A Kinematic Model to Predict a Continuous Range of Human-Like Walking Speed Transitions.

While constant speed gait is well understood, far less is known about how humans change walking speed. It is also unknown if the transition steps smoothly morph between speeds, or if they are unique. Using data from a prior study in which subjects transitioned between five speeds while walking on a treadmill, joint kinematic data were decomposed into trend and periodic components. The trend captured the time-varying nature of the gait, and the periodic component captured the cyclic nature of a stride. The start and end of the transition were found by detecting where the trend diverged from a ±2 standard deviation band around the mean of the pre- and post-transition trend. On average, the transition started within half a step of when the treadmill changed speed ( p << 0.001 for equivalence test). The transition length was 2 to 3 steps long. A predictive kinematic model was fit to the experimental data using Bezier polynomials for the trend and Fourier series for the periodic component. The model was fit using 1) only constant speed walking, 2) only speed transition steps, and 3) a random sample of five step types and then validated using the complement of the training data. Regardless of the training set, the model accurately predicted untrained gaits (normalized RMSE , normalized maximum error generally ). Because the errors were similar for all training sets, this implies that joint kinematics smoothly morph between gaits when humans change speed.

Validation of a modified visual analogue scale to measure user-perceived comfort of a lower-limb exoskeleton.

User perceived exoskeleton comfort is likely important for device acceptance, but there is currently no validated instrument to measure it. The Visual Analogue Scale (VAS) is an existing tool to measure subjective human feedback by asking the user to mark a point on a line with each end of the line representing an opposing anchor statement. It can be modified to show the previous response, allowing the subject to directly indicate if the current condition is better or worse than the previous one. The goal of this study was to determine how well the modified VAS could measure user-perceived comfort as the exoskeleton control parameters were varied. To validate the survey, 14 healthy subjects walked in a pair of ankle exoskeletons with approximately ten distinct sets of control parameters tested in a prescribed order. Each set of control parameters was tested twice. After each trial, user-perceived comfort was measured using a two-question VAS survey. The repeatability coefficient was approximately 40 mm, similar to the total range of responses. The results were also inconsistent, with relative rankings between consecutive pairs of conditions matching for approximately 50% of comparisons. Thus, as tested, the VAS was not repeatable or consistent. It is possible that subject adaptation within the trial and over the course of the experiment may have impacted the results. Additional work is needed to develop a repeatable method to measure comfort and to determine how perceived comfort varies as subjects' gain exoskeleton experience.

Predicting fall risk using multiple mechanics-based metrics for a planar biped model.

For both humans and robots, falls are undesirable, motivating the development of fall prediction models. Many mechanics-based fall risk metrics have been proposed and validated to varying degrees, including the extrapolated center of mass, the foot rotation index, Lyapunov exponents, joint and spatiotemporal variability, and mean spatiotemporal parameters. To obtain a best-case estimate of how well these metrics can predict fall risk both individually and in combination, this work used a planar six-link hip-knee-ankle biped model with curved feet walking at speeds ranging from 0.8 m/s to 1.2 m/s. The true number of steps to fall was determined using the mean first passage times from a Markov chain describing the gaits. In addition, each metric was estimated using the Markov chain of the gait. Because calculating the fall risk metrics from the Markov chain had not been done before, the results were validated using brute force simulations. Except for the short-term Lyapunov exponents, the Markov chains could accurately calculate the metrics. Using the Markov chain data, quadratic fall prediction models were created and evaluated. The models were further evaluated using differing length brute force simulations. None of the 49 tested fall risk metrics could accurately predict the number of steps to fall by themselves. However, when all the fall risk metrics except the Lyapunov exponents were combined into a single model, the accuracy increased substantially. These results suggest that multiple fall risk metrics must be combined to obtain a useful measure of stability. As expected, as the number of steps used to calculate the fall risk metrics increased, the accuracy and precision increased. This led to a corresponding increase in the accuracy and precision of the combined fall risk model. 300 step simulations seemed to provide the best tradeoff between accuracy and using as few steps as possible.

Quantifying the effect of sagittal plane joint angle variability on bipedal fall risk.

Falls are a major issue for bipeds. For elderly adults, falls can have a negative impact on their quality of life and lead to increased medical costs. Fortunately, interventional methods are effective at reducing falls assuming they are prescribed. For biped robots, falls prevent them from completing required tasks. Thus, it is important to understand what aspects of gait increase fall risk. Gait variability may be associated with increased fall risk; however, previous studies have not investigated the variation in the movement of the legs. The purpose of this study was to determine the effect of joint angle variability on falling to determine which component(s) of variability were statistically significant. In order to investigate joint angle variability, a physics-based simulation model that captured joint angle variability as a function of time through Fourier series was used. This allowed the magnitude, the frequency mean, and the frequency standard deviation of the variability to be altered. For the values tested, results indicated that the magnitude of the variability had the most significant impact on falling, and specifically that the stance knee flexion variability magnitude was the most significant factor. This suggests that increasing the joint variability magnitude may increase fall risk, particularly if the controller is not able to actively compensate. Altering the variability frequency had little to no effect on falling.

