Dynamic Stability of Passive Bipedal Walking on Rough Terrain:A Preliminary Simulation Study

A simplified 2D passive dynamic model was simulated to walk down on a rough slope surface defined by deterministic profiles to investigate how the walking stability changes with increasing surface roughness.Our results show that the passive walker can walk on rough surfaces subject to surface roughness up to approximately 0.1％ of its leg length.This indicates that bipedal walkers based on passive dynamics may possess some intrinsic stability to adapt to rough terrains although the maximum roughness they can tolerate is small.Orbital stability method was used to quantify the walking stability before the walker started to fall over.It was found that the average maximum Floquet multiplier increases with surface roughness in a non-linear form.Although the passive walker remained orbitally stable for all the simulation cases,the results suggest that the possibility of the bipedal model moving away from its limit cycle increases with the surface roughness if subjected to additional perturbations.The number of consecutive steps before falling was used to measure the walking stability after the passive walker started to fall over.The results show that the number of steps before falling decreases exponentially with the increase in surface roughness.When the roughness magnitude approached to 0.73％ of the walker's leg length,it fell down to the ground as soon as it entered into the uneven terrain.It was also found that shifting the phase angle of the surface profile has apparent affect on the system stability.This is probably because point contact was used to simulate the heel strikes and the resulted variations in system states at heel strikes may have pronounced impact on the passive gaits,which have narrow basins of attraction.These results would provide insight into how the dynamic stability of passive bipedal walkers evolves with increasing surface roughness.     

Dynamic stability of passive dynamic walking on an irregular surface

Falls that occur during walking are a significant health problem. One of the greatest impediments to solve this problem is that there is no single obviously "correct" way to quantify walking stability. While many people use variability as a proxy for stability, measures of variability do not quantify how the locomotor system responds to perturbations. The purpose of this study was to determine how changes in walking surface variability affect changes in both locomotor variability and stability. We modified an irreducibly simple model of walking to apply random perturbations that simulated walking over an irregular surface. Because the model's global basin of attraction remained fixed, increasing the amplitude of the applied perturbations directly increased the risk of falling in the model. We generated ten simulations of 300 consecutive strides of walking at each of six perturbation amplitudes ranging from zero (i.e., a smooth continuous surface) up to the maximum level the model could tolerate without falling over. Orbital stability defines how a system responds to small (i.e., "local") perturbations from one cycle to the next and was quantified by calculating the maximum Floquet multipliers for the model. Local stability defines how a system responds to similar perturbations in real time and was quantified by calculating short-term and long-term local exponential rates of divergence for the model. As perturbation amplitudes increased, no changes were seen in orbital stability (r(2)=2.43%; p=0.280) or long-term local instability (r(2)=1.0%; p=0.441). These measures essentially reflected the fact that the model never actually "fell" during any of our simulations. Conversely, the variability of the walker's kinematics increased exponentially (r(2)>or=99.6%; p<0.001) and short-term local instability increased linearly (r(2)=88.1%; p<0.001). These measures thus predicted the increased risk of falling exhibited by the model. For all simulated conditions, the walker remained orbitally stable, while exhibiting substantial local instability. This was because very small initial perturbations diverged away from the limit cycle, while larger initial perturbations converged toward the limit cycle. These results provide insight into how these different proposed measures of walking stability are related to each other and to risk of falling.     

Effects of walking speed, strength and range of motion on gait stability in healthy older adults

Falls pose a tremendous risk to those over 65 and most falls occur during locomotion. Older adults commonly walk slower, which many believe helps improve walking stability. While increased gait variability predicts future fall risk, increased variability is also caused by walking slower. Thus, we need to better understand how differences in age and walking speed independently affect dynamic stability during walking. We investigated if older adults improved their dynamic stability by walking slower, and how leg strength and flexibility (passive range of motion (ROM)) affected this relationship. Eighteen active healthy older and 17 healthy younger adults walked on a treadmill for 5min each at each of 5 speeds (80-120% of preferred). Local divergence exponents and maximum Floquet multipliers (FM) were calculated to quantify each subject's inherent local dynamic stability. The older subjects walked with the same preferred walking speeds as the younger subjects (p=0.860). However, these older adults still exhibited greater local divergence exponents (p<0.0001) and higher maximum FM (p<0.007) than the younger adults at all walking speeds. These older adults remained more locally unstable (p<0.04) even after adjusting for declines in both strength and ROM. In both age groups, local divergence exponents decreased at slower speeds and increased at faster speeds (p<0.0001). Maximum FM showed similar changes with speed (p<0.02). Both younger and older adults exhibited decreased instability by walking slower, in spite of increased variability. These increases in dynamic instability might be more sensitive indicators of future fall risk than changes in gait variability.     

