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.

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.

Blood python (Python brongersmai) strike kinematics and forces are robust to variations in substrate geometry

Snake strikes are some of the most rapid accelerations in terrestrial vertebrates. Generating rapid body accelerations requires high ground reaction forces, but on flat surfaces snakes must rely on static friction to prevent slip. We hypothesize that snakes may be able to take advantage of structures in the environment to prevent their body from slipping, potentially allowing them to generate faster and more forceful strikes. To test this hypothesis, we captured high-speed video and forces from defensive strikes of juvenile blood pythons (Python brongersmai) on a platform that was either open on all sides or with two adjacent walls opposite the direction of the strike. Contrary to our predictions, snakes maintained high performance on open platforms by imparting rearward momentum to the posterior body and tail. This compensatory behavior increases robustness to changes in their strike conditions and could allow them to exploit variable environments.

Corn Snakes Show Consistent Sarcomere Length Ranges Across Muscle Groups and Ontogeny

The force-generating capacity of muscle depends upon many factors including the actin-myosin filament overlap due to the relative length of the sarcomere. Consequently, the force output of a muscle may vary throughout its range of motion, and the body posture allowing maximum force generation may differ even in otherwise similar species. We hypothesized that corn snakes would show an ontogenetic shift in sarcomere length range from being centered on the plateau of the length-tension curve in small individuals to being on the descending limb in adults. Sarcomere lengths across the plateau would be advantageous for locomotion, while the descending limb would be advantageous for constriction due to the increase in force as the coil tightens around the prey. To test this hypothesis, we collected sarcomere lengths from freshly euthanized corn snakes, preserving segments in straight and maximally curved postures, and quantifying sarcomere length via light microscopy. We dissected 7 muscles (spinalis, semispinalis, multifidus, longissimus dorsi, iliocostalis (dorsal and ventral), and levator costae) in an ontogenetic series of corn snakes (mass = 80–335 g) at multiple regions along the body (anterior, middle, and posterior). Our data shows all of the muscles analyzed are on the descending limb of the length-tension curve at rest across all masses, regions, and muscles analyzed, with muscles shortening onto or past the plateau when flexed. While these results are consistent with being advantageous for constriction at all sizes, there could also be unknown benefits of this sarcomere arrangement for locomotion or striking.

Snakes combine vertical and lateral bending to traverse uneven terrain

Terrestrial locomotion requires generating appropriate ground reaction forces which depend on substrate geometry and physical properties. The richness of positions and orientations of terrain features in the 3D world gives limbless animals like snakes that can bend their body versatility to generate forces from different contact areas for propulsion. Despite many previous studies of how snakes use lateral body bending for propulsion on relatively flat surfaces with lateral contact points, little is known about whether and how much snakes use vertical body bending in combination with lateral bending in 3D terrain. This lack had contributed to snake robots being inferior to animals in stability, efficiency, and versatility when traversing complex 3D environments. Here, to begin to elucidate this, we studied how the generalist corn snake traversed an uneven arena of blocks of random height variation five times its body height. The animal traversed the uneven terrain with perfect stability by propagating 3D bending down its body with little transverse motion (11° slip angle). Although the animal preferred moving through valleys with higher neighboring blocks, it did not prefer lateral bending. Among body-terrain contact regions that potentially provide propulsion, 52% were formed by vertical body bending and 48% by lateral bending. The combination of vertical and lateral bending may dramatically expand the sources of propulsive forces available to limbless locomotors by utilizing various asperities available in 3D terrain. Direct measurements of contact forces are necessary to further understand how snakes coordinate 3D bending along the entire body via sensory feedback to propel through 3D terrain. These studies will open a path to new propulsive mechanisms for snake robots, potentially increasing the performance and versatility in 3D terrain.

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.

