Hip actuations can be used to control bifurcations and chaos in a passive dynamic walking model

We explored how hip joint actuation can be used to control locomotive bifurcations and chaos in a passive dynamic walking model that negotiated a slightly sloped surface (gamma<0.019 rad). With no hip actuation, our passive dynamic walking model was capable of producing a chaotic locomotive pattern when the ramp angle was 0.01839 rad相似文献   

Chaotic attractor in two-prey one-predator system originates from interplay of limit cycles

We investigate the appearance of chaos in a microbial 3-species model motivated by a potentially chaotic real world system (as characterized by positive Lyapunov exponents (Becks et al., Nature 435, 2005). This is the first quantitative model that simulates characteristic population dynamics in the system. A striking feature of the experiment was three consecutive regimes of limit cycles, chaotic dynamics and a fixed point. Our model reproduces this pattern. Numerical simulations of the system reveal the presence of a chaotic attractor in the intermediate parameter window between two regimes of periodic coexistence (stable limit cycles). In particular, this intermediate structure can be explained by competition between the two distinct periodic dynamics. It provides the basis for stable coexistence of all three species: environmental perturbations may result in huge fluctuations in species abundances, however, the system at large tolerates those perturbations in the sense that the population abundances quickly fall back onto the chaotic attractor manifold and the system remains. This mechanism explains how chaos helps the system to persist and stabilize against migration. In discrete populations, fluctuations can push the system towards extinction of one or more species. The chaotic attractor protects the system and extinction times scale exponentially with system size in the same way as with limit cycles or in a stable situation.     

Repetitive gait of passive bipedal mechanisms in a three-dimensional environment

The inherent dynamics of bipedal, kneed mechanisms are studied with emphasis on the existence and stability, of repetitive gait in a three-dimensional environment, in the absence of external, active control. The investigation is motivated by observations that sustained anthropomorphic locomotion is largely a consequence of geometric and inertial properties of the mechanism. While the modeling excludes active control, the energy dissipated in ground and knee collisions is continuously re-injected by considering gait down slight inclines. The paper describes the dependence of the resulting passive gait in vertically constrained and unconstrained mechanisms on model parameters, such as ground compliance and ground slope. We also show the possibility of achieving statically unstable gait with appropriate parameter choices.     

Kinematics of bipedalism in Propithecus verreauxi

Bipedalism is rare in primates and has evolved in two distantly related groups: hominoids and indrids. Although copious data are available on the mechanics of bipedal locomotion in hominoids and vertical clinging and leaping (VCL) in indrids, no research has addressed the unique mode of bipedal locomotion exhibited by select indrid primates. Propithecus verreauxi is a highly specialized indrid vertical clinger and leaper that uses a peculiar form of bipedalism on the ground. The objectives of this study were to describe the bipedal gait of Propithecus , to assess the influence of VCL specializations on the kinematic patterns and propulsion mechanisms used by Propithecus during bipedalism, and to compare Propithecus bipedalism with the bipedal gaits of other primates capable of using bipedalism. Video was collected of five adult P. verreauxi moving bipedally in a seminatural setting at the Duke University Primate Center. Duty factor, footfall patterns, joint angles and center of mass movement were quantified in the sagittal plane for 73 steps. Propithecus uses a bipedal gallop, a gait unique to Propithecus . The kinematic similarities (e.g. large hip and knee angular excursions and preparatory countermovements) between bipedal galloping and VCL lead us to suggest that Propithecus takes advantage of specializations for VCL to conserve energy during bipedal galloping. Propithecus also walks bipedally at slower speeds. When Propithecus walks, it utilizes a relatively compliant gait similar to that of other primate facultative bipeds ( Pan , Hylobates ). During bipedal walking, energy conservation may be sacrificed for increased balance and reduced joint loads.     

