisms that soft-bodied organisms and soft robots employ for submerging and subterranean locomotion, focusing on how softness enhances efficiency and adaptability in granular media. We analyze the gaps between the capabilities of natural burrowers and soft robotic burrowers, identify grand challenges, and propose opportunities to enhance robotic burrowing performance. By bridging biological principles with engineering innovation, this review aims to inform the development of next-generation burrowing robots capable of operating with the efficiency and efficacy seen in nature.

The Phylogenetic Relationships of Major Lizard Families Using Mitochondrial Genomes and Selection Pressure Analyses in Anguimorpha

Anguimorpha, within the order Squamata, represents a group with distinct morphological and behavioral characteristics in different ecological niches among lizards. Within Anguimorpha, there is a group characterized by limb loss, occupying lower ecological niches, concentrated within the subfamily Anguinae. Lizards with limbs and those without exhibit distinct locomotor abilities when adapting to their habitats, which in turn necessitate varying degrees of energy expenditure. Mitochondria, known as the metabolic powerhouses of cells, play a crucial role in providing approximately 95% of an organism's energy. Functionally, mitogenomes (mitochondrial genomes) can serve as a valuable tool for investigating potential adaptive evolutionary selection behind limb loss in reptiles. Due to the variation of mitogenome structures among each species, as well as its simple genetic structure, maternal inheritance, and high evolutionary rate, the mitogenome is increasingly utilized to reconstruct phylogenetic relationships of squamate animals. In this study, we sequenced the mitogenomes of two species within Anguimorpha as well as the mitogenomes of two species in Gekkota and four species in Scincoidea. We compared these data with the mitogenome content and evolutionary history of related species. Within Anguimorpha, between the mitogenomes of limbless and limbed lizards, a branch-site model analysis supported the presence of 10 positively selected sites: Cytb protein (at sites 183 and 187), ND2 protein (at sites 90, 155, and 198), ND3 protein (at site 21), ND5 protein (at sites 12 and 267), and ND6 protein (at sites 72 and 119). These findings suggested that positive selection of mitogenome in limbless lizards may be associated with the energy requirements for their locomotion. Additionally, we acquired data from 205 mitogenomes from the NCBI database. Bayesian inference (BI) and Maximum Likelihood (ML) trees were constructed using the 13 mitochondrial protein-coding genes (PCGs) and two rRNAs (12S rRNA and 16S rRNA) from 213 mitogenomes. Our phylogenetic tree and the divergence time estimates for Squamata based on mitogenome data are consistent with results from previous studies. Gekkota was placed at the root of Squamata in both BI and ML trees. However, within the Toxicofera clade, due to long-branch attraction, Anguimorpha and (Pleurodonta + (Serpentes + Acrodonta)) were closely related groupings, which might indicate errors and also demonstrate that mitogenome-based phylogenetic trees may not effectively resolve long-branch attraction issues. Additionally, we reviewed the origin and diversification of Squamata throughout the Mesozoic era, suggesting that Squamata originated in the Late Triassic (206.05 Mya), with the diversification of various superfamilies occurring during the Cretaceous period. Future improvements in constructing squamate phylogenetic relationships using mitogenomes will rely on identifying snake and acrodont species with slower evolutionary rates, ensuring comprehensive taxonomic coverage of squamate diversity, and increasing the number of genes analyzed.

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.

Generation of propulsive force via vertical undulations in snakes

Lateral undulation is the most widespread mode of terrestrial vertebrate limbless locomotion, in which posteriorly propagating horizontal waves press against environmental asperities (e.g. grass, rocks) and generate propulsive reaction forces. We hypothesized that snakes can generate propulsion using a similar mechanism of posteriorly propagating vertical waves pressing against suitably oriented environmental asperities. Using an array of horizontally oriented cylinders, one of which was equipped with force sensors, and a motion capture system, we found snakes generated substantial propulsive force and propulsive impulse with minimal contribution from lateral undulation. Additional tests showed that snakes could propel themselves via vertical undulations from a single suitable contact point, and this mechanism was replicated in a robotic model. Vertical undulations can provide snakes with a valuable locomotor tool for taking advantage of vertical asperities in a variety of habitats, potentially in combination with lateral undulation, to fully exploit the 3D structure of the habitat.

Summary: Snakes are capable of generating propulsion via vertical undulations, which allows them to exploit their environment in 3D and allows more effective use of previously overlooked surfaces in cluttered habitats.

