Stability of a compass gait walking model with series elastic ankle actuation

Passive dynamic walkers exhibit stable human-like walking on inclined planes. The simplest model of this behavior is the well known passive compass gait (PCG) model, which consists of a point mass at the hip and two stick legs. Due to their passive nature, these systems rely on a sloped ground to recover energy lost to ground collisions. A variety of methods have been proposed to eliminate this requirement by using different actuation methods. In this study, we propose a simple model to investigate how series elastic actuation at the ankle can be used to achieve stable walking on level ground. The structure we propose is designed to behave in a similar fashion to how humans utilize toe push-off prior to leg liftoff, and is intended to be used for controlling the ankle joint in a lower-body robotic orthosis. We present the derivation of the hybrid equations of motion for this model, resulting in a numerically computed return map for a single stride. We then numerically identify fixed points of this system and investigate their stability. We show that asymptotically stable walking on flat ground is possible with this model and identify the dependence of limit cycles and their stability on system parameters.