Modulation of orthogonal body waves enables high maneuverability in sidewinding locomotion

Chiral Locomotion Transitions of an Active Gel and Their Chemomechanical Origin

Transitions between chiral rotational locomotion modes occur in a variety of active individuals and populations, such as sidewinders, self-propelled chiral droplets, and dense bacterial suspensions. Despite recent progress in the study of active matter, general principles governing rotational chiral transition remain elusive. Here, we study, experimentally and theoretically, rotational locomotion and its chiral transition in a 2D polyacrylamide (PAAm)-based BZ gel driven by Belousov-Zhabotinsky reaction-diffusion waves. Analysis reveals that the phase difference (Δφ) between orthogonal components of kinematic quantities, such as chemomechanical force, displacement, and velocity, determines rotational chirality, i.e., chiral locomotion transition occurs when Δφ changes sign. This criterion is illustrated with a kinematic equation, which can be applied to biological and physical systems, including super-rotational/superhelical locomotion reported recently during E. gracilis swimming and sperm navigation. This work has potential applications for the design of functional materials and intelligent robots.

Effects of surface morphology and chemical composition on friction properties of Xenopeltis hainanensis scales

The scales of Xenopeltis hainanensis, a snake that can crawl in fields, valleys, and other places, can serve as inspiration for the design of scale-like bionic materials. We present a systematic morphological, microstructural, chemical, and mechanical analysis, including elastic modulus, hardness, and wear morphology of the scales to understand the friction basis for achieving the reptile requirements. At the surface level, a comb-like arrangement of microstructures on the ventral scales provides more surface area and reduces pressure. The separation of microstructures, along with the bending and delamination of collagen fibrils could contribute to energy dissipation, which helps prevent catastrophic failure at deeper structural levels. At the cross-sectional level, a greater thickness provides more distribution of stresses over a larger volume, reducing local deformation and increasing the resistance to damage. At the material level, the ventral scales show higher modulus (E = 384.65 ± 19.03 MPa, H = 58.67 ± 6.15 MPa) than other regions of snake scales, which is attributed to the increased thickness of the scales and the higher concentration of sulfur (S). The experimental results, combined with Energy-dispersive X-ray spectroscopy and SEM characterization, provide a complete picture of the fiction properties influenced by surface morphology and chemical composition during scratch extension of the Xenopeltis hainanensis scales.

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.

Sidewinder-Inspired Self-Adjusting, Lateral-Rolling Soft Robots for Autonomous Terrain Exploration

Helical structures of liquid crystal elastomers (LCEs) hold promise in soft robotics for self-regulated rolling motions. The understanding of their motion paths and potentials for terrain exploration remains limited. This study introduces a self-adjusting, lateral-rolling soft robot inspired by sidewinder snakes. The spring-like LCE helical filaments (HFs) autonomously respond to thermal cues, demonstrating dynamic and sustainable locomotion with adaptive rolling along non-linear paths. By fine-tuning the diameter, pitch, and modulus of the LCE HFs, and the environmental temperature, the movements of the LCE HFs, allowing for exploration of diverse terrains over a 600 cm2 area within a few minutes, can be programmed. LCE HFs are showcased to navigate through over nine obstacles, including maze escaping, terrain exploration, target hunting, and successfully surmounting staircases through adaptable rolling.

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.

Locomotor kinematics on sand versus vinyl flooring in the sidewinder rattlesnake Crotalus cerastes

For terrestrial locomotion of animals and machines, physical characteristics of the substrate can strongly impact kinematics and performance. Snakes are an especially interesting system for studying substrate effects because their gait depends more on the environment than on their speed. We tested sidewinder rattlesnakes (Crotalus cerastes) on two surfaces: sand collected from their natural environment and vinyl tile flooring, an artificial surface often used to elicit sidewinding in laboratory settings. Of ten kinematic variables examined, two differed significantly between the substrates: the body's waveform had an average of ∼17% longer wavelength on vinyl flooring (measured in body lengths), and snakes lifted their bodies an average of ∼40% higher on sand (measured in body lengths). Sidewinding may also differ among substrates in ways we did not measure (e.g. ground reaction forces and energetics), leaving open clear directions for future study.

