Nonlinear Dynamics of a Passive Walker: Bifurcation and Stability Insights With Spring and Damper Mechanics

Abstract

This study explores the nonlinear dynamics associated with a passive dynamic walker (PDW), focusing on the bifurcation and stability insights derived from spring and damper mechanics. PDWs, which rely on gravity for stable locomotion without active control, exhibit a rich spectrum of behaviors, from periodic to chaotic motion. The study examines the effects of key system parameters, such as the hip mass ratio, the leg center of mass (CoM) location, spring stiffness, and damper coefficient, on the stability and gait performance of the walker. Through a combination of theoretical analysis and numerical simulations, the paper identifies bifurcation points where periodic orbits transition into chaotic dynamics, shedding light on the critical conditions for stable walking. The results reveal that increased hip mass, spring stiffness, and leg CoM location ratio contribute to faster walking speeds. All of these physical parameters show a non-monotonic effect on stability. Stability first improves and then deteriorates as the parameter values increase. In contrast, the influence of damping on passive walking is relatively minor, and increasing damping does not significantly improve stability, even sometimes leading to the inability to find a stable solution. Moreover, the results also suggest that the addition of the spring can mitigate the bifurcations of the system. This research provides a deeper understanding of the stability transitions in PDWs, with implications for the design of more efficient and robust legged robots.