Leg recirculation in horizontal plane locomotion

A protocol prescribing leg motion during the swing phase is developed for the planar lateral leg spring model of locomotion. Inspired by experimental observations regarding insect leg function when running over rough terrain, the protocol prescribes the angular velocity of the swing-leg relative to the body in a feedforward manner, yielding natural variations in the leg touch-down angle in response to perturbations away from a periodic orbit. Analysis of the reduced order model reveals that periodic gait stability and robustness to external perturbations depends strongly upon the angular velocity of the leg at touch-down. While the leg angular velocity at touch-down provides control over gait stability and can be chosen to stabilize unstable gaits, the resulting basin of stability is much smaller than that observed for the original lateral leg spring model with a fixed leg touch-down angle. Comparisons to experimental leg angular velocity data for running cockroaches reveal that while the proposed protocol is qualitatively correct, smaller leg angular accelerations occur during the second half of the swing phase. Modifications made to the recirculation protocol to better match experimental observations yield large improvements in the basin of stability.     

Interactive effects of leg autotomy and incline on locomotor performance and kinematics of the cellar spider,Pholcus manueli

Leg autotomy can be a very effective strategy for escaping a predation attempt in many animals. In spiders, autotomy can be very common (5–40% of individuals can be missing legs) and has been shown to reduce locomotor speeds, which, in turn, can reduce the ability to find food, mates, and suitable habitat. Previous work on spiders has focused mostly on the influence of limb loss on horizontal movements. However, limb loss can have differential effects on locomotion on the nonhorizontal substrates often utilized by many species of spiders. We examined the effects of leg autotomy on maximal speed and kinematics while moving on horizontal, 45° inclines, and vertical (90°) inclines in the cellar spider Pholcus manueli, a widespread species that is a denizen of both natural and anthropogenic, three‐dimensional microhabitats, which frequently exhibits autotomy in nature. Maximal speeds and kinematic variables were measured in all spiders, which were run on all three experimental inclines twice. First, all spiders were run at all inclines prior to autotomization. Second, half of the spiders had one of the front legs removed, while the other half was left intact before all individuals were run a second time on all inclines. Speeds decreased with increasing incline and following autotomy at all inclines. Autotomized spiders exhibited a larger decrease in speed when moving horizontally compared to on inclines. Stride length decreased at 90° but not after autotomy. Stride cycle time and duty factor increased after autotomy, but not when moving uphill. Results show that both incline and leg autotomy reduce speed with differential effects on kinematics with increasing incline reducing stride length, but not stride cycle time or duty factor, and vice versa for leg autotomy. The lack of a significant influence on a kinematic variable could be evidence for partial compensation to mitigate speed reduction.     

Descending control of body attitude in the cockroach <Emphasis Type="Italic">Blaberus discoidalis</Emphasis> and its role in incline climbing

Unlike intact animals, cockroaches with bilateral circumoesophageal connective lesions have difficulty climbing up smooth inclines. Typically, they slipped badly or even fell over backward before traveling more than 1.5 body lengths up the incline. The major problem involves increased slippage of the front and sometimes middle legs. Periods of front leg slipping are correlated with excess body elevation that pushes the height of the head to 11 mm above the substrate. Intact animals control body attitude very well on the incline, only rarely rearing above 11 mm. Cockroaches with bilateral circumoesophageal connective lesions spend considerable time above this critical amplitude and slipping increases with amplitude above that value. We conclude that circumoesophageal lesion compromises the insects ability to control body attitude on the incline and this deficit contributes to the inability of lesioned cockroaches to climb steep inclines. A separate body attitude deficit was noted on steps. Upon climbing to the top of a barrier, intact animals bend their body between the first and second thoracic segments. This action maintains good leg mechanics throughout the climb. Cockroaches with bilateral circumoesophageal connective lesions fail to perform this downward flexion. A beneficial role for similar body flexion in simple robots is described in the Discussion.     

