Quadrupedal Gait Research Articles

Bio-inspired design of electrically-driven bounding quadrupeds via parametric analysis

This paper attempts to set the basis for a systematic approach in designing quadruped robots employing a dynamically stable quadruped running in the sagittal plane with a bounding gait, which is a simple model commonly used to analyze the basic qualitative properties of quadruped gaits that use the legs in pair. The outcome of the proposed methodology is the optimal shape of the bounding quadruped robot, i.e., the relation between its physical parameters, and the optimal size of the bounding quadruped robot, i.e., the physical magnitude of it, according to desired performance criteria. The performance criterion introduced is based on: (a) the actuator effort to sustain an active gait, very close to a passive one, and (b) the maximum payload capability of the robot for a target overall mass. The parametric study examines the behavior of the performance criterion over a range of non-dimensional variables connected to robot physical parameters and gait characteristics. The study takes into consideration data from experimental biology and ground surface properties, while it is subject to the existing technological limitations and economic restraints, i.e., the fact that there is a limited number of motor/gearbox combinations available from a practical point of view. The findings from simulation results indicate that the proposed methodology can assist in the design of new, and modifications of existing quadruped robots.

Walk–run classification of symmetrical gaits in the horse: a multidimensional approach

Walking and running are two mechanisms for minimizing energy expenditure during terrestrial locomotion. Duty factor, dimensionless speed, existence of an aerial phase, percentage recovery (PR) or phase shift of mechanical energy and shape of the vertical ground reaction force profile have been used to discriminate between walking and running. Although these criteria work well for the classification of most quadrupedal gaits, they result in conflicting evidence for some gaits, such as the tölt (a symmetrical, four-beat gait used by Icelandic horses). We use established pattern recognition methods to test the hypothesis that the tölt is a running gait based on an automated and optimized decision drawn from four features (dimensionless speed, duty factor, length of aerial phase and PR for over 6000 strides from four symmetrical gaits in seven Icelandic horses) simultaneously. We compare this decision with the use of each of these features in isolation. Sensitivity and specificity values were used to determine optimal thresholds for classifying tölt strides based on each feature separately. Duty factor and dimensionless speed indicate that tölt is more similar to running, while aerial phase and PR indicate that it is more similar to walking. Then, two multidimensional pattern recognition approaches, multivariate Gaussian densities and linear discriminant analysis, were used and it was shown that, in terms of stochastic multidimensional discrimination, tölt is more similar to 'running'. The approaches presented here have potential to be extended to studies on similar 'ambling' gaits in other quadrupeds.

Reply to Herz et al. and Humphrey et al. : Genetic heterogeneity of cerebellar hypoplasia with quadrupedal locomotion

Mutations in the very low-density lipoprotein receptor VLDLR are responsible for cerebellar hypoplasia with quadrupedal gait (1). The most likely mechanism leading to this phenotype is that VLDLR deficiency in the brain at a key stage of development precludes the normal formation of neural structures critical for gait. Quadrupedal gait is an integral part of VLDLR-associated cerebellar hypoplasia syndrome in these families (1, 2). It is not necessary to invoke an “epiphenomenon” or “unfavorable environmental conditions” to explain the phenotype (3), but rather simply considering clinical heterogeneity in the context of genomic understanding of complex traits is sufficient.

“Devolution” of bipedality

Ozcelik et al. (1) report mutations in very-low-density lipoprotein receptor (VLDLR) that are associated with quadrupedal gait. They propose a pivotal role for VLDLR in the transition from quadrupedal to bipedal locomotion in man. VLDLR is a key regulator of cerebellar development in vertebrates (2). All VLDLR mutations reported to date result in disequilibirium syndrome (DES) with cerebellar hypoplasia and are neuroanatomically indistinguishable (1, 3, 4). In contrast to the Turkish population reported by Ozcelik et al., Hutterites carrying a complete deletion of VLDLR are bipedal (3). Ozcelik et al. hypothesize that the Hutterites are more severely afflicted because of a chromosomal deletion and that this causes loss of motor skills required for quadrupedal locomotion, thereby forcing them to habitually walk upright. Quadrupedal locomotion in individuals with cerebellar hypoplasia has been proposed to define a distinct genetic syndrome of “human devolution” or “reverse evolution” (“Unertan syndrome”) (5).