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

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

Defibrillate You Later, Alligator: Q10 Scaling and Refractoriness Keeps Alligators from Fibrillation

Effective cardiac contraction during each heartbeat relies on the coordination of an electrical wave of excitation propagating across the heart. Dynamically induced heterogeneous wave propagation may fracture and initiate reentry-based cardiac arrhythmias, during which fast-rotating electrical waves lead to repeated self-excitation that compromises cardiac function and potentially results in sudden cardiac death. Species which function effectively over a large range of heart temperatures must balance the many interacting, temperature-sensitive biochemical processes to maintain normal wave propagation at all temperatures. To investigate how these species avoid dangerous states across temperatures, we optically mapped the electrical activity across the surfaces of alligator (Alligator mississippiensis) hearts at 23°C and 38°C over a range of physiological heart rates and compare them with that of rabbits (Oryctolagus cuniculus). We find that unlike rabbits, alligators show minimal changes in wave parameters (action potential duration and conduction velocity) which complement each other to retain similar electrophysiological wavelengths across temperatures and pacing frequencies. The cardiac electrophysiology of rabbits accommodates the high heart rates necessary to sustain an active and endothermic metabolism at the cost of increased risk of cardiac arrhythmia and critical vulnerability to temperature changes, whereas that of alligators allows for effective function over a range of heart temperatures without risk of cardiac electrical arrhythmias such as fibrillation, but is restricted to low heart rates. Synopsis La contracción cardíaca efectiva durante cada latido del corazón depende de la coordinación de una onda eléctrica de excitación que se propaga a través del corazón. Heterogéidades inducidas dinámicamente por ondas de propagación pueden resultar en fracturas de las ondas e iniciar arritmias cardíacas basadas en ondas de reingreso, durante las cuales ondas espirales eléctricas de rotación rápida producen una autoexcitación repetida que afecta la función cardíaca y pude resultar en muerte súbita cardíaca. Las especies que funcionan eficazmente en una amplia gama de temperaturas cardíacas deben equilibrar los varios procesos bioquímicos que interactúan, sensibles a la temperatura para mantener la propagación normal de ondas a todas las temperaturas. Para investigar cómo estas especies evitan los estados peligrosos a través de las temperaturas, mapeamos ópticamente la actividad eléctrica a través de las superficies de los corazones de caimanes (Alligator mississippiensis) a 23°C and 38°C sobre un rango de frecuencias fisiológicas del corazón y comparamos con el de los conejos (Oryctolagus cuniculus). Encontramos que a diferencia de los conejos, los caimanes muestran cambios mínimos en los parámetros de onda (duración potencial de acción y velocidad de conducción) que se complementan entre sí para retener longitudes de onda electrofisiológicas similares a través de los rangos de temperaturas y frecuencias de ritmo. La electrofisiología cardíaca de los conejos acomoda las altas frecuencias cardíacas necesarias para mantener un metabolismo activo y endotérmico a costa de un mayor riesgo de arritmia cardíaca y vulnerabilidad crítica a los cambios de temperatura, mientras que la de los caimanes permite un funcionamiento eficaz en una serie de temperaturas cardíacas sin riesgo de arritmias eléctricas cardíacas como la fibrilación, pero está restringida a bajas frecuencias cardíacas.

Side-impact collision: mechanics of obstacle negotiation in sidewinding snakes

Snakes excel at moving through cluttered environments, and heterogeneities can be used as propulsive contacts for snakes performing lateral undulation. However, sidewinding, which is often associated with sandy deserts, cuts a broad path through its environment that may increase its vulnerability to obstacles. Our prior work demonstrated that sidewinding can be represented as a pair of orthogonal body waves (vertical and horizontal) that can be independently modulated to achieve high maneuverability and incline ascent, suggesting that sidewinders may also use template modulations to negotiate obstacles. To test this hypothesis, we recorded overhead video of four sidewinder rattlesnakes (Crotalus cerastes) crossing a line of vertical pegs placed in the substrate. Snakes used three methods to traverse the obstacles: a Propagate Through behavior in which the lifted moving portion of the snake was deformed around the peg and dragged through as the snake continued sidewinding (115/160 runs), Reversal turns that reorient the snake entirely (35/160), or switching to Concertina locomotion (10/160). The Propagate Through response was only used if the anterior-most region of static contact would propagate along a path anterior to the peg, or if a new region of static contact could be formed near the head to satisfy this condition; otherwise, snakes could only use Reversal turns or switch to Concertina locomotion. Reversal turns allowed the snake to re-orient and either escape without further peg contact or re-orient into a posture amenable to using the Propagate Through response. We developed an algorithm to reproduce the Propagate Through behavior in a robophysical model using a modulation of the two-wave template. This range of behavioral strategies provides sidewinders with a versatile range of options for effectively negotiating obstacles in their natural habitat, as well as provide insights into the design and control of robotic systems dealing with heterogeneous habitats.