Mechanical models for insect locomotion: dynamics and stability in the horizontal plane I. Theory

We study the dynamics and stability of legged locomotion in the horizontal plane. Motivated by experimental studies of insects, we develop two- and three-degree-of freedom rigid body models with pairs of ‘virtual’ elastic legs in intermittent contact with the ground. We focus on conservative compliant-legged models, but we also consider prescribed forces, prescribed leg displacements, and combined strategies. The resulting mechanical systems exhibit periodic gaits whose stability characteristics are due to intermittent foot contact, and are largely determined by geometrical criteria. Most strikingly, we show that mechanics alone can confer asymptotic stability in heading and body orientation. In a companion paper, we apply our results to rapidly running cockroaches. Received: 6 September 1999 / Accepted in revised form: 8 May 2000     

Improving horizontal plane locomotion via leg angle control

The lateral leg spring model has been shown to accurately represent horizontal plane locomotion characteristics of sprawled posture insects such as the cockroach Blaberus discoidalis. While passively stable periodic gaits result from employing a constant leg touch-down angle for this model, utilizing a similar protocol for a point mass model of locomotion in three dimensions produces only unstable periodic gaits. In this work, we return to the horizontal plane model and develop a simple control law that prescribes variations in the leg touch-down angle in response to external perturbations. The resulting control law applies control once per stance phase, at the instant of leg touch-down, and depends upon previous leg angles defined in the body reference frame. As a result, our control action is consistent with the neural activity evidenced by B. discoidalis during locomotion over flat and rough terrain, and utilizes variables easily sensed by insect mechanoreceptors. Application of control in the lateral leg spring model is shown to improve stability of periodic gaits, enable stabilization of previously unstable periodic gaits, and maintain or improve the basin of stability of periodic gaits. The magnitude of leg touch-down angle variations utilized during stabilization appear consistent with the natural variations evidenced by single legs during locomotion over flat terrain.     

FUNCTIONAL AND EVOLUTIONARY ASPECTS OF THE POSTCRANIAL ANATOMY OF DICYNODONTS (SYNAPSIDA, THERAPSIDA)

Abstract:  Restoration of the major skeletal muscles and functional morphological analysis of the postcranium were carried out on two Triassic dicynodont genera, Wadiasaurus and Lystrosaurus . A phylogenetic analysis of 12 selected Permian and Triassic dicynodont taxa was conducted and the postcranial character states were then mapped onto the most parsimonious tree. The analysis revealed changes in pectoral girdle and forelimb morphology, which included reduction of the coracoid plate, increasing robustness of the deltopectoral crest, change in humeral orientation from lateral to caudolateral, increasing prominence of the humeral head, and increasing robustness of the radius. Such changes can be associated with a functional tendency to reduce the lateral component of the propulsive force while still in an abducted mode. On the other hand, changes associated with the pelvic girdle included expansion of the preacetabular iliac process, reduction of the postacetabular iliac process, craniocaudal expansion of the iliac blade, change in the shape of the pubis from flat and plate-like to small and rod-like with a cranial process, and change in acetabular orientation from lateral to caudolateral. The femoral head, starting from a cranioproximal position, progressively became dorsally pronounced and offset from the body. Other features/changes associated with the femur included increasing robustness of the trochanter major, and increasing flattening of the femoral midshaft. Changes in the axial skeleton included increasing stiffening of the trunk to reduce lateral undulations, increasing dorsoventral flexion, and increasing sacral vertebral count, which can be correlated with the preacetabular iliac expansion. These findings suggest that the dicynodont postcranial skeleton evolved towards more upright hindlimb morphology with the body held well off the ground.     

Does a crouched leg posture enhance running stability and robustness?

Humans and birds both walk and run bipedally on compliant legs. However, differences in leg architecture may result in species-specific leg control strategies as indicated by the observed gait patterns. In this work, control strategies for stable running are derived based on a conceptual model and compared with experimental data on running humans and pheasants (Phasianus colchicus). From a model perspective, running with compliant legs can be represented by the planar spring mass model and stabilized by applying swing leg control. Here, linear adaptations of the three leg parameters, leg angle, leg length and leg stiffness during late swing phase are assumed. Experimentally observed kinematic control parameters (leg rotation and leg length change) of human and avian running are compared, and interpreted within the context of this model, with specific focus on stability and robustness characteristics. The results suggest differences in stability characteristics and applied control strategies of human and avian running, which may relate to differences in leg posture (straight leg posture in humans, and crouched leg posture in birds). It has been suggested that crouched leg postures may improve stability. However, as the system of control strategies is overdetermined, our model findings suggest that a crouched leg posture does not necessarily enhance running stability. The model also predicts different leg stiffness adaptation rates for human and avian running, and suggests that a crouched avian leg posture, which is capable of both leg shortening and lengthening, allows for stable running without adjusting leg stiffness. In contrast, in straight-legged human running, the preparation of the ground contact seems to be more critical, requiring leg stiffness adjustment to remain stable. Finally, analysis of a simple robustness measure, the normalized maximum drop, suggests that the crouched leg posture may provide greater robustness to changes in terrain height.     

