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.

Influence of posture during gliding flight in the flying lizardDraco volans

The agamid lizards of the genusDracoare undoubtedly the most renown reptilian gliders, using their rib-supported patagial wings as lifting surfaces while airborne. Recent investigations into these reptiles highlighted the role of body posture during gliding, however, the aerodynamics of postural changes inDracoremain unclear. Here, we examine the aerodynamics and gliding performances ofDraco volansusing a numerical approach focusing on three postural changes: wing expansion, body camber, and limb positioning. To this aim, we conducted 70 three-dimensional steady-state computational fluid dynamics simulations of gliding flight and 240 two-dimensional glide trajectory calculations. Our results demonstrate that while airborne,D. volansgenerates a separated turbulent boundary layer over its wings characterized by a large recirculation cell that is kept attached to the wing surface by interaction with wing-tip vortices, increasing lift generation. This lift generating mechanism may be controlled by changing wing expansion and shape to modulate the generation of aerodynamic force. Furthermore, our trajectory simulations highlight the influence of body camber and orientation on glide range. This sheds light on howD. volanscontrols its gliding performance, and conforms to the observation that these animals plan their glide paths prior to take off. Lastly,D. volansis mostly neutral in pitch and highly maneuverable, similar to other vertebrate gliders. The numerical study presented here thus provides a better understanding of the lift generating mechanism and the influence of postural changes in flight in this emblematic animal and will facilitate the study of gliding flight in analogous gliding reptiles for which direct observations are unavailable.

Dynamic gap crossing in Dendrelaphis, the sister taxon of flying snakes

Arboreal animals commonly use dynamic gap-crossing behaviors such as jumping. In snakes, however, most species studied to date only employ the quasi-static cantilever crawl, which involves a whole-body reach. One exception is the paradise tree snake (Chrysopelea paradisi), which exhibits kinematic changes as gap distance increases, culminating in dynamic behaviors that are kinematically indistinguishable from those used to launch glides. Because Chrysopelea uses dynamic behaviors when bridging gaps without gliding, we hypothesized that such dynamic behaviors evolved ancestrally to Chrysopelea. To test this predicted occurrence of dynamic behaviors in closely related taxa, we studied gap bridging locomotion in the genus Dendrelaphis, which is the sister lineage of Chysopelea. We recorded 20 snakes from two species (D. punctulatus and D. calligastra) crossing gaps of increasing size, and analyzed their 3D kinematics. We found that, like C. paradisi, both species of Dendrelaphis modulate their use of dynamic behaviors in response to gap distance, but Dendrelaphis exhibit greater inter-individual variation. Although all three species displayed the use of looped movements, the highly stereotyped J-loop movement of Chrysopelea was not observed in Dendrelaphis. These results support the hypothesis that Chrysopelea may have co-opted and refined an ancestral behavior for crossing gaps for the novel function of launching a glide. Overall, these data demonstrate the importance of gap distance in governing behavior and kinematics during arboreal gap crossing.

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.

Complex Three-Dimensional Terrains Traversal of Insect-Scale Soft Robot

This article proposes a piezoelectric-driven insect-scale soft robot with ring-like curved legs, enabling it to traverse complex three-dimensional (3D) terrain only by body-terrain mechanical action. Relying on the repeated deformation of the main body's n and u shapes, the robot's leg-ground mechanical action produces an "elastic gait" to move. Regarding the detailed design, first, a theoretical curve of the front leg with a fixed angle of attack of 75° is designed by finite element simulation and comparative experiments. It ensures no increase in drag and no decrease in the lift when climbing steps. Second, a ring-like leg structure with 100% closed degree is proposed to ensure a smooth pass through small-sized uneven terrain without getting stuck. Then, the design of the overall asymmetrical structure of the robot can improve the conversion ratio of vibration to forward force. The shape of curved legs is controlled by pulling the flexible leg structure with two metal wires working as spokes. The semirigid leg structure made of fully flexible materials has shape stability and structural robustness. Compared with the plane-legged robot, the curved-legged robot can smoothly traverse different rugged 3D terrains and cross the terrain covering obstacles 0.36 times body height (BH) at a speed of >4 body lengths per second. Moreover, the curved-legged robot shows 100% and 64% chances of climbing steps with 1.2- and 1.9-times BH, respectively.

Jumping with adhesion: landing surface incline alters impact force and body kinematics in crested geckos

Arboreal habitats are characterized by a complex three-dimensional array of branches that vary in numerous characteristics, including incline, compliance, roughness, and diameter. Gaps must often be crossed, and this is frequently accomplished by leaping. Geckos bearing an adhesive system often jump in arboreal habitats, although few studies have examined their jumping biomechanics. We investigated the biomechanics of landing on smooth surfaces in crested geckos, Correlophus ciliatus, asking whether the incline of the landing platform alters impact forces and mid-air body movements. Using high-speed videography, we examined jumps from a horizontal take-off platform to horizontal, 45° and 90° landing platforms. Take-off velocity was greatest when geckos were jumping to a horizontal platform. Geckos did not modulate their body orientation in the air. Body curvature during landing, and landing duration, were greatest on the vertical platform. Together, these significantly reduced the impact force on the vertical platform. When landing on a smooth vertical surface, the geckos must engage the adhesive system to prevent slipping and falling. In contrast, landing on a horizontal surface requires no adhesion, but incurs high impact forces. Despite a lack of mid-air modulation, geckos appear robust to changing landing conditions.

