A transport device for transporting a patient support panel or a medical appliance includes a drive unit, which includes a drive motor, an undercarriage having wheels rotatably mounted on it for driving the undercarriage, and a sensor unit for receiving a signal indicating the position of the transport device with respect to a predetermined path line while the transport device moves along the predetermined path line. One or more of the wheels are rotatably drivable by the drive unit, and one or more wheels are steerable.