# Coastal Areas Division and Coverage with Multiple UAVs for Remote Sensing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Problem Statement, Assumptions and Metrics Considered

- The closeness of the cells within ${A}_{i}$ to the initial location ${\mathbf{p}}_{i}$ of the UAV in charge of searching that sub-area should be minimized. This can be achieved by minimizing the sum of distances between each center of cell ${\mathbf{c}}_{ij}$ from the set S and the initial locations ${\mathbf{p}}_{i}$:$$\underset{S}{min}F\left(S\right)=\underset{S}{min}\sum _{i=1}^{n}\sum _{j=1}^{{M}_{i}\left(S\right)}\parallel {\mathbf{p}}_{i}-{\mathbf{c}}_{ij}\parallel \phantom{\rule{0.277778em}{0ex}},$$
- The size of ${A}_{i}$ should be as close as possible to ${Z}_{i}$ for all of the UAVs. This can be achieved by minimizing the sum of differences:$$\underset{S}{min}G\left(S\right)=\underset{S}{min}\sum _{i=1}^{n}\left(\right)open="|"\; close="|">\sum _{j=1}^{{M}_{i}\left(S\right)}\mathrm{area}\left({C}_{j}\right)-{Z}_{i}$$

## 4. Model Considered for the On-Board Sensors

## 5. Area Decomposition and Partition in a Multi-UAV Context

#### 5.1. Exact Cell Decomposition

#### 5.2. Baseline Area Partitioning Algorithm

Algorithm 1: Antagonizing wavefront propagation algorithm that computes the baseline area partition. Q is a queue list managed as an FIFO by functions $insert$ and $getFirst$. |

${v}_{Ik}$: initial vertices/triangular cells for each UAV ${U}_{k}$, ${S}_{v}$: area size of triangular cells v, $N\left(v\right)$: the set of neighbors of vertex v, $A\left(v\right)$: the UAV identifier allocated to triangular cell v, ${Z}_{k}$: area coverage capability of UAV ${U}_{k}$ in square meters ${S}_{vMin}$: area size of the smallest triangular cell in CDT |

#### 5.3. Reverse Watershed Schema

Algorithm 2: RWS algorithm for the generation of the border-to-center cost $D\left({v}_{i}\right)$ attribute. Q is a queue list managed as an FIFO by functions $insert$ and $getFirst$. |

$N\left(v\right)$: the set of neighbors of vertex/triangular cell v, $A\left(v\right)$: the UAV identifier for triangular cell v |

#### 5.4. Adjustment Function for Deadlock Scenarios

Algorithm 3: Multi-UAV partitioning Deadlock Handling (DLH) algorithm. Baseline partitioning is performed by Algorithm 1, whereas this method is for the sub-area size adjustment (if needed). Function $getSurplusUAV\left(L\right)$ gets a UAV identifier from list L that has an area surplus, whereas function $getShortfallUAV\left(L\right)$ gets the identifier of a UAV that has an area shortfall after Algorithm 1. Function $findSequence$ finds a feasible transition sequence ${P}_{ij}$ between UAV ${U}_{i}$ and ${U}_{j}$, whereas the $move$ function performs the transfer between triangular cells. |

${S}_{vMin}$: area size of the smallest triangular cells in CDT |

Algorithm 4: MoveAWP algorithm. ${C}_{v}$ is the transition cost from the AWP algorithm (see Algorithm 1). Then, function $FindBiggest{C}_{v}(P\left[i\right],P[i+1])$ finds the largest transition cost value triangular cell of UAV $P\left[i\right]$ that is adjacent to UAV $P[i+1]$ in the sequence. Then, function $Awp$ takes as variables an initial cell v, the area size that needs to be exchanged and the UAV identifier that needs to be exchanged from. The growing function is similar to Algorithm 1. |

${P}_{ij}$ the transition sequence between ${U}_{i}$ and ${U}_{j}$ for triangular cells exchange, treated as a list ${v}_{init}$: initial triangular cell for identifier exchange S: area size to be moved |