Functional consequences of convergently evolved microscopic skin features on snake locomotion

The small structures that decorate biological surfaces can significantly affect behavior, yet the diversity of animal-environment interactions essential for survival makes ascribing functions to structures challenging. Microscopic skin textures may be particularly important for snakes and other limbless locomotors, where substrate interactions are mediated solely through body contact. While previous studies have characterized ventral surface features of some snake species, the functional consequences of these textures are not fully understood. Here, we perform a comparative study, combining atomic force microscopy measurements with mathematical modeling to generate predictions that link microscopic textures to locomotor performance. We discover an evolutionary convergence in the ventral skin structures of a few sidewinding specialist vipers that inhabit sandy deserts-an isotropic texture that is distinct from the head-to-tail-oriented, micrometer-sized spikes observed on a phylogenetically broad sampling of nonsidewinding vipers and other snakes from diverse habitats and wide geographic range. A mathematical model that relates structural directionality to frictional anisotropy reveals that isotropy enhances movement during sidewinding, whereas anisotropy improves movement during slithering via lateral undulation of the body. Our results highlight how an integrated approach can provide quantitative predictions for structure-function relationships and insights into behavioral and evolutionary adaptations in biological systems.

Locomotor transitions in the potential energy landscape-dominated regime

To traverse complex three-dimensional terrain with large obstacles, animals and robots must transition across different modes. However, the most mechanistic understanding of terrestrial locomotion concerns how to generate and stabilize near-steady-state, single-mode locomotion (e.g. walk, run). We know little about how to use physical interaction to make robust locomotor transitions. Here, we review our progress towards filling this gap by discovering terradynamic principles of multi-legged locomotor transitions, using simplified model systems representing distinct challenges in complex three-dimensional terrain. Remarkably, general physical principles emerge across diverse model systems, by modelling locomotor-terrain interaction using a potential energy landscape approach. The animal and robots' stereotyped locomotor modes are constrained by physical interaction. Locomotor transitions are stochastic, destabilizing, barrier-crossing transitions on the landscape. They can be induced by feed-forward self-propulsion and are facilitated by feedback-controlled active adjustment. General physical principles and strategies from our systematic studies already advanced robot performance in simple model systems. Efforts remain to better understand the intelligence aspect of locomotor transitions and how to compose larger-scale potential energy landscapes of complex three-dimensional terrains from simple landscapes of abstracted challenges. This will elucidate how the neuromechanical control system mediates physical interaction to generate multi-pathway locomotor transitions and lead to advancements in biology, physics, robotics and dynamical systems theory.

Continuous body 3-D reconstruction of limbless animals

Limbless animals such as snakes, limbless lizards, worms, eels and lampreys move their slender, long bodies in three dimensions to traverse diverse environments. Accurately quantifying their continuous body's 3-D shape and motion is important for understanding body-environment interactions in complex terrain, but this is difficult to achieve (especially for local orientation and rotation). Here, we describe an interpolation method to quantify continuous body 3-D position and orientation. We simplify the body as an elastic rod and apply a backbone optimization method to interpolate continuous body shape between end constraints imposed by tracked markers. Despite over-simplifying the biomechanics, our method achieves a higher interpolation accuracy (∼50% error) in both 3-D position and orientation compared with the widely used cubic B-spline interpolation method. Beyond snakes traversing large obstacles as demonstrated, our method applies to other long, slender, limbless animals and continuum robots. We provide codes and demo files for easy application of our method.

Coordination of lateral body bending and leg movements for sprawled posture quadrupedal locomotion

Many animals generate propulsive forces by coordinating legs, which contact and push against the surroundings, with bending of the body, which can only indirectly influence these forces. Such body–leg coordination is not commonly employed in quadrupedal robotic systems. To elucidate the role of back bending during quadrupedal locomotion, we study a model system: the salamander, a sprawled-posture quadruped that uses lateral bending of the elongate back in conjunction with stepping of the limbs during locomotion. We develop a geometric approach that yields a low-dimensional representation of the body and limb contributions to the locomotor performance quantified by stride displacement. For systems where the damping forces dominate inertial forces, our approach offers insight into appropriate coordination patterns, and improves the computational efficiency of optimization techniques. In particular, we demonstrate effect of the lateral undulation coordinated with leg movement in the forward, rotational, and lateral directions of the robot motion. We validate the theoretical results using numerical simulations, and then successfully test these approaches using robophysical experiments on granular media, a model deformable, frictional substrate. Although our focus lies primarily on robotics, we also demonstrate that our tools can accurately predict optimal body bending of a living salamander Salamandra salamandra.

