The primary concern of the work is robust control of hybrid mechanical systems under unilateral constraints with underactuation degree one. Nonlinear H ∞ output feedback synthesis is developed in the hybrid setting, covering collision phenomena. Sufficient conditions are presented to ensure internal asymptotic stability while also attenuating external disturbances and plant uncertainties. The developed synthesis is applied to the orbital stabilization of an underactuated bipedal robot periodically touching the ground. Good performance of the closed-loop system is obtained not only in the presence of measurement noise and external disturbances, affecting the gait of the biped between collision time instants, but also under uncertainties at the velocity restitution when the ground collision occurs. Keywords robust control · unilateral constraints · un-deractuated mechanical systems · orbital stabilization · bipedal robot · walking gait.