  We present a new walking controller based on 3LP, a 3D model of bipedal
walking that is composed of three pendulums to simulate falling, swing and
torso dynamics. Taking advantage of linear equations and closed-form solutions
of 3LP, the proposed controller projects intermediate states of the biped back
to the beginning of the phase for which a discrete LQR controller is designed.
After the projection, a proper control policy is generated by this LQR
controller and used at the intermediate time. The projection controller reacts
to disturbances immediately and compared to the discrete LQR controller, it
provides superior performance in recovering intermittent external pushes.
Further analysis of closed-loop eigenvalues and disturbance rejection strength
show strong stabilization properties for this architecture. An analysis of
viable regions also show that the proposed controller covers most of the
maximal viable set of states. It is computationally much faster than Model
Predictive Controllers (MPC) and yet optimal over an infinite horizon.
