  In this paper we exploit some interesting properties of a class of bipedal
robots which have an inertial disc. One of this properties is the ability to
control every position and speed except for the disc position. The proposed
control is designed in two hierarchic levels. The first will drive the robot
geometry, while the second will control the speed and also the angular
momentum. The exponential stability of this approach is proved around some
neighborhood of the nominal trajectory defining the geometry of the step. This
control will not spend energy to adjust the disc position and neither to
synchronize the trajectory with the time. The proposed control only takes
action to correct the essential aspects of the walking gait. Computational
simulations are presented for different conditions, serving as a empirical test
for the neighborhood of attraction.
