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In order to solve the problem of stable control in the gait transition process of quadruped robots by using model-based control methods, a quadruped robot prototype platform was designed based on bionics and mechanics, and the robot's single leg kinematic model was derived. The robot's leg height and step length were planned within the reachable workspace at the foot end. By using an ideal compound cycloid trajectory and controlling the gait period reasonably, a transition period variable control method was proposed, which achieved fixed speed control and variable step length control before and after gait transition, ensuring that the speed remained unchanged or variable before and after gait transition. In order to verify the correctness and stability of the proposed algorithm, single leg foot trajectory experiments and whole machine gait transformation experiments were conducted, respectively. On the basis of completing the overall motion control, the application of model-based control and central pattern generator based control in the gait transition process of quadruped robots was compared. The simulation and experimental results showed that under the model-based control algorithm, the quadruped robot can achieve smooth gait transformation, and the speed can be adjusted with changes in step size and period, meeting the walking requirements at different speeds, providing a reference for the motion control of quadruped robots.