_applied_  
_sciences_  
_Article_  
Low-Cost Calibration of Matching Error between Lidar and  
Motor for a Rotating 2D Lidar  
[PERSON] 1, [PERSON] 1,*, [PERSON] 1, [PERSON] 2 and [PERSON] 3  
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This question can be further divided into two subcategories. One is to calibrate the mechanical error between the lidar and the rotating unit [1; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. Due to the mechanical error, the relative position and attitude between the 2D lidar and rotating unit are not exactly the same as expected. The error is 6-degrees of freedom (DOF), containing a 3-DOF translation and 3-DOF rotation [4]. The mechanical error can decrease the accuracy of the 3D point cloud in many aspects, including the shape and attitude of the 3D point cloud. The mechanical error is inevitable because machining and assembling errors cannot be eliminated completely. Therefore, calibration is necessary. The other subcategory is to calibrate the matching error between the 2D lidar and rotating unit (that is, the motor) [2; 3; 5; 8; 16; 17; 18; 19; 20; 21; 22; 23]. The working principle of a rotating 2D lidar is to calculate the 3D coordinates of the points by using the data collected by the 2D lidar and the angle of the motor shaft. Therefore, in order to improve the accuracy of the 3D point cloud, it is necessary to match the data from the 2D lidar and the angle of the motor shaft accurately. If we can know the angle of the motor shaft corresponding to each point collected by the 2D lidar during the entire 3D scan of a rotating 2D lidar, the matching error between the 2D lidar and the motor can be eliminated. However, in reality, the situation mentioned above does not exist, so the matching error always exists, which has a negative impact on the accuracy of the 3D point cloud, both in shape and attitude. The first subcategory focuses on the calibration of the mechanical error, and the second subcategory focuses on the calibration of the matching error. They are juxtaposed with each other and cannot be replaced by each other. Only when both the mechanical error and the matching error are calibrated, a rotating 2D lidar can get an accurate 3D point cloud in a static environment. The first subcategory, the calibration method of the installation error between the 2D lidar and the rotating unit, has been thoroughly evaluated. For example, the calibration processes proposed in [1; 4] can work effectively without the need of specific scene, additional equipment, and a priori information about the environment (such as size etc.). The requirement is that there should be at least one plane in the scanning field. Planar features are abundant in man-made indoor environments, such as walls, floors, and ceilings. However, the research on the second subcategory is relatively unexplored. The existing methods used for calibration of the matching error between a 2D lidar and motor mostly utilize expensive servo motors or encoders to output the motor rotation angle with the time stamps, and align it with the data form 2D data with time stamps. In this way, the matching error is calibrated [2; 3; 5; 8; 16; 17; 18; 19; 20; 21; 22; 23].