Undulatory Locomotion Research Articles

A fast non-dominated sorting multi-objective symbiotic organism search algorithm for energy efficient locomotion of snake robot

This paper deals with energy efficient locomotion of a wheel-less snake robot. This is very crucial for potential applications of untethered snake robots. The optimum gait parameters for the energy efficient locomotion of the snake robot are obtained with two different multi-objective algorithms based on symbiotic organism search algorithm by considering both minimizing the average power consumption and maximizing the forward velocity of the robot. This paper also investigates the energy efficient locomotion of the snake robot under different environment conditions. The obtained results demonstrate that both proposed methods achieve satisfying stable results regarding power consumption reduction with optimal forward velocity for lateral undulation motion. However, it is seen that fast non-dominated sorting multi-objective symbiotic organism search algorithm provides advantage on obtaining a uniformly distributed solution set with a good diversity only in a single run. This paper is important in terms of presenting useful results for developing efficient motion and environmental adaptability of the snake robot.

Lateral bending and buckling aids biological and robotic earthworm anchoring and locomotion

Earthworms (Lumbricus terrestris) are characterized by soft, highly flexible and extensible bodies, and are capable of locomoting in most terrestrial environments. Previous studies of earthworm movement focused on the use of retrograde peristaltic gaits in which controlled contraction of longitudinal and circular muscles results in waves of shortening/thickening and thinning/lengthening of the hydrostatic skeleton. These waves can propel the animal across ground as well as into soil. However, worms benefit from axial body bends during locomotion. Such lateral bending and buckling dynamics can aid locomotor function via hooking/anchoring (to provide propulsion), modify travel orientation (to avoid obstacles and generate turns) and even generate snake-like undulatory locomotion in environments where peristaltic locomotion results in poor performance. To the best of our knowledge, lateral bending and buckling of an earthworm’s body has not yet been systematically investigated. In this study, we observed that within confined environments, worms use lateral bending and buckling to anchor their body to the walls of their burrows and tip (anterior end) bending to search the environment. This locomotion strategy improved the performance of our soft-bodied robophysical model of the earthworm both in a confined (in an acrylic tube) and above-ground heterogeneous environment (rigid pegs), where present peristaltic robots are relatively limited in terradynamic capabilities. In summary, lateral bending and buckling facilitates the mobility of earthworm locomotion in diverse terrain and can play an important role in the creation of low cost soft robotic devices capable of traversing a variety of environments.

Turtling the Salamander: Tail Movements Mitigate Need for Kinematic Limb Changes during Walking in Tiger Salamanders (Ambystoma tigrinum) with Restricted Lateral Movement.

SynopsisLateral undulation and trunk flexibility offer performance benefits to maneuverability, stability, and stride length (via speed and distance traveled). These benefits make them key characteristics of the locomotion of tetrapods with sprawling posture, with the exception of turtles. Despite their bony carapace preventing lateral undulations, turtles are able to improve their locomotor performance by increasing stride length via greater limb protraction. The goal of this study was to quantify the effect of reduced lateral flexibility in a generalized sprawling tetrapod, the tiger salamander (Ambystoma tigrinum). We had two potential predictions: (1) either salamanders completely compensate by changing their limb kinematics, or (2) their performance (i.e., speed) will suffer due to the reduced lateral flexibility. This reduction was performed by artificially limiting trunk flexibility by attaching a 2-piece shell around the body between the pectoral and pelvic girdles. Adult tiger salamanders (n = 3; SVL = 9–14.5 cm) walked on a 1-m trackway under three different conditions: unrestricted, flexible shell (Tygon tubing), and rigid shell (PVC tubing). Trials were filmed in a single, dorsal view, and kinematics of entire midline and specific body regions (head, trunk, tail), as well as the fore and hind limbs, were calculated. Tygon individuals had significantly higher curvature than both PVC and unrestricted individuals for the body, but this trend was primarily driven by changes in tail movements. PVC individuals had significantly lower curvature in the trunk region compared with unrestricted individuals or Tygon; however, there was no difference between unrestricted and Tygon individuals suggesting the shells performed as expected. PVC and Tygon individuals had significantly higher curvature in the tails compared with unrestricted individuals. There were no significant differences for any limb kinematic variables among treatments including average, minimum, and maximum angles. Thus, salamanders respond to decreased lateral movement in their trunk by increasing movements in their tail, without changes in limb kinematics. These results suggest that tail undulations may be a more critical component to sprawling-postured tetrapod locomotion than previously recognized.