Mechanical and metabolic requirements for active lateral stabilization in human walking

Walking appears to be passively unstable in the lateral direction, requiring active feedback control for stability. The central nervous system may control stability by adjusting medio-lateral foot placement, but potentially with a metabolic cost. This cost increases with narrow steps and may affect the preferred step width. We hypothesized that external stabilization of the body would reduce the active control needed, thereby decreasing metabolic cost and preferred step width. To test these hypotheses, we provided external lateral stabilization, using springs pulling bilaterally from the waist, to human subjects walking on a force treadmill at 1.25 m/s. Ten subjects walked, with and without stabilization, at a prescribed step width of zero and also at their preferred step width. We measured metabolic cost using indirect calorimetry, and step width from force treadmill data. We found that at the prescribed zero step width, external stabilization resulted in a 33% decrease in step width variability (root-mean-square) and a 9.2% decrease in metabolic cost. In the preferred step width conditions, external stabilization caused subjects to prefer a 47% narrower step width, with a 32% decrease in step width variability and a 5.7% decrease in metabolic cost. These results suggest that (a). human walking requires active lateral stabilization, (b). body lateral motion is partially stabilized via medio-lateral foot placement, (c). active stabilization exacts a modest metabolic cost, and (d). humans avoid narrow step widths because they are less stable.     

Robust and efficient walking with spring-like legs

The development of bipedal walking robots is inspired by human walking. A way of implementing walking could be performed by mimicking human leg dynamics. A fundamental model, representing human leg dynamics during walking and running, is the bipedal spring-mass model which is the basis for this paper. The aim of this study is the identification of leg parameters leading to a compromise between robustness and energy efficiency in walking. It is found that, compared to asymmetric walking, symmetric walking with flatter angles of attack reveals such a compromise. With increasing leg stiffness, energy efficiency increases continuously. However, robustness is the maximum at moderate leg stiffness and decreases slightly with increasing stiffness. Hence, an adjustable leg compliance would be preferred, which is adaptable to the environment. If the ground is even, a high leg stiffness leads to energy efficient walking. However, if external perturbations are expected, e.g. when the robot walks on uneven terrain, the leg should be softer and the angle of attack flatter. In the case of underactuated robots with constant physical springs, the leg stiffness should be larger than k = 14 in order to use the most robust gait. Soft legs, however, lack in both robustness and efficiency.     

Compliance, actuation, and work characteristics of the goat foreleg and hindleg during level, uphill, and downhill running.

We model the action of muscle-tendon system(s) about a given joint as a serial actuator and spring. By this technique, the experimental joint moment is imposed while the combined angular deflection of the actuator and spring are constrained to match the experimental joint angle throughout the stance duration. The same technique is applied to the radial leg (i.e., shoulder/hip-to-foot). The spring constant that minimizes total actuator work is considered optimal, and this minimum work is expressed as a fraction of total joint/radial leg work, yielding an actuation ratio (AR; 1 = pure actuation and 0 = pure compliance). To address work modulation, we determined the specific net work (SNW), the absolute value of net divided by total work. This ratio is unity when only positive or negative work is done and zero when equal energy is absorbed and returned. Our proximodistal predictions of joint function are supported during level and 15 degrees grade running. The greatest AR and SNW are found in the proximal leg joints (elbow and knee). The ankle joint is the principal spring of the hindleg and shows no significant change in SNW with grade, reflecting the true compliance of the common calcaneal tendon. The principal foreleg spring is the metacarpophalangeal joint. The observed pattern of proximal actuation and distal compliance, as well as the substantial SNW at proximal joints, minimal SNW at intermediate joints, and variable energy absorption at distal joints, may emerge as general principles in quadruped limb mechanics and help to inform the leg designs of highly capable running robots.     

