Detecting subtle subterranean movement via laser speckle imaging

A diversity of organisms live within underground environments. However, visualizing subterranean behavior is challenging because of the opacity of most substrates. We demonstrate that laser speckle imaging, a non-invasive technique resolving nanometer-scale movements, facilitates quantifying biological activity in a granular medium. We monitored fire ants (Solenopsis invicta) at different developmental stages, burial depths (1-5 cm) and moisture fractions (0 and 0.1 by volume) in a container of 0.7 mm glass particles. Although the speckle pattern from the backscattered light precludes direct imaging of animal kinematics, analysis of integrated image differences revealed that spiking during ant movement increased with the developmental phase. Greater burial depth and saturation resulted in fewer and lower magnitude spikes. We verified that spiking correlated with movement via quasi-2D experiments. This straightforward method, involving a laser and digital camera, can be applied to laboratory and potentially field situations to gain insight into subterranean organism activities.

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.

Schrödinger Dynamics and Berry Phase of Undulatory Locomotion

Spectral mode representations play an essential role in various areas of physics, from quantum mechanics to fluid turbulence, but they are not yet extensively used to characterize and describe the behavioral dynamics of living systems. Here, we show that mode-based linear models inferred from experimental live-imaging data can provide an accurate low-dimensional description of undulatory locomotion in worms, centipedes, robots, and snakes. By incorporating physical symmetries and known biological constraints into the dynamical model, we find that the shape dynamics are generically governed by Schrödinger equations in mode space. The eigenstates of the effective biophysical Hamiltonians and their adiabatic variations enable the efficient classification and differentiation of locomotion behaviors in natural, simulated, and robotic organisms using Grassmann distances and Berry phases. While our analysis focuses on a widely studied class of biophysical locomotion phenomena, the underlying approach generalizes to other physical or living systems that permit a mode representation subject to geometric shape constraints.

Maneuvering on non-Newtonian fluidic terrain: a survey of animal and bio-inspired robot locomotion techniques on soft yielding grounds

Frictionally yielding media are a particular type of non-Newtonian fluids that significantly deform under stress and do not recover their original shape. For example, mud, snow, soil, leaf litters, or sand are such substrates because they flow when stress is applied but do not bounce back when released. Some robots have been designed to move on those substrates. However, compared to moving on solid ground, significantly fewer prototypes have been developed and only a few prototypes have been demonstrated outside of the research laboratory. This paper surveys the existing biology and robotics literature to analyze principles of physics facilitating motion on yielding substrates. We categorize animal and robot locomotion based on the mechanical principles and then further on the nature of the contact: discrete contact, continuous contact above the material, or through the medium. Then, we extract different hardware solutions and motion strategies enabling different robots and animals to progress. The result reveals which design principles are more widely used and which may represent research gaps for robotics. We also discuss that higher level of abstraction helps transferring the solutions to the robotics domain also when the robot is not explicitly meant to be bio-inspired. The contribution of this paper is a review of the biology and robotics literature for identifying locomotion principles that can be applied for future robot design in yielding environments, as well as a catalog of existing solutions either in nature or man-made, to enable locomotion on yielding grounds.

Walking is like slithering: A unifying, data-driven view of locomotion

Legged movement is ubiquitous in nature and of increasing interest for robotics. Most legged animals routinely encounter foot slipping, yet detailed modeling of multiple contacts with slipping exceeds current simulation capacity. Here we present a principle that unifies multilegged walking (including that involving slipping) with slithering and Stokesian (low Reynolds number) swimming. We generated data-driven principally kinematic models of locomotion for walking in low-slip animals (Argentine ant, 4.7% slip ratio of slipping to total motion) and for high-slip robotic systems (BigANT hexapod, slip ratio 12 to 22%; Multipod robots ranging from 6 to 12 legs, slip ratio 40 to 100%). We found that principally kinematic models could explain much of the variability in body velocity and turning rate using body shape and could predict walking behaviors outside the training data. Most remarkably, walking was principally kinematic irrespective of leg number, foot slipping, and turning rate. We find that grounded walking, with or without slipping, is governed by principally kinematic equations of motion, functionally similar to frictional swimming and slithering. Geometric mechanics thus leads to a unified model for swimming, slithering, and walking. Such commonality may shed light on the evolutionary origins of animal locomotion control and offer new approaches for robotic locomotion and motion planning.