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.

The control of routine fish maneuvers: Connecting midline kinematics to turn outcomes

Maneuverability is an important factor in determining an animal's ability to navigate its environment and succeed in predator-prey interactions. Although fish are capable of a wide range of maneuvers, most of the literature has focused on escape maneuvers while less attention has been paid to routine maneuvers, such as those used for habitat navigation. The quantitative relationships between body deformations and maneuver outcomes (displacement of the center of mass and change in trajectory) are fundamental to understanding how fish control their maneuvers, yet remain unknown in routine maneuvers. We recorded high-speed video of eight giant danios (Devario aquepinnatus) performing routine and escape maneuvers and quantified the deformation of the midline, the heading of the anterior body, and the kinematics of the centroid (a proxy for center of mass). We found that both routine and escape behaviors used qualitatively similar independent body bending events, which we curvature pulses, that propagate from head to tail but show quantitative differences in midline kinematics and turn outcomes. In routine maneuvers, the direction change and acceleration of the fish are influenced by both the magnitude of the bending pulse and by the duration of the pulse, whereas in escape maneuvers, only pulse duration influenced direction change and turn acceleration. The bending pulse appears to be the smallest functional unit of a turn, and can function independently or in combination, enabling a fish to achieve a wide range of complex maneuvers.

The Biomechanics of Multi-articular Muscle-Tendon Systems in Snakes

The geometry of the musculoskeletal system, such as moment arms and linkages, determines the link between muscular functions and external mechanical results, but as the geometry becomes more complex, this link becomes less clear. The musculoskeletal system of snakes is extremely complex, with several muscles that span dozens of vertebrae, ranging from 10 to 45 vertebrae in the snake semispinalis-spinalis muscle (a dorsiflexor). Furthermore, this span correlates with habitat in Caenophidians, with burrowing and aquatic species showing shorter spans while arboreal species show longer spans. Similar multi-articular spans are present in the prehensile tails of primates, the necks of birds, and our own digits. However, no previous analysis has adequately explained the mechanical consequences of these multi-articular spans. This paper uses techniques from the analysis of static systems in engineering to analyze the consequences of multiarticular muscle configurations in cantilevered gap bridging and compares these outcomes to a hypothetical mono-articular system. Multi-articular muscle spans dramatically reduce the forces needed in each muscle, but the consequent partitioning of muscle cross-sectional area between numerous muscles results in a small net performance loss. However, when a substantial fraction of this span is tendinous, performance increases dramatically. Similarly, metabolic cost is increased for purely muscular multi-articular spans, but decreases rapidly with increasing tendon ratio. However, highly tendinous spans require increased muscle strain to achieve the same motion, while purely muscular systems are unaffected. These results correspond well with comparative data from snakes and offer the potential to dramatically improve the mechanics of biomimetic snake robots.

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.

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.

Comparative and functional analysis of the digital mucus glands and secretions of tree frogs

Background

Mucus and mucus glands are important features of the amphibian cutis. In tree frogs, the mucus glands and their secretions are crucial components of the adhesive digital pads of these animals. Despite a variety of hypothesised functions of these components in tree frog attachment, the functional morphology of the digital mucus glands and the chemistry of the digital mucus are barely known. Here, we use an interdisciplinary comparative approach to analyse these components, and discuss their roles in tree frog attachment.

