Biped Walking Pattern Generation Based on 3-dimensional Spatially Quantized Dynamics

Abstract

This paper reviews a dynamics discretization method called spatially quantized dynamics (SQD) and shows that time scale transformation yields the SQD. Time scale transformation also derives continuous spatial dynamics representations, which are equivalent to the original dynamics. By introducing a path parameter and path frames, the SQD are expanded into the 3-dimensional Euclidean space. An efficient method to calculate actual time steps evolving system state is proposed. As a result, trajectory optimization using the proposed SQD enables a kinematic walking pattern to satisfy dynamic constraints, and how to generate a biped gait with stretched knees along an arc on a horizontal plane is presented.