As a result of the increase in robots in various fields, the mechanical stability of specific robots has become an important subject of research. This study is concerned with the development of a two-wheeled inverted pendulum robot that can be applied to an intelligent, mobile home robot. This kind of robotic mechanism has an innately clumsy motion for stabilizing the robot's body posture. To analyze and execute this robotic mechanism, we investigated the exact dynamics of the mechanism with the aid of 3-DOF modeling. By using the governing equations of motion, we analyzed important issues in the dynamics of a situation with an inclined surface and also the effect of the turning motion on the stability of the robot. For the experiments, the mechanical robot was constructed with various sensors. Its application to a two-dimensional floor environment was confirmed by experiments on factors such as balancing, rectilinear motion, and spinning motion.