Multilegged matter transport: A framework for locomotion on noisy landscapes

Whereas the transport of matter by wheeled vehicles or legged robots can be guaranteed in engineered landscapes such as roads or rails, locomotion prediction in complex environments such as collapsed buildings or crop fields remains challenging. Inspired by the principles of information transmission, which allow signals to be reliably transmitted over "noisy" channels, we developed a "matter-transport" framework that demonstrates that noninertial locomotion can be provably generated over noisy rugose landscapes (heterogeneities on the scale of locomotor dimensions). Experiments confirm that sufficient spatial redundancy in the form of serially connected legged robots leads to reliable transport on such terrain without requiring sensing and control. Further analogies from communication theory coupled with advances in gaits (coding) and sensor-based feedback control (error detection and correction) can lead to agile locomotion in complex terradynamic regimes.

Self-propulsion via slipping: Frictional swimming in multilegged locomotors

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

Estimation of interface frictional anisotropy between sand and snakeskin-inspired surfaces

The transmission of loads across the soil-structure mobilizes direction-dependent shear resistance, which can be selectively used to design geo-structures. A previous study confirmed the frictional anisotropy induced by the interface between the soil and snakeskin-inspired surfaces. However, it is necessary to estimate the interface friction angle quantitatively. In this study, a conventional direct shear apparatus is modified, and 45 cases are performed in two-way shearing directions between bio-inspired surfaces and Jumunjin standard sand under three vertical stresses (50, 100, and 200 kPa). The results show that: (1) shearing against the scales (cranial shearing) mobilizes larger shear resistance and produces a dilative response than shearing along the scales (caudal shearing) and (2) higher scale height or shorter scale length exhibits dilative tendency and produces higher interface friction angle. Further analysis is conducted to capture the frictional anisotropy as a function of the scale geometry ratio, which reveals that the interface anisotropy response is more pronounced during cranial shearing in all the cases, and the difference in the interface friction angle for the caudal → cranial test is higher than that for the cranial → caudal test at the given scale ratio.

Snakes on a slope: strong anti-gravitactic responses and differential habitat use in the Saharan horned viper (Cerastes cerastes) in the Negev desert

The way species use their habitat dictates their intra- and interspecific interactions. We studied the effects of the microhabitat type and slope on the movement behaviour of the Saharan horned viper (Cerastes cerastes) in its natural habitat. This viper occurs in sand dunes and moves mostly by sidewinding. Additionally, we studied the microhabitat preference of desert rodents-the vipers' main prey. We placed the vipers on different natural dune slopes and recorded their behaviour. We found a strong anti-gravitactic response: vipers moved more frequently towards the top of the dune than in any other direction, despite a decrease in stride length with increasing slope. The foraging-related behaviour of the vipers was concentrated in the dune semi-stable areas rather than its stable or shifting sand areas. We measured rodent activity by placing seed trays in the dune allowing the rodents to collect seeds. Rodent activity was the highest in the shifting sands, closely followed by the semi-stable microhabitat. These results suggest the vipers use the semi-stable microhabitat mainly for foraging and may use the shifting sand areas as commuting routes between such areas. This study may be of use for conservation efforts of psammophilic species in desert dunes.

Efficient bending and lifting patterns in snake locomotion

We optimize three-dimensional snake kinematics for locomotor efficiency. We assume a general space-curve representation of the snake backbone with small-to-moderate lifting off the ground and negligible body inertia. The cost of locomotion includes work against friction and internal viscous dissipation. When restricted to planar kinematics, our population-based optimization method finds the same types of optima as a previous Newton-based method. With lifting, a few types of optimal motions prevail. We have an s-shaped body with alternating lifting of the middle and ends at small-to-moderate transverse friction. With large transverse friction, curling and sliding motions are typical at small viscous dissipation, replaced by large-amplitude bending at large viscous dissipation. With small viscous dissipation, we find local optima that resemble sidewinding motions across friction coefficient space. They are always suboptimal to alternating lifting motions, with average input power 10–100% higher.

