Dynamics and Stability of Locomotion for Actively Powered Simplest Walkers

In this paper we explore methods to achieve actively powered walking on level ground using a simple 2D walker model. The walker is activated either by applying equal joint torques at hip and ankle, or by an impulse applied at toe-off immediately before heel-strike, or by the combination of both. We show that activating the walker by equal joint torques at hip and ankle on level ground is equivalent to the dynamics of the passive walker on a downhill slope. We calculate the stability of the gait cycle by an analytical approximation to the Jacobian of the walking map. Results indicate that short-period gait cycle always has an unstable eigenvalue, whereas stability of the long-period gait cycle depends on the selection of initial stance angle.