# A Survey of Low-Cost 3D Laser Scanning Technology
## 3 Classification of the Prototypes
### Discussion of the Classification of the Prototypes  
Until now, we have classified a moving 2D LiDAR by the movement of the 2D LiDAR, namely (1) a rotating 2D LiDAR, (2) a pitching 2D LiDAR, (3) a push-broom 2D LiDAR. These three categories are most commonly used. Besides, there are other categories: (4) an irregularly rotating 2D LiDAR, in which the rotation of the 2D LiDAR is non-periodic and irregular. (5) An obliquely rotating 2D LiDAR, compared with a rotating 2D LiDAR, the 2D LiDAR of an obliquely rotating 2D LiDAR is installed obliquely to make the distribution of the collected 3D point cloud is grid-like, so that it is less likely to miss the obstacles. (6) An irregularly moving 2D LiDAR, in which the movement of the 2D LiDAR is irregular. In the above six categories, the 2D LiDARs in (1), (2), (4), (5), and (6) move relative to the mobile platforms on which the prototypes are carried. For the 2D LiDAR in (3), it is fixed relative to the mobile platform, and there is no relative movement between the two. Figure 12: The prototypes in [86; 87; 88; 89]. (**a**) Left: the prototype in [86]; right: the field of view of this prototype; (**b**) the prototypes in [87]. Left: the first-generation prototype; right: the second-generation prototype, it is placed between a commercial 2D LiDAR and a mobile phone to show its size; (**c**) the prototype in [88]; (**d**) the prototype in [89]. For categories (1), (2), (4), (5), and (6), it is also necessary to distinguish two situations, that is, whether the mobile platform is moving or stationary. Unlike a camera, which can take a picture at a fast speed, for a moving 2D LiDAR, it takes a long time (usually a few seconds) to finish once 3D scan. During this period, if the mobile platform on which the prototype is carried is moved, the distortion of the collected 3D point cloud will be caused. For category 3, a 3D map of the environment can be built only when the platform is moving. If the platform is stationary, the field of view of the 2D LiDAR is limited to a plane, as the result of which, it cannot be used to build 3D point clouds of the environment. For categories (1), (2), (4), (5), and (6), in order to eliminate the distortion of the 3D point cloud, it should be noted that the movement of the 2D LiDAR in the world coordinate frame is the superposition of two movements, one is the movement of the 2D LiDAR relative to the mobile platform, the other is the movement of the mobile platform relative to the world coordinate frame. For category 3, since the 2D LiDAR is fixed relative to the mobile platform, so there is no movement between the 2D LiDAR and the mobile platform, the movement of the 2D LiDAR in the world coordinate frame depends on the movement of the mobile platform relative to the world coordinate frame. In Figure 13, a rotating 2D LiDAR and a push-broom 2D LiDAR are taken as examples to analyze the process of converting the sampling point \(\mathbf{p}\) from the 2D LiDAR coordinate frame \(L\) to the world coordinate frame \(W\). There are four kinds of coordinate frames in Figure 13, among which, the coordinate frame \(W\) is the world coordinate frame, the coordinate frame \(L\) is the coordinate frame of the 2D LiDAR, the position of its original point in the world coordinate frame represents the position of the 2D LiDAR in the world coordinate frame. These two coordinate frames are defined in Section 2 of this paper. In addition, the coordinate frame \(P\) is the coordinate frame of the prototype--that is, the coordinate frame of a rotating 2D LiDAR. The position of its original point in the world coordinate frame represents the position of the prototype in the world coordinate frame. The coordinate frame \(M\) is the coordinate frame of the mobile platform, the position of its original point in the world coordinate frame represents the position of the mobile platform in the world coordinate frame. The raw data collected by a 2D LiDAR is the ranging data and the azimuth angle.