A general locomotion control framework for multi-legged locomotors

Serially connected robots are promising candidates for performing tasks in confined spaces such as search and rescue in large-scale disasters. Such robots are typically limbless, and we hypothesize that the addition of limbs could improve mobility. However, a challenge in designing and controlling such devices lies in the coordination of high-dimensional redundant modules in a way that improves mobility. Here we develop a general framework to discover templates to control serially connected multi-legged robots. Specifically, we combine two approaches to build a general shape control scheme which can provide baseline patterns of self-deformation ('gaits') for effective locomotion in diverse robot morphologies. First, we take inspiration from a dimensionality reduction and a biological gait classification scheme to generate cyclic patterns of body deformation and foot lifting/lowering, which facilitate the generation of arbitrary substrate contact patterns. Second, we extend geometric mechanics, which was originally introduced to study swimming at low Reynolds numbers, to frictional environments, allowing the identification of optimal body-leg coordination in this common terradynamic regime. Our scheme allows the development of effective gaits on flat terrain with diverse numbers of limbs (4, 6, 16, and even 0 limbs) and backbone actuation. By properly coordinating the body undulation and leg placement, our framework combines the advantages of both limbless robots (modularity and narrow profile) and legged robots (mobility). Our framework can provide general control schemes for the rapid deployment of general multi-legged robots, paving the way toward machines that can traverse complex environments. In addition, we show that our framework can also offer insights into body-leg coordination in living systems, such as salamanders and centipedes, from a biomechanical perspective.

Flexible Superlubricity Unveiled in Sidewinding Motion of Individual Polymeric Chains

A combination of low temperature atomic force microcopy and molecular dynamic simulations is used to demonstrate that soft designer molecules realize a sidewinding motion when dragged over a gold surface. Exploiting their longitudinal flexibility, pyrenylene chains are indeed able to lower diffusion energy barriers via on-surface directional locking and molecular strain. The resulting ultralow friction reaches values on the order of tens of pN reported so far only for rigid chains sliding on an incommensurate surface. Therefore, we demonstrate how molecular flexibility can be harnessed to realize complex nanomotion while retaining a superlubric character. This is in contrast with the paradigm guiding the design of most superlubric nanocontacts (mismatched rigid contacting surfaces).

Scaling and relations of morphology with locomotor kinematics in the sidewinder rattlesnake Crotalus cerastes

The movement of limbless terrestrial animals differs fundamentally from that of limbed animals, yet few scaling studies of their locomotor kinematics and morphology are available. We examined scaling and relations of morphology and locomotion in sidewinder rattlesnakes (Crotalus cerastes). During sidewinding locomotion, a snake lifts sections of its body up and forward while other sections maintain static ground contact. We used high-speed video to quantify whole-animal speed and acceleration; the height to which body sections are lifted; and the frequency, wavelength, amplitude and skew angle (degree of tilting) of the body wave. Kinematic variables were not sexually dimorphic, and most did not deviate from isometry, except wave amplitude. Larger sidewinders were not faster, contrary to many results from limbed terrestrial animals. Free from the need to maintain dynamic similarity (because their locomotion is dominated by friction rather than inertia), limbless species may have greater freedom to modulate speed independently of body size. Path analysis supported: (1) a hypothesized relationship between body width and wavelength, indicating that stouter sidewinders form looser curves; (2) a strong relationship between cycle frequency and whole-animal speed; and (3) weaker effects of wavelength (positive) and amplitude (negative) on speed. We suggest that sidewinding snakes may face a limit on stride length (to which amplitude and wavelength both contribute), beyond which they sacrifice stability. Thus, increasing frequency may be the best way to increase speed. Finally, frequency and skew angle were correlated, a result that deserves future study from the standpoint of both kinematics and physiology.

