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

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.

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.

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.

The relative contributions of multiarticular snake muscles to movement in different planes

Muscles spanning multiple joints play important functional roles in a wide range of systems across tetrapods; however, their fundamental mechanics are poorly understood, particularly the consequences of anatomical position on mechanical advantage. Snakes provide an excellent study system for advancing this topic. They rely on the axial muscles for many activities, including striking, constriction, defensive displays, and locomotion. Moreover, those muscles span from one or a few vertebrae to over 30, and anatomy varies among muscles and among species. We characterized the anatomy of major epaxial muscles in a size series of corn snakes (Pantherophis guttatus) using diceCT scans, and then took several approaches to calculating contributions of each muscle to force and motion generated during body bending, starting from a highly simplistic model and moving to increasingly complex and realistic models. Only the most realistic model yielded equations that included the consequence of muscle span on torque-displacement trade-offs, as well as resolving ambiguities that arose from simpler models. We also tested whether muscle cross-sectional areas or lever arms (total magnitude or pitch/yaw/roll components) were related to snake mass, longitudinal body region (anterior, middle, posterior), and/or muscle group (semispinalis-spinalis, multifidus, longissimus dorsi, iliocostalis, and levator costae). Muscle cross-sectional areas generally scaled with positive allometry, and most lever arms did not depart significantly from geometric similarity (isometry). The levator costae had lower cross-sectional area than the four epaxial muscles, which did not differ significantly from each other in cross-sectional area. Lever arm total magnitudes and components differed among muscles. We found some evidence for regional variation, indicating that functional regionalization merits further investigation. Our results contribute to knowledge of snake muscles specifically and multiarticular muscle systems generally, providing a foundation for future comparisons across species and bioinspired multiarticular systems.

Chronic Multi-Electrode Electromyography in Snakes

Knowledge about body motion kinematics and underlying muscle contraction dynamics usually derives from electromyographic (EMG) recordings. However, acquisition of such signals in snakes is challenging because electrodes either attached to or implanted beneath the skin may unintentionally be removed by force or friction caused from undulatory motion, thus severely impeding chronic EMG recordings. Here, we present a reliable method for stable subdermal implantation of up to eight bipolar electrodes above the target muscles. The mechanical stability of the inserted electrodes and the overnight coverage of the snake body with a “sleeping bag” ensured the recording of reliable and robust chronic EMG activity. The utility of the technique was verified by daily acquisition of high signal-to-noise activity from all target sites over four consecutive days during stimulus-evoked postural reactions in Amazon tree boas and Western diamondback rattlesnakes. The successful demonstration of the chronic recording suggests that this technique can improve acute experiments by enabling the collection of larger data sets from single individuals.

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.

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.

Morphological function of toe fringe in the sand lizard Phrynocephalus mystaceus

Toe fringe is the most typical morphological feature of lizards adapted to sandy environments, and it is simple in shape, can evolve repeatedly, and has a high degree of repetition; therefore, this feature is suitable for testing the adaptive convergence suggested by form-environment correlations. Phrynocephalus mystaceus mainly lives in dune habitats, has a developed bilateral toe fringe, and exhibits fast sand-burying behavior for predator avoidance. We tested the effects of resecting the medial and bilateral toe fringes on the locomotor performance and sand-burying performance of P. mystaceus. The results showed that the maximum sprint speed and acceleration on sand substrate did not significantly differ under different conditions (P > 0.05). Sand-burying performance scores of the unresected individuals were significantly greater than those of the resected individuals (P < 0.05). A partial least squares (PLS) regression analysis showed that the relative area of toe fringe was the main factor affecting the sand-burying performance of unresected P. mystaceus. For lizards without fringe, the PLS regression showed that the swinging index of the hind-limb was the main factor affecting the sand-burying performance of the lizard. A comparison of the swinging indexes of the hind-limb of the lizard under three states revealed that under the unresected states, the frequency of the swinging of the hind-limb was significantly higher than those of lizards with resected bilateral fringes, further indicating that the lizards compensated for the loss of fringe by increasing the time and frequency of swinging of the hind-limb. A path analysis also showed that the fringe affected the sand-burying performance of P. mystaceus not only directly but also indirectly by affecting the frequency of the swinging of the hind-limb. After the bilateral toe fringe was removed, a significant negative correlation between locomotor and sand-burying performance was observed (P < 0.05). Taken together, these results provide experimental evidence that toe fringe is positively associated with the sand-burying performance of P. mystaceus.