Evolutionary and morphological patterns underlying carnivoran body shape diversity

The diversity of body shapes is one of the most prominent features of phenotypic variation in vertebrates. Biologists, however, still lack a full understanding of the underlying morphological components that contribute to its diversity, particularly in endothermic vertebrates such as mammals. In this study, hypotheses pertaining to the evolution of the cranial and axial components that contribute to the diversity of carnivoran body shapes were tested. Three trends were found in the evolution of carnivoran body shapes: (1) carnivorans exhibit diverse body shapes with intrafamilial variation predicted best by family clade age, (2) body shape is driven by strong allometric effects of body size where species become more elongate with decreasing size, and (3) the thoracic and lumbar regions and rib length contribute the most to body shape variation, albeit pathways differ between different families. These results reveal the morphological patterns that led to increased diversity in carnivoran body shapes and elucidate the similarities and dissimilarities that govern body shape diversity across vertebrates.

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.

Burrowing behaviour of the European eel (Anguilla anguilla): Effects of life stage

The European eel (Anguilla anguilla) is a fascinating species, exhibiting a complex life cycle. The species is, however, listed as critically endangered on the IUCN Red List due to an amalgam of factors, including habitat loss. This study investigated the burrowing behaviour and substrate preference of glass, elver and yellow stages of A. anguilla. Preference was determined by introducing eels in aquaria with different substrates and evaluating the chosen substrate for burrowing. In addition, burrowing was recorded using a camera in all substrate types and analysed for kinematics. The experiments showed that all of these life stages sought refuge in the sediments with particle sizes ranging from sand to coarse gravel. Starting from a resting position, they shook their head horizontally in combination with rapid body undulations until half of their body was within the substrate. High-speed X-ray videography revealed that once partly in the sediment, eels used only horizontal head sweeps to penetrate further, without the use of their tail. Of the substrates tested, burrowing performance was highest in fine gravel (diameter 1-2 mm; lower burrowing duration, less body movements and/or lower frequency of movements), and all eels readily selected this substrate for burrowing. However, glass eels and elvers were able to use coarse gravel (diameter >8 mm) because their smaller size allowed manoeuvring through the spaces between the grains. Further, burrowing performance increased with body size: glass eels required more body undulations compared to yellow eels. Interestingly, the urge to hide within the sediment was highest for glass eels and elvers. Documentation of substrate preference and burrowing behaviour of A. anguilla provides new information about their potential habitat use. Considering that habitat alterations and deteriorations are partly responsible for the decline of the eel, this information can contribute to the development of more effective conservation measures.

Long Limbless Locomotors Over Land: The Mechanics and Biology of Elongate, Limbless Vertebrate Locomotion

Elongate, limbless body plans are widespread in nature and frequently converged upon (with over two dozen independent convergences in Squamates alone, and many outside of Squamata). Despite their lack of legs, these animals move effectively through a wide range of microhabitats, and have a particular advantage in cluttered or confined environments. This has elicited interest from multiple disciplines in many aspects of their movements, from how and when limbless morphologies evolve to the biomechanics and control of limbless locomotion within and across taxa to its replication in elongate robots. Increasingly powerful tools and technology enable more detailed examinations of limbless locomotor biomechanics, and improved phylogenies have shed increasing light on the origins and evolution of limblessness, as well as the high frequency of convergence. Advances in actuators and control are increasing the capability of "snakebots" to solve real-world problems (e.g., search and rescue), while biological data have proven to be a potent inspiration for improvements in snakebot control. This collection of research brings together prominent researchers on the topic from around the world, including biologists, physicists, and roboticists to offer new perspective on locomotor modes, musculoskeletal mechanisms, locomotor control, and the evolution and diversity of limbless locomotion.

Lateral Oscillation and Body Compliance Help Snakes and Snake Robots Stably Traverse Large, Smooth Obstacles