Towards a general neural controller for quadrupedal locomotion

Our study aims at the design and implementation of a general controller for quadruped locomotion, allowing the robot to use the whole range of quadrupedal gaits (i.e. from low speed walking to fast running). A general legged locomotion controller must integrate both posture control and rhythmic motion control and have the ability to shift continuously from one control method to the other according to locomotion speed. We are developing such a general quadrupedal locomotion controller by using a neural model involving a CPG (Central Pattern Generator) utilizing ground reaction force sensory feedback. We used a biologically faithful musculoskeletal model with a spine and hind legs, and computationally simulated stable stepping motion at various speeds using the neuro-mechanical system combining the neural controller and the musculoskeletal model. We compared the changes of the most important locomotion characteristics (stepping period, duty ratio and support length) according to speed in our simulations with the data on real cat walking. We found similar tendencies for all of them. In particular, the swing period was approximately constant while the stance period decreased with speed, resulting in a decreasing stepping period and duty ratio. Moreover, the support length increased with speed due to the posterior extreme position that shifted progressively caudally, while the anterior extreme position was approximately constant. This indicates that we succeeded in reproducing to some extent the motion of a cat from the kinematical point of view, even though we used a 2D bipedal model. We expect that such computational models will become essential tools for legged locomotion neuroscience in the future.

Locomotion and posture from the common hominoid ancestor to fully modern hominins, with special reference to the last common panin/hominin ancestor.

Based on our knowledge of locomotor biomechanics and ecology we predict the locomotion and posture of the last common ancestors of (a) great and lesser apes and their close fossil relatives (hominoids); (b) chimpanzees, bonobos and modern humans (hominines); and (c) modern humans and their fossil relatives (hominins). We evaluate our propositions against the fossil record in the context of a broader review of evolution of the locomotor system from the earliest hominoids of modern aspect (crown hominoids) to early modern Homo sapiens. While some early East African stem hominoids were pronograde, it appears that the adaptations which best characterize the crown hominoids are orthogrady and an ability to abduct the arm above the shoulder - rather than, as is often thought, manual suspension sensu stricto. At 7-9 Ma (not much earlier than the likely 4-8 Ma divergence date for panins and hominins, see Bradley, 2008) there were crown hominoids in southern Europe which were adapted to moving in an orthograde posture, supported primarily on the hindlimb, in an arboreal, and possibly for Oreopithecus, a terrestrial context. By 7 Ma, Sahelanthropus provides evidence of a Central African hominin, panin or possibly gorilline adapted to orthogrady, and both orthogrady and habitually highly extended postures of the hip are evident in the arboreal East African protohominin Orrorin at 6 Ma. If the traditional idea that hominins passed through a terrestrial 'knuckle-walking' phase is correct, not only does it have to be explained how a quadrupedal gait typified by flexed postures of the hindlimb could have preadapted the body for the hominin acquisition of straight-legged erect bipedality, but we would have to accept a transition from stem-hominoid pronogrady to crown hominoid orthogrady, back again to pronogrady in the African apes and then back to orthogrady in hominins. Hand-assisted arboreal bipedality, which is part of a continuum of orthograde behaviours, is used by modern orangutans to forage among the small branches at the periphery of trees where the core hominoid dietary resource, ripe fruit, is most often to be found. Derivation of habitual terrestrial bipedality from arboreal hand-assisted bipedality requires fewer transitions, and is also kinematically and kinetically more parsimonious.

Mutations in the very low-density lipoprotein receptor VLDLR cause cerebellar hypoplasia and quadrupedal locomotion in humans.