Results

Using synchrotron micro-computer-tomography, we discovered in the arboreal frog Hyla cinerea that the ventral digital mucus glands differ in their morphology from regular anuran mucus glands and form a subdermal gland cluster. We show the presence of this gland cluster also in several other—not exclusively arboreal—anuran families. Using cryo-histochemistry as well as infrared and sum frequency generation spectroscopy on the mucus of two arboreal (H. cinerea and Osteopilus septentrionalis) and of two terrestrial, non-climbing frog species (Pyxicephalus adspersus and Ceratophrys cranwelli), we find neutral and acidic polysaccharides, and indications for proteinaceous and lipid-like mucus components. The mucus chemistry varies only little between dorsal and ventral digital mucus in H. cinerea, ventral digital and abdominal mucus in H. cinerea and O. septentrionalis, and between the ventral abdominal mucus of all four studied species.

Conclusions

The presence of a digital mucus gland cluster in various anuran families, as well as the absence of differences in the mucus chemistry between arboreal and non-arboreal frog species indicate an adaptation towards generic functional requirements as well as to attachment-related requirements. Overall, this study contributes to the understanding of the role of glands and their secretions in tree frog attachment and in bioadhesion in general, as well as the evolution of anurans.

Electronic supplementary material

The online version of this article (10.1186/s12983-019-0315-z) contains supplementary material, which is available to authorized users.

The diversity and evolution of locomotor muscle properties in anurans

Anuran jumping is a model system for linking muscle physiology to organismal performance. However, anuran species display substantial diversity in their locomotion, with some species performing powerful leaps from riverbanks or tree branches, while other species move predominantly via swimming, short hops or even diagonal-sequence gaits. Furthermore, many anurans with similar locomotion and morphology are actually convergent (e.g. multiple independent evolutions of 'tree frogs'), while closely related species may differ drastically, as with the walking toad (Melanophryniscus stelzneri) and bullfrog-like river toad (Phrynoides aspera) compared with other Bufonid toads. These multiple independent evolutionary changes in locomotion allow us to test the hypothesis that evolutionary increases in locomotor performance will be linked to the evolution of faster, high-power muscles. I tested the jumping, swimming and walking (when applicable) performance of 14 species of anurans and one salamander, followed by measurement of the contractile properties of the semimembranosus and plantaris longus muscles and anatomical measurements, using phylogenetic comparative methods. I found that increased jumping performance correlated to muscle contractile properties associated with muscle speed (e.g. time to peak tetanus, maximum shortening speed, peak isotonic power), and was tightly linked to relevant anatomical traits (e.g. leg length, muscle mass). Swimming performance was not correlated to jumping, and was correlated with fewer anatomical and muscular variables. Thus, muscle properties evolve along with changes in anatomy to produce differences in overall locomotor performance.

Robust jumping performance and elastic energy recovery from compliant perches in tree frogs

Arboreal animals often move on compliant branches, which may deform substantially under loads, absorbing energy. Energy stored in a compliant substrate may be returned to the animal or it may be lost. In all cases studied so far, animals jumping from a static start lose all of the energy imparted to compliant substrates and performance is reduced. Cuban tree frogs (Osteopilus septentrionalis) are particularly capable arboreal jumpers, and we hypothesized that these animals would be able to recover energy from perches of varying compliance. In spite of large deflections of the perches and consequent substantial energy absorption, frogs were able to regain some of the energy lost to the perch during the recoil. Takeoff velocity was robust to changes in compliance, but was lower than when jumping from flat surfaces. This highlights the ability of animals to minimize energy loss and maintain dependable performance on challenging substrates via behavioral changes.

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.

