## 4 Experiments
### Autonomous Deployment  
How to deploy the mobile sensor nodes into the target environments is an important problem we need to tackle first, especially when they are going to be used in the so-called unfriendly environments [13-14]. Here we propose a sequenced grid based autonomous deployment method for our mobile sensor network system. We divide the region waiting to be covered into a number of small sections and deploy at least one mobile node into every section. In order to avoid coverage holes, we have to abandon the idea to pursue maximum coverage area. Instead, when the deployment task is completed, we expect the sensor coverage circles to lap over each other and the inscribed squares of every four neighboring circles are connected together to form a bigger square, as shown in Figure 15.  
Then we can divide the target region into many identical square cells that connect with each other. The side length of each cell is \(L_{s=}\sqrt{2}R_{s}\). We set a starting point \(S\) at the entrance and each mobile node has to start its deployment motion from this point. Each cell is then assigned to one of the mobile nodes and the end point is the centroid of each cell. Due to the positioning errors, the mobile nodes in fact can not precisely reach the starting point or the end points. So we have to add target circles to surround those points. The radius of the target circle \(R_{d}\) is in proportion to the positioning accuracy of the mobile node. We number the cells according to the distances between the starting point and the end points. The nearest cell to the starting point is assigned a sequence number one; the second nearest one is assigned a sequence number two, and so on. In order to improve the deployment efficiency and avoid unnecessary obstructions by the previously deployed nodes, the mobile nodes are commanded to occupy the cells with the bigger sequence numbers first. Figure 16 shows the pseudocodes of the algorithm for autonomous deployment. The \(Rc\) value used in this experiment is about 20 meters, which is much longer than the physical size of the testbed. Every node communicates with the base station by only one hop. So the influences of communication range are not considered here. Figure 15: The principle of autonomous deployment of mobile sensor nodes. Before running the deployment routines, we have to assign a timing limit to each mobile sensor node in order to avoid trapping by obstacles. The timing limit of the mobile node to reach \(C_{i}\) is in proportion to the moving speed and the traveling distance to the target point. If the mobile node can not reach \(C_{i}\) before \(\tau_{i}\), then we consider \(C_{i}\) as unreachable and the mobile node stops. The obstacles are randomly distributed in the testbed. The node can autonomously avoid those obstacles on the deployment path by using the two infrared sensors. Here we suppose that there are at least \(n\) mobile nodes available for deployment. Figure 17 shows the process of the deployment experiment on the tabletop testbed. The target area is divided into 12 identical square cells. The value of \(L_{s}\) is 700 mm and the value of \(R_{d}\) is 100 mm. The position of the entrance and the adjacent start point can be localized by GPS or other general positioning methods. The mobile sensor nodes are put in front of the entrance to start its mission of deployment in turn. The average moving speed of each node is about 60 mm/s. Each node pauses for 3 seconds after every 100 encoder counts. During the pause, the node gets its current position data and routes the data back to the base station outside. The deployment experiment was repeated for several times and the stability of the deployment results was satisfying. Figure 16: Pseudocodes of the algorithm for autonomous deployment. Figure 17: Deployment of a group of twelve mobile sensor nodes. The coverage routes measured by the mobile sensor nodes during one of the deployment experiments are shown in Figure 18. One of the target circles can not be reached due to being trapped in the obstacle.