The Strange Attractor Model of Bipedal Locomotion and its Consequences on Motor Control

TL;DR

This paper introduces a novel attractor-based model of human bipedal locomotion that incorporates ankle strategies, improving the accuracy of trajectory predictions and offering insights for rehabilitation and assistive technology development.

Contribution

It presents a new mathematical model combining CoM dynamics with ankle strategies, validated against motion capture data from healthy subjects.

Findings

The model accurately replicates human walking trajectories.

It captures the regulation of stance phase similar to humans.

Supports the nonlinear attractor dynamics hypothesis in locomotion.

Abstract

Despite decades of study, many unknowns exist about the mechanisms governing human locomotion. Current models and motor control theories can only partially capture the phenomenon. This may be a major cause of the reduced efficacy of lower limb rehabilitation therapies. Recently, it has been proposed that human locomotion can be planned in the task-space by taking advantage of the gravitational pull acting on the Centre of Mass (CoM) by modelling the attractor dynamics. The model proposed represents the CoM transversal trajectory as a harmonic oscillator propagating on the attractor manifold. However, the vertical trajectory of the CoM, controlled through ankle strategies, has not been accurately captured yet. Research Questions: Is it possible to improve the model accuracy by introducing a mathematical model of the ankle strategies by coordinating the heel-strike and toe-off strategies with the CoM movement? Our solution consists of closed-form equations that plan human-like trajectories for the CoM, the foot swing, and the ankle strategies. We have tested our model by extracting the biomechanics data and postural during locomotion from the motion capture trajectories of 12 healthy subjects at 3 self-selected speeds to generate a virtual subject using our model. Our virtual subject has been based on the average of the collected data. The model output shows our virtual subject has walking trajectories that have their features consistent with our motion capture data. Additionally, it emerged from the data analysis that our model regulates the stance phase of the foot as humans do. The model proves that locomotion can be modelled as an attractor dynamics, proving the existence of a nonlinear map that our nervous system learns. It can support a deeper investigation of locomotion motor control, potentially improving locomotion rehabilitation and assistive technologies.