Corollary discharge enables proprioception from lateral line sensory feedback.

Animals modulate sensory processing in concert with motor actions. Parallel copies of motor signals, called corollary discharge (CD), prepare the nervous system to process the mixture of externally and self-generated (reafferent) feedback that arises during locomotion. Commonly, CD in the peripheral nervous system cancels reafference to protect sensors and the central nervous system from being fatigued and overwhelmed by self-generated feedback. However, cancellation also limits the feedback that contributes to an animal's awareness of its body position and motion within the environment, the sense of proprioception. We propose that, rather than cancellation, CD to the fish lateral line organ restructures reafference to maximize proprioceptive information content. Fishes' undulatory body motions induce reafferent feedback that can encode the body's instantaneous configuration with respect to fluid flows. We combined experimental and computational analyses of swimming biomechanics and hair cell physiology to develop a neuromechanical model of how fish can track peak body curvature, a key signature of axial undulatory locomotion. Without CD, this computation would be challenged by sensory adaptation, typified by decaying sensitivity and phase distortions with respect to an input stimulus. We find that CD interacts synergistically with sensor polarization to sharpen sensitivity along sensors' preferred axes. The sharpening of sensitivity regulates spiking to a narrow interval coinciding with peak reafferent stimulation, which prevents adaptation and homogenizes the otherwise variable sensor output. Our integrative model reveals a vital role of CD for ensuring precise proprioceptive feedback during undulatory locomotion, which we term external proprioception.

Swarming Aqua Sperm Micromotors for Active Bacterial Biofilms Removal in Confined Spaces (Adv. Sci. 19/2021)

Aqua Sperm Micromotors Aqua sperm based micromotors are used for the efficient destruction of bacterial biofilms in less than one minute. This is their speed and their undulatory locomotion as well as a head size similar to bacterial cells, allowing the Aqua Sperm micromotors to enter and navigate inside the biofilm matrix. More details can be found in article number 2101301 by Martin Pumera and co-workers.

Lateral Undulation of the Bendable Body of a Gecko-Inspired Robot for Energy-Efficient Inclined Surface Climbing

Sprawling posture animals with their bendable spine, such as salamanders, and geckos, can perform agile and versatile locomotion including walking, swimming, and climbing. Therefore, several roboticists have used them as templates for robot designs to investigate and generate efficient locomotion. Typically, walking and/or swimming abilities are realized by salamander-inspired robots with a bendable body, whereas climbing ability is achieved on gecko-inspired robots with an over-simplified fixed body. In this study, we propose optimal bendable body design with three degrees of freedom (DOFs). Its implementation on a sprawling posture robot is inspired by geckos for climbing enhancement. The robot leg and body movements are coordinated and driven by central pattern generator (CPG)-based neural control. As a consequence, the robot can climb using a combination of trot gait and lateral undulation of the bendable body with a C-shaped standing wave. Through the real robot experiments on a 3D force measuring platform, we demonstrate that, due to the dynamics of the bendable body movement, the robot can gain higher medio-lateral (F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> ) ground reaction forces (GRFs) at its front legs as well as anterior-posterior (F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sub> ) GRFs at its hind legs to increase the bending angular momentum (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> ). This results in 52% and 54% reduced energy consumptions during climbing on steeper inclined solid and soft surfaces, respectively, compared to climbing with a fixed body. To this end, the study provides a basis for developing sprawling posture robots with a bendable body and neural control for energy-efficient inclined surface climbing with a possible extension towards agile and versatile locomotion, such as sprawling posture animals.

Phase response analyses support a relaxation oscillator model of locomotor rhythm generation in Caenorhabditis elegans.

