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

Low-dimensional models are ubiquitous in the bipedal robotics literature. On the one hand, are the simplified pendulum models selected to capture the center of mass dynamics. On the other hand, is the passive low-dimensional model induced by virtual constraints. In the first case, the low-dimensional model is valued for its physical insight and analytical tractability. In the second case, the low-dimensional model is integral to a rigorous analysis of the stability of walking gaits in the full-dimensional model of the robot. This paper brings these two approaches together, clarifying their commonalities and differences. 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 is more accurate on a physical robot (e.g., legs with mass) than is a related approximate model parameterized in terms of linear velocity. We implement an associated angular-momentum-based controller on Cassie, a 3D robot, and demonstrate high agility and robustness in experiments.