This study presents the development and validation of a control framework for a quadruped wheeled robot capable of stable and efficient spiral stair ascent and descent. The proposed system integrates the advantages of legged and wheeled locomotion, enabling both high terrain adaptability and mobility efficiency. In particular, the research focuses on addressing the challenging problem of coordinated control between leg mechanisms and wheels in complex environments such as spiral staircases.

A Model Predictive Control (MPC)-based approach was adopted to generate optimal motion trajectories while considering the robot's dynamic constraints. By predicting future states over a finite time horizon and optimizing control inputs in real time, the controller enables adaptive behavior under varying stair geometries. The dynamic model of the robot was constructed to accurately capture interactions between the robot and the environment, including contact forces, posture stability, and wheel-ground interactions.

To improve maneuverability, the robot design incorporates an additional yaw degree of freedom in each leg, allowing flexible trajectory adjustment during curved motion. The MPC framework was designed with multiple cost functions to achieve trajectory tracking, posture stabilization, impact force reduction, and balance maintenance. This formulation enables the robot to minimize slippage and maintain stability during both ascent and descent.

Simulation results demonstrate that the proposed method significantly improves motion smoothness and stability compared to conventional approaches. In particular, the robot successfully navigates spiral stairs with continuous trajectory tracking and reduced impact forces, even under dynamically changing conditions. The system adapts to different stair geometries without requiring extensive parameter tuning or retraining, highlighting its robustness and generalization capability.

Furthermore, the results indicate that the integration of yaw-axis control and MPC contributes to enhanced locomotion performance, enabling efficient turning and alignment along curved paths. This is especially important for spiral staircases, where conventional robots often experience instability due to asymmetric terrain.

Overall, this research demonstrates that the proposed MPC-based control framework provides a practical and effective solution for enabling quadruped wheeled robots to operate in complex, unstructured environments. The findings contribute to advancing robotic mobility in real-world applications such as disaster response, inspection, and infrastructure maintenance, where reliable navigation over stairs and irregular terrains is essential.