Application of Floquet Theory to Human Gait Kinematics and Dynamics

Abstract

In this work, the lower extremity physiological parameters are recorded during normal walking gait, and the dynamical systems theory is applied to determine a stability analysis. The human walking gait pattern of kinematic and dynamical data is approximated to periodic behavior. The embedding dimension analysis of the kinematic variable's time trace and use of Taken's theorem allows us to compute a reduced-order time series that retains the essential dynamics. In conjunction with Floquet theory, this approach can help determine the system's stability characteristics. The Lyapunov–Floquet (L-F) transformation application results in constructing an invariant manifold resembling the form of a simple oscillator system. It is also demonstrated that the simple oscillator system, when re-mapped back to the original domain, reproduces the original system's time evolution (hip angle or knee angle, for example). A reinitialization procedure is suggested that improves the accuracy between the processed data and actual data. The theoretical framework proposed in this work is validated with the experiments using a motion capture system.