Neural circuits coordinate with muscles and sensory feedback to generate motor behaviors appropriate to an animal's environment. In C. elegans, the mechanisms by which the motor circuit generates undulations and modulates them based on the environment are largely unclear. We quantitatively analyzed C. elegans locomotion during free movement and during transient optogenetic muscle inhibition. Undulatory movements were highly asymmetrical with respect to the duration of bending and unbending during each cycle. Phase response curves induced by brief optogenetic inhibition of head muscles showed gradual increases and rapid decreases as a function of phase at which the perturbation was applied. A relaxation oscillator model based on proprioceptive thresholds that switch the active muscle moment was developed and is shown to quantitatively agree with data from free movement, phase responses, and previous results for gait adaptation to mechanical loadings. Our results suggest a neuromuscular mechanism underlying C. elegans motor pattern generation within a compact circuit.

Bio-Inspired Design, Modeling, and Control of Robotic Fish Propelled by a Double-Slider-Crank Mechanism Driven Tail

Abstract This paper presents the design, modeling, and control of a three-joint robotic fish propelled by a double-slider-crank (DSC) driven caudal fin. DSC is a mechanism that can use one direct current motor to achieve oscillating foil propulsion. Its design is guided by a traveling wave equation that mimics a fish's undulatory locomotion. After multiple tests, the robotic fish displayed good performance in mimicking a real fish's swimming motion. DSC mechanism is proven to be an effective propulsion technique for a robotic fish. With the help of another servomotor at the first joint of the fish's tail, the robotic fish can have a two-dimensional free-swimming capability. In experiments, the robotic fish can achieve a swimming speed of 0.35 m/s at 3 Hz, equivalent to 0.98 body length (BL) per second. Its steering rate is proportional to a bias angle. The DSC benefits the control of the robotic fish by independently adjusting its steering and swimming speed. This characteristic is studied in a hydrodynamic model that derives the thrust within a DSC frame. Besides the dynamic model, a semiphysics-based and data-driven linear model is established to connect bias angle to robotic fish's heading angle. The linear model is used for designing an observed-state feedback control control, and the controller has been examined in simulation and experiments.

Shape memory alloy-driven undulatory locomotion of a soft biomimetic ray robot

The objective of this study was to imitate undulatory motion, which is a commonly observed swimming mechanism of rays, using a soft morphing actuator. To achieve the undulatory motion, an artificial muscle built with shape memory alloy-based soft actuators was exploited to control the shape-changing behavior of a soft fin membrane. Artificial undulating fins were divided into two categories according to the method of generating the wave motion: single and multiple actuator-driven fins. For empirical research on the transformation and propulsion behavior of each fin type, the design and construction of bound propulsors were undertaken to mimic the structural and behavioral aspects of animals. To visualize the effect of undulatory motion on the swimming efficiency test of the fin beat frequency, a simplified soft undulating fin with a rectangular propulsor was constructed and tested. Additionally, dynamic modeling of the fin tip in wave-traveling was conducted for comparison and optimization. To optimize the thrust and propulsion efficiency of robot speed, the effects of the wave amplitude control and actuator sequence on the fin behavior were examined. An untethered robot was constructed according to the experimental results of the propulsors. Both exhibited exceptional swimming efficiency and maneuverability. The multiple actuator-driven ray robot exhibited a maximum swimming speed of 0.25 body lengths per second which is almost a similar swimming speed with previously reported robots. The developed robot achieved directional swimming (forward and backward) and turning (including rotation). Underwater exploration in an artificial environment was performed using the robot.

Collective Synchronization of Undulatory Movement through Contact

Physical contact among simple robots with undulatory gaits leads to rich collective dynamics including synchronization, thus showing how some populations in nature sync their movements when in close proximity.

On the snake-like lateral un-dulatory locomotion in terrestrial, aquatic and sand environments

Terrestrial snakes, aquatic snakes, and sandfish lizards are observed to adopt different configurations for locomotion, although they all employ the snake-like un-dulatory wriggling motion. Here we show that these differences may be dominated by the movement and energy efficiencies imposed by mechanical deformation and interaction with environments. Based on a slender soft beam model, a systematical framework is developed to explore and compare the movement and energy efficiencies of the snake-like lateral undulation in terrestrial, aquatic and sand environments. Indeed, it is found that the locomotion configuration of the soft body is highly relevant to the efficiency factors. Optimal un-dulatory configurations are obtained for each environment, which are qualitatively consistent with the biological ones. The present study reveals the mechanism behind the locomotion adaptation of the un-dulatory wriggling motion for navigating through different environments, which sheds light on developing amphibious/all-terrain soft robots, while, at the same time, broadens our cognition of nature's strategies for locomotion.

