  This paper presents an online walking synthesis methodology to enable dynamic
and stable walking on constrained footholds for underactuated bipedal robots.
Our approach modulates the change of angular momentum about the foot-ground
contact pivot at discrete impact using pre-impact vertical center of mass (COM)
velocity. To this end, 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. Desired outputs are
constructed via online optimization combined with closed-form polynomials and
tracked via a quadratic program (QP) based controller. This method is
demonstrated on two robots, AMBER and 3D Cassie, for which stable walking
behaviors with constrained footholds are realized on flat ground, stairs, and
randomly located stepping stones.
