  We present a real-time pattern generator for dynamic walking over rough
terrains. Our method automatically finds step durations, a critical issue over
rough terrains where they depend on terrain topology. To achieve this level of
generality, we consider a Floating-base Inverted Pendulum (FIP) model where the
center of mass can translate freely and the zero-tilting moment point is
allowed to leave the contact surface. This model is equivalent to a linear
inverted pendulum with variable center-of-mass height, but its equations of
motion remain linear. Our solution then follows three steps: (i) we
characterize the FIP contact-stability condition; (ii) we compute feedforward
controls by solving a nonlinear optimization over receding-horizon FIP
trajectories. Despite running at 30 Hz in a model-predictive fashion,
simulations show that the latter is too slow to stabilize dynamic motions. To
remedy this, we (iii) linearize FIP feedback control into a constrained
linear-quadratic regulator that runs at 300 Hz. We finally demonstrate our
solution in simulations with a model of the HRP-4 humanoid robot, including
noise and delays over state estimation and foot force control.