Body Caudal Undulation Measured by Soft Sensors and Emulated by Soft Artificial Muscles.

We propose the use of bio-inspired robotics equipped with soft sensor technologies to gain a better understanding of the mechanics and control of animal movement. Soft robotic systems can be used to generate new hypotheses and uncover fundamental principles underlying animal locomotion and sensory capabilities, which could subsequently be validated using living organisms. Physical models increasingly include lateral body movements, notably back and tail bending, which are necessary for horizontal plane undulation in model systems ranging from fish to amphibians and reptiles. We present a comparative study of the use of physical modeling in conjunction with soft robotics and integrated soft and hyperelastic sensors to monitor local pressures, enabling local feedback control, and discuss issues related to understanding the mechanics and control of undulatory locomotion. A parallel approach combining live animal data with biorobotic physical modeling promises to be beneficial for gaining a better understanding of systems in motion.

Swarming Aqua Sperm Micromotors for Active Bacterial Biofilms Removal in Confined Spaces.

Microscale self‐propelled robots show great promise in the biomedical field and are the focus of many researchers. These tiny devices, which move and navigate by themselves, are typically based on inorganic microstructures that are not biodegradable and potentially toxic, often using toxic fuels or elaborate external energy sources, which limits their real‐world applications. One potential solution to these issues is to go back to nature. Here, the authors use high‐speed Aqua Sperm micromotors obtained from North African catfish (Clarias gariepinus, B. 1822) to destroy bacterial biofilm. These Aqua Sperm micromotors use water‐induced dynein ATPase catalyzed adenosine triphosphate (ATP) degradation as biocompatible fuel to trigger their fast speed and snake‐like undulatory locomotion that facilitate biofilm destruction in less than one minute. This efficient biofilm destruction is due to the ultra‐fast velocity as well as the head size of Aqua Sperm micromotors being similar to bacteria, which facilitates their entry to and navigation within the biofilm matrix. In addition, the authors demonstrate the real‐world application of Aqua Sperm micromotors by destroying biofilms that had colonized medical and laboratory tubing. The implemented system extends the biomedical application of Aqua Sperm micromotors to include hybrid robots for fertilization or cargo tasks.

Characterization of cephalic and non-cephalic sensory cell types provides insight into joint photo- and mechanoreceptor evolution.

Rhabdomeric opsins (r-opsins) are light sensors in cephalic eye photoreceptors, but also function in additional sensory organs. This has prompted questions on the evolutionary relationship of these cell types, and if ancient r-opsins were non-photosensory. A molecular profiling approach in the marine bristleworm Platynereis dumerilii revealed shared and distinct features of cephalic and non-cephalic r-opsin1-expressing cells. Non-cephalic cells possess a full set of phototransduction components, but also a mechanosensory signature. Prompted by the latter, we investigated Platynereis putative mechanotransducer and found that nompc and pkd2.1 co-expressed with r-opsin1 in TRE cells by HCR RNA-FISH. To further assess the role of r-Opsin1 in these cells, we studied its signaling properties and unraveled that r-Opsin1 is a Gαq-coupled blue light receptor. Profiling of cells from r-opsin1 mutants versus wild-types, and a comparison under different light conditions reveals that in the non-cephalic cells light - mediated by r-Opsin1 - adjusts the expression level of a calcium transporter relevant for auditory mechanosensation in vertebrates. We establish a deep-learning-based quantitative behavioral analysis for animal trunk movements and identify a light- and r-Opsin-1-dependent fine-tuning of the worm's undulatory movements in headless trunks, which are known to require mechanosensory feedback. Our results provide new data on peripheral cell types of likely light sensory/mechanosensory nature. These results point towards a concept in which such a multisensory cell type evolved to allow for fine-tuning of mechanosensation by light. This implies that light-independent mechanosensory roles of r-opsins may have evolved secondarily.

