Improved Computation of the Humanoid Centroidal Dynamics and Application for Whole-Body Control

The control of centroidal momentum has recently emerged as an important component of whole-body humanoid control, resulting in emergent upper-body motions and increased robustness to pushes when included in whole-body frameworks. Previous work has developed specialized computational algorithms for the Centroidal Momentum Matrix (CMM) and its derivative, which relate rates of change in centroidal momentum to joint rates and accelerations of the humanoid. This article instead shows that specialized algorithms are in fact not always required. Since the dynamics of the centroidal momentum are embedded in the joint-space dynamic equations of motion, the CMM and terms involving its derivative can be computed from the joint-space mass matrix and Coriolis terms. This new approach presents improvements in terms of its generality, compactness, and efficiency in comparison to previous specialized algorithms. The new computation method is then applied to perform whole-body control of a dynamic kicking motion, where the mass matrix and Coriolis terms are already required by the controller. This example motivates how centroidal momentum can be used as an aggregate descriptor of motion in order to ease whole-body motion authoring from a task-space perspective. It further demonstrates emergent upper-body motion from centroidal angular momentum control that is shown to provide desirable regulation of the net yaw moment under the foot. Finally, a few perspectives are provided on the use of centroidal momentum control.