Dynamic movements facilitate extreme gap crossing in flying snakes

In arboreal habitats, direct routes between two locations can be impeded by gaps in the vegetation. Arboreal animals typically use dynamic movements, such as jumping, to navigate these gaps if the distance between supports exceeds their reaching ability. In contrast, most snakes only use the cantilever crawl to cross gaps. This behavior imposes large torques on the animal, inhibiting their gap-crossing capabilities. Flying snakes (Chrysopelea), however, are known to use dynamic behaviors in a different arboreal context: they use a high-acceleration jump to initiate glides. We hypothesized that flying snakes also use jumping take-off behaviors to cross gaps, allowing them to cross larger distances. To test this hypothesis, we used a six-camera motion-capture system to investigate the effect of gap size on crossing behavior in Chrysopelea paradisi, and analyzed the associated kinematics and torque requirements. We found that C. paradisi typically uses cantilevering for small gaps (<47.5% snout-vent length, SVL). Above this distance, C. paradisi were more likely to use dynamic movements than cantilevers, either arching upward or employing a below-branch loop of the body. These dynamic movements extended the range of horizontal crossing to ∼120% SVL. The behaviors used for the largest gaps were kinematically similar to the J-loop jumps used in gliding, and involved smaller torques than the cantilevers. These data suggest that the ability to jump allows flying snakes to access greater resources in the arboreal environment, and supports the broader hypothesis that arboreal animals jump across gaps only when reaching is not mechanically possible.

Tail Control Enhances Gliding in Arboreal Lizards: An Integrative Study Using a 3D Geometric Model and Numerical Simulation

The ability to glide through an arboreal habitat has been acquired by several mammals, amphibians, snakes, lizards, and even invertebrates. Lizards of the genus Draco possess specialized morphological structures for gliding, including a patagium, throat lappets, and modified hindlimbs. Despite being among the most specialized reptilian gliders, it is currently unknown how Draco is able to maneuver effectively during flight. Here, we present a new computational method for characterizing the role of tail control on Draco glide distance and stability. We first modeled Draco flight dynamics as a function of gravitational, lift, and drag forces. Lift and drag estimates were derived from wind tunnel experiments of 3D printed models based on photos of Draco during gliding. Initial modeling leveraged the known mass and planar surface area of the Draco to estimate lift and drag coefficients. We developed a simplified, 3D simulation for Draco gliding, calculating longitudinal and lateral position and a pitch angle of the lizard with respect to a cartesian coordinate frame. We used PID control to model the lizards' tail adjustment to maintain an angle of attack. Our model suggests an active tail improves both glide distance and stability in Draco. These results provide insight toward the biomechanics of Draco; however, future in vivo studies are needed to provide a complete picture for gliding mechanics of this genus. Our approach enables the replication and modification of existing gliders to better understand their performance and mechanics. This can be applied to extinct species, but also as a way of exploring the biomimetic potential of different morphological features.

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.

Lasso locomotion expands the climbing repertoire of snakes

The diverse ways and environments in which animals move are correlated with morphology¹, but morphology is not sufficient to predict how animals move because behavioral innovations can create new capacities. We document a new mode of snake locomotion - 'lasso locomotion' - that allows the brown treesnake (Boiga irregularis) to ascend much larger smooth cylinders than any previously known behavior. This lasso locomotion may facilitate exploiting resources that might otherwise be unobtainable and contribute to the success and impact of this highly invasive species. VIDEO ABSTRACT.

Morphological evolution in relationship to sidewinding, arboreality and precipitation in snakes of the family Viperidae

Compared with other squamates, snakes have received relatively little ecomorphological investigation. We examined morphometric and meristic characters of vipers, in which both sidewinding locomotion and arboreality have evolved multiple times. We used phylogenetic comparative methods that account for intraspecific variation (measurement error models) to determine how morphology varied in relationship to body size, sidewinding, arboreality and mean annual precipitation (which we chose over other climate variables through model comparison). Some traits scaled isometrically; however, head dimensions were negatively allometric. Although we expected sidewinding specialists to have different body proportions and more vertebrae than non-sidewinding species, they did not differ significantly for any trait after correction for multiple comparisons. This result suggests that the mechanisms enabling sidewinding involve musculoskeletal morphology and/or motor control, that viper morphology is inherently conducive to sidewinding (‘pre-adapted’) or that behaviour has evolved faster than morphology. With body size as a covariate, arboreal vipers had long tails, narrow bodies and lateral compression, consistent with previous findings for other arboreal snakes, plus reduced posterior body tapering. Species from wetter environments tended to have longer tails, wider heads and reduced anterior tapering. This study adds to the growing evidence that, despite superficial simplicity, snakes have evolved various morphological specializations in relationship to behaviour and ecology.

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.