Snakes can move through almost any terrain. Similarly, snake robots hold the promise as a versatile platform to traverse complex environments such as earthquake rubble. Unlike snake locomotion on flat surfaces which is inherently stable, when snakes traverse complex terrain by deforming their body out of plane, it becomes challenging to maintain stability. Here, we review our recent progress in understanding how snakes and snake robots traverse large, smooth obstacles such as boulders and felled trees that lack "anchor points" for gripping or bracing. First, we discovered that the generalist variable kingsnake combines lateral oscillation and cantilevering. Regardless of step height and surface friction, the overall gait is preserved. Next, to quantify static stability of the snake, we developed a method to interpolate continuous body in three dimensions (3D) (both position and orientation) between discrete tracked markers. By analyzing the base of support using the interpolated continuous body 3-D kinematics, we discovered that the snake maintained perfect stability during traversal, even on the most challenging low friction, high step. Finally, we applied this gait to a snake robot and systematically tested its performance traversing large steps with variable heights to further understand stability principles. The robot rapidly and stably traversed steps nearly as high as a third of its body length. As step height increased, the robot rolled more frequently to the extent of flipping over, reducing traversal probability. The absence of such failure in the snake with a compliant body inspired us to add body compliance to the robot. With better surface contact, the compliant body robot suffered less roll instability and traversed high steps at higher probability, without sacrificing traversal speed. Our robot traversed large step-like obstacles more rapidly than most previous snake robots, approaching that of the animal. The combination of lateral oscillation and body compliance to form a large, reliable base of support may be useful for snakes and snake robots to traverse diverse 3-D environments with large, smooth obstacles.

Variation of the frictional anisotropy on ventral scales of snakes caused by nanoscale steps

The ventral scales of most snakes feature micron-sized fibril structures with nanoscale steps oriented towards the snake's tail. We examined these structures by microtribometry as well as atomic force microscopy (AFM) and observed that the nanoscale steps of the micro-fibrils cause a frictional anisotropy, which varies along the snake's body in dependence of the height of the nanoscale steps. A significant frictional behavior is detected when a sharp AFM tip scans the nanoscale steps up or down. Larger friction peaks appear during upward scans (tail to head direction), while considerably lower peaks are observed for downward scans (head to tail direction). This effect causes a frictional anisotropy on the nanoscale, i.e. friction along the head to tail direction is lower than in the opposite direction. The overall effect increases linearly with the step height of the micro-fibrils. Although the step heights are different for each snake, the general step height distribution along the body of the examined snakes follows a common pattern. The frictional anisotropy, induced by the step height distribution, is largest close to the tail, intermediate in the middle, and lower close to the head. This common distribution of frictional anisotropy suggests that snakes even optimized nanoscale features like the height of micro-fibrils through evolution in order to achieve optimal friction performance for locomotion. Finally, ventral snake scales are replicated by imprinting their micro-fibril structures into a polymer. As the natural prototype, the artificial surface exhibits frictional anisotropy in dependence of the respective step height. This feature is of high interest for the design of tribological surfaces with artificial frictional anisotropy.

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.

Experimental modification of morphology reveals the effects of the zygosphene-zygantrum joint on the range of motion of snake vertebrae

Variation in joint shape and soft tissue can alter range of motion (ROM) and create trade-offs between stability and flexibility. The shape of the distinctive zygosphene-zygantrum joint of snake vertebrae has been hypothesized to prevent axial torsion (twisting), but its function has never been tested experimentally. We used experimental manipulation of morphology to determine the role of the zygosphene-zygantrum articulation by micro-computed tomography (μCT) scanning and 3D printing two mid-body vertebrae with unaltered shape and with the zygosphene digitally removed for four species of phylogenetically diverse snakes. We recorded the angular ROM while manipulating the models in yaw (lateral bending), pitch (dorsoventral bending) and roll (axial torsion). Removing the zygosphene typically increased yaw and dorsal pitch ROM. In the normal vertebrae, roll was <2.5 deg for all combinations of pitch and yaw. Roll increased in altered vertebrae but only for combinations of high yaw and ventral pitch that were near or beyond the limits of normal vertebra ROM. In the prairie rattlesnake and brown tree snake, roll in the altered vertebrae was always limited by bony processes other than the zygosphene, whereas in the altered vertebrae of the corn snake and boa constrictor, roll ROM was unconstrained when the pre- and post-zygapophyses no longer overlapped. The zygosphene acts as a bony limit for yaw and dorsal pitch, indirectly preventing roll by precluding most pitch and yaw combinations where roll could occur and potentially allowing greater forces to be applied across the vertebral column than would be possible with only soft-tissue constraints.

Evolution of fossorial locomotion in the transition from tetrapod to snake-like in lizards

Dramatic evolutionary transitions in morphology are often assumed to be adaptive in a new habitat. However, these assumptions are rarely tested because such tests require intermediate forms, which are often extinct. In vertebrates, the evolution of an elongate, limbless body is generally hypothesized to facilitate locomotion in fossorial and/or cluttered habitats. However, these hypotheses remain untested because few studies examine the locomotion of species ranging in body form from tetrapod to snake-like. Here, we address these functional hypotheses by testing whether trade-offs exist between locomotion in surface, fossorial and cluttered habitats in Australian Lerista lizards, which include multiple intermediate forms. We found that snake-like species penetrated sand substrates faster than more lizard-like species, representing the first direct support of the adaptation to fossoriality hypothesis. By contrast, body form did not affect surface locomotion or locomotion through cluttered leaf litter. Furthermore, all species with hindlimbs used them during both fossorial and surface locomotion. We found no evidence of a trade-off between fossorial and surface locomotion. This may be either because Lerista employed kinematic strategies that took advantage of both axial- and limb-based propulsion. This may have led to the differential occupation of their habitat, facilitating diversification of intermediate forms.