Quadrupedal gait in humans, also known as Unertan syndrome, is a rare phenotype associated with dysarthric speech, mental retardation, and varying degrees of cerebrocerebellar hypoplasia. Four large consanguineous kindreds from Turkey manifest this phenotype. In two families (A and D), shared homozygosity among affected relatives mapped the trait to a 1.3-Mb region of chromosome 9p24. This genomic region includes the VLDLR gene, which encodes the very low-density lipoprotein receptor, a component of the reelin signaling pathway involved in neuroblast migration in the cerebral cortex and cerebellum. Sequence analysis of VLDLR revealed nonsense mutation R257X in family A and single-nucleotide deletion c2339delT in family D. Both these mutations are predicted to lead to truncated proteins lacking transmembrane and signaling domains. In two other families (B and C), the phenotype is not linked to chromosome 9p. Our data indicate that mutations in VLDLR impair cerebrocerebellar function, conferring in these families a dramatic influence on gait, and that hereditary disorders associated with quadrupedal gait in humans are genetically heterogeneous.

P2.107 A new syndrome with quadrupedal gait and primitive cognition

P2.107 A new syndrome with quadrupedal gait and primitive cognition

“Unertan Syndrome” in two Turkish Families in Relation to Devolution and Emergence of Homo Erectus: Neurological Examination, MRI, and pet Scans

“Unertan syndrome” consists of two main symptoms: quadrupedal gait and primitive cognitive abilities including language and conscious experience. To assess the central mechanisms involved in this syndrome, the authors performed MRI and PET scans on affected and unaffected individuals from both families. All affected individuals were also subjected to neurological examination. To assess the integrity of the peripheral and central vestibular system, Barany's caloric test was applied to the affected individuals. Brain MRI and PET scans were performed on normal subjects (n = 7) and patients (n = 7). Right- and left-cerebral and cerebellar areas, including the vermial and callosal areas, were measured on the MRI scans using a computer cursor. Quadrupedal gait, mental retardation, dysartric speech, nystagmus, severe truncal ataxia, hyperreflexia, astasia, and abasia were observed in the affected individuals from both families. Cerebellum and vermis were atrophic in the MRI and PET scans of the first family. In contrast, the brain MRI seemed to be normal in the MRI and PET scans of affected individuals from the second family. The caloric test revealed central vestibular damage in patients from the first family and peripheral vestibular damage in patients from the second family. The results suggest that “Unertan syndrome,” discovered in two unrelated families, may be caused by peripheral or central vestibular damage resulting from different genetic defects. Cerebellar hypoplasia may not be a prerequisite for the emergence of this syndrome. Primitive mental abilities may be explained by damage within the vestibulo-cerebellar system, whereas the quadrupedal gait may be due to a genetic defect within the higher brain centers that suppress the atavistic brain networks controlling quadrupedal gait and helped in the emergence of the habitual bipedal gait during human evolution. This retarded development of human locomotion—devolution—may illuminate the brain mechanisms responsible for the transition from quadrupedality to bipedality in human evolution.