Virtual slope control of a forward dynamic bipedal walker

Active joint torques are the primary source of power and control in dynamic walking motion. However the amplitude, rate, timing and phasic behavior of the joint torques necessary to achieve a natural and stable performance are difficult to establish. The goal of this study was to demonstrate the feasibility and stable behavior of an actively controlled bipedal walking simulation wherein the natural system dynamics were preserved by an active, nonlinear, state-feedback controller patterned after passive downhill walking. A two degree-of-freedom, forward-dynamic simulation was implemented with active joint torques applied at the hip joints and stance leg ankle. Kinematic trajectories produced by the active walker were similar to passive dynamic walking with active joint torques influenced by prescribed walking velocity. The control resulted in stable steady-state gait patterns, i.e. eigenvalue magnitudes of the stride function were less than one. The controller coefficient analogous to the virtual slope was modified to successfully control average walking velocity. Furture developments are necessary to expand the range of walking velocities.     

Speed modulation in hylobatid bipedalism: a kinematic analysis

Gibbons are highly arboreal apes, and it is expected that their bipedal locomotion will show some particularities related to the arboreal environment. Previous research has shown that, during hylobatid bipedalism, unsupported phases are rare and stride frequencies are relatively low. This study confirms previous findings, and we suggest that low stride frequencies and the absence of unsupported phases are ways to reduce disadvantageous branch oscillations during arboreal travel. Despite these restrictions, gibbons are able to locomote at a wide range of speeds, implying that they likely exploit other mechanisms to modulate their locomotor speed. To investigate this possibility, we collected video images of a large number of spontaneous bipedal bouts of four untrained white-handed gibbons by using an instrumented walkway with four synchronized cameras. These video images were digitized to obtain a quantification of the 3D kinematics of hylobatid bipedalism. We defined a large number of spatiotemporal and kinematic gait variables, and the relationship between these gait variables and (dimensionless) speed was statistically tested. It was found that gibbons mainly increase stride length to increase their locomotor speed; the main speed-modulating mechanisms are hip and ankle excursion and coupled knee and ankle extension at toe-off. Although aerial phases are rare, gibbons generally adopt a bipedal bouncing gait at most speeds and a clear-cut gait transition, as seen in human locomotion, is absent. Comparison with human and bonobo bipedalism showed that the variability of the 3D joint angles of the hind limb are comparable during human and gibbon bipedalism, and much lower than during bonobo bipedalism. The low variability found in gibbons might be related to constraints imposed by the arboreal environment. These arboreal constraints clearly affect the bipedal gait characteristics of gibbons, but do not constrain the ability to adopt a bipedal bouncing gait during terrestrial locomotion.     

Forward dynamic simulation of bipedal walking in the Japanese macaque: investigation of causal relationships among limb kinematics, speed, and energetics of bipedal locomotion in a nonhuman primate

Japanese macaques that have been trained for monkey performances exhibit a remarkable ability to walk bipedally. In this study, we dynamically reconstructed bipedal walking of the Japanese macaque to investigate causal relationships among limb kinematics, speed, and energetics, with a view to understanding the mechanisms underlying the evolution of human bipedalism. We constructed a two-dimensional macaque musculoskeletal model consisting of nine rigid links and eight principal muscles. To generate locomotion, we used a trajectory-tracking control law, the reference trajectories of which were obtained experimentally. Using this framework, we evaluated the effects of changes in cycle duration and gait kinematics on locomotor efficiency. The energetic cost of locomotion was estimated based on the calculation of mechanical energy generated by muscles. Our results demonstrated that the mass-specific metabolic cost of transport decreased as speed increased in bipedal walking of the Japanese macaque. Furthermore, the cost of transport in bipedal walking was reduced when vertical displacement of the hip joint was virtually modified in the simulation to be more humanlike. Human vertical fluctuations in the body's center of mass actually contributed to energy savings via an inverted pendulum mechanism.     

