Virtual slope control of a forward dynamic bipedal walker

Altering gait variability with an ankle exoskeleton

Exoskeletons can influence human gait. A healthy gait is characterized by a certain amount of variability compared to a non-healthy gait that has more inherent variability; however which exoskeleton assistance parameters are necessary to avoid increasing gait variability or to potentially lower gait variability below that of unassisted walking are unknown. This study investigated the interaction effects of exoskeleton timing and power on gait variability. Ten healthy participants walked on a treadmill with bilateral ankle-foot exoskeletons under ten conditions with different timing (varied from 36% to 54% of the stride) and power (varied from 0.2 to 0.5 W∙kg-1) combinations. We used the largest Lyapunov exponent (LyE) and maximum Floquet multiplier (FM) to evaluate the stride-to-stride fluctuations of the kinematic time series. We found the lowest LyE at the ankle and a significant reduction versus powered-off with exoskeleton power (summed for both legs) of 0.45 W∙kg-1 and actuation timing at 48% of the stride cycle. At the knee, a significant positive effect of power and a negative interaction effect of power and timing were found for LyE. We found significant positive interaction effects of the square of timing and power for LyE at the knee and hip joints. In contrast, the FM at the ankle increased with increasing power and later timing. We found a significant negative effect of power and a positive interaction effect of power and timing for FM at the knee and no significant effects of any of the exoskeleton parameters for FM at the hip. The ability of the exoskeleton to reduce the LyE at the ankle joint offers new possibilities in terms of altering gait variability, which could have applications for using exoskeletons as rehabilitation devices. Further efforts could examine if it is possible to simultaneously reduce the LyE and FM at one or more lower limb joints.

Formation mechanism of a basin of attraction for passive dynamic walking induced by intrinsic hyperbolicity

Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the difficulty in producing stable passive dynamic walking. The underlying mechanism that produces these geometric characteristics was not known. In this paper, we consider this from the viewpoint of dynamical systems theory, and we use the simplest walking model to clarify the mechanism that forms the basin of attraction for passive dynamic walking. We show that the intrinsic saddle-type hyperbolicity of the upright equilibrium point in the governing dynamics plays an important role in the geometrical characteristics of the basin of attraction; this contributes to our understanding of the stability mechanism of bipedal walking.

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 10min 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⩽0.012 for subject × 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⩽19.8%; p⩾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).