# Research on 2D Laser Automatic Navigation Control for Standardized Orchard
## 2 Materials and Methods
### Fruit Tree Position Information Determination  
When using the 2D laser to scan the orchard environment, the laser receiver will receive signal feedback with different lengths due to the occlusion of the laser pulse by the trunk. According to this principle, the position of the fruit tree can be determined. As shown in Figure 5, we have established a rectangular coordinate system with the laser scanner's mounting position \(O\) as the origin and the \(Y\)-axis in the vehicle's forward direction. The \(p_{i}\) is the distance between the laser scanner's emission point and the target. The \(\lambda_{i}\) is the angle formed laser beam with the coordinate axis. The point \((x_{i},y_{i})\) is the Cartesian coordinates of the \(i\)-th point scanned by the 2D laser. By the Equation (1), we complete the process of the Cartesian coordinate transformation of the fruit tree position information. \[\left\{ \begin{array}{l}x_{i}=\rho_{i}\times\cos\lambda_{i}\\ y_{i}=\rho_{i}\times\sin\lambda_{i}\end{array} \right. \tag{1}\]  
Figure 4: Sine wave signal tracking results. Figure 5: Laser scanning Cartesian coordinate system. Due to the complex environment of the orchard, there were more interference points or outlier noise in the point cloud data acquired by the 2D laser, which seriously affects the accuracy of the navigation path identification. Therefore, the acquired point cloud data needs to be filtered first. As shown in Figure 6a, when the heading direction of the vehicle differs greatly from the navigation path, the laser beam can obtain the fruit tree information at a long distance through the spacing of the plant spacing between the fruit trees, thereby causing interference to obtain effective information. We set the i-th data point to \(q_{i}\). Its eigenvector is shown in Equation (2). Set the distance thresholds to \(\rho_{max}\) and \(x_{max}\). If \(\rho_{i}<\rho_{max}\) and \(x_{i}<x_{max}\), \(q_{i}\) is retained. Otherwise it is eliminated. \[q_{i}=\left[\rho_{i},\lambda_{i},x_{i},y_{i}\right]^{T} \tag{2}\]  
When there were small obstacles such as weeds, it does not affect the travel of the vehicle. The laser data of this experiment often contains some discrete points, as shown in Figure 6b. The \(d_{i}\) is the Euclidean distance from point \(q_{i}\) to any point. The \(D_{arr\cdot i}\) is the average distance of \(q_{i}\) to all its \(k\) neighbors and the \(H_{i}\) is the standard range of calculation. \[\left\{ \begin{array}{l}D_{arr\cdot i}=\frac{1}{k}\sum\limits_{i=1}^{k}d_{i} \\ H_{i}=\mu\pm g\times\sigma\end{array} \right. \tag{3}\]  
As shown in the Equation (3), we can see that \(\mu\) is the distance mean, \(\sigma\) is the distance standard deviation and \(g\) is the constant coefficient of standard range \(H_{i}\). When \(D_{arr\cdot i}>H_{i}\), the point is regarded as a discrete point and culled. Otherwise it is retained. When we obtain the complete fruit tree coordinate points, we use European clustering to cluster all the coordinate points on the same fruit tree. As shown in the equations (4), \(M_{i,i+1}\) is the Euclidean distance of the laser data points \(q_{i}\) and \(q_{i+1}\). The cluster search radius is \(r\) and its value is related to the average radius of the fruit trees. \[M_{i,i+1}=\sqrt{\left(x_{i+1}-x_{i}\right)^{2}+\left(y_{i+1}-y_{i}\right)^{2}} \tag{4}\]  
When \(M_{i,i+1}<r\), we think that two points come from the same fruit tree and gather into one kind; when \(M_{i,i+1}>r\), we think that two points come from different fruit trees. Through this experiment, we found that the point cloud data region obtained by the 2D laser scanner is the outer surface of the fruit tree trunk at the current laser height. The trunk of the fruit tree  
Figure 6: Laser data interference point type: (**a**) laser data cross-line interference point, (**b**) orbital noise between orchards. can be approximated as a cylinder, and the central feature point of the trunk can be extracted using the important geometric theorem of three points collinearity.