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.     

Trunk muscle activation patterns during walking at different speeds.

Investigations of trunk muscle activation during gait are rare in the literature. As yet, the small body of literature on trunk muscle activation during gait does not include any systematic study on the influence of walking speed. Therefore, the aim of this study was to analyze trunk muscle activation patterns at different walking speeds. Fifteen healthy men were investigated during walking on a treadmill at speeds of 2, 3, 4, 5 and 6 km/h. Five trunk muscles were investigated using surface EMG (SEMG). Data were time normalized according to stride time and grand averaged SEMG curves were calculated. From these data stride characteristics were extracted: mean SEMG amplitude, minimum SEMG level and the variation coefficient (VC) over the stride period. With increasing walking speed, muscle activation patterns remained similar in terms of phase dependent activation during stride, but mean amplitudes increased generally. Phasic activation, indicated by VC, increased also, but remained almost unchanged for the back muscles (lumbar multifidus and erector spinae) between 4 and 6 km/h. During stride, minimum amplitude reached a minimum at 4 km/h for the back muscles, but for internal oblique muscle it decreased continuously from 2 to 6 km/h. Cumulative sidewise activation of all investigated muscles reached maximum amplitudes during the contralateral heel strike and propulsion phases. The observed changes argue for a speed dependent modulation of activation of trunk muscles within the investigated range of walking speeds prior to strictly maintaining certain activation characteristics for all walking speeds.     

Divergence patterns of banding sequences in different polytene chromosome arms reflect relatively independent evolution of different genome components

Divergence patterns of the banding sequences of the chromosomal arms A, C, D, E, and F were compared in 63 species of the genus Chironomus. Evaluation of the number of breakpoints between the pairs of inverted banding sequences and the analysis of the lengths of the conserved segments in the chromosomal arms in the chironomid species examined showed that different arms evolved relatively independently and at different rates. No direct correlation between the arm length and the breakpoints number was observed. The length of the conservative segment was not fixed, but was arm-specific. Robustness and reliability of the estimates of phylogenetic relationships between the species examined increased with the arm number, i.e., with the genome proportion included in the analysis.__________Translated from Genetika, Vol. 41, No. 4, 2005, pp. 549–558.Original Russian Text Copyright © 2005 by Gunderina, Kiknadze, Istomina, Gusev, Miroshnichenko.     

Divergence patterns of banding sequences in different polytene chromosome arms reflect relatively independent evolution of different genome components

Divergence patterns of the banding sequences from the chromosomal arms A, C, D, E, and F were compared in 63 species of the genus Chironomus. Evaluation of the number of breakpoints between the pairs of inverted banding sequences and the analysis of the lengths of the conserved segments in the chromosomal arms in the chironomid species examined showed that different arms evolved relatively independently and at different rates. No direct correlation between the arm length and the breakpoints number was observed. The length of the conservative segment was not fixed, but was arm-specific. Robustness and fidelity of the estimates of phylogenetic relationships between the species examined increased with the arm number, i.e., with the genome proportion included in the analysis.     

Coordination of legs during straight walking and turning in Drosophila melanogaster

Leg coordination of Drosophila melanogaster was studied using frame-by-frame film analysis. 1. For fastest walking alternating tripod coordination is observed which slightly deviates towards tetrapody as a function of step period. During acceleration or deceleration legs may transiently recover in diagonal pairs. 2. Mean step length increases with step frequency. 3. Mean recovery stroke duration increases with step period and plateaus beyond a period of about 110 ms. Middle legs recover significantly faster than others. 4. Ipsilateral footprints are transversally separated. 5. Walking is usually initiated in tripod coordination (frequently in combination with a turn), otherwise in an accelerating sequence which rapidly shifts towards tripod pattern. Flies can stop abruptly or decelerate over about one metachronal wave. 6. Short interruptions in walking are observed. Legs interrupted during swing phase stay lifted and finish recovery thereafter. 7. Slight changes in walking direction are obtained by altering step lengths only. Tight turns are composed of two or three phases with backward, zero and forward translatory components. In fast turning tripod coordination is maintained. Otherwise body sides can decouple widely. In all turns numbers of contralateral metachronal waves were equal. Results are compared to those for other walking insects and their relevance in screens for locomotor mutants is discussed.     

