The evolutionary transition to sideways-walking gaits in brachyurans was accompanied by a reduction in the number of motor neurons innervating proximal leg musculature

The forwards-walking portly crab, Libinia emarginata is an ancient brachyuran. Its phylogenetic position and behavioral repertoire make it an excellent candidate to reveal the adaptations, which were required for brachyuran crabs to complete their transition to sideways-walking from their forwards-walking ancestors. Previously we showed that in common with other forwards-walking (but distantly related) crustaceans, L. emarginata relies more heavily on its more numerous proximal musculature to propel itself forward than its sideways-walking closer relatives. We investigated if the proximal musculature of L. emarginata is innervated by a greater number of motor neurons than that of sideways-walking brachyurans. We found the distal musculature of spider crabs is innervated by a highly conserved number of motor neurons. However, innervation of its proximal musculature is more numerous than in closely-related (sideways-walking) species, resembling in number and morphology those described for forwards-walking crustaceans. We propose that transition from forward- to sideways-walking in crustaceans involved a decreased role for the proximal leg in favor of the more distal merus–carpus joint.     

Degree of neuromuscular facilitation is correlated with contribution to walking in leg muscles of two species of crab

Despite decades of work on the neuromuscular physiology of crustacean leg muscles, little is known about how physiological differences between these muscles relate to their behavioral usage. We studied a sideways walking shore crab, Carcinus maenas, and a forward walking spider crab, Libinia emarginata, as part of our work to understand the neural control of locomotion. The two species differed significantly in facilitation at neuromuscular junctions for every muscle studied. Further, these differences are correlated exactly with the walking use of the muscles. The forward walking spider crab showed more facilitation in muscles which operate joints having larger ranges of motion in forward walking. Likewise, greater facilitation was seen in muscles more active during sideways walking in the predominantly sideways walking shore crab. These differences even occur between muscles innervated by the same motor neuron, and become more evident with higher stimulus frequency. The increased presynaptic facilitation might allow selective recruitment of fibers innervated by the same motor neuron and aid in temporal filtering. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Behaviour-based modelling of hexapod locomotion: linking biology and technical application

Walking in insects and most six-legged robots requires simultaneous control of up to 18 joints. Moreover, the number of joints that are mechanically coupled via body and ground varies from one moment to the next, and external conditions such as friction, compliance and slope of the substrate are often unpredictable. Thus, walking behaviour requires adaptive, context-dependent control of many degrees of freedom. As a consequence, modelling legged locomotion addresses many aspects of any motor behaviour in general. Based on results from behavioural experiments on arthropods, we describe a kinematic model of hexapod walking: the distributed artificial neural network controller walknet. Conceptually, the model addresses three basic problems in legged locomotion. (I) First, coordination of several legs requires coupling between the step cycles of adjacent legs, optimising synergistic propulsion, but ensuring stability through flexible adjustment to external disturbances. A set of behaviourally derived leg coordination rules can account for decentralised generation of different gaits, and allows stable walking of the insect model as well as of a number of legged robots. (II) Second, a wide range of different leg movements must be possible, e.g. to search for foothold, grasp for objects or groom the body surface. We present a simple neural network controller that can simulate targeted swing trajectories, obstacle avoidance reflexes and cyclic searching-movements. (III) Third, control of mechanically coupled joints of the legs in stance is achieved by exploiting the physical interactions between body, legs and substrate. A local positive displacement feedback, acting on individual leg joints, transforms passive displacement of a joint into active movement, generating synergistic assistance reflexes in all mechanically coupled joints.     

How locomotion sub-functions can control walking at different speeds?