UNERTAN SYNDROME: REVIEW AND REPORT OF FOUR NEW CASES

The aim of this study was to describe additional patients (n= 3) exhibiting the Unertan syndrome (UTS), resident in rural areas of Canakkale. The 8th and 9th families with the UTS, with a total of 16 members affected, have not been previously characterized. A single, non-familial case (Bayramic, Canakkale) occurred during early childhood after an infection with a high fever. Three cases of familial UTS were located in another village in Canakkale. All cases exhibited the three key symptoms of the UTS: (1) walking on all four extremities, (2) primitive language (only sounds), and (3) rudimentary intelligence. Magnetic resonance imaging showed mild vermial hypoplasia in the non-familial case, while there was cerebellar and vermial hypoplasia with a flattened cerebral cortex in the familial cases. Dexterity of the fingers was normal. The man from the latter family was fond of dragging a wooden box after fastening a string around his belt. The collective observations and clinical findings suggest two etiologies for the UTS: (1) genetic, via autosomal recessive transmission and (2) viral, likely the poliovirus affecting the cerebro-cerebellar structures. At a minimum, vermial hypoplasia is suggested to cause fully developed UTS. The subjects could stand upright and even walk bipedally, despite difficulties in balance (ataxia), but they preferred quadrupedal walking. The main difficulty with gait was maintaining a dynamic-asymmetric lateral balance and initiation of the first step during standing. Apparently, a quadrupedal gait in an adult is a developmental regression with absence of the higher control mechanisms for asymmetric lateral balance during bipedal walking. It is suggested that these individuals exhibit ancestral traits; the quadrupedal gait with rudimentary intelligence and primitive speech resulting from viral infections and/or genetic damage may cause devolution (reverse evolution), a manifestation of an experiment of nature as well as experimental studies in animal models. The results support the notion of punctuated evolution, in contrast to Darwin's theory of graded evolution. Dragging a wooden box using a string wrapped around the belt may also be an example of reverse evolution with regard to tool making, illuminating the very long-lasting period before the invention of the wheel. Herein, there has been no intent to insult or injure these individuals affected by the UTS; rather, this is an endeavor to better understand the mystery of human evolution. Go to the publisher's online edition of International Journal of Neuroscience for the following free supplemental resource: video clips.

A New Theory on the Evolution of Human Mind. Unertan Syndrome: Quadrupedality, Primitive Language, and Severe Mental Retardation

Please see suppl. section for video, Download mpg (4483 KB) The recently discovered “UNERTAN SYNDROME” consists of quadrupedal gait, severe mental retardation, and primitive language. This syndrome can be considered as devolution of human being, throwing a light into the transition from quadrupedality to bipedality with co-evolution of human mind. The genetic nature of this syndrome supports the punctuated evolution during transition from quadrupedality to bipedality. In light of Tan’s psychomotor theory, accentuating the major role of the motor system in human mind, a new theory was suggested for the human evolution. Namely, the unique behavioral trait of man, the emergence of the habitual bipedality with Homo erectus (1.6 million and 250.000 tears ago) may be coupled with a resistive mind, which forced man to stand up against the gravitational forces with consequent success in tool making and hunting, using free hands for survival. The second stage in the evolution of modern human beings may be coupled with the emergence of language (circa 40.000 years ago), playing a major role in the origins of human mind.

An early pliocene pangolin (Mammalia; Pholidota) from Langebaanweg, South Africa

ABSTRACT A fossil pangolin is described from the early Pliocene of Langebaanweg, South Africa. Morphological adaptations indicate that the specimen was not arboreal as are the living African species Manis tricuspis and M. tetradactyla, but was probably ground dwelling and may have engaged in a quadrupedal gait similar to that of the living representatives of the African species, Manis gigantea. In addition, it may have used its forelimbs for more extensive digging than does the living African Manis temminckii. The tail length, limb bone widths and proportions, and humeral morphology support the assignment of this specimen to Manis gigantea, making it the oldest known fossil representative of this species and the only confirmed fossil pangolin from South Africa.

Trackway Ratio: A New Look at Trackway Gauge in the Analysis of Quadrupedal Dinosaur Trackways and its Implications for Ichnotaxonomy