Mechanical work performed by the individual legs during uphill and downhill walking

Previous studies of the mechanical work performed during uphill and downhill walking have neglected the simultaneous negative and positive work performed by the leading and trailing legs during double support. Our goal was to quantify the mechanical work performed by the individual legs across a range of uphill and downhill grades. We hypothesized that during double support, (1) with steeper uphill grade, the negative work performed by the leading leg would become negligible and the trailing leg would perform progressively greater positive work to raise the center of mass (CoM), and (2) with steeper downhill grade, the leading leg would perform progressively greater negative work to lower the CoM and the positive work performed by the trailing leg would become negligible. 11 healthy young adults (6 M/5 F, 71.0±12.3 kg) walked at 1.25 m/s on a dual-belt force-measuring treadmill at seven grades (0, ±3, ±6, ±9°). We collected three-dimensional ground reaction forces (GRFs) and used the individual limbs method to calculate the mechanical work performed by each leg. As hypothesized, the trailing leg performed progressively greater positive work with steeper uphill grade, and the leading leg performed progressively greater negative work with steeper downhill grade (p<0.005). To our surprise, unlike level-ground walking, during double support the leading leg performed considerable positive work when walking uphill and the trailing leg performed considerable negative work when walking downhill (p<0.005). To understand how humans walk uphill and downhill, it is important to consider these revealing biomechanical aspects of individual leg function and interaction during double support.     

Relative contribution of arms and legs in humans to propulsion in 25-m sprint front-crawl swimming

Eight male subjects were asked to swim 25 m at maximal velocity while the use of the arm(s) and legs was alternately restricted. Four situations were examined using one arm (1A), two arms (2A), one arm and two legs (1A2L) and both arms and legs (2A2L, normal swim) for propulsion. A significant mean increase of 10% on maximal velocity was obtained in 1A2L and 2A2L compared to 1A and 2A. A non-significant 4% effect was obtained in 1A. This study focused on the actual contribution of leg kick in the 10% gain in maximal velocity. It was clear that the underwater trajectory of the wrist was modified by the action of the legs (most comparisons P < 0.001). Therefore it was thought that the legs enhanced the generated propulsive force by improving the propulsive action of the arm. The arm action was quantified by selecting typical phases from the filmed trajectory of the wrist, namely forward (F), downwards (D) and backwards (B). Although there was a tendency for individual changes in kinematic parameters (F, D and B) to occur with individual changes in velocity when 2A was compared to 2A2L, no relationship was found between the relative changes in F, D and B and relative changes in velocity. This was illustrated by describing the responses of three individuals who could represent three patterns of contribution by legs and arms to propulsion in high speed swimming.     

Sequence landmark patterns identify and characterize protein families

The three-dimensional structures of homologous proteins are usually conserved during evolution, as are critical residues in a few short sequence motifs that often constitute the active site in enzymes. The precise spatial organization of such sites depends on the lengths and positions of the secondary structural elements connecting the motifs. We show how members of protein superfamilies, such as kinesins, myosins, and G(alpha) subunits of trimeric G proteins, are identified and classed by simply counting the number of amino acid residues between important sequence motifs in their nucleotide triphosphate-hydrolyzing domains. Subfamily-specific landmark patterns (motif to motif scores) are principally due to inserts and gaps in surface loops. Unusual protein sequences and possible sequence prediction errors are detected.     

Stride lengths and frequencies of arboreal walking in seven species of didelphid marsupials

Didelphid marsupials differ in their use of the forest strata, with corresponding differences in morphology and arboreal walking performances. Similar performances may be reached by different combinations of stride length and frequency, but it has been suggested that arboreal walkers increase velocity by longer strides. Our objective was to determine how stride length and frequency contribute to the velocity in the arboreal walking of seven species of didelphid marsupials of the Atlantic Forest of Brazil. Animals were stimulated to cross five 3-m long horizontal supports of different diameters. The cycle of maximum velocity was chosen to measure relative stride length, frequency, and relative velocity. Except forCaluromys philander, the more arboreal species were faster than the terrestrial species, but maximum velocity of arboreal species was reached by two strategies, increasing stride frequency (Gracilinanus microtarsus, Micoureus demerarae, andDidelphis aurita), or reducing frequency and increasing stride length (Marmosops incanus andC. philander). Increasing velocity in arboreal walking by more frequent strides may reduce oscillations of the body, whereas longer strides may reduce branch swaying. Among the terrestrial species,Philander frenatus performed similarly to more arboreal species, suggesting a potential ability to use the canopy, undetected in field observations.     

