This paper presents three feedback controllers that achieve an asymptotically
stable, periodic, and fast walking gait for a 3D (spatial) bipedal robot
consisting of a torso, two legs, and passive (unactuated) point feet. 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. The interest of studying robots with point feet is that the robot's
natural dynamics must be explicitly taken into account to achieve balance while
walking. We use an extension of the method of virtual constraints and hybrid
zero dynamics, in order to simultaneously compute a periodic orbit and an
autonomous feedback controller that realizes the orbit. This method allows the
computations to be carried out on a 2-DOF subsystem of the 8-DOF robot model.
The stability of the walking gait under closed-loop control is evaluated with
the linearization of the restricted Poincar\'e map of the hybrid zero dynamics.
Three strategies are explored. The first strategy consists of imposing a
stability condition during the search of a periodic gait by optimization. The
second strategy uses an event-based controller. In the third approach, the
effect of output selection is discussed and a pertinent choice of outputs is
proposed, leading to stabilization without the use of a supplemental
event-based controller