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Fig. 9 Cumulative Distribution Function (CDF) of the time spent to fully cover the area for the PdUC, PdUC-D, Billiard and Spiral mobility models

Figure 9 Cumulative Distribution Function (CDF) of the time spent to fully cover the area for the PdUC, PdUC-D, Billiard and Spiral mobility models

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REESE MAIR ER ce eee SS ERTL, Sue NETO US eee eee Nes mee Eo EE EEE Despite PdUC [6] being more effective than other mobility patterns (Spiral and Billiard) in terms of polluted areas monitoring times, finding the most highly polluted locations earlier, it still spends too much time focusing on small variations. Tracking these variations, that can also be produced by sensor errors, is not too efficient in obtaining the global pollution map. On the contrary, the Spiral and Billiard models present simpler mobility patterns that, by themselves, avoid such redundant sampling. So, in this work, the main idea is to optimize PdUC by discretizing the whole target area, creating a grid composed of small tiles. Notice that discretization is one of the most efficient mathematical approaches to optimize a system by transforming a continuous domain into its discrete counterpart [14], as shown in Fig. 1. Notice that the UAV can only move to the center of each tile, and each tile can only be monitored once, thereby reducing redundant sampling, which in turn reduces the full coverage time significantly.
REESE MAIR ER ce eee SS ERTL, Sue NETO US eee eee Nes mee Eo EE EEE Despite PdUC [6] being more effective than other mobility patterns (Spiral and Billiard) in terms of polluted areas monitoring times, finding the most highly polluted locations earlier, it still spends too much time focusing on small variations. Tracking these variations, that can also be produced by sensor errors, is not too efficient in obtaining the global pollution map. On the contrary, the Spiral and Billiard models present simpler mobility patterns that, by themselves, avoid such redundant sampling. So, in this work, the main idea is to optimize PdUC by discretizing the whole target area, creating a grid composed of small tiles. Notice that discretization is one of the most efficient mathematical approaches to optimize a system by transforming a continuous domain into its discrete counterpart [14], as shown in Fig. 1. Notice that the UAV can only move to the center of each tile, and each tile can only be monitored once, thereby reducing redundant sampling, which in turn reduces the full coverage time significantly.
Fig.2 Change of the PAUC to PdUC-D algorithm
Fig.2 Change of the PAUC to PdUC-D algorithm
First, both matrices are initialized, P with NaN (null), and B with 0’s. In the Search phase, when monitoring a tile ¢;,; (@ and j are the row and the column position, respectively), the obtained pollution values are stored in P;,;, and B;,; are set to 1. When monitoring a tile either With regard to movement control, and to avoid re-visiting previously monitored areas, we use two matrices: Py, and By ,n, to store the sampled values and the monitored tiles, respectively. Notice that n x m represents the size of the grid (rows and columns respectively).
First, both matrices are initialized, P with NaN (null), and B with 0’s. In the Search phase, when monitoring a tile ¢;,; (@ and j are the row and the column position, respectively), the obtained pollution values are stored in P;,;, and B;,; are set to 1. When monitoring a tile either With regard to movement control, and to avoid re-visiting previously monitored areas, we use two matrices: Py, and By ,n, to store the sampled values and the monitored tiles, respectively. Notice that n x m represents the size of the grid (rows and columns respectively).
Fig. 4 Change of the PAUC to PdUC-D algorithm in the Explore phase: Adaptive Spiral (top), Alternate direction (middle), and Avoidance of previously monitored areas (bottom)
Fig. 4 Change of the PAUC to PdUC-D algorithm in the Explore phase: Adaptive Spiral (top), Alternate direction (middle), and Avoidance of previously monitored areas (bottom)
First of all, we analyze the impact of varying the tile size between 50[m] and 400[m]. Our goal is to determine which is the best size considering our restrictions.
First of all, we analyze the impact of varying the tile size between 50[m] and 400[m]. Our goal is to determine which is the best size considering our restrictions.
Table 1 Simulation parameters
Table 1 Simulation parameters
Fig. 7 Cumulative Distribution Function of the time spent by PdUC- D to fully cover the area for different tile sizes: 50, 100, 200, and 400 meters, respectively In the equation, e; is the relative error at time ¢, Sy,y,1 is the recreated pollution value at position (x, y) using the samples taken during simulation until time f, by.) is the reference pollution value at position (x, y), and n and m are the dimensions of the target area, respectively.
Fig. 7 Cumulative Distribution Function of the time spent by PdUC- D to fully cover the area for different tile sizes: 50, 100, 200, and 400 meters, respectively In the equation, e; is the relative error at time ¢, Sy,y,1 is the recreated pollution value at position (x, y) using the samples taken during simulation until time f, by.) is the reference pollution value at position (x, y), and n and m are the dimensions of the target area, respectively.
Fig. 8 Relative error comparison for PAUC-D varying tile sizes: 50, 100, 200, and 400 meters, respectively
Fig. 8 Relative error comparison for PAUC-D varying tile sizes: 50, 100, 200, and 400 meters, respectively
Fig. 10 Relative error comparison between the PdUC, PdUC-D, Billiard and Spiral mobility models at different times can observe that all mobility models roughly exhibit the same behavior: they start with a high relative error, which is foreseeable since we are using Kriging interpolation to recreate the pollution distribution, and it gradually decreases toward the mean error value as the number of samples increases. Then, as more and more samples become available, the spatial interpolation process quickly becomes
Fig. 10 Relative error comparison between the PdUC, PdUC-D, Billiard and Spiral mobility models at different times can observe that all mobility models roughly exhibit the same behavior: they start with a high relative error, which is foreseeable since we are using Kriging interpolation to recreate the pollution distribution, and it gradually decreases toward the mean error value as the number of samples increases. Then, as more and more samples become available, the spatial interpolation process quickly becomes
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Computer ScienceDistributed ComputingFlexibility in engineering designAir Pollution MonitoringOther Engineering
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