Segment and joint angles of hind limb during bipedal and quadrupedal walking of the bonobo (Pan paniscus)

We describe segment angles (trunk, thigh, shank, and foot) and joint angles (hip, knee, and ankle) for the hind limbs of bonobos walking bipedally ("bent-hip bent-knee walking," 17 sequences) and quadrupedally (33 sequences). Data were based on video recordings (50 Hz) of nine subjects in a lateral view, walking at voluntary speed. The major differences between bipedal and quadrupedal walking are found in the trunk, thigh, and hip angles. During bipedal walking, the trunk is approximately 33-41 degrees more erect than during quadrupedal locomotion, although it is considerably more bent forward than in normal human locomotion. Moreover, during bipedal walking, the hip has a smaller range of motion (by 12 degrees ) and is more extended (by 20-35 degrees ) than during quadrupedal walking. In general, angle profiles in bonobos are much more variable than in humans. Intralimb phase relationships of subsequent joint angles show that hip-knee coordination is similar for bipedal and quadrupedal walking, and resembles the human pattern. The coordination between knee and ankle differs much more from the human pattern. Based on joint angles observed throughout stance phase and on the estimation of functional leg length, an efficient inverted pendulum mechanism is not expected in bonobos.     

Theories of bipedal walking: an odyssey

In this paper six theories of bipedal walking, and the evidence in support of the theories, are reviewed. They include: evolution, minimising energy consumption, maturation in children, central pattern generators, linking control and effect, and robots on two legs. Specifically, the six theories posit that: (1) bipedalism is the fundamental evolutionary adaptation that sets hominids--and therefore humans--apart from other primates; (2) locomotion is the translation of the centre of gravity along a pathway requiring the least expenditure of energy; (3) when a young child takes its first few halting steps, his or her biomechanical strategy is to minimise the risk of falling; (4) a dedicated network of interneurons in the spinal cord generates the rhythm and cyclic pattern of electromyographic signals that give rise to bipedal gait; (5) bipedal locomotion is generated through global entrainment of the neural system on the one hand, and the musculoskeletal system plus environment on the other; and (6) powered dynamic gait in a bipedal robot can be realised only through a strategy which is based on stability and real-time feedback control. The published record suggests that each of the theories has some measure of support. However, it is important to note that there are other important theories of locomotion which have not been covered in this review. Despite such omissions, this odyssey has explored the wide spectrum of bipedal walking, from its origins through to the integration of the nervous, muscular and skeletal systems.     

A passive dynamic walking robot that has a deterministic nonlinear gait

There is a growing body of evidence that the step-to-step variations present in human walking are related to the biomechanics of the locomotive system. However, we still have limited understanding of what biomechanical variables influence the observed nonlinear gait variations. It is necessary to develop reliable models that closely resemble the nonlinear gait dynamics in order to advance our knowledge in this scientific field. Previously, Goswami et al. [1998. A study of the passive gait of a compass-like biped robot: symmetry and chaos. International Journal of Robotic Research 17(12)] and Garcia et al. [1998. The simplest walking model: stability, complexity, and scaling. Journal of Biomechanical Engineering 120(2), 281-288] have demonstrated that passive dynamic walking computer models can exhibit a cascade of bifurcations in their gait pattern that lead to a deterministic nonlinear gait pattern. These computer models suggest that the intrinsic mechanical dynamics may be at least partially responsible for the deterministic nonlinear gait pattern; however, this has not been shown for a physical walking robot. Here we use the largest Laypunov exponent and a surrogation analysis method to confirm and extend Garcia et al.'s and Goswami et al.'s original results to a physical passive dynamic walking robot. Experimental outcomes from our walking robot further support the notion that the deterministic nonlinear step-to-step variations present in gait may be partly governed by the intrinsic mechanical dynamics of the locomotive system. Furthermore the nonlinear analysis techniques used in this investigation offer novel methods for quantifying the nature of the step-to-step variations found in human and robotic gait.     

Chimpanzee bipedal locomotion in the Gombe National Park,East Africa

An adult male chimpanzee in the natural habitat has been observed to walk predominantly bipedally after a total forelimb paralysis in 1966. The major differences from previously described bipedal chimpanzee gait are (1) one third of the femoral extension is posterior to the hip joint in propulsion, (2) excursion of the swinging foot is close to midline, due to adduction of the lower hindlimb in swing and propulsive phases, (3) depressed pelvic tilt is on the side of the swinging limb, (4) thoracic vertebrae rotate and are vertical and erect, and (5) there is only a moderate lateral sway of the midline. This locomotory complex is interpreted as individual variability and suggests an evolutionary model for the origin of hominid bipedal locomotion.     

