Compliant bipedal model with the center of pressure excursion associated with oscillatory behavior of the center of mass reproduces the human gait dynamics

Although the compliant bipedal model could reproduce qualitative ground reaction force (GRF) of human walking, the model with a fixed pivot showed overestimations in stance leg rotation and the ratio of horizontal to vertical GRF. The human walking data showed a continuous forward progression of the center of pressure (CoP) during the stance phase and the suspension of the CoP near the forefoot before the onset of step transition. To better describe human gait dynamics with a minimal expense of model complexity, we proposed a compliant bipedal model with the accelerated pivot which associated the CoP excursion with the oscillatory behavior of the center of mass (CoM) with the existing simulation parameter and leg stiffness. Owing to the pivot acceleration defined to emulate human CoP profile, the arrival of the CoP at the limit of the stance foot over the single stance duration initiated the step-to-step transition. The proposed model showed an improved match of walking data. As the forward motion of CoM during single stance was partly accounted by forward pivot translation, the previously overestimated rotation of the stance leg was reduced and the corresponding horizontal GRF became closer to human data. The walking solutions of the model ranged over higher speed ranges (~1.7 m/s) than those of the fixed pivoted compliant bipedal model (~1.5 m/s) and exhibited other gait parameters, such as touchdown angle, step length and step frequency, comparable to the experimental observations. The good matches between the model and experimental GRF data imply that the continuous pivot acceleration associated with CoM oscillatory behavior could serve as a useful framework of bipedal model.     

A model of human walking energetics with an elastically-suspended load

Elastically-suspended loads have been shown to reduce the peak forces acting on the body while walking with a load when the suspension stiffness and damping are minimized. However, it is not well understood how elastically-suspended loads can affect the energetic cost of walking. Prior work shows that elastically suspending a load can yield either an increase or decrease in the energetic cost of human walking, depending primarily on the suspension stiffness, load, and walking speed. It would be useful to have a simple explanation that reconciles apparent differences in existing data. The objective of this paper is to help explain different energetic outcomes found with experimental load suspension backpacks and to systematically investigate the effect of load suspension parameters on the energetic cost of human walking. A simple two-degree-of-freedom model is used to approximate the energetic cost of human walking with a suspended load. The energetic predictions of the model are consistent with existing experimental data and show how the suspension parameters, load mass, and walking speed can affect the energetic cost of walking. In general, the energetic cost of walking with a load is decreased compared to that of a stiffly-attached load when the natural frequency of a load suspension is tuned significantly below the resonant walking frequency. The model also shows that a compliant load suspension is more effective in reducing the energetic cost of walking with low suspension damping, high load mass, and fast walking speed. This simple model could improve our understanding of how elastic load-carrying devices affect the energetic cost of walking with a load.     

Predicting human walking gaits with a simple planar model

Models of human walking with moderate complexity have the potential to accurately capture both joint kinematics and whole body energetics, thereby offering more simultaneous information than very simple models and less computational cost than very complex models. This work examines four- and six-link planar biped models with knees and rigid circular feet. The two differ in that the six-link model includes ankle joints. Stable periodic walking gaits are generated for both models using a hybrid zero dynamics-based control approach. To establish a baseline of how well the models can approximate normal human walking, gaits were optimized to match experimental human walking data, ranging in speed from very slow to very fast. The six-link model well matched the experimental step length, speed, and mean absolute power, while the four-link model did not, indicating that ankle work is a critical element in human walking models of this type. Beyond simply matching human data, the six-link model can be used in an optimization framework to predict normal human walking using a torque-squared objective function. The model well predicted experimental step length, joint motions, and mean absolute power over the full range of speeds.     

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.     