Friction modulation in limbless, three-dimensional gaits and heterogeneous terrains

Motivated by a possible convergence of terrestrial limbless locomotion strategies ultimately determined by interfacial effects, we show how both 3D gait alterations and locomotory adaptations to heterogeneous terrains can be understood through the lens of local friction modulation. Via an effective-friction modeling approach, compounded by 3D simulations, the emergence and disappearance of a range of locomotory behaviors observed in nature is systematically explained in relation to inhabited environments. Our approach also simplifies the treatment of terrain heterogeneity, whereby even solid obstacles may be seen as high friction regions, which we confirm against experiments of snakes ‘diffracting’ while traversing rows of posts, similar to optical waves. We further this optic analogy by illustrating snake refraction, reflection and lens focusing. We use these insights to engineer surface friction patterns and demonstrate passive snake navigation in complex topographies. Overall, our study outlines a unified view that connects active and passive 3D mechanics with heterogeneous interfacial effects to explain a broad set of biological observations, and potentially inspire engineering design.

A long puzzle in snake’s locomotion, sidewinding allows them to travel at an angle and reorient in some environments without loss of speed. Here, authors provide a mathematical argument to the evolution of sidewinding gaits and reinforce an analogy between limbless terrestrial locomotion and optics.

Frequency modulation of body waves to improve performance of sidewinding robots

Sidewinding is a form of locomotion executed by certain snakes and has been reconstructed in limbless robots; the gait is beneficial because it is effective in diverse terrestrial environments. Sidewinding gaits are generated by coordination of horizontal and vertical traveling waves of body undulation: the horizontal wave largely sets the direction of sidewinding with respect to the body frame while the vertical traveling wave largely determines the contact pattern between the body and the environment. When the locomotor’s center of mass leaves the supporting polygon formed by the contact pattern, undesirable locomotor behaviors (such as unwanted turning or unstable oscillation of the body) can occur. In this article, we develop an approach to generate desired translation and turning by modulating the vertical wave. These modulations alter the distribution of body–environment contact patches and can stabilize configurations that were previously statically unstable. The approach first identifies the spatial frequency of the vertical wave that statically stabilizes the locomotor for a given horizontal wave. Then, using geometric mechanics tools, we design the coordination between body waves that produces the desired translation or rotation. We demonstrate the effectiveness of our technique in numerical simulations and on experiments with a 16-joint limbless robot locomoting on flat hard ground. Our scheme broadens the range of movements and behaviors accessible to sidewinding locomotors at low speeds, which can lead to limbless systems capable of traversing diverse terrain stably and/or rapidly.

Functional consequences of convergently evolved microscopic skin features on snake locomotion

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

Onsager's variational principle in active soft matter

Onsagers variational principle (OVP) was originally proposed by Lars Onsager in 1931 [L. Onsager, Phys. Rev., 1931, 37, 405]. This fundamental principle provides a very powerful tool for formulating thermodynamically consistent models. It can also be employed to find approximate solutions, especially in the study of soft matter dynamics. In this work, OVP is extended and applied to the dynamic modeling of active soft matter such as suspensions of bacteria and aggregates of animal cells. We first extend the general formulation of OVP to active matter dynamics where active forces are included as external non-conservative forces. We then use OVP to analyze the directional motion of individual active units: a molecular motor walking on a stiff biofilament and a toy two-sphere microswimmer. Next we use OVP to formulate a diffuse-interface model for an active polar droplet on a solid substrate. In addition to the generalized hydrodynamic equations for active polar fluids in the bulk region, we have also derived thermodynamically consistent boundary conditions. Finally, we consider the dynamics of a thin active polar droplet under the lubrication approximation. We use OVP to derive a generalized thin film equation and then employ OVP as an approximation tool to find the spreading laws for the thin active polar droplet. By incorporating the activity of biological systems into OVP, we develop a general approach to construct thermodynamically consistent models for better understanding the emergent behaviors of individual animal cells and cell aggregates or tissues.

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.

