Fractional central pattern generators for bipedal locomotion

Locomotion has been a major research issue in the last few years. Many models for the locomotion rhythms of quadrupeds, hexapods, bipeds and other animals have been proposed. This study has also been extended to the control of rhythmic movements of adaptive legged robots. In this paper, we consider a fractional version of a central pattern generator (CPG) model for locomotion in bipeds. A fractional derivative D α f(x), with α non-integer, is a generalization of the concept of an integer derivative, where α=1. The integer CPG model has been proposed by Golubitsky, Stewart, Buono and Collins, and studied later by Pinto and Golubitsky. It is a network of four coupled identical oscillators which has dihedral symmetry. We study parameter regions where periodic solutions, identified with legs’ rhythms in bipeds, occur, for 0<α≤1. We find that the amplitude and the period of the periodic solutions, identified with biped rhythms, increase as α varies from near 0 to values close to unity.

Bipedal Locomotion: A Fractional CPG for Generating Patterns

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

Gait Regulation for Bipedal Locomotion

This work explores regulation of forward speed, step length, and slope walking for the passive-dynamic class of bipedal robots. Previously, an energy-shaping control for regulating forward speed has appeared in the literature; here we show that control to be a special case of a more general time-scaling control that allows for speed transitions in arbitrary time. As prior work has focused on potential energy shaping for fully actuated bipeds, we study in detail the shaping of kinetic energy for bipedal robots, giving special treatment to issues of underactuation. Drawing inspiration from features of human walking, an underactuated kinetic-shaping control is presented that provides efficient regulation of walking speed while adjusting step length. Previous results on energetic symmetries of bipedal walking are also extended, resulting in a control that allows regulation of speed and step length while walking on any slope. Finally we formalize the optimal gait regulation problem and propose a dynamic programming solution seeded with passive-dynamic limit cycles. Observations of the optimal solutions generated by this method reveal further similarities between passive dynamic walking and human locomotion and give insight into the structure of minimum-effort controls for walking.

Complex order biped rhythms

Animal locomotion is a complex process, involving the central pattern generators (neural networks, located in the spinal cord, that produce rhythmic patterns), the brainstem command systems, the steering and posture control systems and the top layer structures that decide which motor primitive is activated at a given time. Pinto and Golubitsky studied an integer CPG model for legs rhythms in bipeds. It is a four-coupled identical oscillators' network with dihedral symmetry. This paper considers a new complex order central pattern generator (CPG) model for locomotion in bipeds. A complex derivative Dα±jβ, with α, β ∈ ℜ+, j = √-1, is a generalization of the concept of an integer derivative, where α = 1, β = 0. Parameter regions where periodic solutions, identified with legs' rhythms in bipeds, occur, are analyzed. Also observed is the variation of the amplitude and period of periodic solutions with the complex order derivative.

Neogene antecedents of the modern human hand and its relation to bipedalism

El present projecte s'ha dut a terme a l'American Museum of Natural History (AMNH, New York) entre el 31 de Desembre de 2010 i el 30 de Desembre de 2012. L'objectiu del projecte era elucidar la història evolutiva de la mà humana: traçar els canvis evolutius en la seva forma i proporcions que van propiciar la seva estructura moderna que permet als humans manipular amb precisió. El treball realitzat ha inclòs recol•lecció de dades i anàlisis, redacció de resultats i formació en mètodes analítics específics. Durant aquest temps, l'autor a completat la seva de base de dades existent en mesures lineals de la mà a hominoides. També s'han agafat dades del peu; d'aquesta forma ara mateix es compta amb una base de dades amb més de 500 individus, amb més de 200 mesures per cada un. També s'han agafat dades en tres imensions utilitzant un làser escàner. S'han après tècniques de morfometria geomètrica 3D directament dels pioners al camp a l'AMNH. Com a resultat d'aquesta feina s'han produït 10 resums (publicats a congressos internacionals) i 9 manuscrits (molts d'ells ja publicats a revistes internacionals) amb resultats de gran rellevància: La mà humana posseeix unes proporcions relativament primitives, que són més similars a les proporciones que tenien els hominoides fòssils del Miocè que no pas a la dels grans antropomorfs actuals. Els darrers tenen unes mans allargades amb un polzes molt curts que reflexen l'ús de la mà com a eina de suspensió sota les branques. En canvi, els hominoides del Miocè tenien unes mans relativament curtes amb un polze llarg que feien servir per estabilitzar el seu pes quan caminaven per sobre de les branques. Una vegada els primers homínids van aparèixer al final del Miocè (fa uns 6 Ma) i van començar a fer servir el bipedisme com a mitjà més comú de locomoció, les seves mans van ser "alliberades" de les seves funcions locomotores. La selecció natural—ara només treballant en la manipulació—va convertir les proporcions ja existents de la mà d'aquests primats en l'òrgan manipulatori que representa la mà humana avui dia.