Robotic swimming in curved space via geometric phase

Locomotion by shape changes or gas expulsion is assumed to require environmental interaction, due to conservation of momentum. However, as first noted in [J. Wisdom, Science 299, 1865-1869 (2003)] and later in [E. Guéron, Sci. Am. 301, 38-45 (2009)] and [J. Avron, O. Kenneth, New J. Phys, 8, 68 (2006)], the noncommutativity of translations permits translation without momentum exchange in either gravitationally curved spacetime or the curved surfaces encountered by locomotors in real-world environments. To realize this idea which remained unvalidated in experiments for almost 20 y, we show that a precision robophysical apparatus consisting of motors driven on curved tracks (and thereby confined to a spherical surface without a solid substrate) can self-propel without environmental momentum exchange. It produces shape changes comparable to the environment's inverse curvatures and generates movement of [Formula: see text] cm per gait. While this simple geometric effect predominates over short time, eventually the dissipative (frictional) and conservative forces, ubiquitous in real systems, couple to it to generate an emergent dynamics in which the swimming motion produces a force that is counter-balanced against residual gravitational forces. In this way, the robot both swims forward without momentum and becomes fixed in place with a finite momentum that can be released by ceasing the swimming motion. We envision that our work will be of use in a broad variety of contexts, such as active matter in curved space and robots navigating real-world environments with curved surfaces.

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.

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.

The neuroecology of the water-to-land transition and the evolution of the vertebrate brain

The water-to-land transition in vertebrate evolution offers an unusual opportunity to consider computational affordances of a new ecology for the brain. All sensory modalities are changed, particularly a greatly enlarged visual sensorium owing to air versus water as a medium, and expanded by mobile eyes and neck. The multiplication of limbs, as evolved to exploit aspects of life on land, is a comparable computational challenge. As the total mass of living organisms on land is a hundredfold larger than the mass underwater, computational improvements promise great rewards. In water, the midbrain tectum coordinates approach/avoid decisions, contextualized by water flow and by the animal's body state and learning. On land, the relative motions of sensory surfaces and effectors must be resolved, adding on computational architectures from the dorsal pallium, such as the parietal cortex. For the large-brained and long-living denizens of land, making the right decision when the wrong one means death may be the basis of planning, which allows animals to learn from hypothetical experience before enactment. Integration of value-weighted, memorized panoramas in basal ganglia/frontal cortex circuitry, with allocentric cognitive maps of the hippocampus and its associated cortices becomes a cognitive habit-to-plan transition as substantial as the change in ecology. This article is part of the theme issue 'Systems neuroscience through the lens of evolutionary theory'.

Data-driven geometric system identification for shape-underactuated dissipative systems

Modeling system dynamics becomes challenging when the properties of individual system components cannot be directly measured, and often requires identification of properties from observed motion. In this paper, we show that systems whose movement is highly dissipative have features which provide an opportunity to more easily identify models and more quickly optimize motions than would be possible with general techniques. Geometric mechanics provides means for reduction of the dynamics by environmental homogeneity, while the dissipative nature minimizes the role of second order (inertial) features in the dynamics. Here we extend the tools of geometric system identification to 'shape-underactuated dissipative systems (SUDS)'-systems whose motions are more dissipative than inertial, but whose actuation is restricted to a subset of the body shape coordinates. Many animal motions are SUDS, including micro-swimmers such as nematodes and flagellated bacteria, and granular locomotors such as snakes and lizards. Many soft robots are also SUDS, particularly robots that incorporate highly damped series elastic actuators to reduce the rigidity of their interactions with their environments during locomotion and manipulation. We motivate the use of SUDS models, and validate their ability to predict motion of a variety of simulated viscous swimming platforms. For a large class of SUDS, we show how the shape velocity actuation inputs can be directly converted into torque inputs, suggesting that systems with soft pneumatic or dielectric elastomer actuators can be modeled with the tools presented. Based on fundamental assumptions in the physics, we show how our model complexity scales linearly with the number of passive shape coordinates. This scaling offers a large reduction on the number of trials needed to identify the system model from experimental data, and may reduce overfitting. The sample efficiency of our method suggests its use in modeling, control, and optimization in robotics, and as a tool for the study of organismal motion in friction dominated regimes.