Facultatively Sidewinding Snakes and the Origins of Locomotor Specialization

Specialist species often possess adaptations that strongly distinguish them from their relatives, obscuring the transitional steps leading to specialization. Sidewinding snakes represent an example of locomotor specialization in an elongate, limbless terrestrial vertebrate. We typically think of sidewinding as a gait that only a handful of very specialized snake species perform, mostly vipers from sandy desert environments. Some of these desert-dwelling vipers are so specialized that they only rarely use more common types of locomotion. However, some non-viper species sidewind facultatively in particular circumstances, and a few may regularly sidewind under natural conditions. Numerous accounts report facultative sidewinding in species that more typically perform other types of locomotion. I have compiled these accounts, uncovering evidence that dozens of species perform sidewinding with varying proficiency under a variety of conditions. These facultative sidewinders can reveal insight into the evolution and biomechanics of sidewinding, and they provide ample opportunities for future study.

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.

Decoding Decentralized Control Mechanism Underlying Adaptive and Versatile Locomotion of Snakes

Snakes have no limbs and can move in various environments using a simple elongated limbless body structure obtained through a long-term evolutionary process. Specifically, snakes have various locomotion patterns, which they change in response to conditions encountered. For example, on an unstructured terrain, snakes actively utilize the terrain's irregularities and move effectively by actively pushing their bodies against the "scaffolds" that they encounter. In a narrow aisle, snakes exhibit concertina locomotion, in which the tail part of the body is pulled forward with the head part anchored, and this is followed by the extension of the head part with the tail part anchored. Furthermore, snakes often exhibit three-dimensional (3-D) locomotion patterns wherein the points of ground contact change in a spatiotemporal manner, such as sidewinding and sinus-lifting locomotion. This ability is achieved possibly by a decentralized control mechanism, which is still mostly unknown. In this study, we address this aspect by employing a synthetic approach to understand locomotion mechanisms by developing mathematical models and robots. We propose a Tegotae-based decentralized control mechanism and use a 2-D snake-like robot to demonstrate that it can exhibit scaffold-based and concertina locomotion. Moreover, we extend the proposed mechanism to 3D and use a 3-D snake-like robot to demonstrate that it can exhibit sidewinding and sinus-lifting locomotion. We believe that our findings will form a basis for developing snake-like robots applicable to search-and-rescue operations as well as understanding the essential decentralized control mechanism underlying animal locomotion.

Rapid two-anchor crawling from a milliscale prismatic-push-pull (3P) robot

Many crawling organisms such as caterpillars and worms use a method of movement in which two or more anchor points alternately push and pull the body forward at a constant frequency. In this paper we present a milliscale push-pull robot which is capable of operating across a wide range of actuation frequencies thus enabling us to expand our understanding of two-anchor locomotion beyond the low-speed regime. We designed and fabricated a milliscale robot which uses anisotropic friction at two oscillating contact points to propel itself forward in a push-pull fashion. In experiments we varied the oscillation frequency,f, over a wide range (10-250 Hz) and observe a non-linear relationship between robot speed over this full frequency range. At low frequency (f< 100 Hz) forward speed increased linearly with frequency. However, at an intermediate push-pull frequency (f> 100 Hz) speed was relatively constant with increasing frequency. Lastly, at higher frequency (f> 170 Hz) the linear speed-frequency relationship returned. The speed-frequency relationship at low actuation frequencies is consistent with previously described two-anchor models and experiments in biology and robotics, however the higher frequency behavior is inconsistent with two-anchor frictional behavior. To understand the locomotion behavior of our system we first develop a deterministic two-anchor model in which contact forces are determined exactly from static or dynamic friction. Our experiments deviate from the model predictions, and through 3D kinematics measurements we confirm that ground contact is intermittent in robot locomotion at higher frequencies. By including probabilistic foot slipping behavior in the two-anchor friction model we are able to describe the three-regimes of robot locomotion.