A self-organizing model of walking patterns of insects

Insects generate walking patterns which depend upon external conditions. For example, when an insect is exposed to an additional load parallel to the direction in which it is walking, the walking pattern changes according to the magnitude of the load. Furthermore, even after some of its legs have been amputated, an insect will produce walking patterns with its remaining legs. These adaptations in insect walking could not previously be explained by a mathematical model, since the mathemati cal models were based upon the hypothesis that the relationship between walking velocity and walking patterns is fixed under all conditions. We have produced a mathematical model which describes self-organizing insect walking patterns in real-time by using feedback information regarding muscle load (Kimura et al. 1993). As part of this model, we introduced a new rule to coordinate leg movement, in which the information is circulated to optimize the efficiency of the energy transduction of each effector orga n. We describe this mechanism as ‘the least dissatisfaction for the greatest number of elements’. In this paper, we introduce the following aspects of this model, which reflect adaptability to changing circumstances: (1) after one leg is exposed to a transient perturbation, the walking pattern recovers swiftly; (2) when the external load parallel to the walking direction is continuously increased or decreased, the pattern transition point is shifted according to the magnitude of the load increme nt or decrement. This model generates a walking pattern which optimizes energy consumption at a given walking velocity even under these conditions; and (3) when some of the legs are amputated, the model generates walking patterns which are consistent with experimental results. We also discuss the ability of a hierarchical self-organizing model to describe a swift and flexible information processing system. Received: 8 February 1993/Accepted in revised form: 12 November 1993     

A self-organizing model of walking patterns of insects

It is well known that the motor systems of animals are controlled by a hierarchy consisting of a brain, central pattern generator, and effector organs. An animal's walking patterns change depending on its walking velocities, even when it has been decerebrated, which indicates that the walking patterns may, in fact, be generated in the subregions of the neural systems of the central pattern generator and the effector organs. In order to explain the self-organization of the walking pattern in response to changing circumstances, our model incorporates the following ideas: (1) the brain sends only a few commands to the central pattern generator (CPG) which act as constraints to self-organize the walking patterns in the CPG; (2) the neural network of the CPG is composed of oscillating elements such as the KYS oscillator, which has been shown to simulate effectively the diversity of the neural activities; and (3) we have introduced a rule to coordinate leg movement, in which the excitatory and inhibitory interactions among the neurons act to optimize the efficiency of the energy transduction of the effector organs. We describe this mechanism as the least dissatisfaction for the greatest number of elements, which is a self-organization rule in the generation of walking patterns. By this rule, each leg tends to share the load as efficiently as possible under any circumstances. Using this self-organizing model, we discuss the control mechanism of walking patterns.     

Interlimb interactions during cyclic in-phase and antiphase movements of arms and legs and their dependence on afferent influences

Coordinated arm and leg movements imply neural interactions between the rhythmic generators of the upper and lower extremities. In ten healthy subjects in the lying position, activity of the muscles of the upper and lower extremities was recorded during separate and joint cyclic movements of the arms and legs with different phase relationships between the movements of the limbs and under various conditions of the motor task. Antiphase active arm movements were characterized by higher muscle activity than during the inphase mode. The muscle activity during passive arm movements imposed by the experimentalist was significantly lower than muscle activity during passive arm movements imposed by the other arm. When loading one arm, the muscle activity in the other, passively moving, arm increased independently from the synergy of arm movements. During a motor task implementing joint antiphase movements of both upper and lower extremities, compared to a motor task implementing their joint in-phase movements, we observed a significant increase in activity in the biceps brahii muscle, the tibialis anterior muscle, and the biceps femoris muscle. Loading of arms in these motor tasks has been accompanied by increased activity in some leg muscles. An increase in the frequency of rhythmic movements resulted in a significant growth of the muscle activity of the arms and legs during their cooperative movements with a greater rate of rise in the flexor muscle activity of the arms and legs during joint antiphase movements. Thus, both the spatial organization of movements and the type of afferent influences are significant factors of interlimb interactions, which, in turn, determine the type of neural interconnections that are involved in movement regulation.     

