<p>Dynamically stable gait control for quadruped robots remains an active area of research. This study develops a model-based dynamic control approach, leveraging the time-invariant hybrid zero dynamics (HZD)&#xa0;method to enhance the dynamically stable locomotion of underactuated quadruped robots. The proposed approach is exemplified on a rigid, straight-legged quadruped robot model in the trotting gait. To validate the results, we establish a multibody modeling framework for simulating quadruped locomotion using the multibody dynamics software, e.g., MSC ADAMS. The multibody simulation framework in MSC ADAMS exhibits a high degree of consistency with the mathematical model in MATLAB and eliminates the need for deriving complex mathematical dynamic equations of motion, significantly simplifying the dynamic simulation of quadruped robots. Building on this validated foundation, the proposed controller is benchmarked against a conventional control strategy within the developed multibody framework, which serves as a superior evaluation platform for both nominal and physically disturbed conditions that closely resemble real-world scenarios. The results demonstrate superior performance and robust behavior of the proposed control method in generating a dynamically stable locomotion at situations. This study advances the control of quadruped locomotion and establishes a solid foundation for the future development of more efficient and robust quadruped robots.</p>