Dynamic stability of human walking in visually and mechanically destabilizing environments

Understanding how humans remain stable during challenging locomotor activities is critical to developing effective tests to diagnose patients with increased fall risk. This study determined if different continuous low-amplitude perturbations would induce specific measureable changes in measures of dynamic stability during walking. We applied continuous pseudo-random oscillations of either the visual scene or support surface in either the anterior-posterior or mediolateral directions to subjects walking in a virtual environment with speed-matched optic flow. Floquet multipliers and short-term local divergence exponents both increased (indicating greater instability) during perturbed walking. These responses were generally much stronger for body movements occurring in the same directions as the applied perturbations. Likewise, subjects were more sensitive to both visual and mechanical perturbations applied in the mediolateral direction than to those applied in the anterior-posterior direction, consistent with previous experiments and theoretical predictions. These responses were likewise consistent with subjects' anecdotal perceptions of which perturbation conditions were most challenging. Contrary to the Floquet multipliers and short-term local divergence exponents, which both increased, long-term local divergence exponents decreased during perturbed walking. However, this was consistent with specific changes in the mean log divergence curves, which indicated that subjects' movements reached their maximum local divergence limits more quickly during perturbed walking. Overall, the Floquet multipliers were less sensitive, but reflected greater specificity in their responses to the different perturbation conditions. Conversely, the short-term local divergence exponents exhibited less specificity in their responses, but were more sensitive measures of instability in general.     

Can stability really predict an impending slip-related fall among older adults?

The primary purpose of this study was to systematically evaluate and compare the predictive power of falls for a battery of stability indices, obtained during normal walking among community-dwelling older adults. One hundred and eighty seven community-dwelling older adults participated in the study. After walking regularly for 20 strides on a walkway, participants were subjected to an unannounced slip during gait under the protection of a safety harness. Full body kinematics and kinetics were monitored during walking using a motion capture system synchronized with force plates. Stability variables, including feasible-stability-region measurement, margin of stability, the maximum Floquet multiplier, the Lyapunov exponents (short- and long-term), and the variability of gait parameters (including the step length, step width, and step time), were calculated for each subject. Sensitivity of predicting slip outcome (fall vs. recovery) was examined for each stability variable using logistic regression. Results showed that the feasible-stability-region measurement predicted fall incidence among these subjects with the highest sensitivity (68.4%). Except for the step width (with an sensitivity of 60.2%), no other stability variables could differentiate fallers from those who did not fall for the sample included in this study. The findings from the present study could provide guidance to identify individuals at increased risk of falling using the feasible-stability-region measurement or variability of the step width.     

Kinematic variability and local dynamic stability of upper body motions when walking at different speeds

A ubiquitous characteristic of elderly and patients with gait disabilities is that they walk slower than healthy controls. Many clinicians assume these patients walk slower to improve their stability, just as healthy people slow down when walking across ice. However, walking slower also leads to greater variability, which is often assumed to imply deteriorated stability. If this were true, then slowing down would be completely antithetical to the goal of maintaining stability. This study sought to resolve this paradox by directly quantifying the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability. Eleven young healthy subjects walked on a motorized treadmill at five different speeds. Three-dimensional movements of a single marker placed over the first thoracic vertebra were recorded during continuous walking. Mean stride-to-stride standard deviations and maximum finite-time Lyapunov exponents were computed for each time series to quantify the variability and local dynamic stability, respectively, of these movements. Quadratic regression analyses of the dependent measures vs. walking speed revealed highly significant U shaped trends for all three mean standard deviations, but highly significant linear trends, with significant or nearly significant quadratic terms, for five of the six finite-time Lyapunov exponents. Subjects exhibited consistently better local dynamic stability at slower speeds for these five measures. These results support the clinically based intuition that people who are at increased risk of falling walk slower to improve their stability, even at the cost of increased variability.     