A new parameter, the Trackway Ratio (TR), is proposed to supplement the previously used trackway gauge to describe and quantify the relative width of trackways in dinosaur quadrupedal gaits. It is expressed as the ratio of the width of the tracks relative to the total width of the trackway (both measured perpendicular to the long axis of the trackway). The ratio may be used with either pes (PTR) or manus (MTR) tracks. The PTR range of values for wide-, medium- and narrow-gauge trackways of previous authors are provisionally suggested to be ≤35%, 36–49% and ≥50%, respectively. The application of such a ratio would permit a more consistent ichnotaxonomy to be adopted where both track morphology and trackway parameters are used to define ichnotaxa. Determination of the TR, as well as other parameters, will be affected by track preservation quality. Recent experiments on track simulation in the laboratory have shed further light on observations made in the field concerning the value of track measurements (in particular track length and width) recorded from below the surface on which the maker was moving. Experimental track simulations in the laboratory have shown that the dimensions of transmitted tracks preserved below the surface on which the foot was impressed may vary from 65% to 135% of the true dimensions of the indenter. Two case studies are presented that quantify the errors that may be made on calculating TR and the size, gait and speed of the maker, from trackways if the preservation of the tracks are not fully understood. It is shown that in individual trackways the PTR may vary along the length of the trackway; so that part of the trackway may be classified as wide-gauge and other parts medium-gauge. There is a relationship between variation in PTR and that of pace angulation along the length of a single trackway. An analysis of 42 trackways, principally sauropod, shows a temporal distribution that does not agree closely with previous suggestions relating to narrow- and wide-gauge trackways.

Growth plate formation and development in alligator and mouse metapodials: evolutionary and functional implications

Mammalian metapodials (metacarpals and metatarsals), unlike most long bones, form a single growth plate, and undergo longitudinal growth at only one end. The growth dynamics of non-mammalian tetrapod metapodials have not been systematically examined in order to determine if unidirectional growth is unique to mammals. Here we compare murine metapodial ossification in growth stages that parallel those of embryonic, juvenile and subadult American alligators (Alligator mississippiensis). Safranin O staining was used for qualitative histology, and chondrocyte differentiation and proliferation were assessed via immunohistochemistry for type X collagen and proliferative cell nuclear antigen (PCNA). We establish that growth plates form at both ends of alligator metapodials and are maintained in the subadult. PCNA results show that alligators and mice share common patterns of chondrocyte proliferation during growth plate formation. In addition, while alligators and mice differ initially in the degree of organization and pace of chondrocyte differentiation, these parameters are largely similar in established growth plates. However, the replacement of cartilage by bone is highly irregular throughout growth in the alligator, in contrast to the more uniform process in the mouse. These results indicate that while alligators and mammals share common mechanisms of chondrocyte regulation, they differ substantially in their processes of ossification. Phylogenetic analysis indicates that the direct ossification of one epiphysis and reliance on a single growth plate is a derived character (synapomorphy) in therian mammals and likely indicates an adaptation for erect quadrupedal gait.

Ground forces applied by galloping dogs

The gallop differs from most other quadrupedal gaits in that each limb plays a unique role. This study compares the ground forces applied by the four limbs and uses force differences between limbs to address the question of why the gallop is the fastest quadrupedal gait. Individual ground forces were recorded from each of the four limbs as six dogs galloped down a runway at constant speed. Trials were videotaped at high speed using a camera positioned perpendicular to the runway, and velocity was measured using photosensors. The trailing forelimb applied greater peak vertical forces than the lead forelimb, however the vertical impulses from the two forelimbs were similar because the lead forelimb had a longer contact interval. The trailing forelimb and lead hindlimb applied greater peak accelerating forces and accelerating force impulses than their contralateral limbs despite their tendency to have shorter contact intervals. The accelerating impulse of both forelimbs combined did not differ significantly from that of both hindlimbs. The forelimbs applied a greater decelerating impulse than the hindlimbs, such that their net fore-aft impulse was decelerating whereas that of the hindlimbs was accelerating. The greater accelerating impulse applied by the trailing forelimb and greater decelerating impulse applied by the lead forelimb are consistent with the forelimbs acting as elastic struts rather than being actively retracted. In contrast, greater accelerating forces were produced by the lead hindlimb while the center of mass was lifted, suggesting that the hindlimbs are more actively extended or retracted during stance. The differences in ground forces measured between paired limbs suggest that the lead forelimb and trailing hindlimb are limited in their ability to apply forces by their positions in the stride cycle rather than by their muscular capacity. Although a bound or half-bound would allow more limbs to produce their maximal forces, a gallop may generate higher speeds because it is more efficient. Galloping could be more efficient than other gaits involving sagittal bending if the increased number of ground contact intervals decreased either the decelerating forces applied at the onset of ground contact or the vertical motion of the center of mass.