Estimation of unmeasured ground reaction force data based on the oscillatory characteristics of the center of mass during human walking

To enhance the wearability of portable motion-monitoring devices, the size and number of sensors are minimized, but at the expense of quality and quantity of data collected. For example, owing to the size and weight of low-frequency force transducers, most currently available wearable gait measurement systems provide only limited, if any, elements of ground reaction force (GRF) data. To obtain the most GRF information possible with a minimal use of sensors, we propose a GRF estimation method based on biomechanical knowledge of human walking. This includes the dynamics of the center of mass (CoM) during steady human gait resembling the oscillatory behaviors of a mass-spring system. Available measurement data were incorporated into a spring-loaded inverted pendulum with translating pivot. The spring stiffness and simulation parameters were tuned to match, as accurately as possible, the available data and oscillatory characteristics of walking. Our results showed that the model simulation estimated reasonably well the unmeasured GRF. Using the vertical GRF and CoP profile for gait speeds ranging from 0.93 to 1.89 m/s, the anterior-posterior (A-P) GRF was estimated and resulted in an average correlation coefficient of R = 0.982 ± 0.009. Even when the ground contact timing and gait speed information were alone available, our method estimated GRFs resulting in R = 0.969 ± 0.022 for the A-P and R = 0.891 ± 0.101 for the vertical GRFs. This research demonstrates that the biomechanical knowledge of human walking, such as inherited oscillatory characteristics of the CoM, can be used to gain unmeasured information regarding human gait dynamics.     

Consequences of forward translation of the point of force application for the mechanics of running

In running humans, the point of force application between the foot and the ground moves forwards during the stance phase. Our aim was to determine the mechanical consequences of this 'point of force translation' (POFT). We modified the planar spring-mass model of locomotion to incorporate POFT, and then compared spring-mass simulations with and without POFT. We found that, if leg stiffness is adjusted appropriately, it is possible to maintain very similar values of peak vertical ground reaction force (GRF), stance time, contact length and vertical centre of mass displacement, whether or not POFT occurs. The leg stiffness required to achieve this increased as the distance of POFT increased. Peak horizontal GRF and mechanical work per step were lower when POFT occurred. The results indicate that the lack of POFT in the traditional spring-mass model should not prevent it from providing good predictions of peak vertical GRF, stance time, contact length and vertical centre of mass displacement in running humans, if an appropriate spring stiffness is used. However, the model can be expected to overestimate peak horizontal GRF and mechanical work per step. When POFT occurs, the spring stiffness in the traditional spring-mass model is not equivalent to leg stiffness. Therefore, caution should be exercised when using spring stiffness to understand how the musculoskeletal system adapts to different running conditions. This can explain the contradictory results in the literature regarding the effect of running speed on leg stiffness.     

A model of cerebrocerebello-spinomuscular interaction in the sagittal control of human walking

A computationally developed model of human upright balance control (Jo and Massaquoi on Biol cybern 91:188–202, 2004) has been enhanced to describe biped walking in the sagittal plane. The model incorporates (a) non-linear muscle mechanics having activation level -dependent impedance, (b) scheduled cerebrocerebellar interaction for control of center of mass position and trunk pitch angle, (c) rectangular pulse-like feedforward commands from a brainstem/ spinal pattern generator, and (d) segmental reflex modulation of muscular synergies to refine inter-joint coordination. The model can stand when muscles around the ankle are coactivated. When trigger signals activate, the model transitions from standing still to walking at 1.5 m/s. Simulated natural walking displays none of seven pathological gait features. The model can simulate different walking speeds by tuning the amplitude and frequency in spinal pattern generator. The walking is stable against forward and backward pushes of up to 70 and 75 N, respectively, and with sudden changes in trunk mass of up to 18%. The sensitivity of the model to changes in neural parameters and the predicted behavioral results of simulated neural system lesions are examined. The deficit gait simulations may be useful to support the functional and anatomical correspondences of the model. The model demonstrates that basic human-like walking can be achieved by a hierarchical structure of stabilized-long loop feedback and synergy-mediated feedforward controls. In particular, internal models of body dynamics are not required.     

Optimum walking techniques for idealized animals

The vertical component of the force exerted by a foot on the ground, in the course of a step, may rise to a single maximum and decline again (as in human running) or may show two distinct maxima (as in human walking). A foot may remain on the ground for a large or small fraction of the duration of a stride. Mathematical models are used to investigate the effects of these differences of technique on the energy cost of locomotion. The optimum technique for a biped at a given speed is different from the optimum for a hypothetical many-legged animal. The optima for quadrupedal walking are likely to lie between these extremes.
The walking techniques adopted by men at different speeds are close to the optima indicated by the bipedal model. The two maxima of the force exerted by a foot are higher, and have a lower minimum between them, at higher speeds of walking. The techniques adopted by a sheep are close to the optima indicated by the many-legged model but dogs use techniques rather closer to the optima for bipeds.
The limitations of the models are discussed.     

