Asymptotically Stable Walking of a Simple Underactuated 3D Bipedal Robot

This paper presents a feedback controller that achieves an asymptotically stable, periodic, and fast walking gait for a 3D bipedal robot consisting of 3-links and passive (unactuated) point-feet. The robot has 6 DOF in the single support phase and four actuators. In addition to the reduced number of actuators, the interest of studying robots with point feet is that the feedback control solution must exploit the robot's natural dynamics in order to achieve balance while walking. We use an extension of the method of virtual constraints, a very successful method for planar bipeds, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit, for a 3D (spatial) bipedal walking robot. This method allows the computations for the controller design and the periodic orbit to be carried out on a 2-DOF subsystem of the 6-DOF robot model. The linearization of the Poincare map of the closed-loop system proves that the achieved periodic walking motion, at a speed of approximately one and a half body lengths per second, is exponentially stable.