Distinct Gaits Research Articles

A Horner’s polynomial based quadrupedal multi-gaits signal generation controller

<p>Animal locomotion is the process through which animals move from one location to another. Self-propelled locomotion is based on the animal performing a series of actions to move towards a predetermined target. All of these motions occur sequentially and repeat themselves during a gait cycle. A gait cycle may be simulated by duplicating each motion in the cycle sequentially. To achieve this goal, a problem known as the gait planning issue was formulated, in which various systems were created to provide suitable signals for the execution of distinct gaits (patterns of steps of an animal at a specified speed). This research approaches the problem using Horner's polynomials for quadruped robots. The approach entails first creating a sequence table for each gait and fit two polynomial equations. In this study, an attempt is made to combine several gaits using Horner's polynomials. An algorithm uses elaborated polynomials to generate the desired gaits signals.</p>

Acinonyx jubatus-Inspired Quadruped Robotics: Integrating Neural Oscillators for Enhanced Locomotion Control.

This study presents the design, simulation, and prototype creation of a quadruped robot inspired by the Acinonyx jubatus (cheetah), specifically designed to replicate its distinctive walking, trotting, and galloping locomotion patterns. Following a detailed examination of the cheetah's skeletal muscle anatomy and biomechanics, a simplified model of the robot with 12 degrees of freedom was conducted. The mathematical transformation hierarchy model was established, and direct kinematics were simulated. A bio-inspired control approach was introduced, employing a Central Pattern Generator model based on Wilson-Cowan neural oscillators for each limb, interconnected by synaptic weights. This approach assisted in the simulation of oscillatory signals for relative phases corresponding to four distinct gaits in a system-level simulation platform. The design phase was conducted using CAD software (SolidWorks 2018), resulting in a 1:3-scale robot mirroring the cheetah's actual proportions. Movement simulations were performed in a virtual mechanics software environment, leading to the construction of a prototype measuring 35.5 cm in length, 21 cm in width, 27 cm in height (when standing), and weighing approximately 2.1 kg. The experimental validation of the prototype's limb angular positions and trajectories was achieved through the image processing of video-recorded movements, demonstrating a high correlation (0.9025 to 0.9560) in joint angular positions, except for the knee joint, where a correlation of 0.7071 was noted. This comprehensive approach from theoretical analysis to practical implementation showcases the potential of bio-inspired robotics in emulating complex biological locomotion.

Multiflagellate Swimming Controlled by Hydrodynamic Interactions.

Many eukaryotic microorganisms propelled by multiple flagella can swim very rapidly with distinct gaits. Here, we model a three-dimensional mutiflagellate swimmer, resembling the microalgae. When the flagella are actuated synchronously, the swimming efficiency can be enhanced or reduced by interflagella hydrodynamic interactions (HIs), determined by the intrinsic tilting angle of the flagella. The asynchronous gait with a phase difference between neighboring flagella can reduce oscillatory motion via the basal mechanical coupling. In the presence of a spherical body, simulations taking into account the flagella-body interactions reveal the advantage of anterior configuration compared with posterior configuration, where in the latter case an optimal flagella number arises. Apart from understanding the role of HIs in the multiflagellate microorganisms, this work could also guide laboratory fabrications of novel microswimmers.

Dimensionality of locomotor behaviors in developing C. elegans.

Adult animals display robust locomotion, yet the timeline and mechanisms of how juvenile animals acquire coordinated movements and how these movements evolve during development are not well understood. Recent advances in quantitative behavioral analyses have paved the way for investigating complex natural behaviors like locomotion. In this study, we tracked the swimming and crawling behaviors of the nematode Caenorhabditis elegans from postembryonic development through to adulthood. Our principal component analyses revealed that adult C. elegans swimming is low dimensional, suggesting that a small number of distinct postures, or eigenworms, account for most of the variance in the body shapes that constitute swimming behavior. Additionally, we found that crawling behavior in adult C. elegans is similarly low dimensional, corroborating previous studies. Further, our analysis revealed that swimming and crawling are distinguishable within the eigenworm space. Remarkably, young L1 larvae are capable of producing the postural shapes for swimming and crawling seen in adults, despite frequent instances of uncoordinated body movements. In contrast, late L1 larvae exhibit robust coordination of locomotion, while many neurons crucial for adult locomotion are still under development. In conclusion, this study establishes a comprehensive quantitative behavioral framework for understanding the neural basis of locomotor development, including distinct gaits such as swimming and crawling in C. elegans.

Effect of internal damping on locomotion in frictional environments.