A BRAZILIAN FAMILY WITH QUADRUPEDAL GAIT, SEVERE MENTAL RETARDATION, COARSE FACIAL CHARACTERISTICS, AND HIRSUTISM

This article describes the case of four brothers, born of a consanguineous couple, that present a severe mental retardation syndrome, coarse facial characteristics, hirsutism, quadrupedal gait (pithecoid walk), small stature, absence of speech, strabismus as well as having small hands and feet. This case seems to be a behavioral syndrome, which was inherited in an autosomal recessive manner not previously recorded.

A WRIST-WALKER EXHIBITING NO “UNER TAN SYDNROME”: A THEORY FOR POSSIBLE MECHANISMS OF HUMAN DEVOLUTION TOWARD THE ATAVISTIC WALKING PATTERNS

After discovering two families with handicapped children exhibiting the “Uner Tan syndrome,” the author discovered a man exhibiting only wrist-walking with no primitive mental abilities including language. According to his mother, he had an infectious disease with high fever as a three months old baby; as a result, the left leg had been paralyzed after a penicilline injection. This paralysis most probably resulted from a viral disease, possibly poliomyelitis. He is now (2006) 36 years old; the left leg is flaccid and atrophic, with no tendon reflexes; however, sensation is normal. The boy never stood up on his feet while maturing. The father forced him to walk upright using physical devices and making due exercises, but the child always rejected standing upright and walking in erect posture; he always preferred wrist-walking; he expresses that wrist-walking is much more comfortable for him than upright-walking. He is very strong now, making daily body building exercises, and walking quite fast using a “three legs,” although he cannot stand upright. Mental status, including the language and conscious experience, is quite normal. There was no intra-familiar marriage as in the two families mentioned earlier, and there is no wrist-walking in his family and relatives. There were no cerebellar signs and symptoms upon neurological examination. The brain-MRI was normal; there was no atrophy in cerebellum and vermis. It was concluded that there may be sporadic wrist-walkers exhibiting no “Uner Tan Syndrome.” The results suggest that the cerebellum has nothing to do with human wrist-walking, which may rather be an atavistic trait appearing from time to time in normal individuals, indicating a live model for human reverse evolution. It was concluded that pure quadrupeds may sporadically appear due to random fluctuations in genotypes and/or environmental factors (hormonal or nutritional); the human development following the human evolution may be stopped in the stage of transition from quadrupedality to bipedality. That is, the activity of the philogenetically youngest supraspinal centers for bipedal walking responsible for suppression of the older supraspinal centers for quadrupedal gait may be interrupted at the atavistic level due to genetic and/or environmental factors. Consequently, it is assumed that these individuals prefer their natural wrist-walking to move around more quickly and efficiently.

The locomotor kinematics of Asian and African elephants: changes with speed and size