The sandfish lizard's aerodynamic filtering system

Particulate air pollution has an adverse effect on cardiovascular and respiratory health. Air filtration systems are therefore essential in closed indoor environments. While mechanical filtration is described as an efficient technology, particle filters may act as a source of pollution if not correctly installed and frequently maintained. The sandfish lizard, a sand swimmer that spends nearly its whole life in fine desert sand, inspired us to rethink traditional filtering systems due to its unique ability of filtering sand from its nasal cavity. During a slow, prolonged inhalation, strong cross-flow velocities develop in a certain region of the upper respiratory tract; these cross-flows enhance gravitational settling and force inhaled sand grains towards the wall where they adhere to mucus, which covers the walls in this region. During an intense, cough-like exhalation the particles are blasted out. In this work, the sandfish's aerodynamic filtering system was analyzed experimentally and by computational fluid dynamics simulations to study the flow profile and particle trajectories. Based on these findings, we discuss the development of a biomimetic filtering system, which could have the following advantages: due to the absence of a membrane, total pressure losses can be reduced. The mucus-covered surface would be mimicked by a specifically treated surface to trap particulate matter. Also, the device would contain a self-cleaning mechanism that simulates the lizard's exhalation. This biomimetic filtering system would therefore have an enhanced life-time and it would be low-maintenance and therefore economical and sustainable.

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.

Snakes partition their body to traverse large steps stably

Many snakes live in deserts, forests and river valleys and traverse challenging 3-D terrain such as rocks, felled trees and rubble, with obstacles as large as themselves and variable surface properties. By contrast, apart from branch cantilevering, burrowing, swimming and gliding, laboratory studies of snake locomotion have focused on locomotion on simple flat surfaces. Here, to begin to understand snake locomotion in complex 3-D terrain, we studied how the variable kingsnake, a terrestrial generalist, traversed a large step of variable surface friction and step height (up to 30% snout-vent length). The snake traversed by partitioning its body into three sections with distinct functions. Body sections below and above the step oscillated laterally on horizontal surfaces for propulsion, whereas the body section in between cantilevered in a vertical plane to bridge the large height increase. As the animal progressed, these three sections traveled down its body, conforming overall body shape to the step. In addition, the snake adjusted the partitioned gait in response to increase in step height and decrease in surface friction, at the cost of reduced speed. As surface friction decreased, body movement below and above the step changed from a continuous lateral undulation with little slip to an intermittent oscillatory movement with much slip, and initial head lift-off became closer to the step. Given these adjustments, body partitioning allowed the snake to be always stable, even when initially cantilevering but before reaching the surface above. Such a partitioned gait may be generally useful for diverse, complex 3-D terrain.

Dynamics of scattering in undulatory active collisions

Natural and artificial self-propelled systems must manage environmental interactions during movement. In complex environments, these interactions include active collisions, in which propulsive forces create persistent contacts with heterogeneities. Due to the driven and dissipative nature of these systems, such collisions are fundamentally different from those typically studied in classical physics. Here we experimentally and numerically study the effects of active collisions on a laterally undulating sensory-deprived robophysical model, whose dynamics are relevant to self-propelled systems across length scales and environments. Interactions with a single rigid post scatter the robot, and this deflection is dominated by head-post contact. These results motivate a model which reduces the snake to a circular particle with two key features: The collision dynamics are set by internal driving subject to the geometric constraints of the post, and the particle has an effective length equal to the wavelength of the snake. Interactions with a single row of evenly spaced posts (with interpost spacing d) produce distributions reminiscent of far-field diffraction patterns: As d decreases, distinct secondary peaks emerge as large deflections become more likely. Surprisingly, we find that the presence of multiple posts does not change the nature of individual collisions; instead, multimodal scattering patterns arise from multiple posts altering the likelihood of individual collisions to occur. As d decreases, collisions near the leading edges of the posts become more probable, and we find that these interactions are associated with larger deflections. Our results, which highlight the surprising dynamics that can occur during active collisions of self-propelled systems, can inform control principles for locomotors in complex terrain and facilitate design of task-capable active matter.