The mechanics of elastic loading and recoil in anuran jumping

Many animals use catapult mechanisms to produce extremely rapid movements for escape or prey capture, resulting in power outputs far beyond the limits of muscle. In these catapults, muscle contraction loads elastic structures, which then recoil to release the stored energy extremely rapidly. Many arthropods employ anatomical ‘catch mechanisms’ to lock the joint in place during the loading period, which can then be released to allow joint motion via elastic recoil. Jumping vertebrates lack a clear anatomical catch, yet face the same requirement to load the elastic structure prior to movement. There are several potential mechanisms to allow loading of vertebrate elastic structures, including the gravitational load of the body, a variable mechanical advantage, and moments generated by the musculature of proximal joints. To test these hypothesized mechanisms, we collected simultaneous 3D kinematics via X-ray Reconstruction of Moving Morphology (XROMM) and single-foot forces during the jumps of three Rana pipiens. We calculated joint mechanical advantage, moment and power using inverse dynamics at the ankle, knee, hip and ilio-sacral joints. We found that the increasing proximal joint moments early in the jump allowed for high ankle muscle forces and elastic pre-loading, and the subsequent reduction in these moments allowed the ankle to extend using elastic recoil. Mechanical advantage also changed throughout the jump, with the muscle contracting against a poor mechanical advantage early in the jump during loading and a higher mechanical advantage late in the jump during recoil. These ‘dynamic catch mechanisms’ serve to resist joint motion during elastic loading, then allow it during elastic recoil, functioning as a catch mechanism based on the balance and orientation of forces throughout the limb rather than an anatomical catch.

Chasing maximal performance: a cautionary tale from the celebrated jumping frogs of Calaveras County

Maximal performance is an essential metric for understanding many aspects of an organism's biology, but it can be difficult to determine because a measured maximum may reflect only a peak level of effort, not a physiological limit. We used a unique opportunity provided by a frog jumping contest to evaluate the validity of existing laboratory estimates of maximum jumping performance in bullfrogs (Rana catesbeiana). We recorded video of 3124 bullfrog jumps over the course of the 4-day contest at the Calaveras County Jumping Frog Jubilee, and determined jump distance from these images and a calibration of the jump arena. Frogs were divided into two groups: 'rental' frogs collected by fair organizers and jumped by the general public, and frogs collected and jumped by experienced, 'professional' teams. A total of 58% of recorded jumps surpassed the maximum jump distance in the literature (1.295 m), and the longest jump was 2.2 m. Compared with rental frogs, professionally jumped frogs jumped farther, and the distribution of jump distances for this group was skewed towards long jumps. Calculated muscular work, historical records and the skewed distribution of jump distances all suggest that the longest jumps represent the true performance limit for this species. Using resampling, we estimated the probability of observing a given jump distance for various sample sizes, showing that large sample sizes are required to detect rare maximal jumps. These results show the importance of sample size, animal motivation and physiological conditions for accurate maximal performance estimates.

Getting around when you're round: quantitative analysis of the locomotion of the blunt-spined brittle star, Ophiocoma echinata

Brittle stars (Ophiuroidea, Echinodermata) are pentaradially symmetrical echinoderms that use five multi-jointed limbs to locomote along the seafloor. Prior qualitative descriptions have claimed coordinated movements of the limbs in a manner similar to tetrapod vertebrates, but this has not been evaluated quantitatively. It is uncertain whether the ring-shaped nervous system, which lacks an anatomically defined anterior, is capable of generating rhythmic coordinated movements of multiple limbs. This study tested whether brittle stars possess distinct locomotor modes with strong inter-limb coordination as seen in limbed animals in other phyla (e.g. tetrapods and arthropods), or instead move each limb independently according to local sensory feedback. Limb tips and the body disk were digitized for 56 cycles from 13 individuals moving across sand. Despite their pentaradial anatomy, all individuals were functionally bilateral, moving along the axis of a central limb via synchronous motions of contralateral limbs (±~13% phase lag). Two locomotor modes were observed, distinguishable mainly by whether the central limb was directed forwards or backwards. Turning was accomplished without rotation of the body disk by defining a different limb as the center limb and shifting other limb identities correspondingly, and then continuing locomotion in the direction of the newly defined anterior. These observations support the hypothesis that, in spite of their radial body plan, brittle stars employ coordinated, bilaterally symmetrical locomotion.