Reaction Forces and Rib Function During Locomotion in Snakes

Locomotion in most tetrapods involves coordinated efforts between appendicular and axial musculoskeletal systems, where interactions between the limbs and the ground generate vertical (GV), horizontal (GH), and mediolateral (GML) ground-reaction forces that are transmitted to the axial system. Snakes have a complete absence of external limbs and represent a fundamental shift from this perspective. The axial musculoskeletal system of snakes is their primary structure to exert, transmit, and resist all motive and reaction forces for propulsion. Their lack of limbs makes them particularly dependent on the mechanical interactions between their bodies and the environment to generate the net GH they need for forward locomotion. As organisms that locomote on their bellies, the forces that enable the various modes of snake locomotion involve two important structures: the integument and the ribs. Snakes use the integument to contact the substrate and produce a friction-reservoir that exceeds their muscle-induced propulsive forces through modulation of scale stiffness and orientation, enabling propulsion through variable environments. XROMM work and previous studies suggest that the serially repeated ribs of snakes change their cross-sectional body shape, deform to environmental irregularities, provide synergistic stabilization for other muscles, and differentially exert and transmit forces to control propulsion. The costovertebral joints of snakes have a biarticular morphology, relative to the unicapitate costovertebral joints of other squamates, that appears derived and not homologous with the ancestral bicapitate ribs of Amniota. Evidence suggests that the biarticular joints of snakes may function to buttress locomotor forces, similar to other amniotes, and provide a passive mechanism for resisting reaction forces during snake locomotion. Future comparisons with other limbless lizard taxa are necessary to tease apart the mechanics and mechanisms that produced the locomotor versatility observed within Serpentes.

Intermittent sliding locomotion of a two-link body

We study the possibility of efficient intermittent locomotion for two-link bodies that slide by changing their interlink angle periodically in time. We find that the anisotropy ratio of the sliding friction coefficients is a key parameter, while solutions have a simple scaling dependence on the friction coefficients' magnitudes. With very anisotropic friction, efficient motions involve coasting in low-drag states, with rapid and asymmetric power and recovery strokes. As the anisotropy decreases, burst-and-coast motions change to motions with long power strokes and short recovery strokes, and roughly constant interlink angle velocity on each. These motions are seen in the spaces of sinusoidal and power-law motions described by two and five parameters, respectively. Allowing the duty cycle to vary greatly increases the motions' efficiency compared to the case of symmetric power and recovery strokes. Allowing further variations in the concavity of the power and recovery strokes improves the efficiency further only when friction is very anisotropic. Near isotropic friction, a variety of optimally efficient motions are found with more complex waveforms. Many of the optimal sinusoidal and power-law motions are similar to those that we find with an optimization search in the space of more general periodic functions (truncated Fourier series). When we increase the resistive force's power-law dependence on velocity, the optimal motions become smoother, slower, and less efficient, particularly near isotropic friction.

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.

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

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

Limbless animals like snakes inhabit most terrestrial environments, generating thrust to overcome drag on the elongate body via contacts with heterogeneities. The complex body postures of some snakes and the unknown physics of most terrestrial materials frustrates understanding of strategies for effective locomotion. As a result, little is known about how limbless animals contend with unplanned obstacle contacts. We studied a desert snake, Chionactis occipitalis, which uses a stereotyped head-to-tail traveling wave to move quickly on homogeneous sand. In laboratory experiments, we challenged snakes to move across a uniform substrate and through a regular array of force-sensitive posts. The snakes were reoriented by the array in a manner reminiscent of the matter-wave diffraction of subatomic particles. Force patterns indicated the animals did not change their self-deformation pattern to avoid or grab the posts. A model using open-loop control incorporating previously described snake muscle activation patterns and body-buckling dynamics reproduced the observed patterns, suggesting a similar control strategy may be used by the animals. Our results reveal how passive dynamics can benefit limbless locomotors by allowing robust transit in heterogeneous environments with minimal sensing.