Gait synchronized force modulation during the stance period of one limb achieved by an active partial body weight support system

Our purpose was to demonstrate the ability of an actively controlled partial body weight support (PBWS) system to provide gait synchronized support during the stance period of a single lower extremity while examining the affect of such a support condition on gait asymmetry. Using an instrumented treadmill and a motion capture system, we compared gait parameters of twelve healthy elderly subjects (age 65-80 years) during unsupported walking to those while walking with 20% body weight support provided during only the stance period of the right limb. Specifically, we examined peak three-dimensional ground reaction force (GRF) data and the symmetry of lower extremity sagittal plane joint angles and of time and distance parameters. A reduction in all three GRF components was observed for the supported limb during modulated support. Reductions observed in the vertical GRF were comparable to the desired 20% support level. Additionally, GRF components examined for the unsupported limb during modulated support were consistently similar to those measured during unsupported walking. Modulated support caused statistically significant increases in asymmetry for knee flexion during stance (increased 5.9%), hip flexion during late swing (increased 9.1%), and the duration of single limb support (increased 2.8%). However, the observed increases were similar or considerably less than the natural variability in the asymmetry of these parameters during unsupported walking. The ability of the active PBWS device to provide unilateral support may offer new and possibly improved applications of PBWS rehabilitation for patients with unilateral walking deficits such as hemiparesis or orthopaedic injury.     

Simple and complex models for studying muscle function in walking

While simple models can be helpful in identifying basic features of muscle function, more complex models are needed to discern the functional roles of specific muscles in movement. In this paper, two very different models of walking, one simple and one complex, are used to study how muscle forces, gravitational forces and centrifugal forces (i.e. forces arising from motion of the joints) combine to produce the pattern of force exerted on the ground. Both the simple model and the complex one predict that muscles contribute significantly to the ground force pattern generated in walking; indeed, both models show that muscle action is responsible for the appearance of the two peaks in the vertical force. The simple model, an inverted double pendulum, suggests further that the first and second peaks are due to net extensor muscle moments exerted about the knee and ankle, respectively. Analyses based on a much more complex, muscle-actuated simulation of walking are in general agreement with these results; however, the more detailed model also reveals that both the hip extensor and hip abductor muscles contribute significantly to vertical motion of the centre of mass, and therefore to the appearance of the first peak in the vertical ground force, in early single-leg stance. This discrepancy in the model predictions is most probably explained by the difference in model complexity. First, movements of the upper body in the sagittal plane are not represented properly in the double-pendulum model, which may explain the anomalous result obtained for the contribution of a hip-extensor torque to the vertical ground force. Second, the double-pendulum model incorporates only three of the six major elements of walking, whereas the complex model is fully 3D and incorporates all six gait determinants. In particular, pelvic list occurs primarily in the frontal plane, so there is the potential for this mechanism to contribute significantly to the vertical ground force, especially during early single-leg stance when the hip abductors are activated with considerable force.     

Estimation of temporal gait parameters using Bayesian models on acceleration signals

The purpose of this study is to develop a system capable of performing calculation of temporal gait parameters using two low-cost wireless accelerometers and artificial intelligence-based techniques as part of a larger research project for conducting human gait analysis. Ten healthy subjects of different ages participated in this study and performed controlled walking tests. Two wireless accelerometers were placed on their ankles. Raw acceleration signals were processed in order to obtain gait patterns from characteristic peaks related to steps. A Bayesian model was implemented to classify the characteristic peaks into steps or nonsteps. The acceleration signals were segmented based on gait events, such as heel strike and toe-off, of actual steps. Temporal gait parameters, such as cadence, ambulation time, step time, gait cycle time, stance and swing phase time, simple and double support time, were estimated from segmented acceleration signals. Gait data-sets were divided into two groups of ages to test Bayesian models in order to classify the characteristic peaks. The mean error obtained from calculating the temporal gait parameters was 4.6%. Bayesian models are useful techniques that can be applied to classification of gait data of subjects at different ages with promising results     

Minimizing center of mass vertical movement increases metabolic cost in walking.