Comparing system identification techniques for identifying human-like walking controllers.

While human walking has been well studied, the exact controller is unknown. This paper used human experimental walking data and system identification techniques to infer a human-like controller for a spring-loaded inverted pendulum (SLIP) model. Because the best system identification technique is unknown, three methods were used and compared. First, a linear system was found using ordinary least squares. A second linear system was found that both encoded the linearized SLIP model and matched the first linear system as closely as possible. A third nonlinear system used sparse identification of nonlinear dynamics (SINDY). When directly mapping states from the start to the end of a step, all three methods were accurate, with errors below 10% of the mean experimental values in most cases. When using the controllers in simulation, the errors were significantly higher but remained below 10% for all but one state. Thus, all three system identification methods generated accurate system models. Somewhat surprisingly, the linearized system was the most accurate, followed closely by SINDY. This suggests that nonlinear system identification techniques are not needed when finding a discrete human gait controller, at least for unperturbed walking. It may also suggest that human control of normal, unperturbed walking is approximately linear.

Inertial sensing of step kinematics in ambulatory patients with ALS and related motor neuron diseases.

Amyotrophic lateral sclerosis (ALS) is a progressive disorder which impairs gait and elevates the risk for falls. Current methods of assessing gait in these patients are infrequent and subjective. The goal of this study was to evaluate wearable-based methods for assessing gait to facilitating better monitoring of ambulatory health and ultimately lessen fall risk. Thirty ambulatory patients seen in ALS clinic were guided by a physical therapist on a short walk, during which inertial sensors recorded their movement. Two methods, utilising sensors at the waist or foot, were used independently to estimate gait parameters. Decreased stride length, increased stride duration and decreased walking speed were associated with lower functional walking scores, and the presence of a cane or walker. Overall, there was no group-wide mean walking speed differences between methods, though the waist method overestimated stride length and walking speed in those with more significant gait dysfunction compared to the foot method. Reconstruction of movement using the foot-based sensor resulted in route segments that were 94 ± 1% standard error of the mean (SEM) the length of a centre-to-centre hallway reference vector, with an angular error of 0.66 ± 0.28° SEM.

Quantification of spatiotemporal parameter behavior during walking speed transitions.

The biomechanics of constant speed walking have been well quantified, but little is known about transitions between walking speeds. Spatiotemporal behavior (step time, length, and speed) has been investigated in starting, stopping, and walking to running transitions, but speed transitions during walking have yet to be investigated. This study quantified the spatiotemporal parameter behavior during walking speed transitions with a range of magnitudes (or differences between pre- and post-transition normalized speeds ranging from 0.03 to 0.13, or approximately 1.18 m/s to 1.58 m/s). 23 healthy adults walked on a treadmill at five different constant speeds for one minute each to establish a baseline. They then performed walking speed transitions, in which they walked on the treadmill as it randomly changed between the five speeds. Linear mixed effect models showed that subjects converged to slightly different post-transition step time and step length averages than established in the constant speed baseline, but the differences are likely too small to be meaningful (on the order of 0.01 s and 0.01 m). When diverging from the pre-transition speed, subjects either diverged in only step time (with step length remaining the same), only step length (with step time remaining the same), or both step time and step length to reach the post-transition speed, with the behavior strongly tied to the magnitude of the speed transition (p<0.001). Step time often overshot the new value before converging. The number of steps required for each parameter to converge increased with increasing transition magnitude (p<0.001) and was consistently higher at all magnitudes for speed than step time and length (p<0.001). In summary, transition magnitude affected the spatiotemporal behavior during walking speed transitions. Further, step time, length, and speed all exhibited slightly different divergence and convergence behavior during transitions.

The Effect of Stiff Foot Plate Length on Walking Gait Mechanics.

Exoskeletons are increasingly being used to treat gait pathologies. Many of these exoskeletons use a foot plate to actuate the foot, altering the effective stiffness of the foot. Stiffness of the biological foot and ankle plays an important role in the energy modulating function of the leg, so it is important to examine how a foot plate in and of itself impacts gait. Therefore, this study quantified how foot plates themselves alter the walking gait of 16 healthy young adults. The effect of the foot plate length was also examined through the use of two foot plates, one that ended at the metatarsals and one that extended past the toes, about 20% longer. Gait parameters examined included walking speed, step frequency, joint angles for the hip, knee, ankle, forefoot, and toe, ground reaction forces (GRF), and foot-ankle power. The most significant changes were caused by the full plate, which caused an average 13% decrease in the ankle range of motion (ROM) and a 23% decrease in forward GRF at push off. The shorter plate also decreased ankle ROM to a lesser degree. This indicates that the presence of a foot plate impacted foot and ankle kinematics. However, the presence of the tested foot plate had no effect on walking speed or hip or knee kinematics. This indicates that subjects were mostly able to compensate both kinematically and energetically via their foot and ankle for the increased foot stiffness due to the tested foot plate.