Stable bipedal walking with a swing-leg protraction strategy

In bipedal locomotion, swing-leg protraction and retraction refer to the forward and backward motion, respectively, of the swing-leg before touchdown. Past studies have shown that swing-leg retraction strategy can lead to stable walking. We show that swing-leg protraction can also lead to stable walking. We use a simple 2D model of passive dynamic walking but with the addition of an actuator between the legs. We use the actuator to do full correction of the disturbance in a single step (a one-step dead-beat control). Specifically, for a given limit cycle we perturb the velocity at mid-stance. Then, we determine the foot placement strategy that allows the walker to return to the limit cycle in a single step. For a given limit cycle, we find that there is swing-leg protraction at shallow slopes and swing-leg retraction at steep slopes. As the limit cycle speed increases, the swing-leg protraction region increases. On close examination, we observe that the choice of swing-leg strategy is based on two opposing effects that determine the time from mid-stance to touchdown: the walker speed at mid-stance and the adjustment in the step length for one-step dead-beat control. When the walker speed dominates, the swing-leg retracts but when the step length dominates, the swing-leg protracts. This result suggests that swing-leg strategy for stable walking depends on the model parameters, the terrain, and the stability measure used for control. This novel finding has a clear implication in the development of controllers for robots, exoskeletons, and prosthetics and to understand stability in human gaits.     

An upper-body can improve the stability and efficiency of passive dynamic walking

The compass-gait walker proposed by McGeer can walk down a shallow slope with a self-stabilizing gait that requires no actuation or control. However, as the slope goes to zero so does the walking speed, and dynamic gait stability is only possible over a very narrow range of slopes. Gomes and Ruina have results demonstrating that by adding a torso to the compass-gait walker, it can walk passively on level-ground with a non-infinitesimal constant average speed. However, the gait involves exaggerated joint movements, and for energetic reasons horizontal passive dynamic walking cannot be stable. We show in this research that in addition to collision-free walking, adding a torso improves stability and walking speed when walking downhill. Furthermore, adding arms to the torso results in a collision-free periodic gait with natural-looking torso and limb movements. Overall, in contrast to the suggestions that active control may be needed to balance an upper-body on legs, it turns out that the upper and lower bodies can be integrated to improve the stability, efficiency and speed of a passive dynamic walker.     

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.     

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.     

Effects of perturbation magnitude on dynamic stability when walking in destabilizing environments

External perturbations applied to the walking surface or visual field can challenge an individual's ability to maintain stability during walking. Accurately quantifying and predicting changes in stability during walking will further our understanding of how individuals respond to challenges encountered during daily life and guide the development of assessments and rehabilitation interventions for individuals at increased risk of falling. This study is the first to determine how orbital and local dynamic stability metrics, including maximum Floquet multipliers and local divergence exponents, change in response to continuous mediolateral visual and surface perturbations of different amplitudes. Eleven healthy individuals walked in a fully immersive virtual environment. Participants completed two 3-min walking trials each under the following nine conditions: no perturbations, surface perturbations at each of 3 amplitudes, and visual perturbations at each of 5 amplitudes. All perturbations were applied as continuous pseudo-random oscillations. During both surface and visual perturbations, individuals were significantly more orbitally and locally unstable compared to un-perturbed walking. As walking surface perturbation amplitudes increased, individuals were more orbitally (but not locally) unstable. As visual perturbation amplitudes increased, individuals were more locally (but not orbitally) unstable between lower and higher amplitudes. Overall, these dynamic stability metrics were much less sensitive to changes in perturbation amplitudes than to differences between un-perturbed and perturbed walking, or to differences between mechanical and visual perturbations. This suggests that the type of perturbation(s) applied has a far greater impact than the magnitude of those perturbations in determining the response that will be elicited.     