The legs: a key to bird evolutionary success

Birds are the most diverse and largest group of extant tetrapods. They show marked variability, yet much of this variation is superficial and due to feather and bill color and shape. Under the feathers, the skeleto-muscular system is rather constant throughout the bird group. The adaptation to flight is the explanation for this uniformity. The more obvious morphological adaptations for flight are the wings, but the trunk is always rigid, the tail is short and the neck is flexible, since all these features are correlated with flying behaviour. Unrelated to the exigencies of flight, the legs always have three long bones, and all the birds walk on their toes. This leg structure is a striking plesiomorphic feature that was already present in related dinosaurs. The multi-purpose potential of the legs is the result of the skeletal architecture of a body with three segmented flexed legs. This configuration provides mechanical properties that allow the use of the legs as propulsive, paddling, foraging or grooming tools. It is the association of diverse modes of locomotion-walking, running, hopping, flying and swimming-that have enabled the birds to colonize almost all the environments on Earth.

Predicting the metabolic energy costs of bipedalism using evolutionary robotics

To understand the evolution of bipedalism among the homnoids in an ecological context we need to be able to estimate theenerrgetic cost of locomotion in fossil forms. Ideally such an estimate would be based entirely on morphology since, except for the rare instances where footprints are preserved, this is hte only primary source of evidence available. In this paper we use evolutionary robotics techniques (genetic algoritms, pattern generators and mechanical modeling) to produce a biomimentic simulation of bipedalism based on human body dimensions. The mechnaical simulation is a seven-segment, two-dimensional model with motive force provided by tension generators representing the major muscle groups acting around the lower-limb joints. Metabolic energy costs are calculated from the muscel model, and bipedal gait is generated using a finite-state pattern generator whose parameters are produced using a genetic algorithm with locomotor economy (maximum distance for a fixed energy cost) as the fitness criterion. The model is validated by comparing the values it generates with those for modern humans. The result (maximum efficiency of 200 J m-1) is within 15% of the experimentally derived value, which is very encouraging and suggests that this is a useful analytic technique for investigating the locomotor behaviour of fossil forms. Initial work suggests that in the future this technique could be used to estimate other locomotor parameters such as top speed. In addition, the animations produced by this technique are qualitatively very convincing, which suggests that this may also be a useful technique for visualizing bipedal locomotion.

The ontogeny of bipedalism: insights from the study of talar growth

The development of bipedal locomotion was gradual during evolution, and with the increase in discoveries of fossils and, in particular, in discoveries of pedal bones, the attention to this problematic has grown in the last decades. Moreover, the discoveries of juveniles fossil foot bones has led the attention to the evolution and the development of bipedal locomotion. The study of the development of human gait in children may help in shedding light to the development of human locomotion. The human talus plays a pivotal role, linking the leg to the foot and receiving and distributing the weight, while permitting a wide range of foot movements. It is also present at birth, and this makes a perfect bone to study to disentangle how the bone structure acts to cope with the changes in locomotion and body weight. Here, I analyze the external and internal morphology of the human talus from the perinatal period to adolescence, to investigate how the different phases of the acquisition of bipedal gait affect talar morphology, and how the bone copes with the weight gain during growth. Results show that the talar internal and external morphologies change in line with the different activities and loading of the foot. Initially, at around birth, the talus has a very globular and immature external shape, with a very dense trabecular architecture, composed of thin, numerous, and densely packed trabeculae, with a rather isotropic structure. External and internal morphologies change in relation to the different loading patterns which follow during growth, showing a more specialized structure, both in the external and internal morphology, linked to the maturation of bipedal locomotion, until the adult-like pattern is reached, during adolescence.