A bipedal compliant walking model generates periodic gait cycles with realistic swing dynamics

A simple spring mechanics model can capture the dynamics of the center of mass (CoM) during human walking, which is coordinated by multiple joints. This simple spring model, however, only describes the CoM during the stance phase, and the mechanics involved in the bipedality of the human gait are limited. In this study, a bipedal spring walking model was proposed to demonstrate the dynamics of bipedal walking, including swing dynamics followed by the step-to-step transition. The model consists of two springs with different stiffnesses and rest lengths representing the stance leg and swing leg. One end of each spring has a foot mass, and the other end is attached to the body mass. To induce a forward swing that matches the gait phase, a torsional hip joint spring was introduced at each leg. To reflect the active knee flexion for foot clearance, the rest length of the swing leg was set shorter than that of the stance leg, generating a discrete elastic restoring force. The number of model parameters was reduced by introducing dependencies among stiffness parameters. The proposed model generates periodic gaits with dynamics-driven step-to-step transitions and realistic swing dynamics. While preserving the mimicry of the CoM and ground reaction force (GRF) data at various gait speeds, the proposed model emulated the kinematics of the swing leg. This result implies that the dynamics of human walking generated by the actuations of multiple body segments is describable by a simple spring mechanics.     

Passive bipedal walking with phasic muscle contraction

The existence of self-organizing walking patterns is often considered the result of a mechanical system interacting with the environment and a (neural) oscillating unit. The pattern generators might be thought of as an indispensable component for the existence of limit cycle behavior. This paper shows that this is not a necessity for the existence of a self-organizing bipedal walking pattern. Stable walking cycles emerge from a simple passive bipedal structure, with an energy source inevitably present to sustain the oscillation. In this work the energy source is chosen to be phasic muscle contraction. A two-dimensional model is composed of two legs and a hip mass, symbolizing the trunk. The stance leg stiffness is generated by two muscles. The hip stiffness is generated by four muscles. Muscle activation is caused by two reflex-like trigger signals, without feedback control. Human equivalent model parameters such as geometry and mass distribution were assumed. With return map analysis, the model is analyzed on periodic behavior. Stable walking cycles were found and could be manipulated during walking by varying the muscle or reflex parameters, forcing the oscillation to converge to a new attractor. Received: 5 November 1998 / Accepted in revised form: 26 March 1999     

Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment

A new principle of sensorimotor control of legged locomotion in an unpredictable environment is proposed on the basis of neurophysiological knowledge and a theory of nonlinear dynamics. Stable and flexible locomotion is realized as a global limit cycle generated by a global entrainment between the rhythmic activities of a nervous system composed of coupled neural oscillators and the rhythmic movements of a musculo-skeletal system including interaction with its environment. Coordinated movements are generated not by slaving to an explicit representation of the precise trajectories of the movement of each part but by dynamic interactions among the nervous system, the musculo-skeletal system and the environment. The performance of a bipedal model based on the above principle was investigated by computer simulation. Walking movements stable to mechanical perturbations and to environmental changes were obtained. Moreover, the model generated not only the walking movement but also the running movement by changing a single parameter nonspecific to the movement. The transitions between the gait patterns occurred with hysteresis.     

Trunk orientation causes asymmetries in leg function in small bird terrestrial locomotion

In contrast to the upright trunk in humans, trunk orientation in most birds is almost horizontal (pronograde). It is conceivable that the orientation of the heavy trunk strongly influences the dynamics of bipedal terrestrial locomotion. Here, we analyse for the first time the effects of a pronograde trunk orientation on leg function and stability during bipedal locomotion. For this, we first inferred the leg function and trunk control strategy applied by a generalized small bird during terrestrial locomotion by analysing synchronously recorded kinematic (three-dimensional X-ray videography) and kinetic (three-dimensional force measurement) quail locomotion data. Then, by simulating quail gaits using a simplistic bioinspired numerical model which made use of parameters obtained in in vivo experiments with real quail, we show that the observed asymmetric leg function (left-skewed ground reaction force and longer leg at touchdown than at lift-off) is necessary for pronograde steady-state locomotion. In addition, steady-state locomotion becomes stable for specific morphological parameters. For quail-like parameters, the most common stable solution is grounded running, a gait preferred by quail and most of the other small birds. We hypothesize that stability of bipedal locomotion is a functional demand that, depending on trunk orientation and centre of mass location, constrains basic hind limb morphology and function, such as leg length, leg stiffness and leg damping.     