The gaits of undulating animals arise from a complex interaction of their central nervous system, muscle, connective tissue, bone, and environment. As a simplifying assumption, many previous studies have often assumed that sufficient internal force is available to produce observed kinematics, thus not focusing on quantifying the interconnection between muscle effort, body shape, and external reaction forces. This interplay, however, is critical to locomotion performance in crawling animals, especially when accompanied by body viscoelasticity. Moreover, in bioinspired robotic applications, the body's internal damping is indeed a parameter that the designer can tune. Still, the effect of internal damping is not well understood. This study explores how internal damping affects the locomotion performance of a crawler with a continuous, viscoelastic, nonlinear beam model. Crawler muscle actuation is modeled as a traveling wave of bending moment propagating posteriorly along the body. Consistent with the friction properties of the scales of snakes and limbless lizards, environmental forces are modeled using anisotropic Coulomb friction. It is found that by varying the crawler body's internal damping, the crawler's performance can be altered, and distinct gaits could be achieved, including changing the net locomotion direction from forward to back. We will discuss this forward and backward control and identify the optimal internal damping for peak crawling speed.

An Insect-Inspired Terrains-Adaptive Soft Millirobot with Multimodal Locomotion and Transportation Capability.

Inspired by the efficient locomotion of insects in nature, researchers have been developing a diverse range of soft robots with simulated locomotion. These robots can perform various tasks, such as carrying medicines and collecting information, according to their movements. Compared to traditional rigid robots, flexible robots are more adaptable and terrain-immune and can even interact safely with people. Despite the development of biomimetic principles for soft robots, how their shapes, morphology, and actuation systems respond to the surrounding environments and stimuli still need to be improved. Here, we demonstrate an insect-scale soft robot with multi-locomotion modes made by Ecoflex and magnetic particles, which can be actuated by a magnetic field. Our robot can realize four distinct gaits: horizontal tumbling for distance, vertical tumbling for height, imitation of gastropod writhing, and inchworm-inspired crawling for cargo delivery. The soft compliant structure and four locomotion modes make the robot ideal for maneuvering in congested or complex spaces. In addition to linear motion (~20 mm/s) and turning (50°/s) on a flat terrain, the robot can also maneuver on various surface conditions (such as gaps, smooth slopes, sand, muddy terrain, and water). These merits, together with the robot’s high load-carrying capacity (5 times its weight), low cost, obstacle-crossing capability (as high as ~50% its length), and pressure resistance (70 kg), allow for a wide variety of applications.

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 ). 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.

Gait change in tongue movement

During locomotion, humans switch gaits from walking to running, and horses from walking to trotting to cantering to galloping, as they increase their movement rate. It is unknown whether gait change leading to a wider movement rate range is limited to locomotive-type behaviours, or instead is a general property of any rate-varying motor system. The tongue during speech provides a motor system that can address this gap. In controlled speech experiments, using phrases containing complex tongue-movement sequences, we demonstrate distinct gaits in tongue movement at different speech rates. As speakers widen their tongue-front displacement range, they gain access to wider speech-rate ranges. At the widest displacement ranges, speakers also produce categorically different patterns for their slowest and fastest speech. Speakers with the narrowest tongue-front displacement ranges show one stable speech-gait pattern, and speakers with widest ranges show two. Critical fluctuation analysis of tongue motion over the time-course of speech revealed these speakers used greater effort at the beginning of phrases—such end-state-comfort effects indicate speech planning. Based on these findings, we expect that categorical motion solutions may emerge in any motor system, providing that system with access to wider movement-rate ranges.

Universal Features in Panarthropod Inter-Limb Coordination during Forward Walking.

SynopsisTerrestrial animals must often negotiate heterogeneous, varying environments. Accordingly, their locomotive strategies must adapt to a wide range of terrain, as well as to a range of speeds to accomplish different behavioral goals. Studies in Drosophila have found that inter-leg coordination patterns (ICPs) vary smoothly with walking speed, rather than switching between distinct gaits as in vertebrates (e.g., horses transitioning between trotting and galloping). Such a continuum of stepping patterns implies that separate neural controllers are not necessary for each observed ICP. Furthermore, the spectrum of Drosophila stepping patterns includes all canonical coordination patterns observed during forward walking in insects. This raises the exciting possibility that the controller in Drosophila is common to all insects, and perhaps more generally to panarthropod walkers. Here, we survey and collate data on leg kinematics and inter-leg coordination relationships during forward walking in a range of arthropod species, as well as include data from a recent behavioral investigation into the tardigrade Hypsibius exemplaris. Using this comparative dataset, we point to several functional and morphological features that are shared among panarthropods. The goal of the framework presented in this review is to emphasize the importance of comparative functional and morphological analyses in understanding the origins and diversification of walking in Panarthropoda.Introduction