Let your feet do the walking: constraints on the stability of bipedal coordination

In this paper we consider whether the behaviour of the neural circuitry that controls lower limb movements in humans is shaped primarily by the spatiotemporal characteristics of bipedal gait patterns, or by selective pressures that are sensitive to considerations of balance and energetics. During the course of normal locomotion, the full dynamics of the neural circuitry are masked by the inertial properties of the limbs. In the present study, participants executed bipedal movements in conditions in which their feet were either unloaded or subject to additional inertial loads. Two patterns of rhythmic coordination were examined. In the in-phase mode, participants were required to flex their ankles and extend their ankles in synchrony. In the out-of-phase mode, the participants flexed one ankle while extending the other and vice versa. The frequency of movement was increased systematically throughout each experimental trial. All participants were able to maintain both the in-phase and the out-of-phase mode of coordination, to the point at which they could no longer increase their frequency of movement. Transitions between the two modes were not observed, and the stability of the out-of-phase and in-phase modes of coordination was equivalent at all movement frequencies. These findings indicate that, in humans, the behaviour of the neural circuitry underlying coordinated movements of the lower limbs is not constrained strongly by the spatiotemporal symmetries of bipedal gait patterns.

Le développement des proportions métaphysaires chez les hominoïdes : croissance et influence de la locomotion

Dans le cadre de ce mémoire, les relations entre morphologie, locomotion et croissance chez les hominoïdes sont analysées sous l'angle des proportions métaphysaires et de leur acquisition. Plusieurs niveaux d'analyse — intermembre, supérieur et inférieur — sont abordés dans une perspective ontogénique. La masse corporelle et la direction des charges influencent la morphologie des surfaces articulaires et métaphysaires mais aussi leur développement. Les charges étant dépendantes du mode locomoteur et celui-ci se modifiant en fonction de l'âge, on tente de voir à quel(s) moment(s) les changements proportionnels ont lieu et pourquoi ils apparaissent. Des mesures linéaires ont été recueillies sur l'humérus, le radius, le fémur et le tibia sur un échantillon squelettique des espèces H. sapiens, P. troglodytes, G. gorilla et P. pygmaeus. À partir de ces mesures et du calcul de certains ratios, des comparaisons intra et interspécifiques ont été réalisées. Les différences les plus significatives entre les espèces se dévoilent au niveau intermembre et sont relatives aux différents pourcentages d'utilisation des membres supérieurs ou inférieurs. Au sein des espèces, les résultats révèlent une similarité dans les réactions des surfaces métaphysaires au niveau intermembre, supérieur et inférieur. Les changements proportionnels ont lieu entre les stades 0 et 1 pour H. sapiens (première marché indépendante), entre les stades 2 et 4 pour P. troglodytes (majorité du poids corporel soutenue par les membres inférieurs) et entre les stades 3 et 5 pour G. gorilla (taille adulte et quadrupédie très majoritaire). Pour P. pygmaeus aucun stade en particulier n'a été ciblé par les analyses et cela concorde avec l'homogénéité de ses modes de locomotion employés au cours de la vie. Les différences proportionnelles répondent à des changements locomoteurs majeurs. Australopithecus afarensis est intermédiaire entre H. sapiens et les grands singes pour de nombreuses comparaisons. Au niveau du genou, les plus jeunes individus A. afarensis ne montrent pas de morphologie bipède, similaire aux humains.

Locomotion and gaits of the northern brown bandicoot, Isoodon macrourus (Marsupalia: Peramelidae)

Gait repertoires of the northern brown bandicoot, Isoodon macrourus, were studied over a wide range of locomotor speeds. At low relative speeds, bandicoots used symmetrical gaits that included pacing, trotting, and lateral sequence strides. Forefoot contact duration was generally shorter than hind foot contact duration at all speeds. At moderate relative speeds bandicoots used half-bounding gaits with either no period of suspension or with a short gathered suspension. At high speeds the predominant gait had both a short extended and a short gathered suspension, although some strides comprised only an extended suspension. Increases in speed were accompanied by increases in spinal extension, presumably leading to the extended suspensions. On a stationary treadmill individuals occasionally used a bipedal gait. Maximum half-bounding speeds appear to be relatively low in this species.

Visual Feedforward Control in Human Locomotion During Avoidance of Obstacles that Change Size

The purpose of the current study was to understand how visual information about an ongoing change in obstacle size is used during obstacle avoidance for both lead and trail limbs. Participants were required to walk in a dark room and to step over an obstacle edged with a special tape visible in the dark. The obstacle's dimensions were manipulated one step before obstacle clearance by increasing or decreasing its size. Two increasing and two decreasing obstacle conditions were combined with seven control static conditions. Results showed that information about the obstacle's size was acquired and used to modulate trail limb trajectory, but had no effect on lead limb trajectory. The adaptive step was influenced by the time available to acquire and process visual information. In conclusion, visual information about obstacle size acquired during lead limb crossing was used in a feedforward manner to modulate trail limb trajectory.

