This paper introduces a planar positioning sensing system based on orthogonal wheels and encoders for some surfaces that may float (such as ship decks). The positioning sensing system can obtain the desired position and angle information on any such ground that floats. In view of the current method of using the IMU gyroscope for positioning, the odometer data on these floating grounds are not consistent with the real-time data in the world coordinate system. The system takes advantage of the characteristic of the orthogonal wheel, using four vertical omnidirectional wheels and encoders to position on the floating ground. We design a new structure and obtain the position and angle information of a mobile robot by solving the encoder installed on four sets of omnidirectional wheels. Each orthogonal wheel is provided with a sliding mechanism. This is a good solution to the problem of irregular motion of the system facing the floating grounds. In the experiment, it is found that under the condition that the parameters of the four omnidirectional wheels are obtained by the encoder, the influence of the angle change of the robot in the world coordinate system caused by the flotation of the ground can be ignored, and the position and pose of the robot on the fluctuating ground can be well obtained. Regardless of straight or curved motion, the error can reach the centimeter level. In the mobile floating platform experiment, the maximum error of irregular movement process is 2.43 (±0.075) cm and the RMSE is 1.51 cm.