Evaluation of Bio-Inspired Scales on Locomotion Performance of Snake-Like Robots

The unique frictional properties conferred by snake ventral scales inspired the engineering and fabrication of surrogate mechanisms for a robotic snake. These artificial, biologically inspired scales produce anisotropic body-ground forcing patterns with various locomotion surfaces. The benefits they confer to robotic snake-like locomotion were evaluated in experimental trials employing rectilinear, lateral undulation, and sidewinding gaits over several distinct surface types: carpet, inhomogeneous concrete and homogeneous concrete. Enhanced locomotive performance, with respect to net displacement and heading stability, was consistently measured in scenarios that utilized the engineered scales, over equivalent scenarios where the anisotropic effects of scales were absent.

Bioinspired 3D Printed Locomotion Devices Based on Anisotropic Friction

Anisotropic friction plays a key role in natural systems, particularly for realizing the purpose of locomotion and strong attachment for the survival of organisms. Of particular interest, here, is the observation that friction anisotropy is promoted numerous times by nature, for example, by wild wheat awn for its targeted and successful seed anchorage and dispersal. Such feature is, however, not fully exploited in man-made systems, such as microbots, due to technical limitations and lack of full understanding of the mechanisms. To unravel the complex dynamics occurring in the sliding interaction between anisotropic microstructured surfaces, the friction induced by asymmetric plant microstructures is first systematically investigated. Inspired by this, anisotropic polymer microactuators with three-dimensional (3D) printed microrelieves are then prepared. By varying geometric parameters, the capability of microactuators to generate strong friction anisotropy and controllable motion in remotely stretched cylindrical tubes is investigated. Advanced theoretical models are proposed to understand and predict the dynamic behavior of these synthetic systems and to shed light on the parameters and mechanisms governing their behavior. Finally, a microbot prototype is developed and cargo transportation functions are successfully realized. This research provides both in-depth understanding of anisotropic friction in nature and new avenues for developing intelligent actuators and microbots.

Robotics-inspired biology

For centuries, designers and engineers have looked to biology for inspiration. Biologically inspired robots are just one example of the application of knowledge of the natural world to engineering problems. However, recent work by biologists and interdisciplinary teams have flipped this approach, using robots and physical models to set the course for experiments on biological systems and to generate new hypotheses for biological research. We call this approach robotics-inspired biology; it involves performing experiments on robotic systems aimed at the discovery of new biological phenomena or generation of new hypotheses about how organisms function that can then be tested on living organisms. This new and exciting direction has emerged from the extensive use of physical models by biologists and is already making significant advances in the areas of biomechanics, locomotion, neuromechanics and sensorimotor control. Here, we provide an introduction and overview of robotics-inspired biology, describe two case studies and suggest several directions for the future of this exciting new research area.

Towards autonomous locomotion: CPG-based control of smooth 3D slithering gait transition of a snake-like robot

Snake-like robots with 3D locomotion ability have significant advantages of adaptive travelling in diverse complex terrain over traditional legged or wheeled mobile robots. Despite numerous developed gaits, these snake-like robots suffer from unsmooth gait transitions by changing the locomotion speed, direction, and body shape, which would potentially cause undesired movement and abnormal torque. Hence, there exists a knowledge gap for snake-like robots to achieve autonomous locomotion. To address this problem, this paper presents the smooth slithering gait transition control based on a lightweight central pattern generator (CPG) model for snake-like robots. First, based on the convergence behavior of the gradient system, a lightweight CPG model with fast computing time was designed and compared with other widely adopted CPG models. Then, by reshaping the body into a more stable geometry, the slithering gait was modified, and studied based on the proposed CPG model, including the gait transition of locomotion speed, moving direction, and body shape. In contrast to sinusoid-based method, extensive simulations and prototype experiments finally demonstrated that smooth slithering gait transition can be effectively achieved using the proposed CPG-based control method without generating undesired locomotion and abnormal torque.

