Since the quadruped robot possesses predominant environmental adaptability,it is expected to be employed in nature environments. In some situations,such as ice surface and tight space,the quadruped robot is required to lower the height of center of gravity( COG) to enhance the stability and maneuverability. To properly handle these situations,a quadruped controller based on the central pattern generator( CPG) model,the discrete tracking differentiator( TD) and proportional-derivative( PD) sub-controllers is presented. The CPG is used to generate basic rhythmic motion for the quadruped robot. The discrete TD is not only creatively employed to implement the transition between two different rhythmic medium values of the CPG which results in the adjustment of the height of COG of the quadruped robot,but also modified to control the transition duration which enables the quadruped robot to achieve the stable transition. Additionally,two specific PD sub-controllers are constructed to adjust the oscillation amplitude of the CPG,so as to avoid the severe deviation in the transverse direction during transition locomotion. Finally,the controller is validated on a quadruped model. A tunnel with variable height is built for the quadruped model to travel through. The simulation demonstrates the severe deviation without the PD sub-controllers,and the reduced deviation with the PD sub-controllers. Since the quadruped robot possesses predominant environmental adaptability, it is expected to be employed in nature environments. It is expected to be employed in nature environments. stability and maneuverability. To handle the situations, a quadruped controller based on the central pattern generator (CPG) model, the discrete tracking differentiator (TD) and the proportional-derivative (PD) sub-controllers is presented. The rhythmic motion for the quadruped robot. The discrete TD is not only creatively employed to implement the transition between two different rhythmic medium values ​​of the CPG which results in the adjustment of the height of COG of the quadruped robot, but also modified to control the transition duration which enables the quadruped robot to achieve the stable transition. Additionally, two specific PD sub-controllers are constructed to adjust t he oscillation amplitude of the CPG, so as to avoid the severe deviation in the transverse direction during transition locomotion. Finally, the controller is validated on a quadruped model. A tunnel with variable height is built for the quadruped model to travel through. demonstrates the severe deviation without the PD sub-controllers, and the reduced deviation with the PD sub-controllers.