Inspired from template models explaining biological locomotory systems and Raibert׳s pioneering legged robots, locomotion can be realized by basic sub-functions: elastic axial leg function, leg swinging and balancing. Combinations of these three can generate different gaits with diverse properties. In this paper we investigate how locomotion sub-functions contribute to stabilize walking at different speeds. Based on this trilogy, we introduce a conceptual model to quantify human locomotion sub-functions in walking. This model can produce stable walking and also predict human locomotion sub-function control during swing phase of walking. Analyzing experimental data based on this modeling shows different control strategies which are employed to increase speed from slow to moderate and moderate to fast gaits.     

A collisional model of the energetic cost of support work qualitatively explains leg sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition

Terrestrial legged locomotion requires repeated support forces to redirect the body's vertical velocity component from down to up. We assume that the redirection is accomplished by impulsive leg forces that cause small-angle glancing collisions of a point-mass model of the animal. We estimate the energetic costs of these collisions by assuming a metabolic cost proportional to positive muscle work involved in generating the impulses. The cost of bipedal running estimated from this collisional model becomes less than that of walking at a Froude number (v2/gl) of about 0.7. Two strategies to reduce locomotion costs associated with the motion redirection are: (1) having legs simulate purely elastic springs, as is observed in human running; and (2) sequencing the leg forces during the redirection phase; examples of this sequencing are the ba-da-dump pattern of a horse gallop and having push-off followed by heel-strike in human walking.     

Compliant leg behaviour explains basic dynamics of walking and running

The basic mechanics of human locomotion are associated with vaulting over stiff legs in walking and rebounding on compliant legs in running. However, while rebounding legs well explain the stance dynamics of running, stiff legs cannot reproduce that of walking. With a simple bipedal spring-mass model, we show that not stiff but compliant legs are essential to obtain the basic walking mechanics; incorporating the double support as an essential part of the walking motion, the model reproduces the characteristic stance dynamics that result in the observed small vertical oscillation of the body and the observed out-of-phase changes in forward kinetic and gravitational potential energies. Exploring the parameter space of this model, we further show that it not only combines the basic dynamics of walking and running in one mechanical system, but also reveals these gaits to be just two out of the many solutions to legged locomotion offered by compliant leg behaviour and accessed by energy or speed.     

Extended Evolutionary Fast Learn-to-Walk Approach for Four-Legged Robots

Robot locomotion is an active research area. In this paper we focus on the locomotion of quadruped robots. An effective walking gait of quadruped robots is mainly concerned with two key aspects, namely speed and stability. The large search space of potential parameter settings for leg joints means that hand tuning is not feasible in general. As a result walking parameters are typically determined using machine learning techniques. A major shortcoming of using machine learning techniques is the significant wear and tear of robots since many parameter combinations need to be evaluated before an optimal solution is found.This paper proposes a direct walking gait learning approach, which is specifically designed to reduce wear and tear of robot motors, joints and other hardware. In essence we provide an effective learning mechanism that leads to a solution in a faster convergence time than previous algorithms. The results demonstrate that the new learning algorithm obtains a faster convergence to the best solutions in a short run. This approach is significant in obtaining faster walking gaits which will be useful for a wide range of applications where speed and stability are important. Future work will extend our methods so that the faster convergence algorithm can be applied to a two legged humanoid and lead to less wear and tear whilst still developing a fast and stable gait.     

Insects Use Two Distinct Classes of Steps during Unrestrained Locomotion

Background

Adaptive, context-dependent control of locomotion requires modulation of centrally generated rhythmic motor patterns through peripheral control loops and postural reflexes. Thus assuming that the modulation of rhythmic motor patterns accounts for much of the behavioural variability observed in legged locomotion, investigating behavioural variability is a key to the understanding of context-dependent control mechanisms in locomotion. To date, the variability of unrestrained locomotion is poorly understood, and virtually nothing is known about the features that characterise the natural statistics of legged locomotion. In this study, we quantify the natural variability of hexapedal walking and climbing in insects, drawing from a database of several thousand steps recorded over two hours of walking time.