Predicting path from undulations for C. elegans using linear and nonlinear resistive force theory

A basic issue in the physics of behaviour is the mechanical relationship between an animal and its surroundings. The model nematode C. elegans provides an excellent platform to explore this relationship due to its anatomical simplicity. Nonetheless, the physics of nematode crawling, in which the worm undulates its body to move on a wet surface, is not completely understood and the mathematical models often used to describe this phenomenon are empirical. We confirm that linear resistive force theory, one such empirical model, is effective at predicting a worm's path from its sequence of body postures for forward crawling, reversing, and turning and for a broad range of different behavioural phenotypes observed in mutant worms. Worms recently isolated from the wild have a higher effective drag anisotropy than the laboratory-adapted strain N2 and most mutant strains. This means the wild isolates crawl with less surface slip, perhaps reflecting more efficient gaits. The drag anisotropies required to fit the observed locomotion data (70  ±  28 for the wild isolates) are significantly larger than the values measured by directly dragging worms along agar surfaces (3-10 in Rabets et al (2014 Biophys. J. 107 1980-7)). A proposed nonlinear extension of the resistive force theory model also provides accurate predictions, but does not resolve the discrepancy between the parameters required to achieve good path prediction and the experimentally measured parameters. We confirm that linear resistive force theory provides a good effective model of worm crawling that can be used in applications such as whole-animal simulations and advanced tracking algorithms, but that the nature of the physical interaction between worms and their most commonly studied laboratory substrate remains unresolved.

Phototactic guidance of a tissue-engineered soft-robotic ray

Inspired by the relatively simple morphological blueprint provided by batoid fish such as stingrays and skates, we created a biohybrid system that enables an artificial animal--a tissue-engineered ray--to swim and phototactically follow a light cue. By patterning dissociated rat cardiomyocytes on an elastomeric body enclosing a microfabricated gold skeleton, we replicated fish morphology at 1/10 scale and captured basic fin deflection patterns of batoid fish. Optogenetics allows for phototactic guidance, steering, and turning maneuvers. Optical stimulation induced sequential muscle activation via serpentine-patterned muscle circuits, leading to coordinated undulatory swimming. The speed and direction of the ray was controlled by modulating light frequency and by independently eliciting right and left fins, allowing the biohybrid machine to maneuver through an obstacle course.

Advantage of straight walk instability in turning maneuver of multilegged locomotion: a robotics approach

Multilegged locomotion improves the mobility of terrestrial animals and artifacts. Using many legs has advantages, such as the ability to avoid falling and to tolerate leg malfunction. However, many intrinsic degrees of freedom make the motion planning and control difficult, and many contact legs can impede the maneuverability during locomotion. The underlying mechanism for generating agile locomotion using many legs remains unclear from biological and engineering viewpoints. The present study used a centipede-like multilegged robot composed of six body segments and twelve legs. The body segments are passively connected through yaw joints with torsional springs. The dynamic stability of the robot walking in a straight line changes through a supercritical Hopf bifurcation due to the body axis flexibility. We focused on a quick turning task of the robot and quantitatively investigated the relationship between stability and maneuverability in multilegged locomotion by using a simple control strategy. Our experimental results show that the straight walk instability does help the turning maneuver. We discuss the importance and relevance of our findings for biological systems and propose a design principle for a simple control scheme to create maneuverable locomotion of multilegged robots.

Scrunching: a novel escape gait in planarians

The ability to escape a predator or other life-threatening situations is central to animal survival. Different species have evolved unique strategies under anatomical and environmental constraints. In this study, we describe a novel musculature-driven escape gait in planarians, 'scrunching', which is quantitatively different from other planarian gaits, such as gliding and peristalsis. We show that scrunching is a conserved gait among different flatworm species, underlying its importance as an escape mechanism. We further demonstrate that it can be induced by a variety of physical stimuli, including amputation, high temperature, electric shock and low pH. We discuss the functional basis for scrunching as the preferential gait when gliding is impaired due to a disruption of mucus production. Finally, we show that the key mechanical features of scrunching are adequately captured by a simple biomechanical model that is solely based on experimental data from traction force microscopy and tissue rheology without fit parameters. Together, our results form a complete description of this novel form of planarian locomotion. Because scrunching has distinct dynamics, this gait can serve as a robust behavioral readout for studies of motor neuron and muscular functions in planarians and in particular the restoration of these functions during regeneration.

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.