This paper presents three feedback controllers that achieve an asymptoticallystable, periodic, and fast walking gait for a 3D (spatial) bipedal robotconsisting of a torso, two legs, and passive (unactuated) point feet. Thecontact between the robot and the walking surface is assumed to inhibit yawrotation. The studied robot has 8 DOF in the single support phase and 6actuators. The interest of studying robots with point feet is that the robot'snatural dynamics must be explicitly taken into account to achieve balance whilewalking. We use an extension of the method of virtual constraints and hybridzero dynamics, in order to simultaneously compute a periodic orbit and anautonomous feedback controller that realizes the orbit. This method allows thecomputations 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 withthe linearization of the restricted Poincar\'e map of the hybrid zero dynamics.Three strategies are explored. The first strategy consists of imposing astability condition during the search of a periodic gait by optimization. Thesecond strategy uses an event-based controller. In the third approach, theeffect of output selection is discussed and a pertinent choice of outputs isproposed, leading to stabilization without the use of a supplementalevent-based controller.
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