Shared extremes by ectotherms and endotherms: Body elongation in mustelids is associated with small size and reduced limbs

An elongate body with reduced or absent limbs has evolved independently in many ectothermic vertebrate lineages. While much effort has been spent examining the morphological pathways to elongation in these clades, quantitative investigations into the evolution of elongation in endothermic clades are lacking. We quantified body shape in 61 musteloid mammals (red panda, skunks, raccoons, and weasels) using the head-body elongation ratio. We also examined the morphological changes that may underlie the evolution toward more extreme body plans. We found that a mustelid clade comprised of the subfamilies Helictidinae, Guloninae, Ictonychinae, Mustelinae, and Lutrinae exhibited an evolutionary transition toward more elongate bodies. Furthermore, we discovered that elongation of the body is associated with the evolution of other key traits such as a reduction in body size and a reduction in forelimb length but not hindlimb length. This relationship between body elongation and forelimb length has not previously been quantitatively established for mammals but is consistent with trends exhibited by ectothermic vertebrates and suggests a common pattern of trait covariance associated with body shape evolution. This study provides the framework for documenting body shapes across a wider range of mammalian clades to better understand the morphological changes influencing shape disparity across all vertebrates.

Mechanical diffraction reveals the role of passive dynamics in a slithering snake

Snakes inhabit environments composed of heterogeneous materials, controlling their body–terrain interactions to generate propulsion. Such complexity makes it challenging to understand the interplay of body mechanics and neural control during obstacle collisions. To simplify, we studied a desert-dwelling snake with a stereotyped waveform moving in a laboratory heterogeneous terrain, an array of posts embedded in a sand-mimic substrate. Compilation of hundreds of trials revealed multipeaked “scattering” patterns, reminiscent of diffraction of subatomic particles. A model incorporating muscle activation patterns and body buckling recovered the mechanical diffraction pattern, indicating passive dynamics facilitates obstacle negotiation without additional neural input. Our study demonstrates the importance of mechanics in snake locomotion as well as the rich dynamics in collisions of self-propelled systems.

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 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.

Burrowing fishes: Kinematics, morphology and phylogeny of sand-diving wrasses (Labridae)

Burrowing through the substrate is a common behaviour in many organisms, both invertebrate and vertebrate. Sand-diving, a burrowing behaviour in the fish family Labridae, consists of a quick and forceful headfirst plunge into the sediment followed by undulatory axial body movements until the fish is completely concealed beneath the surface. This study determined that sand-diving of the slippery dick wrasse Halichoeres bivittatus is composed of two distinct phases of undulatory axial body movements. In the first phase, body undulations occur at high frequencies and wave speeds and low amplitudes, while in the second phase, frequencies and wave speeds decrease while amplitude increases. Furthermore, this study examined several morphological features of sand-diving labrids, including narrow, elongated bodies and lengthened neural spines that overlap with the dorsal pterygiophores, that may be anatomical traits that contribute to burrowing ability. Finally, ancestral state reconstruction showed that sand-diving occurs exclusively in the upper half of the labrid phylogenetic tree with an evolutionary history indicating that sand-diving may have evolved once and then been lost three to five times or may have evolved independently at least three times in family Labridae.

Characterization of the microscopic tribological properties of sandfish (Scincus scincus) scales by atomic force microscopy

Lizards of the genus Scincus are widely known under the common name sandfish due to their ability to swim in loose, aeolian sand. Some studies report that this fascinating property of sandfish is accompanied by unique tribological properties of their skin such as ultra-low adhesion, friction and wear. The majority of these reports, however, is based on experiments conducted with a non-standard granular tribometer. Here, we characterise microscopic adhesion, friction and wear of single sandfish scales by atomic force microscopy. The analysis of frictional properties with different types of probes (sharp silicon tips, spherical glass tips and sand debris) demonstrates that the tribological properties of sandfish scales on the microscale are not exceptional if compared to snake scales or technical surfaces such as aluminium, Teflon, or highly oriented pyrolytic graphite.

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.