Visual Contrast and Intensity Affect Perch Choice of Brown Tree Snakes (Boiga irregularis) and Boa Constrictors (Boa constrictor)

Habitat structure can affect animal movement both by affecting the mechanical demands of locomotion and by influencing where animals choose to go. Arboreal habitats facilitate studying path choice by animals because variation in branch structure has known mechanical consequences, and different branches create discrete choices. Recent laboratory studies have found that arboreal snakes can use vision to select shapes and locations of destinations that mechanically facilitate bridging gaps. However, the extent to which the appearance of objects unrelated to biomechanical demands affects the choice of destinations remains poorly understood for most animal taxa including snakes. Hence, we manipulated the intensity (black, gray, or white), contrast, structure, and locations of destinations to test for their combined effects on perch choice during gap bridging of brown tree snakes and boa constrictors. For a white background and a given perch structure and location, both species had significant preferences for darker perches. The preference for darker destinations was strong enough to override or reduce some preferences for biomechanically advantageous destinations such as those having secondary branches or being located closer or along a straighter trajectory. These results provide a striking example of how visual cues unrelated to the physical structure of surfaces, such as contrast and intensity, can bias choice and, in some cases, supersede a preference for mechanically beneficial surfaces. Because these two species are so phylogenetically distant, some of their similar preferences suggest a sensory bias that may be widespread in snakes. The manipulation of surface color may facilitate management of invasive species, such as the brown tree snakes, by enhancing the efficiency of traps or making certain objects less attractive to them.

Going the distance: The biomechanics of gap-crossing behaviors

The discontinuity of the canopy habitat is one of the principle differences between the terrestrial and arboreal environments. An animal's ability to cross gaps-to move from one support to another across an empty space-is influenced by both the physical structure of the gap and the animal's locomotor capabilities. In this review, we discuss the range of behaviors animals use to cross gaps. Focusing on the biomechanics of these behaviors, we suggest broad categorizations that facilitate comparisons between taxa. We also discuss the importance of gap distance in determining crossing behavior, and suggest several mechanical characteristics that may influence behavior choice, including the degree to which a behavior is dynamic, and whether or not the behavior is airborne. Overall, gap crossing is an important aspect of arboreal locomotion that deserves further in-depth attention, particularly given the ubiquity of gaps in the arboreal habitat.

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.

Dynamic traversal of large gaps by insects and legged robots reveals a template

It is well known that animals can use neural and sensory feedback via vision, tactile sensing, and echolocation to negotiate obstacles. Similarly, most robots use deliberate or reactive planning to avoid obstacles, which relies on prior knowledge or high-fidelity sensing of the environment. However, during dynamic locomotion in complex, novel, 3D terrains, such as a forest floor and building rubble, sensing and planning suffer bandwidth limitation and large noise and are sometimes even impossible. Here, we study rapid locomotion over a large gap-a simple, ubiquitous obstacle-to begin to discover the general principles of the dynamic traversal of large 3D obstacles. We challenged the discoid cockroach and an open-loop six-legged robot to traverse a large gap of varying length. Both the animal and the robot could dynamically traverse a gap as large as one body length by bridging the gap with its head, but traversal probability decreased with gap length. Based on these observations, we developed a template that accurately captured body dynamics and quantitatively predicted traversal performance. Our template revealed that a high approach speed, initial body pitch, and initial body pitch angular velocity facilitated dynamic traversal, and successfully predicted a new strategy for using body pitch control that increased the robot's maximal traversal gap length by 50%. Our study established the first template of dynamic locomotion beyond planar surfaces, and is an important step in expanding terradynamics into complex 3D terrains.

Three-dimensional trajectories affect the epaxial muscle activity of arboreal snakes crossing gaps

The need for long-axis support is widespread among non-aquatic vertebrates and may be particularly acute for arboreal snakes when many vertebrae span sizable gaps between branches with diverse orientations. Hence, we used brown tree snakes (Boiga irregularis) bridging gaps to test how three-dimensional trajectories affected muscle activity and whether these motor patterns differed from those for the locomotion of terrestrial snakes and movements of other vertebrates. We used five trajectories: pitch angles of 90, 0 and -90 deg (downward) when yaw=0, and 90 deg yaw angles to the left and right when pitch=0 deg. We recorded movement and EMGs from the three largest epaxial muscles, which from dorsal to ventral are the semispinalis-spinalis (SSP), longissimus dorsi (LD), and iliocostalis (IL). Overall, the SSP had extensive bilateral activity, which resembled the motor pattern during the dorsiflexion of sidewinding snakes. Unlike any previously described terrestrial snake locomotion, bilateral activity of the LD and IL was also common during gap bridging. The largest amounts of muscle activity usually occurred for horizontal gaps, and muscle activity decreased markedly as soon as the snake's head touched the far edge of the gap. Snakes had the least amount of muscle activity for pitch=-90 deg. While turning sideways, muscles on the convex side had less activity when turning compared to the concave side. Hence, the orientation relative to gravity profoundly affected muscle activity during gap bridging, and these complex three-dimensional movements involved several previously undescribed variants of axial motor pattern.

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.