Angular Momentum about the Contact Point for Control of Bipedal Locomotion: Validation in a LIP-based Controller

In the control of bipedal locomotion, linear velocity of the center of mass has been widely accepted as a primary variable for summarizing a robot's state vector. The ubiquitous massless-legged linear inverted pendulum (LIP) model is based on it. In this paper, we argue that angular momentum about the contact point has several properties that make it superior to linear velocity for feedback control. So as not to confuse the benefits of angular momentum with any other control design decisions, we first reformulate the standard LIP controller in terms of angular momentum. We then implement the resulting feedback controller on the 20 degree-of-freedom bipedal robot, Cassie Blue, where each leg accounts for nearly one-third of the robot's total mass of 35~Kg. Under this controller, the robot achieves fast walking, rapid turning while walking, large disturbance rejection, and locomotion on rough terrain. The reasoning developed in the paper is applicable to other control design philosophies, whether they be Hybrid Zero Dynamics or Reinforcement Learning.