Zero moment point manipulability ellipsoid

In this paper, we propose zero moment point (ZMP) manipulability ellipsoid as an extension to the existing ZMP balance criterion. The ZMP manipulability ellipsoid was developed by combining the ZMP balance criterion, the humanoid robot dynamics and the manipulability of robotic manipulators. The ZMP manipulability ellipsoid represents the ability of a humanoid robot to instantly move the ZMP from its current ZMP location within the balance criterion. The size and shape of the ZMP manipulability ellipsoid are a function of the joint-torque limitation of a humanoid robot. Thus, the ellipsoid forms an area in which the ZMP can be manipulated instantly, and the larger the ellipsoid, the better the propensity of a humanoid robot will be to recover from an unbalanced situation. We also show that the gravity force of a humanoid robot affects neither the shape nor the translation of the ellipsoid. Furthermore, we show that the ZMP manipulability ellipsoid can aid the humanoid-robot design process by choosing appropriate actuators. Finally, a four degree-of-freedom walking robot was used to illustrate the proposed ZMP manipulability ellipsoid