Zero Dynamics, Pendulum Models, and Angular Momentum in Feedback Control of Bipedal Locomotion

Abstract

Lowdimensional models are ubiquitous in the bipedal robotics literature. On the one hand is the community of researchers that bases feedback control design on pendulum models selected to capture the center of mass dynamics of the robot during walking. On the other hand is the community that bases feedback control design on virtual constraints, which induce an exact lowdimensional model in the closedloop system. In the first case, the lowdimensional model is valued for its physical insight and analytical tractability. In the second case, the lowdimensional model is integral to a rigorous analysis of the stability of walking gaits in the fulldimensional model of the robot. This paper seeks to clarify the commonalities and differences in the two perspectives for using lowdimensional models. In the process of doing so, we argue that angular momentum about the contact point is a better indicator of robot state than linear velocity. Concretely, we show that an approximate (pendulum and zero dynamics) model parameterized by angular momentum provides better predictions for foot placement on a physical robot (e.g., legs with mass) than does a related approximate model parameterized in terms of linear velocity. We implement an associated angularmomentumbased controller on Cassie, a 3D robot, and demonstrate high agility and robustness in experiments.