The primary concern of the work is robust control of hybrid mechanical systems under unilateral constraints of co-dimension one. Nonlinear H∞ output feedback synthesis is developed in the hybrid setting, covering collision phenomena. Robustness issues of the proposed synthesis are numerically illustrated in two benchmark applications. First, the regulation and orbital stabilization of a simple mass-spring-damper system, impacting a barrier, illustrate the capability of the proposed approach via state feedback and position feedback designs, respectively. In order to add a practical value to the present investigation the tracking synthesis of a walking gait is then addressed for a complex bipedal robot with feet. In both applications, good performances are achieved despite imperfect measurements and the presence of both external disturbances, affecting the collision-free motion phase, and uncertainties that occur in the collision phase.