# Collision Risk Assessment and Operation Assistant Strategy for Teleoperation System
## 4 Collision Risk Assessment
### Calculation of the Evaluation Factors  
1. Calculation of the relative shortest distance  
Due to the irregular shape of the obstacles and the robot, it is challenging to calculate the distance between the connecting rod of the robot and the surrounding assembly parts using the conventional method. To simplify this problem, the method of the bounding box [27] was applied in this paper. Additionally, when measuring the nearest distance with conventional techniques, the two closest positions of the robot and the obstacles must be obtained, which can be challenging to accomplish [23]. Therefore, in this study, the discrete expandable bounding box approach was proposed as a solution to tackle this issue. To illustrate this method briefly, only one obstacle is introduced. As is shown in Figure 7, the connecting rods of the robot are wrapped with expanding capsule envelopes of various radii. The radii of the capsules are \(R_{0}\), \(R_{0}+d_{1}\), \(R_{0}+d_{2}\), and \(\dots\)\(R_{0}+d_{nt}\), respectively, where \(R_{0}\) denotes the smallest radius needed to completely enclose the robot arm. These preset envelope boxes move in tandem with the robot arm as it moves. Therefore, the shortest distance between the robot connecting rod surface and the surrounding obstacles can be converted into a collision detection problem between the bounding boxes and the surrounding obstacles. The smallest radius in all bounding boxes that collides with obstacles is considered as the relative shortest distance. The aforementioned procedure was performed utilizing the designed digital interface whose image processing function can handle the mentioned bounding box collision detection and offer feedback on the radii of contact layers. Despite the discretization method's limitations of precision, the issue is made more solvable, and the inaccuracy is within acceptable bounds. The specific calculation process is shown in Equations (1) and (2):  
\[R_{box-i}=R_{0}+d_{i}(d_{i}<d_{i-1}) \tag{1}\]  
\[D=\min(d_{i,\_contacted}) \tag{2}\]  
where, \(R_{box-i}\) represents the radius of the \(i\) layer bounding box, \(R_{0}\) denotes the smallest radius needed to completely enclose the robot arm, \(d_{i}\) denotes the increase in the radius of the \(i\)-th bounding box compared to the minimum radius bounding box, and \(d_{i,\_contacted}\) indicates the increase in the radius of the bounding box where contact occurs. 2. Calculation of delay time \(T\)  
The delay time comprises the delay in signal transmission brought on by radio transmission speed restrictions as well as the delay in data processing at sending and receiving stations and satellite relay stations [30]. As a result, the delay time is the amount of time that passes between sending a response signal by the local side and getting it from the remote side. To gauge the delay time, a master signal was created. It was initially transmitted by  
Figure 7: The discrete expandable bounding box method. the local side, if it was accepted by the slave, the response signal was sent back to the host. The time gap was used as the delay time of the current command period. The formula for calculating the delay time of the current command cycle is as follows:  
\[T_{i}=T_{i\_receive}-T_{i\_send} \tag{3}\]  
where, \(T_{i}\) represents the delay time of the \(i\) command cycle, \(T_{i\_send}\) is the the time of sending signal, \(T_{i\_receive}\) presents the time of receiving response signal, and \(i\) is the command cycle. 3. Calculation of operation speed \(V\)  
The operating speed of the current state is directly proportional to the movement distance, so the speed is calculated by the movement distance, which is calculated as follows.