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.

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.

Angles and waves: intervertebral joint angles and axial kinematics of limbed lizards, limbless lizards, and snakes

Segmentation gives rise to the anterior-posterior axis in many animals, and in vertebrates this axis comprises serially arranged vertebrae. Modifications to the vertebral column abound, and a recurring, but functionally understudied, change is the elongation of the body through the addition and/or elongation of vertebrae. Here, we compared the vertebral and axial kinematics of the robustly limbed Fire skink (Riopa fernandi) representing the ancestral form, the limbless European glass lizard (Ophisaurus apodus), and the Northern water snake (Nerodia sipedon). We induced these animals to traverse through channels and peg arrays of varied widths and densities, respectively, using high-speed X-ray and light video. We found that even though the snake had substantially more and shorter vertebrae than either lizard, intervertebral joint angles did not differ between species in most treatment levels. All three species decreased the amplitude and wavelength of their undulations as channels narrowed and the lizard species increased wave frequency in narrower channels. In peg arrays, both lizard species decreased wave amplitude, while the snake showed no differences. All three species maintained similar wavelengths and frequencies as peg density increased in most cases. Our results suggest that amplitude is decoupled from wavelength and frequency in all three focal taxa. The combination of musculoskeletal differences and the decoupling of axial kinematic traits likely facilitates the formation of different undulatory waves, thereby allowing limbless species to adopt different modes 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.

A review on locomotion robophysics: the study of movement at the intersection of robotics, soft matter and dynamical systems

Discovery of fundamental principles which govern and limit effective locomotion (self-propulsion) is of intellectual interest and practical importance. Human technology has created robotic moving systems that excel in movement on and within environments of societal interest: paved roads, open air and water. However, such devices cannot yet robustly and efficiently navigate (as animals do) the enormous diversity of natural environments which might be of future interest for autonomous robots; examples include vertical surfaces like trees and cliffs, heterogeneous ground like desert rubble and brush, turbulent flows found near seashores, and deformable/flowable substrates like sand, mud and soil. In this review we argue for the creation of a physics of moving systems-a 'locomotion robophysics'-which we define as the pursuit of principles of self-generated motion. Robophysics can provide an important intellectual complement to the discipline of robotics, largely the domain of researchers from engineering and computer science. The essential idea is that we must complement the study of complex robots in complex situations with systematic study of simplified robotic devices in controlled laboratory settings and in simplified theoretical models. We must thus use the methods of physics to examine both locomotor successes and failures using parameter space exploration, systematic control, and techniques from dynamical systems. Using examples from our and others' research, we will discuss how such robophysical studies have begun to aid engineers in the creation of devices that have begun to achieve life-like locomotor abilities on and within complex environments, have inspired interesting physics questions in low dimensional dynamical systems, geometric mechanics and soft matter physics, and have been useful to develop models for biological locomotion in complex terrain. The rapidly decreasing cost of constructing robot models with easy access to significant computational power bodes well for scientists and engineers to engage in a discipline which can readily integrate experiment, theory and computation.

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.

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.