Characterization of statistical persistence in joint angle variation during walking.

The objective of this study was to characterize joint angle variation across strides. Specifically, the statistical persistence of variations were quantified using the Hurst exponent. If a time series exhibits statistical persistence, then a parameter which is smaller (or larger) than average will tend to be followed by additional values that are also smaller (or larger) than average. Human walking has statistical persistence between stride durations. Variation in stride duration must arise from variation in the motion of the leg segments during walking. It is unclear, however, if the joint angle variation also exhibits statistical persistence. This study examined kinematic data collected from nine healthy adults walking for 10 min at a self-selected comfortable speed on a treadmill. The joint angle variation in the lower limbs was parameterized using first-order Fourier series which in turn were described by frequency and magnitude coefficients for each stride. To determine if the joint angle variation exhibited statistical persistence, the Hurst exponent was found for each coefficient at each joint. The mean Hurst exponents were 0.54 for the frequency coefficients and 0.61 for the magnitude coefficients. Neither the frequency or magnitude coefficients exhibited statistically significant persistence, although some of the magnitude coefficients were close to reaching statistical significance. This suggests that joint angle variability in healthy adults does not directly produce the statistical persistence observed in stride duration fluctuations.

Gait modification when decreasing double support percentage.

Much is still unknown about walking stability, including which aspects of gait contribute to higher stability. Walking stability appears to be related to walking speed, although the exact relationship is unclear. As walking speed decreases, the double support (DS) period of gait increases both in time and as a percentage of the gait cycle. Because humans have more control over their center of mass movement during DS, increasing DS duration may alter stability. This study examined how human gait is affected by changing DS percentage independent of walking speed. Sixteen young, healthy adults walked on a treadmill at a single speed for six one-minute trials. These trials included normal gait as well as longer- and shorter-than-normal DS percentage gaits. Subjects were consistently able to decrease DS percentage but had difficulty increasing DS percentage. In some cases, subjects altered their cadence when changing DS percentage, particularly when attempting to increase DS percentage. The changes to gait when decreasing DS percentage were similar to changes when increasing walking speed but occurred mainly during the swing period. These changes include increased hip and knee flexion during the swing period, increased swing foot height, and larger magnitude peaks in ground reaction forces. The changes in gait when attempting to increase DS percentage trended toward changes when decreasing walking speed. Altering DS percentage induced gait changes that were similar to, yet clearly distinct from, gait changes due to walking speed. Further, the difficulty of increasing DS percentage when walking at a constant speed suggests that people walk more slowly when they want to increase time spent in DS.

Toward Unified Control of a Powered Prosthetic Leg: A Simulation Study.

This brief presents a novel control strategy for a powered knee-ankle prosthesis that unifies the entire gait cycle, eliminating the need to switch between controllers during different periods of gait. A reduced-order Discrete Fourier Transformation (DFT) is used to define virtual constraints that continuously parameterize periodic joint patterns as functions of a mechanical phasing variable. In order to leverage the provable stability properties of Hybrid Zero Dynamics (HZD), hybrid-invariant Bézier polynomials are converted into unified DFT virtual constraints for various walking speeds. Simulations of an amputee biped model show that the unified prosthesis controller approximates the behavior of the original HZD design under ideal scenarios and has advantages over the HZD design when hybrid invariance is violated by mismatches with the human controller. Two implementations of the unified virtual constraints, a feedback linearizing controller and a more practical joint impedance controller, produce similar results in simulation.

Stable, Robust Hybrid Zero Dynamics Control of Powered Lower-Limb Prostheses.

To improve the quality of life for lower-limb amputees, powered prostheses are being developed. Advanced control schemes from the field of bipedal robots, such as hybrid zero dynamics (HZD), may provide great performance. HZD-based control specifies the motion of the actuated joints using output functions to be zeroed, and the required torques are calculated using input-output linearization. For one-step periodic gaits, there is an analytic metric of stability. To apply HZD-based control on a powered prosthesis, several modifications must be made. Because the prosthesis and amputee are only connected via the socket, the prosthesis controller does not have access to the full state of the biped, which decentralizes the form of the input-output linearization. The differences between the amputated and contralateral sides result in a two-step periodic gait, which requires the orbital stability metric to be extended. In addition, because human gait is variable, the prosthesis controller must be robust to continuous moderate perturbations. This robustness is proved using local input-to-state stability and demonstrated with simulations of an above-knee amputee model.