SMALLBug: A 30-mg Crawling Robot Driven by a High-Frequency Flexible SMA Microactuator

We present the design, fabrication and experimental testing of SMALLBug, a 30-mg crawling microrobot that is 13 mm in length and can locomote at actuation frequencies of up to 20 Hz. The robot is driven by an electrically-powered 6-mg bending actuator that is composed of a thin shape-memory alloy (SMA) wire and a carbon-fiber piece that acts as a loading leaf-spring. This configuration enables the generation of high-speed thermally-induced phase transformations of the SMA material to produce high-frequency periodic actuation. During development, several actuator prototypes with different mechanical stiffnesses were tested and characterized by measuring their bending motions when excited with pulse-width modulation (PWM) voltages with a variety of frequencies and duty cycles (DCs). In a similar manner, the displacement-force characteristic of the actuator chosen to drive SMALLBug was identified by measuring its bending displacements under a number of different loads ranging from 4.22 to 83.8 mN. The locomotion capabilities of SMALLBug were experimentally tested at three different input actuation frequencies, which were observed to produce three distinct gaits. At the low frequency of 2 Hz, the robot locomotes with a crawling gait similar to that of inchworms; at the moderate frequency of 10 Hz, the robot advances smoothly at an approximately constant speed using a shuffling gait; and at the high frequency of 20 Hz, the robot generates small and fast jumps in a galloping gait, reaching average speeds of up to 17 $\boldsymbol{\text {mm}} \cdot \boldsymbol{\text {s}}^{\boldsymbol{\text {--}}\boldsymbol{\text {1}}}$, equivalent to 1.3 body-lengths per second (BLPS).

What Defines Different Modes of Snake Locomotion?

SynopsisAnimals move in diverse ways, as indicated in part by the wide variety of gaits and modes that have been described for vertebrate locomotion. Much variation in the gaits of limbed animals is associated with changing speed, whereas different modes of snake locomotion are often associated with moving on different surfaces. For several decades different types of snake locomotion have been categorized as one of four major modes: rectilinear, lateral undulation, sidewinding, and concertina. Recent empirical work shows that the scheme of four modes of snake locomotion is overly conservative. For example, during aquatic lateral undulation, the timing between muscle activity and lateral bending changes along the length of the snake, which is unlike terrestrial lateral undulation. The motor pattern used to prevent sagging while bridging gaps also suggests that arboreal lateral undulation on narrow surfaces or with a few discrete points of support has a different motor pattern than terrestrial lateral undulation when the entire length of the snake is supported. In all types of concertina locomotion, the distance from the head to the tail changes substantially as snakes alternately flex and then extend different portions of their body. However, snakes climbing cylinders with concertina exert forces medially to attain a purchase on the branch, whereas tunnels require pushing laterally to form an anchoring region. Furthermore, different motor patterns are used for these two types of concertina movement. Some snakes climb vertical cylinders with helical wrapping completely around the cylinder, whereas all other forms of concertina bend regions of the body alternately to the left and right. Current data support rectilinear locomotion and sidewinding as being distinct modes, whereas lateral undulation and concertina are best used for defining categories of gaits with some unifying similarities. Partly as a result of different motor patterns, I propose recognizing five and four distinct types of lateral undulation and concertina, respectively, resulting in a total of 11 distinct gaits previously recognized as only four.

Design Principles for Central Pattern Generators With Preset Rhythms.

This article is concerned with the design of synthetic central pattern generators (CPGs). Biological CPGs are neural circuits that determine a variety of rhythmic activities, including locomotion, in animals. A synthetic CPG is a network of dynamical elements (here called cells) properly coupled by various synapses to emulate rhythms produced by a biological CPG. We focus on CPGs for locomotion of quadrupeds and present our design approach, based on the principles of nonlinear dynamics, bifurcation theory, and parameter optimization. This approach lets us design the synthetic CPG with a set of desired rhythms and switch between them as the parameter representing the control actions from the brain is varied. The developed four-cell CPG can produce four distinct gaits: walk, trot, gallop, and bound, similar to the mouse locomotion. The robustness and adaptability of the network design principles are verified using different cell and synapse models.

Designing minimal and scalable insect-inspired multi-locomotion millirobots.

