Data-Driven Modelling of the Non-Linear Dynamics of Passive Lower-Limb Prosthetic Systems

Abstract

Modelling the non-linear dynamics of prosthetic feet is an important tool for linking prosthesis mechanical properties to end-user outcomes. There has been a renewed interest in data-driven modelling of dynamical systems, with the development of the Extended Dynamic Mode Decomposition with control (eDMDc), and the Sparse Identification of Non-Linear Dynamics with Control (SINDYc). These algorithms do not require prior information about the system, including mechanical configuration, and are data-driven. The aim of this study was to assess feasibility and accuracy of applying these data-driven algorithms to model prosthesis non-linear load response dynamics. Different combinations of a dynamic response foot, a hydraulic ankle unit, and three shock absorbing pylons of varying resistance were tested loaded and unloaded at three orientations reflecting critical positions during the stance phase of walking. We tested two different data-driven algorithms, the eDMDc, with two different kernels, and the SINDYc, which regresses the coefficients for a non-linear ordinary differential equation. Each algorithm was able to model the non-linear prosthesis dynamics, but the SINDYc outperformed the eDMDc methods with a root mean square error across orientations < 1.50 mm and a maximum error in peak displacement of 1.28 mm or 4% relative error. From the estimated SINDYc governing equation of the system dynamics, we were able to simulate different mechanical behavior by systematically varying parameter values, which offers a novel foundation for designing, controlling, and classifying prosthetic systems ultimately aimed at improving prosthesis user outcomes.