Human leg model predicts ankle muscle-tendon morphology, state, roles and energetics in walking

A common feature in biological neuromuscular systems is the redundancy in joint actuation. Understanding how these redundancies are resolved in typical joint movements has been a long-standing problem in biomechanics, neuroscience and prosthetics. Many empirical studies have uncovered neural, mechanical and energetic aspects of how humans resolve these degrees of freedom to actuate leg joints for common tasks like walking. However, a unifying theoretical framework that explains the many independent empirical observations and predicts individual muscle and tendon contributions to joint actuation is yet to be established. Here we develop a computational framework to address how the ankle joint actuation problem is resolved by the neuromuscular system in walking. Our framework is founded upon the proposal that a consideration of both neural control and leg muscle-tendon morphology is critical to obtain predictive, mechanistic insight into individual muscle and tendon contributions to joint actuation. We examine kinetic, kinematic and electromyographic data from healthy walking subjects to find that human leg muscle-tendon morphology and neural activations enable a metabolically optimal realization of biological ankle mechanics in walking. This optimal realization (a) corresponds to independent empirical observations of operation and performance of the soleus and gastrocnemius muscles, (b) gives rise to an efficient load-sharing amongst ankle muscle-tendon units and (c) causes soleus and gastrocnemius muscle fibers to take on distinct mechanical roles of force generation and power production at the end of stance phase in walking. The framework outlined here suggests that the dynamical interplay between leg structure and neural control may be key to the high walking economy of humans, and has implications as a means to obtain insight into empirically inaccessible features of individual muscle and tendons in biomechanical tasks.     

Dynamic stability of superior vs. inferior body segments in individuals with transtibial amputation walking in destabilizing environments

Interestingly, young and highly active people with lower limb amputation appear to maintain a similar trunk and upper body stability during walking as able-bodied individuals. Understanding the mechanisms underlying how this stability is achieved after lower-leg amputation is important to improve training regimens for improving walking function in these patients. This study quantified how superior (i.e., head, trunk, and pelvis) and inferior (i.e., thigh, shank, and feet) segments of the body respond to continuous visual or mechanical perturbations during walking. Nine persons with transtibial amputation (TTA) and 12 able-bodied controls (AB) walked on a 2 m×3 m treadmill in a Computer Assisted Rehabilitation Environment (CAREN). Subjects were perturbed by continuous pseudo-random mediolateral movements of either the treadmill platform or the visual scene. TTA maintained a similar local and orbital stability in their superior body segments as AB throughout both perturbation types. However, for their inferior body segments, TTA subjects exhibited greater dynamic instability during perturbed walking. In TTA subjects, these increases in instability were even more pronounced in their prosthetic limb compared to their intact leg. These findings demonstrate that persons with unilateral lower leg amputation maintain upper body stability in spite of increased dynamic instability in their impaired lower leg. Thus, transtibial amputation does significantly impair sensorimotor function, leading to substantially altered dynamic movements of their lower limb segments. However, otherwise relatively healthy patients with unilateral transtibial amputation appear to retain sufficient remaining sensorimotor function in their proximal and contralateral limbs to adequately compensate for their impairment.     

Effect of muscular activity on valgus/varus laxity and stiffness of the knee

Quantitative changes in valgus/varus knee stability with different levels of muscular activity were determined for five subjects. A specially designed machine was used to measure resistance to angulation in the frontal plane. This device held the thigh stationary, the knee straight, an cycled the leg from side to side at a constant rate between present moment limits. Resistance to this forced valgus/varus motion was measured simultaneously with torque about the knee in the sagittal plane. Muscle activity was monitored by electromyography (EMG). Direct comparison of moment-rotation characteristics allowed changes in stability to be quantified as a function of extension and flexion torque. Extension torques less than 20% of the maximum increased varus stability more than valgus stability. Flexion torques of the same relative magnitude increased valgus stability more than varus stability. Comparison with the literature suggested that prevention of opening of the lateral side of the joint under varus loading was responsible for increased varus stability with increasing torque, both with extension and flexion torques.     

