# Robot Delay-Tolerant Sensor Network for Overhead Transmission Line Monitoring
## 3 RDTSN Model and Data Delivery Strategy
### Robot Delay-Tolerant Sensor Network (RDTSN) Model
#### 3.1.1 Motion Model of Inspection Robot  
In the network model, the simplified robot movement rule is shown in Figure 4. The robot moves along the ground wire between power towers. It will maintain a rest or uniform motion between the towers of \(N\) to \(N+n\) (\(n\), \(N\in N^{*}\)). When the robot is crossing the tower, it will walk at a low speed for obstacle climbing. Its movement model is consistent with the Random Waypoint [31], but the motion is along the power line. In order to identify the more-accurate kinematic relationship of the network, this paper introduces Path-constraint Random Waypoint (PRW), Bidirectional Path-constraint Random Waypoint (BPRW) and the new movement rules.  
A denotes the maximum motion range, S denotes the constraint path, P denotes the constraint point which the path S must pass through. In the network, static nodes are randomly distributed on the constraint point P. All robots follow the rules of movement and are independent of each other. Path-constraint Random Waypoint (PRW) is described as follows:  
1. Randomly select the movement starting point B and end point D on the S, where the point B and D should be on the same line.
2. Set random movement rate \(\
u\in(\
u_{\text{min}},\
u_{\text{max}})\) as the movement rate.
3. Robot moves at constant speed on the S's broken line of BD.
4. At point D, it takes the time of T\({}_{\text{pause}}\in(\text{T}_{\text{min}},\text{T}_{\text{max}})\) to remain stationary or complete an obstacle-climbing process.
5. Repeat the movement and select the last exercise endpoint D\({}_{X}\) as the starting point for the next movement \(B_{X+1}\).
6. All motion paths in Path-constraint Random Waypoint do not cross.  
Bidirectional Path-constraint Random Waypoint (BPRW) is similar to PRW, and it imitates the vehicle traffic and introduces two-way traffic rule. There are two parallel constraint paths in BPRW, the distribution of the constraint points P on the two constraint paths of S and S' are consistent. On each path, the moving node can only move in one direction. It moves in opposite direction on the S to S'. Excluding the above differences, BPRW and PRW are consistent with the two motion models.  
To a certain extent, the simplified rules can reflect the movement of robots in the network. However, in a multi-robot system, the motion model based on formation control will be more advantageous in reliability and efficiency. Therefore, a more capable Bidirectional Multi-robot Inspection(BMI) model is proposed. BMI model combines BPRW and formation control strategy, as shown in Figure 5 and described as follows.  
Figure 4: Tow movement models of robot. (**a**) PRW movement model; (**b**) BPRW movement model.  
1. The coordinates at unit center are the average of the multiple robots in a short time.
2. Robots perform uniform distribution in inspection tasks, as shown in Figure 5. * The whole transmission line is divided into two heterogeneity regions. * The robots are evenly distributed on different ground lines in the two regions.
3. The distance between any two robots on each ground line satisfies \(d\in(\frac{L}{n-1}-a,\frac{L}{n-1})\), \(n>1\).
4. All movements follow BPRW.  
In the BMI model, d denotes the distance between the two robots on each ground line; L denotes the length of each ground line; n denotes the number of robots; a denotes the accuracy of formation. All robots need to configure GPS or network-based localization algorithm. The robots can inspect all the transmission lines around it, including two ground lines. Therefore, the uniform distribution formation can achieve the best inspection efficiency.  
For the inspection robot network model, high-voltage ground wire is regarded as the path-constraint S, treat power tower as the constraint point P, the robot as mobile node. Each robot acts in accordance with PRW, BPRW or BMI and they are independent of each other.