Results

We show that the range of step length used by unrestrained climbing stick insects is large, showing that step length can be changed substantially for adaptive locomotion. Step length distributions were always bimodal, irrespective of leg type and walking condition, suggesting the presence of two distinct classes of steps: short and long steps. Probability density of step length was well-described by a gamma distribution for short steps, and a logistic distribution for long steps. Major coefficients of these distributions remained largely unaffected by walking conditions. Short and long steps differed concerning their spatial occurrence on the walking substrate, their timing within the step sequence, and their prevalent swing direction. Finally, ablation of structures that serve to improve foothold increased the ratio of short to long steps, indicating a corrective function of short steps.

Conclusions

Statistical and functional differences suggest that short and long steps are physiologically distinct classes of leg movements that likely reflect distinct control mechanisms at work.     

Suspending loads decreases load stability but may slightly improve body stability

Here, we seek to determine how compliantly suspended loads could affect the dynamic stability of legged locomotion. We theoretically model the dynamic stability of a human carrying a load using a coupled spring-mass-damper model and an actuated spring-loaded inverted pendulum model, as these models have demonstrated the ability to correctly predict other aspects of locomotion with a load in prior work, such as body forces and energetic cost. We report that minimizing the load suspension natural frequency and damping ratio significantly reduces the stability of the load mass but may slightly improve the body stability of locomotion when compared to a rigidly attached load. These results imply that a highly-compliant load suspension could help stabilize body motion during human, animal, or robot load carriage, but at the cost of a more awkward (less stable) load.     

Lower extremity coupling parameters during locomotion and landings

During ballistic locomotion and landing activities, the lower extremity joints must function synchronously to dissipate the impact. The coupling of subtalar motion to tibial and knee rotation has been hypothesized to depend on the dynamic requirements of the task. This study was undertaken to look for differences in the coupling of 3-D foot and knee motions during walking, jogging, and landing from a jump. Twenty recreationally active young women with normal foot alignment (as assessed by a licensed physical therapist) were videotaped with high-speed cameras (250 Hz) during walking, jogging, hopping, and jumping trials. Coupling coefficients were compared among the four activities. The ratio of eversion to tibial rotation increased from the locomotion to the landing trials, indicating that with the increased loading demands of the activity, the requirements of foot motion increased. However, this increased motion was not proportionately translated into rotation of the tibia through the subtalar joint. Furthermore, the ratio of knee flexion to knee internal rotation increased significantly from the walking to landing trials. Together these findings suggest that femoral rotation may compensate for the increase in tibial rotation as the force-dissipating demands of the task increase. The relative unbalance among the magnitude of foot, tibial, and knee rotations observed with increasing task demands may have direct implications on clinical treatments aimed at reducing knee motion via controlling motion at the foot during landing tasks.     

Human odometer is gait-symmetry specific

In 1709, Berkeley hypothesized of the human that distance is measurable by ‘the motion of his body, which is perceivable by touch’. To be sufficiently general and reliable, Berkeley''s hypothesis must imply that distance measured by legged locomotion approximates actual distance, with the measure invariant to gait, speed and number of steps. We studied blindfolded human participants in a task in which they travelled by legged locomotion from a fixed starting point A to a variable terminus B, and then reproduced, by legged locomotion from B, the A–B distance. The outbound (‘measure’) and return (‘report’) gait could be the same or different, with similar or dissimilar step sizes and step frequencies. In five experiments we manipulated bipedal gait according to the primary versus secondary distinction revealed in symmetry group analyses of locomotion patterns. Berkeley''s hypothesis held only when the measure and report gaits were of the same symmetry class, indicating that idiothetic distance measurement is gait-symmetry specific. Results suggest that human odometry (and perhaps animal odometry more generally) entails variables that encompass the limbs in coordination, such as global phase, and not variables at the level of the single limb, such as step length and step number, as traditionally assumed.     

