Bipedal robots with instantaneous impact form a subclass of the dynamic systems with hybrid and under-actuation properties. Because of these two complex properties, finding an effective control method to show a rule base motion is difficult. In particular, few works are focused on how to regulate gate speed based on analytical stability and its own model which boost the robustness and accuracy. This is, thereby, still an open and challenging issue. In this paper, we present a solution for

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... regulating walking gait speed of bipedal robot based on its model while simultaneously stabilizing a closed orbit in the constraint manifold space. Suitable paths are therefore taken as the virtual holonomic constraints, which are then characterized by some parameters. By proposing a stability theorem, a hierarchical controller is designed in two levels. At the low-level, the controller stabilizes the constraints as an output of the system state space, thereby creating the constraint manifold. In order to achieve the desired gate speed, the high-level controller adaptively deforms this manifold through the characterization parameters. In this design, the robustness of the controller is taken into consideration to prevent the system from being affected by disturbances. Simulation results show that the control method has a good performance and works smoothly in regulating the robot gate speed. Furthermore, the robot is also resistant to disturbance during movement and performs a stable motion over time.