Adiabatic Invariant of Center-of-Mass Motion during Walking as a Dynamical Stability Constraint on Stride Interval Variability and Predictability

Abstract

Human walking exhibits properties of both stability and variability. On the one hand, the variability of the interval of time between heel strikes is autocorrelated, i.e., not randomly organized. On the other hand, walking is highly stereotyped and arguments from general mechanics suggest that the stability of gait can be assessed according to invariant properties. This study aims at proposing one of those invariants. Participants walked for 10 min at a natural pace, with and without a metronome indicating participants’ preferred step frequency. In both cases, we use different parameters to assess both the variability and stability of walking. We verify a known result: the metronome strongly alters the variability of the motion. However, despite the large variability changes, our proposed adiabatic invariant is preserved in both conditions, demonstrating the stability of gait. It appears as though our model reveals dynamical constraints that are “hidden” beyond apparent walking variability.