Passive Frontal Plane Stabilization in 3D Walking

This paper explores the use of a single passive design to stabilize frontal plane dynamics for 3D biped walking across a range of forward velocities and/or step lengths. Particular goals are to determine if design of sagittal plane control can be done independently from design of frontal plane stabilization mechanisms, and to explore how dynamic coupling between the two planned motions affects energetic efficiency of walking. Passive dynamic walkers have long utilized curved feet for low energy frontal plane stabilization in 3d walking, with the current design practice of matching the linearized resonance of the curvature to match a particular, steady-state walking gait to achieve stable coupled limit cycle in the 3D dynamics. However, practical legged walking systems should operate across a range of velocities and step widths. We examine aspects of the nonlinear dynamics that contribute to the energy efficiency and stability of the system through simulations. Specifically, we focus on the frontal plane dynamics and the resulting variability of time-ofreturn for frontal plane wobbles, as a function of impact velocity. Our decoupled analysis explains some aspects of the 3D motions; however, the actual effects on cost of transport demonstrate interesting phenomena we had not anticipated. Specifically, while a general trend of increasing cost of transport for 3D vs 2D gaits with stride time does hold in our simulations, the 3D gaits sometimes require less energy than their constrained 2D counterparts, which was a surprising and encouraging result. This work provides a promising direction for the development of practical methods to utilize control designed for planar 2D walking models on more sophisticated 3D dynamic models using little or no additional active control.