Surface structure and tribology of legless squamate reptiles

Squamate reptiles (around 10,000 species of snakes and lizards) comprise a myriad of distinct terrestrial vertebrates. The diversity within this biological group offers a great opportunity for customized bio-inspired solutions that address a variety of current technological problems especially within the realm of surface engineering and tribology. One subgroup within squamata is of interest in that context, namely the legless reptiles (mainly snakes and few lizards). The promise of that group lies within their functional adaptation as manifested in optimized surface designs and locomotion that is distinguished by economy of effort even when functioning within hostile tribological environments. Legless reptiles are spread over a wide range in the planet, this geographical diversity demands customized response to local habitats. Customization, in turn, is facilitated through specialized surface design features. In legless reptiles, micro elements of texture, their geometry and topological layout advance mitigation of frictional effects both in locomotion and in general function. Lately, the synergy between functional traits and intrinsic surface features has emerged as focus of research across disciplines. Many investigations have sought to characterize the structural as well as the tribological response of legless species from an engineering point of view. Despite the sizable amount of data that have accumulated in the literature over the past two decades or so, no effort to review the available information, whence this review. This manuscript, therefore, endeavors to assess available data on surface metrology and tribological behavior of legless reptiles and to define aspects of that performance necessary to formulate an advanced paradigm for bio-inspired surface engineering.

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.

Efficient nematode swimming in a shear thinning colloidal suspension

The swimming behavior of a nematode Caenorhabditis elegans (C. elegans) is investigated in a non-Newtonian shear thinning colloidal suspension. At the onset value (ϕ∼ 8%), the suspension begins to exhibit shear thinning behavior, and the average swimming speed of worms jumps by approximately 12% more than that measured in a Newtonian solution exhibiting no shear dependent viscosity. In the shear thinning regime, we observe a gradual yet significant improvement in swimming efficiency with an increase in ϕ while the swimming speed remains nearly constant. We postulate that this enhanced swimming can be explained by the temporal change in the stroke form of the nematode that is uniquely observed in a shear thinning colloidal suspension: the nematode features a fast and large stroke in its head to overcome the temporally high drag imposed by the viscous medium, whose effective viscosity (ηs) is shown to drop drastically, inversely proportional to the strength of its stroke. Our results suggest new insights into how nematodes efficiently maneuver through the complex fluid environment in their natural habitat.

Kinematic gait synthesis for snake robots

Snake robots are highly articulated mechanisms that can perform a variety of motions that conventional robots cannot. Despite many demonstrated successes of snake robots, these mechanisms have not been able to achieve the agility displayed by their biological counterparts. We suggest that studying how biological snakes coordinate whole-body motion to achieve agile behaviors can help improve the performance of snake robots. The foundation of this work is based on the hypothesis that, for snake locomotion that is approximately kinematic, replaying parameterized shape trajectory data collected from biological snakes can generate equivalent motions in snake robots. To test this hypothesis, we collected shape trajectory data from sidewinder rattlesnakes executing a variety of different behaviors. We then analyze the shape trajectory data in a concise and meaningful way by using a new algorithm, called conditioned basis array factorization, which projects high-dimensional data arrays onto a low-dimensional representation. The low-dimensional representation of the recorded snake motion is able to reproduce the essential features of the recorded biological snake motion on a snake robot, leading to improved agility and maneuverability, confirming our hypothesis. This parameterized representation allows us to search the low-dimensional parameter space to generate behaviors that further improve the performance of snake robots.

Controlled preparation of wet granular media reveals limits to lizard burial ability

Many animals move within ground composed of granular media (GM); the resistive properties of such substrates can depend on water content and compaction, but little is known about how such parameters affect locomotion or the physics of drag and penetration. Using apparatus to control compaction of GM, our recent studies of movement in dry GM have revealed locomotion strategies of specialized dry-sand-swimming reptiles. However, these animals represent a small fraction of the diversity and presumed burial strategies of fossorial reptilian fauna. Here we develop a system to create states of wet GM of varying moisture content and compaction in quantities sufficient to study the burial and subsurface locomotion of the Ocellated skink (C. ocellatus), a generalist lizard. X-ray imaging revealed that in wet and dry GM the lizard slowly buried (≈30 s) propagating a wave from head to tail, while moving in a start-stop motion. During forward movement, the head oscillated, and the forelimb on the convex side of the body propelled the animal. Although body kinematics and 'slip' were similar in both substrates, the burial depth was smaller in wet GM. Penetration and drag force experiments on smooth cylinders revealed that wet GM was ≈4× more resistive than dry GM. In total, our measurements indicate that while the rheology of the dry and wet GM differ substantially, the lizard's burial motor pattern is conserved across substrates, while its burial depth is largely constrained by environmental resistance.

