# Collision Risk Assessment and Operation Assistant Strategy for Teleoperation System
## 6 Experiment and Discussion
### Validation of the Collision Risk Assessment Model  
To validate the correctness of the proposed collision risk assessment model, three scenarios were designed in the virtual environment. A different assessment factor was kept for each scenario to verify the correct relationship between the collision risk and the factors. To illustrate the problem intuitively, one obstacle was placed. The coordinate value of the obstacle was (0 mm, 600 mm, 100 mm), and the radius was 50 mm. In each scenario, the robot moves from the starting point A to the end position B according to the red line shown in Figure 17 with the robot's end-effector posture remaining constant, and the collision risk value of each scenario is recorded.  
Figure 16: Screenshot of the shortest distance calculated by the discrete expansion bounding box method. We need to further elaborate the process of theoretical calculation of the shortest distance. The reason why the theoretical distance is accessible is that the obstacle is directly in front of the end of the robot, so the distance from the end of the robot to the center of the obstacle, when removing the diameter of the obstacle, is the shortest distance. When the obstacle is not in front, the theoretical calculation is incorrect, because it is necessary to obtain the shortest distance contact point with the obstacle. This point may not be the end of the robot, and it may be in another link of the robot. Therefore, the theoretical calculation is complex and difficult.  
Scenario A. This scenario verified the positive correlation between the collision risk and the nearest distance. The robot moves to the terminal position B from starting point A with a fixed speed (v = 40 mm/s) and a delay time (T = 2 s). Figure 18a depicts the results.  
Scenario B. In this scenario, the robot moves to the same terminal position from the same starting point with different terminal speed; the velocity of each movement is 10 mm/s, 20 mm/s, and 40 mm/s, respectively. The delay time is all set at 2 s. The results are shown in Figure 18b.  
Scenario C. In this scenario, the delay time of each robot movement was set to 1 s, 2 s, 3 s, and 4 s, respectively, and the speed of each movement was 30 mm/s. The results can be observed in Figure 18c.  
Figure 17: The scenarios in the virtual environment.  
Figure 18: The collision risk assessment results in virtual simulation scenario (**a**) results when T = 2 s, v = 20 mm/s; (**b**) collision risk assessment results with different speeds and T = 2 s; (**c**) collision risk assessment results with different delays at V = 30 mm/s. The smaller the value, the higher the collision risk.  
As can be seen in Figure 18a, the collision risk increased with the decrease in the shortest distance for the same speed and delay time, with a more pronounced trend as the robot approached the obstacle. Moreover, the risk value did not increase linearly, because the results combined the expert experience of risk assessment in different scenarios, which is also the advantage of this method. In addition, when the robot was at the same starting position, the collision risk value of the robot with an end speed magnitude of 40 mm/s was 0.6206, which is lower than the calculated value of 1.8438 for 10 mm/s. According to the fuzzy definition of collision risk and membership function (Figure 12) the smaller the value, the higher the collision risk. Therefore, the result shows that the risk increased with the increase in the speed magnitude. It can be proven that the collision risk assessment model is not only related to the shortest distance, but it is also related to the operation speed. Figure 10c illustrates that the delay time has a similar effect on collision risk as speed.