Prosthetic Leg Control in the Nullspace of Human Interaction.

Recent work has extended the control method of virtual constraints, originally developed for autonomous walking robots, to powered prosthetic legs for lower-limb amputees. Virtual constraints define desired joint patterns as functions of a mechanical phasing variable, which are typically enforced by torque control laws that linearize the output dynamics associated with the virtual constraints. However, the output dynamics of a powered prosthetic leg generally depend on the human interaction forces, which must be measured and canceled by the feedback linearizing control law. This feedback requires expensive multi-axis load cells, and actively canceling the interaction forces may minimize the human's influence over the prosthesis. To address these limitations, this paper proposes a method for projecting virtual constraints into the nullspace of the human interaction terms in the output dynamics. The projected virtual constraints naturally render the output dynamics invariant with respect to the human interaction forces, which instead enter into the internal dynamics of the partially linearized prosthetic system. This method is illustrated with simulations of a transfemoral amputee model walking with a powered knee-ankle prosthesis that is controlled via virtual constraints with and without the proposed projection.

Characterizing and modeling the joint-level variability in human walking.

Although human gait is often assumed to be periodic, significant variability exists. This variability appears to provide different information than the underlying periodic signal, particularly about fall risk. Most studies on variability have either used step-to-step metrics such as stride duration or point-wise standard deviations, neither of which explicitly capture the joint-level variability as a function of time. This work demonstrates that a second-order Fourier series for stance joints and a first-order Fourier series for swing joints can accurately capture the variability in joint angles as a function of time on a per-step basis for overground walking at the self-selected speed. It further demonstrates that a total of seven normal distributions, four linear relationships, and twelve continuity constraints can be used to describe how the Fourier series vary between steps. The ability of the proposed method to create curves that match human joint-level variability was evaluated both qualitatively and quantitatively using randomly generated curves.

Incorporating Human-like Walking Variability in an HZD-Based Bipedal Model.

Predictive simulations of human walking could be used to investigate a wide range of questions. Promising moderately complex models have been developed using the robotics control technique hybrid zero dynamics (HZD). Existing simulations of human walking only consider the mean motion, so they cannot be used to investigate fall risk, which is correlated with variability. This work determines how to incorporate human-like variability into an HZD-based healthy human model to generate a more realistic gait. The key challenge is determining how to combine the existing mathematical description of variability with the dynamic model so that the biped is still able to walk without falling. To do so, the commanded motion is augmented with a sinusoidal variability function and a polynomial correction function. The variability function captures the variation in joint angles while the correction function prevents the variability function from growing uncontrollably. The necessity of the correction function and the improvements with a reduction of stance ankle variability are demonstrated via simulations. The variability in temporal measures is shown to be similar to experimental values.

Hybrid Invariance and Stability of a Feedback Linearizing Controller for Powered Prostheses.

The development of powered lower-limb prostheses has the potential to significantly improve amputees' quality of life. By applying advanced control schemes, such as hybrid zero dynamics (HZD), to prostheses, more intelligent prostheses could be designed. Originally developed to control bipedal robots, HZD-based control specifies the motion of the actuated degrees of freedom using output functions to be zeroed, and the required torques are calculated using feedback linearization. Previous work showed that an HZD-like prosthesis controller can successfully control the stance period of gait. This paper shows that an HZD-based prosthesis controller can be used for the entire gait cycle and that feedback linearization can be performed using only information measured with on-board sensors. An analytic metric for orbital stability of a two-step periodic gait is developed. The results are illustrated in simulation.

Unifying the Gait Cycle in the Control of a Powered Prosthetic Leg.

This paper presents a novel control strategy for an above-knee powered prosthetic leg that unifies the entire gait cycle, eliminating the need to switch between controllers during different periods of gait. Current control methods divide the gait cycle into several sequential periods each with independent controllers, resulting in many patient-specific control parameters and switching rules that must be tuned by clinicians. Having a single controller could reduce the number of control parameters to be tuned for each patient, thereby reducing the clinical time and effort involved in fitting a powered prosthesis for a lower-limb amputee. Using the Discrete Fourier Transformation, a single virtual constraint is derived that exactly characterizes the desired actuated joint motion over the entire gait cycle. Because the virtual constraint is defined as a periodic function of a monotonically increasing phase variable, no switching or resetting is necessary within or across gait cycles. The output function is zeroed using feedback linearization to produce a single, unified controller. The method is illustrated with simulations of a powered knee-ankle prosthesis in an amputee biped model and with examples of systematically generated output functions for different walking speeds.

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.