Reliability and Minimum Detectable Change of Temporal-Spatial,Kinematic, and Dynamic Stability Measures during Perturbed Gait

Temporal-spatial, kinematic variability, and dynamic stability measures collected during perturbation-based assessment paradigms are often used to identify dysfunction associated with gait instability. However, it remains unclear which measures are most reliable for detecting and tracking responses to perturbations. This study systematically determined the between-session reliability and minimum detectable change values of temporal-spatial, kinematic variability, and dynamic stability measures during three types of perturbed gait. Twenty young healthy adults completed two identical testing sessions two weeks apart, comprised of an unperturbed and three perturbed (cognitive, physical, and visual) walking conditions in a virtual reality environment. Within each session, perturbation responses were compared to unperturbed walking using paired t-tests. Between-session reliability and minimum detectable change values were also calculated for each measure and condition. All temporal-spatial, kinematic variability and dynamic stability measures demonstrated fair to excellent between-session reliability. Minimal detectable change values, normalized to mean values ranged from 1–50%. Step width mean and variability measures demonstrated the greatest response to perturbations with excellent between-session reliability and low minimum detectable change values. Orbital stability measures demonstrated specificity to perturbation direction and sensitivity with excellent between-session reliability and low minimum detectable change values. We observed substantially greater between-session reliability and lower minimum detectable change values for local stability measures than previously described which may be the result of averaging across trials within a session and using velocity versus acceleration data for reconstruction of state spaces. Across all perturbation types, temporal-spatial, orbital and local measures were the most reliable measures with the lowest minimum detectable change values, supporting their use for tracking changes over multiple testing sessions. The between-session reliability and minimum detectable change values reported here provide an objective means for interpreting changes in temporal-spatial, kinematic variability, and dynamic stability measures during perturbed walking which may assist in identifying instability.     

Influence of simulated neuromuscular noise on movement variability and fall risk in a 3D dynamic walking model

People at risk of falling exhibit increased gait variability, which may predict future falls. However, the causal mechanisms underlying these correlations are not well known. Increased neuronal noise associated with aging likely leads to increased gait variability, which could in turn lead to increased fall risk. This paper presents a model of how changes in neuromuscular noise independently affect gait variability and probability of falling, and aims to determine the extent to which changes in gait variability directly predict fall risk. We used a dynamic walking model that incorporates a lateral step controller to maintain lateral stability. Noise was applied to this controller to approximate neuromuscular noise in humans. Noise amplitude was varied between low amplitudes that did not induce falls and high amplitudes for which the model always fell. With increases in noise amplitude, the model fell more often and after fewer steps. Gait variability increased with noise amplitude and predicted increased probability of falling. Importantly, these relationships were not linear. At either low gait variability or very high gait variability, small increases in noise and variability affected probability of falling very little. Conversely, at intermediate noise and/or variability levels, the same small increases resulted in large increases in probability of falling. Our results validate the idea that age-related increases in neuromuscular noise likely play a direct contributing role in increasing fall risk. However, neuromuscular noise remains only one of many important factors that need to be considered. These findings have important implications for fall prevention research and practice.     

Differences between local and orbital dynamic stability during human walking

Currently there is no commonly accepted way to define, much less quantify, locomotor stability. In engineering, "orbital stability" is defined using Floquet multipliers that quantify how purely periodic systems respond to perturbations discretely from one cycle to the next. For aperiodic systems, "local stability" is defined by local divergence exponents that quantify how the system responds to very small perturbations continuously in real time. Triaxial trunk accelerations and lower extremity sagittal plane joint angles were recorded from ten young healthy subjects as they walked for 10 min over level ground and on a motorized treadmill at the same speed. Maximum Floquet multipliers (Max FM) were computed at each percent of the gait cycle (from 0% to 100%) for each time series to quantify the orbital stability of these movements. Analyses of variance comparing Max FM values between walking conditions and correlations between Max FM values and previously published local divergence exponent results were computed. All subjects exhibited orbitally stable walking kinematics (i.e., magnitudes of Max FM < 1.0), even though these same kinematics were previously found to be locally unstable. Variations in orbital stability across the gait cycle were generally small and exhibited no systematic patterns. Walking on the treadmill led to small, but statistically significant improvements in the orbital stability of mediolateral (p = 0.040) and vertical (p = 0.038) trunk accelerations and ankle joint kinematics (p = 0.002). However, these improvements were not exhibited by all subjects (p < or = 0.012 for subject x condition interaction effects). Correlations between Max FM values and previously published local divergence exponents were inconsistent and 11 of the 12 comparisons made were not statistically significant (r2 < or = 19.8%; p > or = 0.049). Thus, the variability inherent in human walking, which manifests itself as local instability, does not substantially adversely affect the orbital stability of walking. The results of this study will allow future efforts to gain a better understanding of where the boundaries lie between locally unstable movements that remain orbitally stable and those that lead to global instability (i.e., falling).     