Three‐Legged Locomotion and the Constraints on Limb Number: Why Tripeds Don’t Have a Leg to Stand On

Three‐legged animals do not exist today and such an animal is not found in the fossil record. Which constraints operate to result in the lack of a triped phenotype? Consideration of animal locomotion and robotic studies suggests that physical constraints would not prevent a triped from being functional or advantageous. As is reviewed here, the strongest constraint on the evolution of a triped is phylogenetic: namely, the early genetic adoption of a bilaterally symmetrical body plan occurring before the advent of limbs. Presumably, this would greatly constrain any three‐legged animal from ever evolving. Tripedalism is employed only by a few animals, but many use a tripod stance while engaged in a variety of activities. Because terms are often used interchangeably in the literature, a standardization of locomotion terminology is proposed. Understanding the constraints behind “forbidden” phenotypes forces us to confront gaps in our evolutionary understanding of which we may be unaware.     

Patterns of axial and appendicular movements during aquatic walking in the salamander Siren lacertina

Most studies of salamander locomotion have focused either on swimming or terrestrial walking, but some salamanders also use limb-based locomotion while submerged under water (aquatic walking). In this study we used video motion analysis to describe the aquatic walking gait of Siren lacertina, an elongate salamander with reduced forelimbs and no hindlimbs. We found that S. lacertina uses a bipedal-undulatory gait, which combines alternating use of the forelimbs with a traveling undulatory wave. Each forelimb is in contact with the substrate for about 50% of the stride cycle and forelimbs have little temporal overlap in contact intervals. We quantified the relative timing and frequency of limb and tail movements and found that, unlike the terrestrial gaits of most salamanders, axial and appendicular movements are decoupled during aquatic walking. We found no significant relationship between stride frequency and aquatic walking velocity, but we did find a statistically significant relationship between tailbeat frequency and aquatic walking velocity, which suggests that aquatic walking speed is mainly modulated by axial movements. By comparing axial wavespeed and distance traveled per tailbeat during swimming (forelimbs not used) and aquatic walking (forelimbs used), we found lower wavespeed and greater distance traveled per tailbeat during aquatic walking. These findings suggest that the reduced forelimbs of S. lacertina contribute to forward propulsion during aquatic walking.     

Stable walking with asymmetric legs

Asymmetric leg function is often an undesired side-effect in artificial legged systems and may reflect functional deficits or variations in the mechanical construction. It can also be found in legged locomotion in humans and animals such as after an accident or in specific gait patterns. So far, it is not clear to what extent differences in the leg function of contralateral limbs can be tolerated during walking or running. Here, we address this issue using a bipedal spring-mass model for simulating walking with compliant legs. With the help of the model, we show that considerable differences between contralateral legs can be tolerated and may even provide advantages to the robustness of the system dynamics. A better understanding of the mechanisms and potential benefits of asymmetric leg operation may help to guide the development of artificial limbs or the design novel therapeutic concepts and rehabilitation strategies.     

Freshwater crab origins—Laying Gondwana to rest

We review the available data on the phylogeny, palaeontology and divergence time estimation of primary freshwater crabs in relation to a hypothesized Gondwanan origin of these brachyurans, as postulated by some workers in recent decades. Known phylogenetic relationships within the Old World freshwater crabs do not correspond to the successive fragmentation of the Gondwana continent. This is strong evidence against an ancestral Gondwanan distribution of Afrotropical Potamonautidae and Asian-Australian Gecarcinucidae. The fossil record of freshwater crabs (no older than the Oligocene) and heterotreme brachyurans also postdate the initial break up of Gondwana. Molecular-clock based time estimates for the most common recent ancestor of freshwater crab families differ profoundly, depending on the method of calibration used, and whether freshwater or marine brachyuran fossils are used as calibration points. As such, molecular clock estimates calibrated on freshwater crab fossils favour a post-Gondwanan evolution of freshwater crabs whereas calibration based on marine brachyuran fossils date their last common ancestor before the fragmentation of Gondwana.     

