Garcia Gabriel ; Griffin Robert ; Pratt Jerry

Abstract

One common method for stabilizing robots after a push is the InstantaneousCapture Point, however, this has the fundamental limitation of assumingconstant height. Although there are several works for balancing bipedal robotsincluding height variations in 2D, the amount of literature on 3D models islimited. There are optimization methods using variable Center of Pressure (CoP)and reaction force to the ground, although they do not provide the physicalregion where a robot can step and require a precomputation for the analysis.This work provides the necessary and sufficient conditions to maintain balanceof the 3D Variable Height Inverted Pendulum (VHIP) with both, fixed andvariable CoP. We also prove that the 3D VHIP with Fixed CoP is the same as its2D version, and we generalize controllers working on the 2D VHIP to the 3DVHIP. We also show the generalization of the Divergent Component of Motion tothe 3D VHIP and we provide an alternative motion decomposition for the analysisof height and CoP strategies independently. This allow us to generalizeprevious global feedback controllers done in the 2D VHIP to the 3D VHIP with aVariable CoP.