  Developments for 3D control of the center of mass (CoM) of biped robots are
currently located in two local minima: on the one hand, methods that allow CoM
height variations but only work in the 2D sagittal plane; on the other hand,
nonconvex direct transcriptions of centroidal dynamics that are delicate to
handle. This paper presents an alternative that controls the CoM in 3D via an
indirect transcription that is both low-dimensional and solvable fast enough
for real-time control. The key to this development is the notion of boundedness
condition, which quantifies the capturability of 3D CoM trajectories.
