Abstract: A controlling apparatus for representing the motion of a normal wheeled omni-directional vehicle (ODV) in a relative coordinate system, and for effectively controlling the ODV and a controlling method thereof. Drive wheels are connected to four corners of the body of the ODV through offset links that can be independently steered. With the offset links, even if the body stops, it can be reoriented without a need to perform a forced direction change operation. The traveling speed of the body, the turning radius of the body, and the angle between the horizontal axis of the body and the traveling direction thereof are defined as relative variables of a relative coordinate system. With these relative variables, the motion of the ODV is designated. The designated motion of the body is converted into the time change or the displacement (drive speed) and the steering angle of each wheel by inverse kinematics. The corresponding control signals are sent to a driving unit of the wheels.