Understanding How a 3-dimensional ZMP Exactly Decouples the Horizontal and Vertical Dynamics of the CoM-ZMP Model

The CoM-ZMP model represents the dominant behaviour of bipedal locomotion with surface contact. However, once the centre of mass (CoM) position goes out of a predefined spatial plane, the horizontal dynamics of the model can couple with its vertical dynamics to be nonlinear. This study theoretically investigates the properties of the 3-dimensional zero moment point (ZMP), lying apart from the actual ground to resolve the coupling. The presented discussion includes the compatibility of the 3D ZMP with ZMPs used in preceding research, such as the linear inverted pendulum mode, the existence of a virtual repellent point considering the arbitrary vertical CoM motion, the parameter invariance of the CoM-ZMP model, and feasible regions of the ZMP.