In ant colonies, collectivity enables division of labour and resources1-3 with great scalability. Beyond their intricate social behaviours, individuals of the genus Odontomachus4, also known as trap-jaw ants, have developed remarkable multi-locomotion mechanisms to 'escape-jump' upwards when threatened, using the sudden snapping of their mandibles5, and to negotiate obstacles by leaping forwards using their legs6. Emulating such diverse insect biomechanics and studying collective behaviours in a variety of environments may lead to the development of multi-locomotion robotic collectives deployable in situations such as emergency relief, exploration and monitoring7; however, reproducing these abilities in small-scale robotic systems with simple design and scalability remains a key challenge. Existing robotic collectives8-12 are confined to two-dimensional surfaces owing to limited locomotion, and individual multi-locomotion robots13-17 are difficult to scale up to large groups owing to the increased complexity, size and cost of hardware designs, which hinder mass production. Here we demonstrate an autonomous multi-locomotion insect-scale robot (millirobot) inspired by trap-jaw ants that addresses the design and scalability challenges of small-scale terrestrial robots. The robot's compact locomotion mechanism is constructed with minimal components and assembly steps, has tunable power requirements, and realizes five distinct gaits: vertical jumping for height, horizontal jumping for distance, somersault jumping to clear obstacles, walking on textured terrain and crawling on flat surfaces. The untethered, battery-powered millirobot can selectively switch gaits to traverse diverse terrain types, and groups of millirobots can operate collectively to manipulate objects and overcome obstacles. We constructed the ten-gram palm-sized prototype-the smallest and lightest self-contained multi-locomotion robot reported so far-by folding a quasi-two-dimensional metamaterial18 sandwich formed of easily integrated mechanical, material and electronic layers, which will enable assembly-free mass-manufacturing of robots with high task efficiency, flexibility and disposability.

Hydrodynamic Performance of a Modular Biolocomotion Emulator

This paper presents experimental measurements of the internal and external forces and moments generated during forced oscillation of a modular biolocomotion emulator executing four distinct gaits at three reduced frequencies and three Reynolds numbers (including zero). The purpose of the experimental program is to develop a database of hydrodynamic force measurements that can be used to validate low-order computational methods, such as the unsteady vortex lattice method, for design analysis.

Using step width to compare locomotor biomechanics between extinct, non-avian theropod dinosaurs and modern obligate bipeds.

How extinct, non-avian theropod dinosaurs locomoted is a subject of considerable interest, as is the manner in which it evolved on the line leading to birds. Fossil footprints provide the most direct evidence for answering these questions. In this study, step width-the mediolateral (transverse) distance between successive footfalls-was investigated with respect to speed (stride length) in non-avian theropod trackways of Late Triassic age. Comparable kinematic data were also collected for humans and 11 species of ground-dwelling birds. Permutation tests of the slope on a plot of step width against stride length showed that step width decreased continuously with increasing speed in the extinct theropods (p < 0.001), as well as the five tallest bird species studied (p < 0.01). Humans, by contrast, showed an abrupt decrease in step width at the walk-run transition. In the modern bipeds, these patterns reflect the use of either a discontinuous locomotor repertoire, characterized by distinct gaits (humans), or a continuous locomotor repertoire, where walking smoothly transitions into running (birds). The non-avian theropods are consequently inferred to have had a continuous locomotor repertoire, possibly including grounded running. Thus, features that characterize avian terrestrial locomotion had begun to evolve early in theropod history.

Phenotypic Characterization of Speed-Associated Gait Changes in Mice Reveals Modular Organization of Locomotor Networks

Studies of locomotion in mice suggest that circuits controlling the alternating between left and right limbs may have a modular organization with distinct locomotor circuits being recruited at different speeds. It is not clear, however, whether such a modular organization reflects specific behavioral outcomes expressed at different speeds of locomotion. Here, we use detailed kinematic analyses to search for signatures of a modular organization of locomotor circuits in intact and genetically modified mice moving at different speeds of locomotion. We show that wild-type mice display three distinct gaits: two alternating, walk and trot, and one synchronous, bound. Each gait is expressed in distinct ranges of speed with phenotypic inter-limb and intra-limb coordination. A fourth gait, gallop, closely resembled bound in most of the locomotor parameters but expressed diverse inter-limb coordination. Genetic ablation of commissural V0V neurons completely removed the expression of one alternating gait, trot, but left intact walk, gallop, and bound. Ablation of commissural V0V and V0D neurons led to a loss of walk, trot, and gallop, leaving bound as the default gait. Our study provides a benchmark for studies of the neuronal control of locomotion in the full range of speeds. It provides evidence that gait expression depends upon selection of different modules of neuronal ensembles.

