Energetics of Actively Powered Locomotion Using the Simplest Walking Model

TLDR

The study modifies a minimal passive‑dynamic walking model to investigate human walking energetics and the optimal speed‑step‑length relationship. The model incorporates a toe‑off impulse and stance‑leg torque, a swing‑leg hip torque that adjusts frequency without adding propulsion, and derives power laws linking impulses and spring constants to gait speed and step length. Toe‑off impulses are four times less costly than stance‑leg torques by reducing collision loss, the hip‑torque actuation further lowers collision loss, and the derived power laws hold in simulations of more realistic models.

Abstract

We modified an irreducibly simple model of passive dynamic walking to walk on level ground, and used it to study the energetics of walking and the preferred relationship between speed and step length in humans. Powered walking was explored using an impulse applied at toe-off immediately before heel strike, and a torque applied on the stance leg. Although both methods can supply energy through mechanical work on the center of mass, the toe-off impulse is four times less costly because it decreases the collision loss at heel strike. We also studied the use of a hip torque on the swing leg that tunes its frequency but adds no propulsive energy to gait. This spring-like actuation can further reduce the collision loss at heel strike, improving walking energetics. An idealized model yields a set of simple power laws relating the toe-off impulses and effective spring constant to the speed and step length of the corresponding gait. Simulations incorporating nonlinear equations of motion and more realistic inertial parameters show that these power laws apply to more complex models as well.