  In this paper, we present a new walking controller based on 3LP model. Taking
advantage of linear equations and closed-form solutions of 3LP, the proposed
controller can project the state of the robot at any time during the phase back
to a certain event for which, a discrete LQR controller is designed. After the
projection, a proper control policy is generated by the expert discrete
controller and used online. This projecting architecture reacts to disturbances
with minimal delay and compared to discrete controllers, it provides superior
performance in recovering intermittent external pushes. Further analysis of
closed-loop eigenvalues and disturbance rejection shows that the proposed
time-projecting controller has strong stabilization properties. Controllable
regions also show that the projecting architecture covers most of the maximal
controllable set of states. It is computationally much faster than model
predictive controllers, but still optimal.