Development of Wheel-less Snake Robot with Two Distinct Gaits and Gait Transition Capability

Snake robots are mostly designed based on single mode locomotion. However, single mode gait most likely could not work effectively when the robot is subject to an unstructured working environment with different measures of terrain complexity. As a solution, mixed mode locomotion is proposed in this paper by synchronizing two types of gaits known as serpentine and wriggler gaits used for non-constricted and narrow space environments, respectively, but for straight line locomotion only. A gait transition algorithm is developed to efficiently change the gait from one to another. This study includes the investigation on kinematics analysis followed by dynamics analysis while considering related structural constraints for both gaits. The approach utilizes the speed of the serpentine gait for open area locomotion and exploits the narrow space access capability of the wriggler gait. Hence, it can increase motion flexibility in view of the fact that the robot is able to change its mode of locomotion according to the working environment.

Kinematics and Center of Mass Mechanics During Terrestrial Locomotion in Northern Lapwings (Vanellus vanellus, Charadriiformes)

Avian bipedalism is best studied in derived walking/running specialists. Here, we use kinematics and center of mass (CoM) mechanical energy patterns to investigate gait transitions of lapwings-migratory birds that forage on the ground, and therefore may need a trade-off between the functional demands of terrestrial locomotion and long distance flights. The animals ran on a treadmill while high-speed X-ray videos were recorded within the sustainable speed range. Instantaneous CoM mechanics were computed from integrating kinematics and body segment properties. Lapwings exhibit similar locomotor characteristics to specialized walking/running birds, but have less distinct gaits. At slow speeds no clear separation between vaulting (i.e., walking) and bouncing (i.e., running) energy patterns exists. Mechanical energy recovery of non-bouncing gaits correlates poorly with speed and suggests inefficient use of the inverted pendulum mechanism. Speed ranges of gaits overlap considerably, especially those of grounded running, a gait with CoM mechanics indicative of running but without an aerial phase, and aerial phase running, with no preferential gait at most speeds. Compliant limb morphology and grounded running in birds can be regarded as an evolutionary constraint, but lapwings effectively make use of advantages offered by this gait for a great fraction of their speed range. Thus, effective usage of grounded running during terrestrial locomotion is suggested generally to be a part of striding avian bipedalism-even in species not specialized in walking/running locomotion.

Inter-leg coordination in the control of walking speed inDrosophila

Legged locomotion is the most common behavior of terrestrial animals and it is assumed to have become highly optimized during evolution. Quadrupeds, for instance, use distinct gaits that are optimal with regard to metabolic cost and have characteristic kinematic features and patterns of inter-leg coordination. In insects, the situation is not as clear. In general, insects are able to alter inter-leg coordination systematically with locomotion speed, producing a continuum of movement patterns. This notion, however, is based on the study of several insect species, which differ greatly in size and mass. Each of these species tends to walk at a rather narrow range of speeds. We have addressed these issues by examining four strains of Drosophila, which are similar in size and mass, but tend to walk at different speed ranges. Our data suggest that Drosophila controls its walking speed almost exclusively via step frequency. At high walking speeds, we invariably found tripod coordination patterns, the quality of which increased with speed as indicated by a simple measure of tripod coordination strength (TCS). At low speeds, we also observed tetrapod coordination and wave gait-like walking patterns. These findings not only suggest a systematic speed dependence of inter-leg movement patterns but also imply that inter-leg coordination is flexible. This was further supported by amputation experiments in which we examined walking behavior in animals after the removal of a hindleg. These animals show immediate adaptations in body posture, leg kinematics and inter-leg coordination, thereby maintaining their ability to walk.

Coordination of behavioral hierarchies during environmental transitions inCaenorhabditis elegans

For animals inhabiting multiple environments, the ability to select appropriate behaviors is crucial as their adaptability is often context dependent. Caenorhabditis elegans uses distinct gaits to move on land and in water. Gait transitions can potentially coordinate behaviors associated with distinct environments. We investigated whether land and water differentially affect the behavioral repertoire of C. elegans. Swimming worms interrupted foraging, feeding, egg-laying and defecation. Exogenous dopamine induced bouts of these land-associated behaviors in water. Our finding that worms do not drink fluid while immersed may explain why higher drug doses are required in water than on land to elicit the same effects. C. elegans is a valid model to study behavioral hierarchies and how environmental pressures alter their balance.