Design and Control of a Two-Motor-Actuated Tuna-Inspired Robot System

This article presents the mechanical design and locomotion control of a novel tuna-inspired robot system for both fast swimming and high maneuverability. Mechanically, the developed robotic fish named CasiTuna comprises three important parts, i.e., an innovative two-motor-actuated propulsive mechanism, a buoyancy adjustment structure, and a pair of pectoral fins. Unlike most robotic fishes' multiple concatenated links-based propulsive mechanism, CasiTuna's two-motor-actuated one places both motors in the anterior body and utilizes a transmission system to achieve tuna-like lateral undulations. Meanwhile, the buoyancy adjustment mechanism in conjunction with pectoral fins endows the robot with the capability of three-dimensional maneuverability. Kinematic and dynamic analyses are further conducted to reveal the interactive hydrodynamic forces. Regarding the locomotion control method, a bio-inspired central pattern generator-based controller is adopted to achieve multimodal swimming. In particular, two kinds of turning maneuvers are implemented and discussed. Aquatic experiments, including straight swimming, circular turning, and nearly static pitching validate the effectiveness of proposed mechatronic design and locomotion control methods. Remarkably, CasiTuna achieved a peak forward speed of 0.8 m/s (corresponding to 1.52 body lengths per second) and a minimum turning radius of less than 0.3 body lengths.

Insights on the evolution of synapsid locomotion based on tetrapod tracks from the lower Permian of Mallorca (Balearic Islands, western Mediterranean)

“Pelycosaur”-grade synapsids were a successful group of terrestrial tetrapods that lived during the Carboniferous and Permian, utilising a wide diversity of ecological niches. They are considered the trackmakers of the ichnogenera Dimetropus and possibly also Dromopus and Tambachichnium, found in upper Palaeozoic deposits of North America, North Africa and Europe. Here we describe a new morphotype from the lower Permian of Mallorca (Balearic Islands, western Mediterranean), identified as cf. Dimetropus isp., which was purportedly produced by caseid synapsids. The trackmaker identity is inferred based on the digit proportions, as caseids are the only pelycosaurs with species showing mesaxonic autopodia, and a relative depth pattern (corresponding to the functional prevalence of the autopodia of the trackmaker) showing an overall similarity to that of Dimetropus osageorum, which is also attributed to caseids. A detailed study of the expulsion rims and drag traces makes it possible to infer the mode of locomotion of the trackmaker, with a gait alternating the movement of manus and pedes of the two sides of the body and lateral undulation of the spine. Our results provide new information concerning the locomotion of early synapsids, which would undergo important functional modifications later in their evolutionary history such as a shift from abducted to adducted posture and lateral to sagittal bending of the axial skeleton.

Interactions among multiple selective pressures on the form–function relationship in insular stream fishes

Abstract Relationships between body shape and escape performance are well established for many species. However, organisms can face multiple selection pressures that might impose competing demands. Many fishes use fast starts for escaping predator attacks, whereas some species of gobiid fishes have evolved the ability to climb waterfalls out of predator-dense habitats. The ancestral ‘powerburst’ climbing mechanism uses lateral body undulations to move up waterfalls, whereas a derived ‘inching’ mechanism uses rectilinear locomotion. We examined whether fast-start performance is impacted by selection imposed from the new functional demands of climbing. We predicted that non-climbing species would show morphology and fast-start performance that facilitate predator evasion, because these fish live consistently with predators and are not constrained by the demands of climbing. We also predicted that, by using lateral undulations, powerburst climbers would show escape performance superior to that of inchers. We compared fast starts and body shape across six goby species. As predicted, non-climbing fish exhibited distinct morphology and responded more frequently to an attack stimulus than climbing species. Contrary to our predictions, we found no differences in escape performance among climbing styles. These results indicate that selection for a competing pressure need not limit the ability of prey to escape predator attacks.

Slithering CSF: Cerebrospinal Fluid Dynamics in the Stationary and Moving Viper Boa, Candoia aspera.

