Motion analysis of a multi-joint system with holonomic constraints using Riemannian distance

Abstract

ABSTRACT Multi-joint movement is realized by controlling the nonlinear dynamics induced by the mass of each link. Collaborative link-inertia action towards a goal achieves energy-efficient motion, such as inertial movement. Inertial movement-based motion analysis is beneficial but challenging when walking is considered, owing to the alterations in the nonlinear equations of motion, which correspond to the holonomic constraints between the foot and ground. In this study, we clarified that the shortest curve between two points on holonomically constrained Riemannian manifolds corresponds to the constrained inertial movement of a multi-joint system, and that every constrained inertial movement can be consistently considered by the shortest-curve lengths (Riemannian distances). Accordingly, by comparing the curve length of the measured motion with the Riemannian distance, we developed a quantitative analysis method for measuring the proximity of a measured walk to the inertial movement. This was applied to healthy persons walking under different inertial cadences and load conditions. The results indicate the proximity to the inertial movement during the swing phase under all conditions, including the similarity between the proximity profiles in normal and high-inertia walks. These findings validate the introduction of a Riemannian distance-based evaluation quantity in the motion analysis and control of multi-joint systems.