Active and passive contributions to joint kinetics during walking in older adults

The objectives of this study were to characterize the active and passive contributions to joint kinetics during walking in healthy young and older adults, and assess whether isokinetic ankle strength is associated with ankle power output during walking. Twenty healthy young (18–35 years) and 20 healthy older (65–85 years) adults participated in this study. We measured subject-specific passive-elastic joint moment–angle relationships in the lower extremity and tested maximum isokinetic ankle strength at 30 deg/s. Passive moment–angle relationships were used to estimate active and passive joint moment, power, and work quantities during walking at 80%, 100% and 120% of preferred walking speed. There were no significant differences in walking speed, step length, or cadence between the older and young adults. However, the older adults produced significantly more net positive work at the hip but less net positive work at the ankle at all walking speeds. Passive contributions to hip and ankle work did not significantly differ between groups, inferring that the older adults generated the additional hip work actively. Maximum isokinetic ankle strength was significantly less in the older adults, and correlated with peak positive plantar-flexor power at both the preferred and fast walking speeds. The results of this study suggest that age-related shifts in joint kinetics do not arise as a result of increased passive hip joint stiffness, but seem to be reflected in plantar-flexor weakness.     

The effects of sensory loss and walking speed on the orbital dynamic stability of human walking

Peripheral sensory feedback is believed to contribute significantly to maintaining walking stability. Patients with diabetic peripheral neuropathy have a greatly increased risk of falling. Previously, we demonstrated that slower walking speeds in neuropathic patients lead to improved local dynamic stability. However, all subjects exhibited significant local instability during walking, even though no subject fell or stumbled during testing. The present study was conducted to determine if and how significant changes in peripheral sensation and walking speed affect orbital stability during walking. Trunk and lower extremity kinematics were examined from two prior experiments that compared patients with significant neuropathy to healthy controls and walking at multiple different speeds in young healthy subjects. Maximum Floquet multipliers were computed for each time series to quantify the orbital stability of these movements. All subjects exhibited orbitally stable walking kinematics, even though these same kinematics were previously shown to be locally unstable. Differences in orbital stability between neuropathic and control subjects were small and, with the exception of knee joint movements (p=0.001), not statistically significant (0.380p0.946). Differences in knee orbital stability were not mediated by differences in walking speed. This was supported by our finding that although orbital stability improved slightly with slower walking speeds, the correlations between walking speed and orbital stability were generally weak (r(2)16.7%). Thus, neuropathic patients do not gain improved orbital stability as a result of slowing down and do not experience any loss of orbital stability because of their sensory deficits.     

Energetics of actively powered locomotion using the simplest walking model

We modified an irreducibly simple model of passive dynamic walking to walk on level ground, and used it to study the energetics of walking and the preferred relationship between speed and step length in humans. Powered walking was explored using an impulse applied at toe-off immediately before heel strike, and a torque applied on the stance leg. Although both methods can supply energy through mechanical work on the center of mass, the toe-off impulse is four times less costly because it decreases the collision loss at heel strike. We also studied the use of a hip torque on the swing leg that tunes its frequency but adds no propulsive energy to gait. This spring-like actuation can further reduce the collision loss at heel strike, improving walking energetics. An idealized model yields a set of simple power laws relating the toe-off impulses and effective spring constant to the speed and step length of the corresponding gait. Simulations incorporating nonlinear equations of motion and more realistic inertial parameters show that these power laws apply to more complex models as well.     