Spatial patterns of human gene frequencies in Europe

The aims of this study of spatial patterns of human gene frequencies in Europe are twofold. One is to present new methodology developed for the analysis of such data. The other is to report on the diversity of spatial patterns observed in Europe and their interpretation as evidence of population processes. Spatial variation in 59 allele and haplotype frequencies (26 genetic systems) for polymorphisms in blood antigens, enzymes, and proteins is analyzed for an aggregate of 3,384 localities, using homogeneity tests, one-dimensional and directional spatial correlograms, and SYMAP interpolated surfaces. The data matrices are reduced to reveal the principal patterns by clustering techniques. The findings of this study can be summarized as follows: 1) There is significant heterogeneity in allele frequencies among the localities for all but one genetic system. 2) There are significant spatial patterns for most allele frequencies. 3) There is a substantial minority of clinal patterns in these populations. Clinal trends are found more frequently in HLA alleles than for other variables. North-south and northwest-southwest gradients predominate. 4) There is a strong decline in overall genetic similarity with geographic distance for most variables. 5) There are few, if any, appreciable correlations in pairs of allele frequencies over the continent, and there is little interesting correlation structure in the resulting correlation matrix. 6) Few spatial correlograms are markedly similar to each other, yet they form well-defined clusters. Spatial variation patterns, therefore, differ among allele frequencies. Patterns of human gene frequencies in modern Europe are diverse and complex. No single model suffices for interpretation of the observed genetic structure. Some clinal patterns reported here support the Neolithic demic-expansion hypothesis, others suggest latitudinal selection. Most of the clinal patterns are in HLA alleles, but there is also evidence from ABO for east-west migration diffusion. The majority of patterns are patchy, consistent with hypotheses of isolation by distance or of settlement of genetically differing, subsequently expanding ethnic groups. While undoubtedly there has been an ongoing stochastic process of differentiation consistent with the isolation-by-distance model, this has not obscured the directional patterns caused by migration (demic diffusion), and has perhaps only reinforced the contribution from settlement of ethnic units to patterns of genetic variation. However, the impact of the latter is most difficult to discern and requires further methodological developments.     

Geographic patterns: how to identify them and why

Geographic patterns of genetic diversity allow us to make inferences about population histories and the evolution of inherited disease. The statistical methods describing genetic variation in space, such as estimation of genetic variances, mapping of allele frequencies, and principal components analysis, have opened up the possibility to reconstruct demographic processes whose effects have been tested by a variety of approaches, including spatial autocorrelation, cladistic analyses, and simulations. These studies have significantly contributed to our understanding of human genetic variation; however, the molecular data that have accumulated since the mid-1980s have also created new complications. Reasons include the generally limited sample sizes, but, more generally, it is the nature of molecular variation itself that makes it necessary to develop and apply specific models and methods for the treatment of DNA data. The foreseeable diffusion of laboratory techniques for the rapid typing of many DNA markers will force us to change our approach to the study of human variation anyway, moving from the gene level toward the genome level. Because extensive variation among loci is the rule rather than the exception, an important practical tip is to be skeptical of inferences based on single-locus diversity.     

Venous return from distal regions affects heat loss from the arms and legs during exercise-induced thermal loads

To study the role of venous return from distal parts of the extremities in influencing heat loss from the more proximal parts, changes in mean skin temperature (Tsk) of the non-exercising extremities were measured by color thermography during leg and arm exercise in eight healthy subjects. Thirty minutes of either leg or arm exercise at an ambient temperature (Ta) of 20 degrees C or 30 degrees C produced a greatly increased blood flow in the hand or foot and a great increase in venous return through the superficial skin veins of the extremities. During the first 10 min of recovery from the exercise, blood flow to and venous return from the hand or foot on the tested side was occluded with a wrist or ankle cuff at a pressure of 33.3 kPa (250 mm Hg), while blood flow to the control hand or foot remained undisturbed. During the 10-min wrist occlusion, Tsk increased significantly from 28.3 degrees +/- 0.41 degrees C to 30.1 degrees +/- 0.29 degrees C in the control forearm, but remained at nearly the same level (28.0 degrees +/- 0.34 degrees C to 28.2 degrees +/- 0.25 degrees C) in the occluded forearm. In the legs, although Tsk on both sides was virtually identical (32.0 degrees +/- 0.31 degrees C, control vs 32.0 degrees +/- 0.36 degrees C, tested) before occlusion, Tsk on the control side (32.6 degrees +/- 0.27 degrees C) was significantly higher than that on the tested side (32.2 degrees +/- 0.21 degrees C) after ankle occlusion.(ABSTRACT TRUNCATED AT 250 WORDS)     

Pulmonary ventilation, blood gases, and blood pH after training of the arms or the legs.

In two groups of young healthy subjects who performed arm training (N = 5) and leg training (N = 5), respectively, the respiratory adaptation to submaximal exercise with trained and nontrained muscle groups was compared by measurement of the ventilatory equivalent (Ve/Vo2, pH, and blood gases (Pco2, Po2, and So2) in arterial blood and in venous blood from exercising extremities. After training Ve/Vo2 was significantly reduced during exercise with trained muscles, but unchanged during exercise with nontrained muscles. The reduction in Ve/Vo2 was closely related to a less pronounced increase in heart rate and in arterial lactate content, but showed no quantitative correlation to changes in arterial adaptations in trained muscles are mainly responsible for the reduction in Ve/Vo2. After training during exercise with trained as well as nontrained muscles a shift to the right of the blood oxygen dissociation curve occurred as extremities was lower while corresponding Po2 was higher.