A Simple Controller for Quadrupedal Bounding

In this work, the dynamics of quadrupedal bounding is studied via the reduced-order sagittal-plane model of Fig.1. The model is composed of a rigid torso and two massless springy prismatic legs. Albeit simple, models in this family have been found useful in uncovering many important prop-erties of bounding. For example, it has been shown in [1] that a variety of bounding gaits can be generated passively, suggesting that such motions represent natural interactions between a quadruped and its environment. According to the modeling and control hierarchy intro-duced in [2], reductive locomotion models can be used to inform the control of more accurate high-dimensional rep-resentations of robots (or animals) by suggesting suitable coordination mechanisms. However, passive reduced-order models such as the one in [1] cannot be used directly as con-trol targets for more complete robot models due to their lim-ited ability in rejecting perturbations. For example, the ma-jority of the passively generated fixed points in [1] are un-stable; stable (within a total energy level) fixed points only exist when the forward velocity is in a range that is not re-alizable by most robotic quadrupeds. Even for these stable fixed points, the domain of attraction is not practical