Level-specific role of paraxial mesoderm in regulation of Tbx5/Tbx4 expression and limb initiation

Tetrapod limbs, forelimbs and hindlimbs, emerge as limb buds during development from appropriate positions along the rostro-caudal axis of the main body. In this study, tissue interactions by which rostro-caudal level-specific limb initiation is established were analyzed. The limb bud originates from the lateral plate located laterally to the paraxial mesoderm, and we obtained evidence that level-specific tissue interactions between the paraxial mesoderm and the lateral plate mesoderm are important for the determination of the limb-type-specific gene expression and limb outgrowth. When the wing-level paraxial mesoderm was transplanted into the presumptive leg region, the wing-level paraxial mesoderm upregulated the expression of Tbx5, a wing marker gene, and down regulated the expression of Tbx4 and Pitx1, leg marker genes, in the leg-level lateral plate. The wing-level paraxial mesoderm relocated into the leg level also inhibited outgrowth of the hindlimb bud and down regulated Fgf10 and Fgf8 expression, demonstrating that the wing-level paraxial mesoderm cannot substitute for the function of the leg-level paraxial mesoderm in initiation and outgrowth of the hindlimb. The paraxial mesoderm taken from the neck- and flank-level regions also had effects on Tbx5/Tbx4 expression with different efficiencies. These findings suggest that the paraxial mesoderm has level-specific abilities along the rostro-caudal axis in the limb-type-specific mechanism for limb initiation.     

Biomimetic Design and Optimal Swing of a Hexapod Robot Leg

Biological inspiration has spawned a wealth of solutions to both mechanical design and control schemes in the efforts to develop agile legged machines. This paper presents a compliant leg mechanism for a small six-legged robot, HITCR-ll, based on abstracted anatomy from insect legs. Kinematic structure, relative proportion of leg segment lengths and actuation system were analyzed in consideration of anatomical structure as well as muscle system of insect legs and desired mobility. A spring based passive compliance mechanism inspired by musculoskeletal structures of biological systems was integrated into distal segment of the leg to soften foot impact on touchdown. In addition, an efficient locomotion planner capable of generating natural movements for the legs during swing phase was proposed. The problem of leg swing was formulated as an optimal control procedure that satisfies a series of locomotion task terms while minimizing a biologically-based objective function, which was solved by a Gauss Pseudospectral Method （GPM） based numerical technique. We applied this swing generation algorithm to both a simulation platform and a robot prototype. Results show that the proposed leg structure and swing planner are able to successfully perform effective swing movements on rugged terrains.     

Speed dependent phase shifts and gait changes in cockroaches running on substrates of different slipperiness

Background

Many legged animals change gaits when increasing speed. In insects, only one gait change has been documented so far, from slow walking to fast running, which is characterised by an alternating tripod. Studies on some fast-running insects suggested a further gait change at higher running speeds. Apart from speed, insect gaits and leg co-ordination have been shown to be influenced by substrate properties, but the detailed effects of speed and substrate on gait changes are still unclear. Here we investigate high-speed locomotion and gait changes of the cockroach Nauphoeta cinerea, on two substrates of different slipperiness.

Results

Analyses of leg co-ordination and body oscillations for straight and steady escape runs revealed that at high speeds, blaberid cockroaches changed from an alternating tripod to a rather metachronal gait, which to our knowledge, has not been described before for terrestrial arthropods. Despite low duty factors, this new gait is characterised by low vertical amplitudes of the centre of mass (COM), low vertical accelerations and presumably reduced total vertical peak forces. However, lateral amplitudes and accelerations were higher in the faster gait with reduced leg synchronisation than in the tripod gait with distinct leg synchronisation.

Conclusions

Temporally distributed leg force application as resulting from metachronal leg coordination at high running speeds may be particularly useful in animals with limited capabilities for elastic energy storage within the legs, as energy efficiency can be increased without the need for elasticity in the legs. It may also facilitate locomotion on slippery surfaces, which usually reduce leg force transmission to the ground. Moreover, increased temporal overlap of the stance phases of the legs likely improves locomotion control, which might result in a higher dynamic stability.