The distal femoral anatomy of Australopithecus

The anatomy of the distal femoral fragments from Sterkfontein is reviewed, including its orthopaedic and biomechanical implications with respect to locomotion pattern. Comparisons are made with other hominids and a number of quadrupedal primates. Items which are considered are the obliquity and robustness of the shaft, the anterior intercondylar groove, the intercondylar notch, and the contour of the medial and lateral articular surfaces. The distinctive hominid status of these specimens is shown by their extensive adaptation to bipedal locomotion. No feature is found which is not fully commensurate with completely bipedal locomotion; rather, their distinctive hominid character points to a need for a reanalysis of the gait pattern in these early Pleistocene hominids.     

Construction of an associative memory using unstable periodic orbits of a chaotic attractor

Unstable periodic orbits are the skeleton of a chaotic attractor. We constructed an associative memory based on the chaotic attractor of an artificial neural network, which associates input patterns to unstable periodic orbits. By processing an input, the system is driven out of the ground state to one of the pre-defined disjunctive areas of the attractor. Each of these areas is associated with a different unstable periodic orbit. We call an input pattern learned if the control mechanism keeps the system on the unstable periodic orbit during the response. Otherwise, the system relaxes back to the ground state on a chaotic trajectory. The major benefits of this memory device are its high capacity and low-energy consumption. In addition, new information can be simply added by linking a new input to a new unstable periodic orbit.     

Energy efficient walking with central pattern generators: from passive dynamic walking to biologically inspired control

Like human walking, passive dynamic walking—i.e. walking down a slope with no actuation except gravity—is energy efficient by exploiting the natural dynamics. In the animal world, neural oscillators termed central pattern generators (CPGs) provide the basic rhythm for muscular activity in locomotion. We present a CPG model, which automatically tunes into the resonance frequency of the passive dynamics of a bipedal walker, i.e. the CPG model exhibits resonance tuning behavior. Each leg is coupled to its own CPG, controlling the hip moment of force. Resonance tuning above the endogenous frequency of the CPG—i.e. the CPG’s eigenfrequency—is achieved by feedback of both limb angles to their corresponding CPG, while integration of the limb angles provides resonance tuning at and below the endogenous frequency of the CPG. Feedback of the angular velocity of both limbs to their corresponding CPG compensates for the time delay in the loop coupling each limb to its CPG. The resonance tuning behavior of the CPG model allows the gait velocity to be controlled by a single parameter, while retaining the energy efficiency of passive dynamic walking.     

Paired nonlinear behavior of active and passive joint torques associated with preparation for walk-to-run gait transition

This study investigated the lower extremity torque's active and passive features during the walk-to-run gait transition with continuously increased walking speed. Fourteen volunteers participated in the experiment. Kinematic and kinetic data were collected synchronously. Five strides leading up the gait transition were examined. Peaks of the passive (e.g., contact) and active (e.g., generalized muscle torques), along with net joint torque, and time to peak torques exhibited significant differences at the last stride before gait transition, compared to the first four strides, at the ankle, knee, and hip joints, respectively. Selected peak joint active and passive torques showed significant and opposite trends at critical events within a stride cycle: such ankle joint right after heel-contact, knee joint during weight acceptance, and both hip and knee joints right before toe-off. The magnitude and the corresponding time to active and passive peak torque changed in a nonlinear pattern before the transition from walk to run. The lower extremity segment-interaction during gait transition appeared to be an active reorganization exemplified by the interaction between the lower extremity's active and passive torque components.