Dynamics and stability of muscle activations during walking in healthy young and older adults

To facilitate stable walking, humans must generate appropriate motor patterns and effective corrective responses to perturbations. Yet most EMG analyses do not address the continuous nature of muscle activation dynamics over multiple strides. We compared muscle activation dynamics in young and older adults by defining a multivariate state space for muscle activity. Eighteen healthy older and 17 younger adults walked on a treadmill for 2 trials of 5 min each at each of 5 controlled speeds (80–120% of preferred). EMG linear envelopes of v. lateralis, b. femoris, gastrocnemius, and t. anterior of the left leg were obtained. Interstride variability, local dynamic stability (divergence exponents), and orbital stability (maximum Floquet multipliers; FM) were calculated. Both age groups exhibited similar preferred walking speeds (p=0.86). Amplitudes and variability of individual EMG linear envelopes increased with speed (p<0.01) in all muscles but gastrocnemius. Older adults also exhibited greater variability in b. femoris and t. anterior (p<0.004). When comparing continuous multivariate EMG dynamics, older adults demonstrated greater local and orbital instability of their EMG patterns (p<0.01). We also compared how muscle activation dynamics were manifested in kinematics. Local divergence exponents were strongly correlated between kinematics and EMG, independent of age and walking speed, while variability and max FM were not. These changes in EMG dynamics may be related to increased neuromotor noise associated with aging and may indicate subtle deterioration of gait function that could lead to future functional declines.     

Slower speeds in patients with diabetic neuropathy lead to improved local dynamic stability of continuous overground walking

Patients with diabetic peripheral neuropathy are significantly more likely to fall while walking than subjects with intact sensation. While it has been suggested that these patients walk slower to improve locomotor stability, slower speeds are also associated with increased locomotor variability, and increased variability has traditionally been equated with loss of stability. If the latter were true, this would suggest that slowing down, as a locomotor control strategy, should be completely antithetical to the goal of maintaining stability. The present study resolves these seemingly paradoxical findings by using methods from nonlinear time series analysis to directly quantify the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability. Fourteen patients with severe peripheral neuropathy and 12 gender-, age-, height-, and weight-matched non-diabetic controls participated. Sagittal plane angles of the right hip, knee, and ankle joints and tri-axial accelerations of the trunk were measured during 10 min of continuous overground walking at self-selected speeds. Maximum finite-time Lyapunov exponents were computed for each time series to quantify the local dynamic stability of these movements. Neuropathic patients exhibited slower walking speeds and better local dynamic stability of upper body movements in the horizontal plane than did control subjects. The differences in local dynamic stability were significantly predicted by differences in walking speed, but not by differences in sensory status. These results support the hypothesis that reductions in walking speed are a compensatory strategy used by neuropathic patients to maintain dynamic stability of the upper body during level walking.     

Energetics and passive dynamics of the ankle in downhill walking

This study investigated the energetics of the human ankle during the stance phase of downhill walking with the goal of modeling ankle behavior with a passive spring and damper mechanism. Kinematic and kinetic data were collected on eight male participants while walking down a ramp with inclination varying from 0° to 8°. The ankle joint moment in the sagittal plane was calculated using inverse dynamics. Mechanical energy injected or dissipated at the ankle joint was computed by integrating the power across the duration of the stance phase. The net mechanical energy of the ankle was approximately zero for level walking and monotonically decreased (i.e., became increasingly negative) during downhill walking as the slope decreased. The indication is that the behavior of the ankle is energetically passive during downhill walking, playing a key role in dissipating energy from one step to the next. A passive mechanical model consisting of a pin joint coupled with a revolute spring and damper was fit to the ankle torque and its parameters were estimated for each downhill slope using linear regression. The passive model demonstrated good agreement with actual ankle dynamics as indicated by low root-mean-square error values. These results indicate the stance phase behavior of the human ankle during downhill walking may be effectively duplicated by a passive mechanism with appropriately selected spring and damping characteristics.