Simple SummaryThe cerebrospinal fluid (CSF) flows through and around the central nervous system to nourish, cleanse, and support the brain and spinal cord. Though abnormalities of this CSF flow have been linked to multiple human neural diseases, little is known about the underlying mechanics of CSF flow. This study was designed to test the hypothesis that movement of the body’s trunk could cause CSF flow; hence, the study was conducted on a snake, an animal with prominent trunk movement. The results demonstrate that the resting snake has a CSF pressure profile that is very similar to what is seen in humans and other mammals, and that the CSF dynamics are changed during either artificial (manual) or natural (locomotor) movement of the snake’s bodyIn the viper boa (Candoia aspera), the cerebrospinal fluid (CSF) shows two stable overlapping patterns of pulsations: low-frequency (0.08 Hz) pulses with a mean amplitude of 4.1 mmHg that correspond to the ventilatory cycle, and higher-frequency (0.66 Hz) pulses with a mean amplitude of 1.2 mmHg that correspond to the cardiac cycle. Manual oscillations of anesthetized C. aspera induced propagating sinusoidal body waves. These waves resulted in a different pattern of CSF pulsations with frequencies corresponding to the displacement frequency of the body and with amplitudes greater than those of the cardiac or ventilatory cycles. After recovery from anesthesia, the snakes moved independently using lateral undulation and concertina locomotion. The episodes of lateral undulation produced similar influences on the CSF pressure as were observed during the manual oscillations, though the induced CSF pulsations were of lower amplitude during lateral undulation. No impact on the CSF was found while C. aspera was performing concertina locomotion. The relationship between the propagation of the body and the CSF pulsations suggests that the body movements produce an impulse on the spinal CSF.

A spanwise oscillating plate in a crossflow: Implication for mass transfer and locomotion

AbstractMany aquatic processes (i.e., organism locomotion, macrophyte response to unsteady flow and mass/heat transfer) involve oscillatory or undulatory movements perpendicular to the direction of flow and perpendicular to the plane of oscillation (i.e., spanwise). The reduction of boundary layer (BL) thickness () and increased turbulence have been identified as the mechanisms for faster heat and mass transfer on these moving surfaces. We examined the hydrodynamics of a submerged spanwise‐oscillating plate in a crossflow within turbulent open channel flow at different oscillation frequencies (f) and channel velocity (U). The BL over the plate was characterized using moving particle image velocimetry to understand the effects of f and U on boundary stress, vorticity, and transfer processes. Changes in the velocity gradient at the plate surface depend on the interactions between spanwise vorticities of opposite directions that reversed downstream along the plate. The vorticity structure reduced shear stress at the surface of the plate resulting in &gt; 65% drag reduction near the upstream edge. Whereas was reduced in comparison to a stationary plate, vorticity increased the diffusive sublayer thickness ) over the oscillating plate (≲1.75 thicker than stationary), which would reduce rather than increase mass transfer based on the film model. Conversely, oscillations would enhance the mass transfer by a factor of ≤ 7 due to periodic renewal of water at the DSL. Similar arguments indicate that renewal would lead to increased convective heat transfer along the plate. Results of this work will increase our understanding of the physical and biological processes that occur in environmental boundary layers.

Resilience of neural networks for locomotion.

Locomotion is an essential behaviour for the survival of all animals. The neural circuitry underlying locomotion is therefore highly robust to a wide variety of perturbations, including injury and abrupt changes in the environment. In the short term, fault tolerance in neural networks allows locomotion to persist immediately after mild to moderate injury. In the longer term, in many invertebrates and vertebrates, neural reorganization including anatomical regeneration can restore locomotion after severe perturbations that initially caused paralysis. Despite decades of research, very little is known about the mechanisms underlying locomotor resilience at the level of the underlying neural circuits and coordination of central pattern generators (CPGs). Undulatory locomotion is an ideal behaviour for exploring principles of circuit organization, neural control and resilience of locomotion, offering a number of unique advantages including experimental accessibility and modelling tractability. In comparing three well-characterized undulatory swimmers, lampreys, larval zebrafish and Caenorhabditis elegans, we find similarities in the manifestation of locomotor resilience. To advance our understanding, we propose a comparative approach, integrating experimental and modelling studies, that will allow the field to begin identifying shared and distinct solutions for overcoming perturbations to persist in orchestrating this essential behaviour.