     

Dynamics and stability of insect locomotion: a hexapedal model for horizontal plane motions

We develop a simple hexapedal model for the dynamics of insect locomotion in the horizontal plane. Each leg is a linear spring endowed with two inputs, controlling force-free length and hip position, in a stereotypical feedforward pattern. These represent, in a simplified manner, the effects of neurally activated muscles in the animal and are determined from measured foot force and kinematic body data for cockroaches. We solve the three-degree-of-freedom Newtonian equations for coupled translation-yawing motions in response to the inputs and determine branches of periodic gaits over the animals typical speed range. We demonstrate a close quantitative match to experiments and find both stable and unstable motions, depending upon input protocols.Our hexapedal model highlights the importance of stability in evaluating effective locomotor performance and in particular suggests that sprawled-posture runners with large lateral and opposing leg forces can be stable in the horizontal plane over a range of speeds, with minimalsensory feedback from the environment. Fore–aft force patterns characteristic of upright-posture runners can cause instability in the model. We find that stability can constrain fundamental gait parameters: our model is stable only when stride length and frequency match the patterns measured in the animal. Stability is not compromised by large joint moments during running because ground reaction forces tend to align along the leg and be directed toward the center of mass. Legs radiating in all directions and capable of generating large moments may allow very rapid turning and extraordinary maneuvers. Our results further weaken the hypothesis that polypedal, sprawled-posture locomotion with large lateral and opposing leg forces is less effective than upright posture running with fewer legs.     

Morphological variation does not influence locomotor performance within a cohort of hatchling lizards (Amphibolurus muricatus, Agamidae)

A causal link between morphology and performance is a central tenet of ecomorphological analyses, but there are few detailed analyses of exactly how morphological variation within a hatchling cohort maps onto locomotor performance, and especially whether or not different tasks favour different morphologies (or vice versa). We measured morphological traits (including body length, mass, head size, limb proportions and fluctuating asymmetry [FA]) on a large sample of laboratory-incubated hatchling lizards ( Amphibolurus muricatus , Agamidae), and used principal component analysis to reduce this data set to four major axes of variation (size, shape and two FA axes). Running speeds of each lizard were measured on raceways at four inclines, from level (0°) through to steep (45°). Unsurprisingly, steeper inclines reduced locomotor speeds. Absolute body size was the only morphological trait that was consistently related to sprinting performance, and the relationships were similar at each incline. Within-cohort variation in body shape and FA among this large sample was unrelated to locomotor speeds, thus challenging the common assumption of a causal link between these variables. The only exception was a weak trend for greater hind limb length to enhance locomotor performance more at steep inclines than at shallower angles. In general, our data suggest that different morphological traits do not differentially maximize locomotor performance up variable inclines. Overall, our data provide a cautionary note about the generality of causal connections between within-cohort morphological variation and locomotor performance under different environmental contexts.     

生物鲁棒性的研究进展

生物鲁棒性是指在受到外部扰动或内部参数摄动等不确定因素干扰时,生物系统保持其结构和功能稳定的一种特性。目前已经发现生物鲁棒性普遍存在于生物系统整体、器官、细胞、分子等各种层次,如细菌趋化、细胞周期、细胞信号通讯、基因突变、生物发育、基因网络等等。产生生物鲁棒性的作用机制主要是生物系统的反馈、冗余、模块和结构稳定等。稳定鲁棒性和品质鲁棒性是生物鲁棒性研究的两个重要命题,数学模型是生物鲁棒性研究的重要手段。认识生物鲁棒性对癌症、MDS、糖尿病等疾病的发生、发展和治疗有重要意义。丈章从上述几个方面综述了生物鲁棒性的研究进展。     

Squirrel monkey locomotion on an inclined treadmill: Implications for the evolution of gaits

Three adult squirrel monkeys were trained to run on a motor-driven treadmill that was inclined downwardly and upwardly at 8°, 16° and 28°, and horizontally (0°). Films were used to compare the gait and kinematics of the animals across the inclines. All three animals used both lateral and diagonal sequence gaits, although the former was preferred at all but the upward 16° and 28° inclines. Cycle duration and hind limb stance and swing durations tended to increase as downward inclination decreased. Trunk inclination, except at 28° downward, tended to parallel the changes in treadmill inclination. The most dramatic and consistent change for the hind limb joint displacement patterns was that maximum extension during stance increased as the treadmill inclination increased from 28° downward to 28° upward. In contrast to an earlier study by Prost & Sussman (1969), we could find no evidence that squirrel monkeys are best adapted to run on upward inclines of about 16°. The utilization of diagonal sequence gaits on the upward inclines supports previous suggestions that the preference for these gaits in primates is associated with an evolutionary increase in climbing behaviors.