Morphology and burrowing energetics of semi-fossorial skinks (Liopholis)

Burrowing is an important form of locomotion in reptiles, but no study has examined the energetic cost of burrowing for reptiles. This is significant since burrowing is the most energetically expensive mode of locomotion undertaken by animals, and many burrowing species therefore show specialisations for their subterranean lifestyle. We examined the effect of temperature and substrate characteristics (coarse sand or fine sand) on the net energetic cost of burrowing (NCOB) and burrowing rate in two species of the Egernia group of skinks (Liopholis striata and Liopholis inornata) and compared it with those of other burrowing animals. We further tested for morphological specialisations among burrowing species by comparing the relationship between body shape and retreat preference in Egernia skinks. For L. striata and L. inornata, NCOB is 350 times more expensive than the predicted cost of pedestrian terrestrial locomotion. Temperature had a positive effect on burrowing rate for both species, and a negative effect on NCOB for L. striata but not L. inornata. Both NCOB and burrowing rate were independent of substrate type. Burrows constructed by skinks had smaller cross-sectional area than those constructed by mammals of comparable mass, and NCOB of skinks was lower than that of mammals of similar mass. After accounting for body size, retreat preference was significantly correlated with body shape in Egernia group skinks. Species of Egernia group skinks that use burrows for retreats have narrower bodies and shorter front limbs than other species. We conclude that the morphological specialisations of burrowing skinks allow them to construct relatively narrow burrows, thereby reducing NCOB and the total cost of constructing their burrow retreats.

Flexibility of the axial central pattern generator network for locomotion in the salamander

In tetrapods, limb and axial movements are coordinated during locomotion. It is well established that inter- and intralimb coordination show considerable variations during ongoing locomotion. Much less is known about the flexibility of the axial musculoskeletal system during locomotion and the neural mechanisms involved. Here we examined this issue in the salamander Pleurodeles waltlii, which is capable of locomotion in both aquatic and terrestrial environments. Kinematics of the trunk and electromyograms from the mid-trunk epaxial myotomes were recorded during four locomotor behaviors in freely moving animals. A similar approach was used during rhythmic struggling movements since this would give some insight into the flexibility of the axial motor system. Our results show that each of the forms of locomotion and the struggling behavior is characterized by a distinct combination of mid-trunk motor patterns and cycle durations. Using in vitro electrophysiological recordings in isolated spinal cords, we observed that the spinal networks activated with bath-applied N-methyl-d-aspartate could generate these axial motor patterns. In these isolated spinal cord preparations, the limb motor nerve activities were coordinated with each mid-trunk motor pattern. Furthermore, isolated mid-trunk spinal cords and hemicords could generate the mid-trunk motor patterns. This indicates that each side of the cord comprises a network able to generate coordinated axial motor activity. The roles of descending and sensory inputs in the behavior-related changes in axial motor coordination are discussed.

Locomotor benefits of being a slender and slick sand swimmer

Squamates classified as 'subarenaceous' possess the ability to move long distances within dry sand; body elongation among sand and soil burrowers has been hypothesized to enhance subsurface performance. Using X-ray imaging, we performed the first kinematic investigation of the subsurface locomotion of the long, slender shovel-nosed snake (Chionactis occipitalis) and compared its biomechanics with those of the shorter, limbed sandfish lizard (Scincus scincus). The sandfish was previously shown to maximize swimming speed and minimize the mechanical cost of transport during burial. Our measurements revealed that the snake also swims through sand by propagating traveling waves down the body, head to tail. Unlike the sandfish, the snake nearly followed its own tracks, thus swimming in an approximate tube of self-fluidized granular media. We measured deviations from tube movement by introducing a parameter, the local slip angle, βs, which measures the angle between the direction of movement of each segment and body orientation. The average βs was smaller for the snake than for the sandfish; granular resistive force theory (RFT) revealed that the curvature utilized by each animal optimized its performance. The snake benefits from its slender body shape (and increased vertebral number), which allows propagation of a higher number of optimal curvature body undulations. The snake's low skin friction also increases performance. The agreement between experiment and RFT combined with the relatively simple properties of the granular 'frictional fluid' make subarenaceous swimming an attractive system to study functional morphology and bauplan evolution.