Terradynamically streamlined shapes in animals and robots enhance traversability through densely cluttered terrain

Many animals, modern aircraft, and underwater vehicles use fusiform, streamlined body shapes that reduce fluid dynamic drag to achieve fast and effective locomotion in air and water. Similarly, numerous small terrestrial animals move through cluttered terrain where three-dimensional, multi-component obstacles like grass, shrubs, vines, and leaf litter also resist motion, but it is unknown whether their body shape plays a major role in traversal. Few ground vehicles or terrestrial robots have used body shape to more effectively traverse environments such as cluttered terrain. Here, we challenged forest-floor-dwelling discoid cockroaches (Blaberus discoidalis) possessing a thin, rounded body to traverse tall, narrowly spaced, vertical, grass-like compliant beams. Animals displayed high traversal performance (79 ± 12% probability and 3.4 ± 0.7 s time). Although we observed diverse obstacle traversal strategies, cockroaches primarily (48 ± 9% probability) used a novel roll maneuver, a form of natural parkour, allowing them to rapidly traverse obstacle gaps narrower than half their body width (2.0 ± 0.5 s traversal time). Reduction of body roundness by addition of artificial shells nearly inhibited roll maneuvers and decreased traversal performance. Inspired by this discovery, we added a thin, rounded exoskeletal shell to a legged robot with a nearly cuboidal body, common to many existing terrestrial robots. Without adding sensory feedback or changing the open-loop control, the rounded shell enabled the robot to traverse beam obstacles with gaps narrower than shell width via body roll. Such terradynamically 'streamlined' shapes can reduce terrain resistance and enhance traversability by assisting effective body reorientation via distributed mechanical feedback. Our findings highlight the need to consider body shape to improve robot mobility in real-world terrain often filled with clutter, and to develop better locomotor-ground contact models to understand interaction with 3D, multi-component terrain.

Behavioral and mechanical determinants of collective subsurface nest excavation

Collective construction of topologically complex structures is one of the triumphs of social behavior. For example, many ant species construct underground nests composed of networks of tunnels and chambers. Excavation by these ‘superorganisms’ depends on the biomechanics of substrate manipulation, the interaction of individuals, and media stability and cohesiveness. To discover principles of robust social excavation, we used X-ray computed tomography to monitor the growth in three dimensions of nests built by groups of fire ants (Solenopsis invicta) in laboratory substrates composed of silica particles, manipulating two substrate properties: particle size and gravimetric moisture content. Ants were capable of nest construction in all substrates tested other than completely dry or fully saturated; for a given particle size, nest volume was relatively insensitive to moisture content. Tunnels were deepest at intermediate moisture content and the maximum tunnel depth correlated with measured yield force on small rod-shaped intruders (a proxy for cohesive strength). This implies that increased cohesive strength allowed creation of tunnels that were resistant to perturbation but did not decrease individual excavation ability. Ants used two distinct behaviors to create pellets composed of wetted particles, depending on substrate composition. However, despite the ability to create larger stable pellets in more cohesive substrates, pellet sizes were similar across all conditions. We posit that this pellet size balances the individual's load-carrying ability with the need to carry this pellet through confined crowded tunnels. We conclude that effective excavation of similarly shaped nests can occur in a diversity of substrates through sophisticated digging behaviors by individuals which accommodate both differing substrate properties and the need to work within the collective.

Modulation of orthogonal body waves enables high maneuverability in sidewinding locomotion

Many organisms move using traveling waves of body undulation, and most work has focused on single-plane undulations in fluids. Less attention has been paid to multiplane undulations, which are particularly important in terrestrial environments where vertical undulations can regulate substrate contact. A seemingly complex mode of snake locomotion, sidewinding, can be described by the superposition of two waves: horizontal and vertical body waves with a phase difference of ± 90°. We demonstrate that the high maneuverability displayed by sidewinder rattlesnakes (Crotalus cerastes) emerges from the animal's ability to independently modulate these waves. Sidewinder rattlesnakes used two distinct turning methods, which we term differential turning (26° change in orientation per wave cycle) and reversal turning (89°). Observations of the snakes suggested that during differential turning the animals imposed an amplitude modulation in the horizontal wave whereas in reversal turning they shifted the phase of the vertical wave by 180°. We tested these mechanisms using a multimodule snake robot as a physical model, successfully generating differential and reversal turning with performance comparable to that of the organisms. Further manipulations of the two-wave system revealed a third turning mode, frequency turning, not observed in biological snakes, which produced large (127°) in-place turns. The two-wave system thus functions as a template (a targeted motor pattern) that enables complex behaviors in a high-degree-of-freedom system to emerge from relatively simple modulations to a basic pattern. Our study reveals the utility of templates in understanding the control of biological movement as well as in developing control schemes for limbless robots.