Integrating the effects of angular momentum and changing center of mass height in bipedal locomotion planning

The majority of methods developed for generating locomotion plans for bipedal robots are based upon the linear inverted pendulum model. While this simplified model has proven useful, it possesses certain theoretical limitations such as the inability to account for changes in the height of the center of mass or the effects of angular momentum, the latter of which can be useful for recovering from disturbances and in balancing. It is shown in this paper that if we assume that the robot is closely following a known reference signal for the center of mass height, the equations of motion are linear in the position of the center of pressure and the rate of change of angular momentum about the center of mass. With the dynamics linear in these particular quantities, model predictive control is used to solve for control inputs over a receding horizon resulting in reference trajectories for the center of pressure and the rate of change of angular momentum about the center of mass. Examples are presented for undisturbed walking, double support push recovery, and one leg balancing that utilize the effects of angular momentum while remaining dynamically consistent with a reference signal for the height of the center of mass and regulating critical ground reference points for ensuring the maintenance of postural stability.