Evidence for a vertebrate catapult: elastic energy storage in the plantaris tendon during frog jumping

Anuran jumping is one of the most powerful accelerations in vertebrate locomotion. Several species are hypothesized to use a catapult-like mechanism to store and rapidly release elastic energy, producing power outputs far beyond the capability of muscle. Most evidence for this mechanism comes from measurements of whole-body power output; the decoupling of joint motion and muscle shortening expected in a catapult-like mechanism has not been demonstrated. We used high-speed marker-based biplanar X-ray cinefluoroscopy to quantify plantaris muscle fascicle strain and ankle joint motion in frogs in order to test for two hallmarks of a catapult mechanism: (i) shortening of fascicles prior to joint movement (during tendon stretch), and (ii) rapid joint movement during the jump without rapid muscle-shortening (during tendon recoil). During all jumps, muscle fascicles shortened by an average of 7.8 per cent (54% of total strain) prior to joint movement, stretching the tendon. The subsequent period of initial joint movement and high joint angular acceleration occurred with minimal muscle fascicle length change, consistent with the recoil of the elastic tendon. These data support the plantaris longus tendon as a site of elastic energy storage during frog jumping, and demonstrate that catapult mechanisms may be employed even in sub-maximal jumps.

Evidence for a vertebrate catapult: elastic energy storage in the plantaris tendon during frog jumping

Anuran jumping is one of the most powerful accelerations in vertebrate locomotion. Several species are hypothesized to use a catapult-like mechanism to store and rapidly release elastic energy, producing power outputs far beyond the capability of muscle. Most evidence for this mechanism comes from measurements of whole-body power output; the decoupling of joint motion and muscle shortening expected in a catapult-like mechanism has not been demonstrated. We used high-speed marker-based biplanar X-ray cinefluoroscopy to quantify plantaris muscle fascicle strain and ankle joint motion in frogs in order to test for two hallmarks of a catapult mechanism: (i) shortening of fascicles prior to joint movement (during tendon stretch), and (ii) rapid joint movement during the jump without rapid muscle-shortening (during tendon recoil). During all jumps, muscle fascicles shortened by an average of 7.8 per cent (54% of total strain) prior to joint movement, stretching the tendon. The subsequent period of initial joint movement and high joint angular acceleration occurred with minimal muscle fascicle length change, consistent with the recoil of the elastic tendon. These data support the plantaris longus tendon as a site of elastic energy storage during frog jumping, and demonstrate that catapult mechanisms may be employed even in sub-maximal jumps.

Effects of perch diameter and incline on the kinematics, performance and modes of arboreal locomotion of corn snakes (Elaphe guttata)

Animals moving through arboreal habitats face several functional challenges, including fitting onto and moving on cylindrical branches with variable diameters and inclines. In contrast to lizards and primates, the arboreal locomotion of snakes is poorly understood, despite numerous snake species being arboreal. We quantified the kinematics and performance of corn snakes (Elaphe guttata) moving on seven cylinders (diameters 1.6–21 cm) with five inclines (horizontal, ±45° and±90°) and through horizontal tunnels of corresponding widths. When perches were inclined at either 45° or 90°, snakes were unable to move uphill or downhill on the larger diameters. None of the locomotion on perches conformed to any previously described mode of limbless locomotion. On horizontal and uphill perches snakes performed a variant of concertina locomotion with periodic stopping and gripping. When moving downhill, snakes often slid continuously while grasping the perch to reduce their speed. Mean forward velocity decreased both with increased incline and with increased perch diameter, contrary to the beneficial effect of increased diameter on the speeds of lizards. Both tunnel width and perch diameter had widespread and similar effects on kinematics. When perches and tunnels were narrower, the snakes had more lateral bends at shallower angles. The numerous effects of perch diameter on kinematics and the similarity to tunnel concertina locomotion emphasize the importance of fit as a limitation in arboreal locomotion of snakes. However, the slower speeds on horizontal perches compared to tunnels also suggest that balance and grip may further limit locomotor performance.