HZD-based control of a five-link underactuated 3D bipedal robot

This paper presents a within-stride feedback controller that achieves an exponentially stable, periodic, and fast walking gait for a 3D bipedal robot consisting of a torso, revolute knees, and passive (unactuated) point feet. The walking surface is assumed to be rigid and flat; the contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and 6 actuators. In addition to the reduced number of actuators, the interest of studying robots with point feet is that the feedback control solution must explicitly account for the robot¿s natural dynamics in order to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics (HZD), a very successful method for planar bipeds, in order to determine a periodic orbit and an autonomous feedback controller that realizes the orbit, for a 3D (spatial) bipedal walking robot. The effect of output selection on the zero dynamics is highlighted and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller.