Stably Extending Two-Dimensional Bipedal Walking to Three Dimensions

In this paper we develop a feedback control law that results in stable walking gaits on flat ground for a three-dimensional bipedal robotic walker given stable walking gaits for a two-dimensional bipedal robotic walker. This is achieved by combining disparate techniques that have been employed in the bipedal robotic community: controlled symmetries, geometric reduction and hybrid zero dynamics. Controlled symmetries are utilized to obtain stable walking gaits for a two-dimensional bipedal robot walking on flat ground. These are related to walking gaits for a three-dimensional (hipless) bipedal robot through the use of geometric reduction. Finally, these walking gaits in three dimensions are made stable through the use of hybrid zero dynamics.