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We apply virtual holonomic constraints (VHCs) to a fully actuated Euler-Lagrange system with impacts : a bipedal walking robot consisting of a stance leg, swing leg and hip mass. We call these hybrid virtual holonomic constraints (hVHCs). For any desired gait of the bipedal robot, the angular position of the swing leg is expressed as a function of the angular position of the stance leg. Using this function, a hVHC is formed and the control objective is to constrain the dynamics of the robot to evolve on the constraint manifold. A design procedure is developed to generate feasible hVHCs for a 2-DOF bipedal robot. Simulation results are presented.

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