Pattern Generation of Biped Walking Constrained on Parametric Surface

This paper describes a generation method for spatially natural biped walking. By limiting the COG (Center of Gravity) motion space to a sculptured surface, the degree of freedom of the COG matches to the number of the ZMP (Zero Moment Point) equations. The COG motion can be uniquely generated along a specified surface satisfying the ZMP constraint with low calculation cost. Spatial and time parts are separable by representing motion surface of the COG as parametric variables. The motion surface defines the relative height of the COG from the landing foot position. Thus, the proposed method reflects geometric information directly to the motion planning without considering walk stability. In this paper, we show two actual examples, walking pattern including mostly stretched knee and going up stairs. The validity of the proposed method is confirmed by simulation. Walking with mostly stretched knee is also shown in experiment using HRP-2.