Control of obstacle climbing in the cockroach, Blaberus discoidalis. I. Kinematics

An advantage of legged locomotion is the ability to climb over obstacles. We studied deathhead cockroaches as they climbed over plastic blocks in order to characterize the leg movements associated with climbing. Movements were recorded as animals surmounted 5.5-mm or 11-mm obstacles. The smaller obstacles were scaled with little change in running movements. The higher obstacles required altered gaits, leg positions and body posture. The most frequent sequence used was to first tilt the front of the body upward in a rearing stage, and then elevate the center of mass to the level of the top of the block. A horizontal running posture was re-assumed in a leveling-off stage. The action of the middle legs was redirected by rotations of the leg at the thoracal-coxal and the trochanteral-femoral joints. The subsequent extension movements of the coxal-trochanteral and femoral-tibial joints were within the range seen during horizontal running. The structure of proximal leg joints allows for flexibility in leg use by generating subtle, but effective changes in the direction of leg movement. This architecture, along with the resulting re-direction of movements, provides a range of strategies for both animals and walking machines.     

An Experimental Study on the Gait Patterns and Kinematics of Chinese Mitten Crabs

Despite the many studies on eight-legged animals and the importance of their mechanics of terrestrial locomotion, the mechanical energy of crabs in voluntary locomotion on uneven, unpredictable terrain surfaces has received little attention thus far. In this paper, motion video images of Chinese mitten crab (Eriocheir sinensis Milne-Edwards) locomotion on five types of terrains were recorded using a high-speed three-dimensional (3D) recording video system. The typical variables of locomotion such as gait patterns, duty factor, mechanical energy of the mass center, mass-specific rate of the total mechanical power of the mass center, and percentage recovery, were analyzed. Results show that the Chinese mitten crab uses random gaits instead of the alternating tetrapod gait with the increasing terrain roughness. The duty factors of the rows of the leading legs are greater for all terrains than those of the rows of the trailing legs. On smooth terrain, the duty factors of the rows of the trailing legs are greater than that on rough terrains. Kinematic measurements and calculations reveal that similar to mammals, birds, and arthropods, the Chinese mitten crab uses two fundamental gaits to save mechanical energy: the inverted pendulum gait and the bouncing gait. The bouncing gait is the main pattern of mechanical energy conservation. The low probability of injury and energy expenditure due to adaptations to various terrains induce the Chinese mitten crab to modify the mass-specific rate of the total mechanical power of the mass center. The statistical results of percentage recovery also reveal that the Chinese mitten crab has lower energy recovery efficiency over rough terrains compared with smooth terrains.     

Bird terrestrial locomotion as revealed by 3D kinematics

Most birds use at least two modes of locomotion: flying and walking (terrestrial locomotion). Whereas the wings and tail are used for flying, the legs are mainly used for walking. The role of other body segments remains, however, poorly understood. In this study, we examine the kinematics of the head, the trunk, and the legs during terrestrial locomotion in the quail (Coturnix coturnix). Despite the trunk representing about 70% of the total body mass, its function in locomotion has received little scientific interest to date. This prompted us to focus on its role in terrestrial locomotion. We used high-speed video fluoroscopic recordings of quails walking at voluntary speeds on a trackway. Dorso-ventral and lateral views of the motion of the skeletal elements were recorded successively and reconstructed in three dimensions using a novel method based on the temporal synchronisation of both views. An analysis of the trajectories of the body parts and their coordination showed that the trunk plays an important role during walking. Moreover, two sub-systems participate in the gait kinematics: (i) the integrated 3D motion of the trunk and thighs allows for the adjustment of the path of the centre of mass; (ii) the motion of distal limbs transforms the alternating forward motion of the feet into a continuous forward motion at the knee and thus assures propulsion. Finally, head bobbing appears qualitatively synchronised to the movements of the trunk. An important role for the thigh muscles in generating the 3D motion of the trunk is suggested by an analysis of the pelvic anatomy.