# Collision Risk Assessment and Operation Assistant Strategy for Teleoperation System
## 6 Experiment and Discussion
### System Evaluation  
In this section, the accuracy of the designed localization method was measured. In addition, the setting of the discrete expandable bounding box method was illustrated and its effectiveness in distance measurement was verified.  
1. Localization accuracy  
The UR5 robot arm can provide high-precision position information, and the repeated positioning precision in the x, y, z direction was \(\pm\)0.02 mm, \(\pm\)0.02 mm, and \(\pm\)0.05 mm, respectively. Therefore, the accuracy of the designed positioning method can be evaluated by using the localization information of the robot in different positions. As is shown in Figure 14a, the markers were fixed to the end of the robot. The end of the robot was guided to 10 different points using a point-to-point motion form (Figure 14b). The position of the target marker can be obtained by the visual algorithm. The error between the position obtained by the localization method and the information read by the robot represents the accuracy of the localization algorithm.  
As is shown in Figure 15, the positioning error along \(X\), \(Y\), and \(Z\)-axis did not exceed 0.5 mm, and the angular error around \(X\), \(Y\), and \(Z\)-axis was less than \(1^{\circ}\) in the whole working space. The positioning error was no more than 1 mm and \(2^{\circ}\). Therefore, this method has high accuracy and good stability. In the future, the marker can be printed together with the workpiece through 3D printing.  
Figure 14: (**a**) The setup of the experimental system for testing localization accuracy; (**b**) The Cartesian spatial motion trajectory of the robot arm.  
Figure 15: Positioning error curve.  
Validation of the discrete expandable bounding box method  
This paper proposed a new method for calculating the nearest relative distance based on the discrete expandable bounding box, where the shortest distance can be obtained by pre-setting the bounding boxes with different radius. Empirically, the bounding boxes are divided into 15 layers, and the radius of each layer is \(R_{n}=R_{0}+d_{n}\) and \(d_{n}\) = [1 cm, 2 cm, 3 cm, 4 cm, 5 cm, 6 cm, 7 cm, 8 cm, 9 cm, 10 cm, 12 cm, 15 cm, 20 cm, 25 cm], respectively. \(R_{0}\) is the minimum radius that can just achieve the robot arm enclosing. The smallest added radius of the bounding box (\(d_{n}\)) that is contacted with the surrounding obstacles represents the shortest distance. The design of the radius revealed that the radius was unevenly distributed, which is reasonable, because more precise information is needed when approaching obstacles, for example, the spacing of \(R_{1}\), \(R_{2}\), and \(R_{3}\) was only 1 cm. When the distance was about 20-30 cm, the safety was high and no more effort was needed to focus on the actual distance. A screenshot of the shortest distance acquisition through this method is shown in Figure 16. As is shown in the right of the figure, the robot arm link was enclosed by multiple layers bounding box. The \(D\) in the upper right corner represents the shortest distance calculated theoretically, and the \(Dr\) represents the shortest distance calculated by the discrete expandable bounding box. Therefore, the error did not exceed \(d_{n}/2\).