A human walker vaults up and over each stance limb like an inverted pendulum. This similarity suggests that the vertical motion of a walker's center of mass reduces metabolic cost by providing a mechanism for pendulum-like mechanical energy exchange. Alternatively, some researchers have hypothesized that minimizing vertical movements of the center of mass during walking minimizes the metabolic cost, and this view remains prevalent in clinical gait analysis. We examined the relationship between vertical movement and metabolic cost by having human subjects walk normally and with minimal center of mass vertical movement ("flat-trajectory walking"). In flat-trajectory walking, subjects reduced center of mass vertical displacement by an average of 69% (P = 0.0001) but consumed approximately twice as much metabolic energy over a range of speeds (0.7-1.8 m/s) (P = 0.0001). In flat-trajectory walking, passive pendulum-like mechanical energy exchange provided only a small portion of the energy required to accelerate the center of mass because gravitational potential energy fluctuated minimally. Thus, despite the smaller vertical movements in flat-trajectory walking, the net external mechanical work needed to move the center of mass was similar in both types of walking (P = 0.73). Subjects walked with more flexed stance limbs in flat-trajectory walking (P < 0.001), and the resultant increase in stance limb force generation likely helped cause the doubling in metabolic cost compared with normal walking. Regardless of the cause, these findings clearly demonstrate that human walkers consume substantially more metabolic energy when they minimize vertical motion.     

Predicting the metabolic cost of incline walking from muscle activity and walking mechanics

The goal of this study was to identify which muscle activation patterns and gait features best predict the metabolic cost of inclined walking. We measured muscle activation patterns, joint kinematics and kinetics, and metabolic cost in sixteen subjects during treadmill walking at inclines of 0%, 5%, and 10%. Multivariate regression models were developed to predict the net metabolic cost from selected groups of the measured variables. A linear regression model including incline and the squared integrated electromyographic signals of the soleus and vastus lateralis explained 96% of the variance in metabolic cost, suggesting that the activation patterns of these large muscles have a high predictive value for metabolic cost. A regression model including only the peak knee flexion angle during stance phase, peak knee extension moment, peak ankle plantarflexion moment, and peak hip flexion moment explained 89% of the variance in metabolic cost; this finding indicates that kinematics and kinetics alone can predict metabolic cost during incline walking. The ability of these models to predict metabolic cost from muscle activation patterns and gait features points the way toward future work aimed at predicting metabolic cost when gait is altered by changes in neuromuscular control or the use of an assistive technology.     

Anthropomorphic Design of the Human-Like Walking Robot

In this paper, we present a new concept of the mechanical design of a humanoid robot. The goal is to build a humanoid robot utilizing a new structure which is more suitable for human-like walking with the characteristics of the knee stretch, heel-contact, and toe-off. Inspired by human skeleton, we made an anthropomorphic pelvis for the humanoid robot. In comparison with conventional humanoid robots, with such the anthropomorphic pelvis, our robot is capable of adjusting the center of gravity of the upper body by the motion of pelvic tilt, thus reducing the required torque at the ankle joint and the velocity variations in human-like walking. With more precise analysis of the foot mechanism, the fixed-length inverted pendulum can be used to describe the dynamics of biped walking, thus preventing redundant works and power consumption in length variable inverted pendulum system. As the result of the new structure we propose, a humanoid robot is able to walk with human-like gait.     

Ground reaction force estimation using an insole-type pressure mat and joint kinematics during walking

Kinetic analysis of walking requires joint kinematics and ground reaction force (GRF) measurement, which are typically obtained from a force plate. GRF is difficult to measure in certain cases such as slope walking, stair climbing, and track running. Nevertheless, estimating GRF continues to be of great interest for simulating human walking. The purpose of the study was to develop reaction force models placed on the sole of the foot to estimate full GRF when only joint kinematics are provided (Type-I), and to estimate ground contact shear forces when both joint kinematics and foot pressure are provided (Type-II and Type-II-val). The GRF estimation models were attached to a commercial full body skeletal model using the AnyBody Modeling System, which has an inverse dynamics-based optimization solver. The anterior–posterior shear force and medial–lateral shear force could be estimated with approximate accuracies of 6% BW and 2% BW in all three methods, respectively. Vertical force could be estimated in the Type-I model with an accuracy of 13.75% BW. The accuracy of the force estimation was the highest during the mid-single-stance period with an average RMS for errors of 3.10% BW, 1.48% BW, and 7.48% BW for anterior–posterior force, medial–lateral force, and vertical force, respectively. The proposed GRF estimation models could predict full and partial GRF with high accuracy. The design of the contact elements of the proposed model should make it applicable to various activities where installation of a force measurement system is difficult, including track running and treadmill walking.     

