  This paper presents an online walking gait synthesis and a feedback control
methodology to enable stable walking on constrained footholds for bipedal
robots. For this challenging task, the foot placement and center of pressure
cannot be changed, which hinders the application of state-of-art stepping
controllers or zero-moment-point (ZMP) based approaches for walking generation.
As a result, this paper takes a different approach to modulate the change of
the angular momentum about the foot-ground contact pivot at the discrete impact
with vertical center of mass (COM) velocity. We utilize the underactuated
Linear Inverted Pendulum (LIP) model for approximating the underactuated
walking dynamics to provide the desired post-impact angular momentum for each
step. Outputs are constructed via online optimization combined with closed-form
polynomials and then tracked via a quadratic program based controller. This
method is implemented online on two robot models, AMBER and Cassie, for which
stable walking behaviors with constrained footholds are realized on flat
ground, stairs, and randomly located stepping stones.
