Despite that omni-directional mobile robots have been investigated and used popularly, there are rarely useful command systems and control methods for practical applications. In this research, a command system to describe the navigation task for an omni-directional mobile robot is developed, and a motion generation method considering the robot geometry and the given trajectory is proposed. Furthermore, a control method to track the given linear and circular trajectories is proposed. A closed form kinematic model was utilized for motion generation and control as well. A redundantly actuated omni-directional mobile robot that consists of three caster-type wheel mechanisms with high performance embedded controller module was developed for the experiments. And some experiments in the real environment were carried out to verify the effectiveness of the proposed command system and the performance of the motion generation and the trajectory control method.