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.

A minimal robophysical model of quadriflagellate self-propulsion

Locomotion at the microscale is remarkably sophisticated. Microorganisms have evolved diverse strategies to move within highly viscous environments, using deformable, propulsion-generating appendages such as cilia and flagella to drive helical or undulatory motion. In single-celled algae, these appendages can be arranged in different ways around an approximately 10 μm long cell body, and coordinated in distinct temporal patterns. Inspired by the observation that some quadriflagellates (bearing four flagella) have an outwardly similar morphology and flagellar beat pattern, yet swim at different speeds, this study seeks to determine whether variations in swimming performance could arise solely from differences in swimming gait. Robotics approaches are particularly suited to such investigations, where the phase relationships between appendages can be readily manipulated. Here, we developed autonomous, algae-inspired robophysical models that can self-propel in a viscous fluid. These macroscopic robots (length and width = 8.5 cm, height = 2 cm) have four independently actuated 'flagella' (length = 13 cm) that oscillate under low-Reynolds number conditions (Re∼O(10-1)). We tested the swimming performance of these robot models with appendages arranged two distinct configurations, and coordinated in three distinct gaits. The gaits, namely the pronk, the trot, and the gallop, correspond to gaits adopted by distinct microalgal species. When the appendages are inserted perpendicularly around a central 'body', the robot achieved a net performance of 0.15-0.63 body lengths per cycle, with the trot gait being the fastest. Robotic swimming performance was found to be comparable to that of the algal microswimmers across all gaits. By creating a minimal robot that can successfully reproduce cilia-inspired drag-based swimming, our work paves the way for the design of next-generation devices that have the capacity to autonomously navigate aqueous environments.

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.

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

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

Swimming through the sands of the Sahara and Arabian deserts: Phylogeny of sandfish skinks (Scincidae, Scincus) reveals a recent and rapid diversification

Large parts of the Sahara Desert and Arabia are covered by sand seas and sand dunes, which are inhabited by specialized animal communities. For example, many lizards have developed adaptations to life in loose sand, including sand-swimming behavior. The best-known sand swimmers of the Saharo-Arabia are the sandfish skinks (genus Scincus). Although there are currently only four Scincus species recognized, their phylogenetic relationships have not yet been addressed in detail. We use eight genetic markers (three mitochondrial, five nuclear) and a complete sampling of species to infer the relationships within the genus. We employ multiple phylogenetic approaches to reconstruct the evolutionary history of these skinks and to assess the level of reticulation at the onset of their radiation. Our results indicate the presence of five strongly supported species-level lineages, four represented by the currently recognized species and the fifth by S. scincus conirostris, which does not form a clade with S. scincus. Based on these results we elevate the Iranian and northern Arabian S. conirostris to the species level. The two Saharan species, S. albifasciatus and S. scincus, are sister in all analyses. Deeper relationships within the genus, however, remained largely unresolved despite the extensive genetic data set. This basal polytomy, together with the fact that we detected no sign of hybridization in the history of the genus, indicates that the diversification of the five Scincus species was rapid, burst-like, and not followed by secondary hybridization events. Divergence time estimations show a Middle Pliocene crown radiation of the genus (3.3 Mya). We hypothesize that the aridification of the Saharo-Arabia that began in the Late Miocene triggered the initial diversification of Scincus, and that the subsequent expansion of sand deserts enabled their dispersal over the large Saharan and Arabian range. We discuss the evolution of body form in sand swimming lizards and ponder how Scincus retained their fully limbed morphology despite being sand swimmers that are typically limbless.

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.