Comparing system identification techniques for identifying human-like walking controllers

Abstract

While human walking has been well studied, the exact controller is unknown. This paper used human experimental walking data and system identification techniques to infer a human-like controller for a spring-loaded inverted pendulum (SLIP) model. Because the best system identification technique is unknown, three methods were used and compared. First, a linear system was found using ordinary least squares. A second linear system was found that both encoded the linearized SLIP model and matched the first linear system as closely as possible. A third nonlinear system used sparse identification of nonlinear dynamics (SINDY). When directly mapping states from the start to the end of a step, all three methods were accurate, with errors below 10% of the mean experimental values in most cases. When using the controllers in simulation, the errors were significantly higher but remained below 10% for all but one state. Thus, all three system identification methods generated accurate system models. Somewhat surprisingly, the linearized system was the most accurate, followed closely by SINDY. This suggests that nonlinear system identification techniques are not needed when finding a discrete human gait controller, at least for unperturbed walking. It may also suggest that human control of normal, unperturbed walking is approximately linear.

A control Hamiltonian-preserving discretisation for optimal control

“…Inverted elastic pendulum system is often used to model the self-stabilising characteristics of locomotion in humans, animals and biped robots [33,34]. In this section, we study the non-linear self-stabilising behaviour of inverted elastic pendulum system in the framework of optimal control theory.…”

Identification of a Step-And-Brake Controller of a Human Based on Prediction of Capturability

“…While lots of knowledge about how human body parts contribute to walking has been accumulated particularly in the fields of physiology and clinical medicine, it is also necessary to know how those parts are coordinated into the whole-body motion in order to properly diagnose and effectively aid humans’ locomotion abilities. In this regard, it has been demanded to find a plausible mathematical model of the humans’ locomotion controller ( Cavagna and Margaria, 1966 ; Yamashita et al, 1972 ; Alexander, 1976 ; McMahon, 1984 ; Ren et al, 2006 ; Schmitthenner and Martin, 2021 ), which is still challenging.…”