Emergence of the advancing neuromechanical phase in a resistive force dominated medium

Undulatory locomotion, a gait in which thrust is produced in the opposite direction of a traveling wave of body bending, is a common mode of propulsion used by animals in fluids, on land, and even within sand. As such, it has been an excellent system for discovery of neuromechanical principles of movement. In nearly all animals studied, the wave of muscle activation progresses faster than the wave of body bending, leading to an advancing phase of activation relative to the curvature toward the tail. This is referred to as "neuromechanical phase lags" (NPL). Several multiparameter neuromechanical models have reproduced this phenomenon, but due to model complexity, the origin of the NPL has proved difficult to identify. Here, we use perhaps the simplest model of undulatory swimming to predict the NPL accurately during sand-swimming by the sandfish lizard, with no fitting parameters. The sinusoidal wave used in sandfish locomotion, the friction-dominated and noninertial granular resistive force environment, and the simplicity of the model allow detailed analysis, and reveal the fundamental mechanism responsible for the phenomenon: the combination of synchronized torques from distant points on the body and local traveling torques. This general mechanism should help explain the NPL in organisms in other environments; we therefore propose that sand-swimming could be an excellent system with which to generate and test other neuromechanical models of movement quantitatively. Such a system can also provide guidance for the design and control of robotic undulatory locomotors in complex environments.

Mechanics of undulatory swimming in a frictional fluid

The sandfish lizard (Scincus scincus) swims within granular media (sand) using axial body undulations to propel itself without the use of limbs. In previous work we predicted average swimming speed by developing a numerical simulation that incorporated experimentally measured biological kinematics into a multibody sandfish model. The model was coupled to an experimentally validated soft sphere discrete element method simulation of the granular medium. In this paper, we use the simulation to study the detailed mechanics of undulatory swimming in a "granular frictional fluid" and compare the predictions to our previously developed resistive force theory (RFT) which models sand-swimming using empirically determined granular drag laws. The simulation reveals that the forward speed of the center of mass (CoM) oscillates about its average speed in antiphase with head drag. The coupling between overall body motion and body deformation results in a non-trivial pattern in the magnitude of lateral displacement of the segments along the body. The actuator torque and segment power are maximal near the center of the body and decrease to zero toward the head and the tail. Approximately 30% of the net swimming power is dissipated in head drag. The power consumption is proportional to the frequency in the biologically relevant range, which confirms that frictional forces dominate during sand-swimming by the sandfish. Comparison of the segmental forces measured in simulation with the force on a laterally oscillating rod reveals that a granular hysteresis effect causes the overestimation of the body thrust forces in the RFT. Our models provide detailed testable predictions for biological locomotion in a granular environment.

Multi-functional foot use during running in the zebra-tailed lizard (Callisaurus draconoides)

A diversity of animals that run on solid, level, flat, non-slip surfaces appear to bounce on their legs; elastic elements in the limbs can store and return energy during each step. The mechanics and energetics of running in natural terrain, particularly on surfaces that can yield and flow under stress, is less understood. The zebra-tailed lizard (Callisaurus draconoides), a small desert generalist with a large, elongate, tendinous hind foot, runs rapidly across a variety of natural substrates. We use high speed video to obtain detailed three-dimensional running kinematics on solid and granular surfaces to reveal how leg, foot, and substrate mechanics contribute to its high locomotor performance. Running at ~10 body length/s (~1 m/s), the center of mass oscillates like a spring-mass system on both substrates, with only 15% reduction in stride length on the granular surface. On the solid surface, a strut-spring model of the hind limb reveals that the hind foot saves about 40% of the mechanical work needed per step, significant for the lizard's small size. On the granular surface, a penetration force model and hypothesized subsurface foot rotation indicates that the hind foot paddles through fluidized granular medium, and that the energy lost during irreversible deformation of the substrate does not differ from the reduction in the mechanical energy of the center of mass. The upper hind leg muscles must perform three times as much mechanical work on the granular surface as on the solid surface to compensate for the greater energy lost within the foot and to the substrate.