3D Bipedal Walking with Knees and Feet: A Hybrid Geometric Approach

Abstract—Motivated by the goal of obtaining more-anthropomorphic walking in bipedal robots, this paper con-siders a hybrid model of a 3D hipped biped with feet and locking knees. The main observation of this paper is that functional Routhian Reduction can be used to extend two-dimensional walking to three dimensions—even in the presence of periods of underactuation—by decoupling the sagittal and coronal dynamics of the 3D biped. Specifically, we assume the existence of a control law that yields stable walking for the 2D sagittal component of the 3D biped. The main result of the paper is that utilizing this controller together with “reduction control laws ” yields walking in three dimensions. This result is supported through simulation. I