For centuries, elephant locomotion has been a contentious and confusing challenge for locomotion scientists to understand, not only because of technical difficulties but also because elephant locomotion is in some ways atypical of more familiar quadrupedal gaits. We analyzed the locomotor kinematics of over 2400 strides from 14 African and 48 Asian elephant individuals (body mass 116-4632 kg) freely moving over ground at a 17-fold range of speeds, from slow walking at 0.40 m s(-1) to the fastest reliably recorded speed for elephants, 6.8 m s(-1). These data reveal that African and Asian elephants have some subtle differences in how size-independent kinematic parameters change with speed. Although elephants use a lateral sequence footfall pattern, like many other quadrupeds, they maintain this footfall pattern at all speeds, shifting toward a 25% phase offset between limbs (singlefoot) as they increase speed. The duty factors of elephants are greater for the forelimbs than for the hindlimbs, so an aerial phase for the hindquarters is reached at slower speeds than for the forequarters. This aerial phase occurs at a Froude number of around 1, matching theoretical predictions. At faster speeds, stance and swing phase durations approach asymptotes, with the duty factor beginning to level off, concurrent with an increase in limb compliance that likely keeps peak forces relatively low. This increase of limb compliance is reflected by increased compression of the hindlimbs. Like other tetrapods, smaller elephants are relatively more athletic than larger ones, but still move very similarly to adults even at <500 kg. At any particular speed they adopt greater relative stride frequencies and relative stride lengths compared to larger elephants. This extends to near-maximal locomotor performance as well - smaller elephants reach greater Froude numbers and smaller duty factors, hence likely reach relatively greater peak loads on their limbs and produce this force more rapidly. A variety of lines of kinematic evidence support the inference that elephants change their mechanics near a Froude number of 1 (if not at slower speeds), at least to using more compliant limbs, if not spring-like whole-body kinetics. In some ways, elephants move similarly to many other quadrupeds, such as increasing speed mainly by increasing stride frequency (except at fast speeds), and they match scaling predictions for many stride parameters. The main difference from most other animals is that elephants never change their footfall pattern to a gait that uses a whole-body aerial phase. Our large dataset establishes what the normal kinematics of elephant locomotion are, and can also be applied to identify gait abnormalities that may signal musculoskeletal pathologies, a matter of great importance to keepers of captive elephants.

Dynamics of quadrupedal locomotion of monkeys: implications for central control

We characterized the three-dimensional kinematics and dynamics of quadrupedal gait of young adult rhesus and cynomolgus monkeys while they walked with diagonal and lateral gaits at 0.4-1.0 m/s on a treadmill. Rigid bodies on the wrist, ankle, and back were monitored by an optical motion detection system (Optotrak). Kinematic data could be normalized using characteristic stride length, reducing variance due to different gait styles, to emphasize common characteristics of swing and stance parameters among animals. Mean swing phase durations fell as walking speed increased, but the swing phase durations increased at each walking velocity as a linear function of increases in amplitude, thereby following a main sequence relationship. The phase plane trajectories of the swing phases, i.e., plots of the relation of the rising and falling limb velocity to limb position in the sagittal (X-Z) plane, had unique dynamic characteristics. Trajectories were separable at each walking velocity and increases in swing amplitude were linearly related to peak swing velocities, thus comprising main sequences. We infer that the swing phase dynamics are set by central neural mechanisms at the onset of the swing phases according to the intended amplitude, which in turn is based on the walking velocity in the stance phases. From the many dynamic similarities between swing phases and rapid eye movements, we further suggest that the swing phases may be generated by neural mechanisms similar to those that produce saccades and quick phases of nystagmus from a signal related to sensed or desired walking velocity.

Central pattern generators for bipedal locomotion

Golubitsky, Stewart, Buono and Collins proposed two models for the achitecture of central pattern generators (CPGs): one for bipeds (which we call leg) and one for quadrupeds (which we call quad). In this paper we use symmetry techniques to classify the possible spatiotemporal symmetries of periodic solutions that can exist in leg (there are 10 nontrivial types) and we explore the possibility that coordinated arm/leg rhythms can be understood, on the CPG level, by a small breaking of the symmetry in quad, which leads to a third CPG architecture arm. Rhythms produced by leg correspond to the bipedal gaits of walk, run, two-legged hop, two-legged jump, skip, gallop, asymmetric hop, and one-legged hop. We show that breaking the symmetry between fore and hind limbs in quad, which yields the CPG arm, leads to periodic solution types whose associated leg rhythms correspond to seven of the eight leg gaits found in leg; the missing biped gait is the asymmetric hop. However, when arm/leg coordination rhythms are considered, we find the correct rhythms only for the biped gaits of two-legged hop, run, and gallop. In particular, the biped gait walk, along with its arm rhythms, cannot be obtained by a small breaking of symmetry of any quadruped gait supported by quad.