Stability Principle Underlying Passive Dynamic Walking of Rimless Wheel

TL;DR

This paper analyzes the stability principle of passive dynamic walking in rimless wheels, emphasizing the role of energy conservation and linearized dynamics to deepen understanding of inherent stability.

Contribution

It offers a new mathematical analysis linking energy conservation to stability, expanding theoretical understanding of passive dynamic walking models.

Findings

Passive rimless wheels are asymptotically stable due to impact posture and energy constraints.

Linearization of equations reveals the relation between stability and energy conservation.

Mathematical analysis enhances understanding of the inherent stability principle.

Abstract

Rimless wheels are known as the simplest model for passive dynamic walking. It is known that the passive gait generated only by gravity effect always becomes asymptotically stable and 1-period because a rimless wheel automatically achieves the two necessary conditions for guaranteeing the asymptotic stability; one is the constraint on impact posture and the other is the constraint on restored mechanical energy. The asymptotic stability is then easily shown by the recurrence formula of kinetic energy. There is room, however, for further research into the inherent stability principle. In this paper, we reconsider the stability of the stance phase based on the linearization of the equation of motion, and investigate the relation between the stability and energy conservation law. Through the mathematical analysis, we provide a greater understanding of the inherent stability principle.