  In this paper, we propose a multi-domain control parameter learning framework
that combines Bayesian Optimization (BO) and Hybrid Zero Dynamics (HZD) for
locomotion control of bipedal robots. We leverage BO to learn the control
parameters used in the HZD-based controller. The learning process is firstly
deployed in simulation to optimize different control parameters for a large
repertoire of gaits. Next, to tackle the discrepancy between the simulation and
the real world, the learning process is applied on the physical robot to learn
for corrections to the control parameters learned in simulation while also
respecting a safety constraint for gait stability. This method empowers an
efficient sim-to-real transition with a small number of samples in the real
world, and does not require a valid controller to initialize the training in
simulation. Our proposed learning framework is experimentally deployed and
validated on a bipedal robot Cassie to perform versatile locomotion skills with
improved performance on smoothness of walking gaits and reduction of
steady-state tracking errors.
