The kinematic model of an omnidirectional mobile robot with MY (Mutual YoYo) wheels is built based on the structure of MY wheel to analyze its kinematics characteristics. The performance on vibration, control and errors caused by MY wheels is studied. A control method of both optimizing contact distance and improving rotational speed of MY wheel is proposed to reduce the movement errors. The movement characteristics of tri-wheel platform and four-wheel platform are compared for optimal structure. It can improve the movement stability of the robot by employing sinusoidal control law to control the angular velocity of MY wheel reasonably. Simulation results are provided to demonstrate the performance of the proposed approaches.