# A Survey of Low-Cost 3D Laser Scanning Technology
## 4 Problems of a Moving 2D LiDAR
### Problem I: Accuracy
#### 4.1.2 Problem 1.2--For Categories 1, 2, and 5: The Error Caused by the Motor  
For the prototypes of categories (1) a rotating 2D LiDAR, (2) a pitching 2D LiDAR, and (5) an obliquely rotating 2D LiDAR, motors are needed to rotate the 2D LiDARs. Ideally, the motor shaft should have only one degree of freedom when rotating, but in actual situations, the motor shaft may have an axial or radial runout, or the rotation of the motor shaft may cause the trembling of the prototype. These are due to the lack of the performance and accuracy of the motor. Choosing a smooth-running motor when building a prototype can effectively address this problem. In addition, when a motor is set to a constant speed to rotate its shaft at a uniform speed, whether the motor shaft can rotate accurately at the specified speed under the load is also a point that needs to be considered. For example, if an excessive load is applied to a stepper motor, it will cause the stepper motor to lose steps. For the prototypes of categories (1) a rotating 2D LiDAR, (2) a pitching 2D LiDAR and (5) an obliquely rotating 2D LiDAR, this is allowed, because in these prototypes, the motors are required to rotate at a constant speed within a specific period of time. If the 2D LiDAR is heavy or the output torque of the selected motor is insufficient, the motor will be overloaded. The use of a gear reducer in the prototype (such as the prototype developed by [PERSON] et al. [49,92]) can increase the output torque, while gear transmission errors can also be caused. A harmonic reducer may be more precise, it is also more expensive. Moreover, the use of a reducer will increase the weight, volume, and cost of the prototype. In short, when selecting a motor for the prototypes of categories 1, 2 and 5, its performance in terms of smooth running and output torque should be noted. For the prototypes of category 4) an irregularly rotating 2D LiDAR, the 2D LiDAR may not be rotated by a motor (for example, the rotation of the 2D LiDAR in [79] is driven by airflow), so it is not included in the categories of prototypes corresponding to Problem 1.2. Problem 1.2 may decrease the accuracy of the space 3D rigid body transformation between the 2D LiDAR coordinate frame \(L\) and the prototype coordinate frame \(P\) (which corresponds to Equation (3) in Section 3.6 of this paper), this will eventually decrease the accuracy of the 3D point cloud. 1.3 Problem 1.3--For Categories 1, 2, 4, and 5: The Error Caused by the Assembly Inaccuracy between the 2D LiDAR and the Rotating Unit  
For the prototypes of categories (1) a rotating 2D LiDAR, (2) a pitching 2D LiDAR, (4) an irregularly rotating 2D LiDAR, and (5) an obliquely rotating 2D LiDAR, caused by mechanical error, the relative position and attitude between the 2D LiDAR and the rotating unit are not exactly the same as expected (as mentioned at the end of [62]). The mechanical error can be divided into six components, among which, three are translation errors and three are rotation errors [21]. Since the manufacturing and assembly of the mechanical parts cannot be absolutely precise, mechanical error is unavoidable. In [10; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31], calibration methods of the mechanical error have been studied. Problem 1.3 may decrease the accuracy of the space 3D rigid body transformation between the 2D LiDAR coordinate frame \(L\) and the prototype coordinate frame \(P\) (which corresponds to Equation (3) in Section 3.6 of this paper), this will eventually decrease the accuracy of the 3D point cloud. 1.4 Problem 1.4--For Categories 1, 2, and 5: The Error Caused by the Synchronization Inaccuracy between the 2D LiDAR and the Rotating Unit  
For the prototypes of categories (1) a rotating 2D LiDAR, (2) a pitching 2D LiDAR, and (5) an obliquely rotating 2D LiDAR, the principle of these prototypes is to build 3D point clouds by combining the data of the 2D LiDAR and the rotation angle of the motor shaft.