Synthesis of human walking: A planar model for single support

A mathematical model for the single support phase of normal, level, human walking is formulated. The motion of the lower extremity is synthesized using a preprogrammed set of inputs, recognized by the model as a simple collection of applied joint moments.

Two mechanisms are forwarded as candidates for producing the observed peaks in the vertical ground reaction. The first, stance knee flexion-extension, generates the necessary level of whole-body vertical acceleration during the initial region of single support (opposite toe-off to heel-off). A model accounting for the determinants of foot and knee interaction then predicts the second peak to be the result of an increasing ankle moment in the region from heel-off to opposite heel-strike.     

Resonance-based oscillations could describe human gait mechanics under various loading conditions

The oscillatory behavior of the center of mass (CoM) and the corresponding ground reaction force (GRF) of human gait for various gait speeds can be accurately described in terms of resonance using a spring–mass bipedal model. Resonance is a mechanical phenomenon that reflects the maximum responsiveness and energetic efficiency of a system. To use resonance to describe human gait, we need to investigate whether resonant mechanics is a common property under multiple walking conditions. Body mass and leg stiffness are determinants of resonance; thus, in this study, we investigated the following questions: (1) whether the estimated leg stiffness increased with inertia, (2) whether a resonance-based CoM oscillation could be sustained during a change in the stiffness, and (3) whether these relationships were consistently observed for different walking speeds. Seven healthy young subjects participated in over-ground walking trials at three different gait speeds with and without a 25-kg backpack. We measured the GRFs and the joint kinematics using three force platforms and a motion capture system. The leg stiffness was incorporated using a stiffness parameter in a compliant bipedal model that best fitted the empirical GRF data. The results showed that the leg stiffness increased with the load such that the resonance-based oscillatory behavior of the CoM was maintained for a given gait speed. The results imply that the resonance-based oscillation of the CoM is a consistent gait property and that resonant mechanics may be useful for modeling human gait.     

Evaluation of the roles of passive and active control of balance using a balance control model

At present there is a lack of consensus regarding the relative roles of passive and active control of quiet upright stance. In the current work, this issue was investigated using two simulation models based on contemporary theories. Specifically, the two models, both of which assumed active control torques to be generated from an optimal neural controller, differed with respect to whether or not passive control torques (stiffness and damping) were included. Model parameters were specified using experimental center-of-pressure (COP) time series obtained during upright stance, and comparisons then made between simulated and actual COP-based measures. Including both active and passive joint torques in the control model did not appear to lead to any improvement in the ability to simulate COP compared with only including active joint torque. Further, simulated passive control torques were typically less than 10% of the active control torques, though some exceptions were found. These results, along with existing empirical evidence, suggest that active control torque is dominant in maintaining balance during upright stance.     

The influence of foot position on body dynamics

During locomotion, the human body exhibits inherent dynamic properties such as mass (M), stiffness (K) and damping (B). During the gait cycle, foot contact with the ground progresses from the heel to the toe. Contact forces between the foot and ground are defined as ground reaction forces (GRF). It is unclear how body dynamics are affected by foot landing position. If the shape of GRF is indicative of body dynamics, our understanding of gait patterns in normal and pathologic conditions may improve. The aims of this study were to determine:(1) whether foot landing position affects the inherent dynamics of the human body and (2) the extent to which the GRF curve reflects the response of inherent body dynamics to sudden loading.Eight non-disabled control volunteers performed a series of small jumps and landed on one leg with a fully extended knee in three foot landing positions: heel, mid-foot, and toe. They then walked at self-paced velocity over force plates. For each foot landing position, values of K, B and the dimensionless damping coefficient, ξ, were calculated from the period of vertical body oscillations, T, and compared with an ANOVA test. In addition, the time between the two peaks of the vertical GRF, T_GRF, was compared with T. We found that that K and B decreased and ξ did not change (p<0.01) between heel to toe-landing positions. T_GRF was not different than T for the toe-landing position, which suggests that the dynamic body response has major impact on the shape of GRF.