Effects of chlorogenic acid on neutrophil locomotion functions in response to inflammatory stimulus

Aim of the study: Species of Lychnophora are used in Brazilian folk medicine as analgesic and anti-inflammatory agents. Chlorogenic acid (CGA) and their analogues are important components of polar extracts of these species, as well in several European and Asian medicinal plants. Some of these phenolic compounds display anti-inflammatory effects. In this paper we report the isolation of CGA from Lychnophora salicifolia and its effects on functions involved in neutrophils locomotion. Materials and methods: LC-MS(n) data confirmed the presence of CGA in the plant. Actions of CGA were investigated on neutrophils obtained from peritoneal cavity of Wistar rats (4h after 1% oyster glycogen solution injection; 10 ml), and incubated with vehicle or with 50, 100 or 1000 mu M CGA in presence of lipopolysaccharide from Escherichia coil (LPS, 5 mu g/ml). Nitric oxide (NO; Griess reaction); prostaglandin E(2) (PGE(2)), interleukin-1 beta (IL-1 beta) and tumor necrosis factor-alpha [TNF-alpha; enzyme-linked immunosorbent assay (EIA)]; protein (flow cytometry) and gene (RT-PCR) expression of L-selectin, beta(2)integrin and platelet-endothelial cell adhesion molecule-1 (PECAM-1) were quantified. In vitro neutrophil adhesion to primary culture of microvascular endothelial cell (PMEC) and neutrophil migration in response to formyl-methionil-leucil-phenilalanine (fMLP, 10(-8)M, Boyden chamber) was determined. Results: CGA treatment did not modify the secretion of inflammatory mediators, but inhibited L-selectin cleavage and reduced beta(2) integrin, independently from its mRNA synthesis, and reduced membrane PECAM-1 expression: inhibited neutrophil adhesion and neutrophil migration induced by fMLP. Conclusions: Based on these findings, we highlight the direct inhibitory actions of CGA on adhesive and locomotion properties of neutrophils, which may contribute to its anti-inflammatory effects and help to explain the use of Lychnophora salicifolia as an anti-inflammatory agent. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Unifying principles in terrestrial locomotion: Do hopping Australian marsupials fit in?

Mammalian terrestrial locomotion has many unifying principles. However, the Macropodoidea are a particularly interesting group that exhibit a number of significant deviations from the principles that seem to apply to other mammals. While the properties of materials that comprise the musculoskeletal system of mammals are similar, evidence suggests that tendon properties in macropodoid marsupials may be size or function dependent, in contrast to the situation in placental mammals. Postural differences related to hopping versus running have a dramatic effect on the scaling of the pelvic limb musculoskeletal system. Ratios of muscle fibre to tendon cross-sectional areas for ankle extensors and digital flexors scale with positive allometry in all mammals, but exponents are significantly higher in macropods. Tendon safety factors decline with increasing body mass in mammals, with eutherians at risk of ankle extensor tendon rupture at a body mass of about 150 kg, whereas kangaroos encounter similar problems at a body mass of approximately 35 kg. Tendon strength appears to limit locomotor performance in these animals. Elastic strain energy storage in tendons is mass dependent in all mammals, but exponents are significantly larger in macropodid. Tibial stresses may scale with positive allometry in kangaroos, which result in lower bone safety factors in macropods compared to eutherian mammals.

Locomotion at-1.0 degrees C: burst swimming performance of five species of Antarctic fish

We investigated the burst swimming performance of five species of Antarctic fish at -1.0degreesC. The species studied belonged to the suborder, Notothenioidei, and from the families, Nototheniidae and Bathydraconidae. Swimming performance of the fish was assessed over the initial 300 ms of a startle response using surgically attached miniature accelerometers. Escape responses in all fish consisted of a C-type fast start; consisting of an initial pronounced bending of the body into a C-shape, followed by one or more complete tail-beats and an un-powered glide. We found significant differences in the swimming performance of the five species of fish examined, with average maximum swimming velocities (U-max) ranging from 0.91 to 1.39 m s(-1) and maximum accelerations (A(max)) ranging from 10.6 to 15.6 m s(-2). The cryopelagic species, Pagothenia borchgrevinki, produced the fastest escape response, reaching a U-max and A(max) of 1.39 m s(-1) and 15.6 m s(-2), respectively. We also compared the body shapes of each fish species with their measures of maximum burst performance. The dragonfish, Gymnodraco acuticeps, from the family Bathdraconidae, did not conform to the pattern observed for the other four fish species belonging to the family Nototheniidae. However, we found a negative relationship between buoyancy of the fish species and burst swimming performance. (C) 2002 Elsevier Science Ltd. All rights reserved.