Algorithm 5: MoveRWS algorithm. Function $FindSequence$ finds a valid transition sequence, as can be seen in Figure 8. This function is also called before the initial recursion of the MoveRWS algorithm. Function $ExchangeIdentifiers$ makes use of the information of the RWS algorithm (see Algorithm 2), and it exchanges agent identifiers on two adjacent configuration spaces, by exchanging the amount of triangular cells that have the lowest coverage cost, but are adjacent. It also propagates and extends this cost. Function $RestOfSequence$ returns the remaining sequence for the specific $P\left[i\right]\to P[i+1]$ transition, in order to initially transfer only the amount of triangular cells that are adjacent between i and $i+1$ until the final ${U}_{j}$ UAV. In case this happens, the requested area has not been exchanged yet, so the algorithm runs recursively, and the last line takes a step back in sequence traversal. |

S area size to be moved ${S}_{adj\left(kl\right)}$ the area size of adjacent triangular cells between UAV k and l ${P}_{ij}$ the transition sequence between ${U}_{i}$ and ${U}_{j}$ for triangular cell exchange, treated as a list |

## 6. Simulation Results

#### 6.1. Coordinate Frames

#### 6.2. Simulation Architecture and Configuration

#### 6.3. Partitioning Algorithms Comparison in Simulation

#### 6.4. Coverage Path Planning Simulation Results

Algorithm 6: Waypoint list computation for coverage. ${D}_{c}$ is an auxiliary variable with the current border-to-center cost in each step, whereas ${v}_{{I}_{k}}$ is the starting position of the UAV ${U}_{k}$. Function $findClosest$ finds the closest vertex to the current one that has its same border-to-center cost. $CD{T}_{k}$ is the sub-CDT for UAV ${U}_{k}$. W is the produced waypoint list of vertices. |

${D}_{c}\leftarrow \infty $; $v\leftarrow $ findClosest(${v}_{{I}_{k}},{D}_{c}$); W.insert(v); |

## 7. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

UAV | Unmanned Aerial Vehicle |

FoV | Field of View |

CDT | Constrained Delaunay Triangulation |

AWP | Antagonizing Wavefront Propagation |

RWS | Reverse Watershed Schema |

DLH | Deadlock Handling |

ROS | Robotic Operating System |

SITL | Software In The Loop |

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**Figure 1.**An example with three UAVs, each one with its allocated sub-area. The scheme is composed by two levels: the bottom layer shows the different on-board sensors’ field of view projection on the sea, whereas the upper shows the cell decomposition denoted as a triangular grid on top of each UAV. ${U}_{1}$, ${U}_{2}$ and ${U}_{3}$ denote the UAVs, and ${A}_{1}$, ${A}_{2}$ and ${A}_{3}$ denote the the sub-areas of the total region R, which is constrained by the red borders. The initial positions of the UAVs are ${\mathbf{p}}_{1}$, ${\mathbf{p}}_{2}$ and ${\mathbf{p}}_{3}$.

**Figure 2.**FoV projection calculation is relative to the coordinate frames of the system. For missions in coastal regions, the ground can be considered as flat.

**Figure 3.**The appropriate cell decomposition is proportional to the velocity V, the sample rate T and the FoV projection footprint F. In (

**a**), in every time step ${t}_{0},{t}_{1},\dots ,{t}_{n}$, F is not large enough for the sensor to take a complete sample, whereas in (

**b**), T is not fast enough to obtain a sample from each area. In both cases, the problem could be solved be either reducing the speed, increasing the sample rate if possible or increasing the altitude for increasing the projection of the FoV. In (

**c**), the ideal solution in the limit is shown, whereas in (

**d**), the most usual case of the same portion of the sea being present in many samples is presented.

**Figure 4.**Trondheim fjord area (Norway) with Ytterøya island. The complex coastal area of interest is denoted by the black outer polygon, whereas the red dashed areas indicate regions that are no-fly zones.

**Figure 5.**The FoV footprint, which is used in the test case of this paper, can be seen in (

**a**) and forms a trapezoid T. The pitch angle $\beta $, along with the sensor’s view angle $\theta $, the angle $\psi $ that pitch $\beta $ and the bisector of $\theta $ form and the altitude h from the ground are used for the calculation. The CDT constraint is defined by side d of the inscribed equilateral triangle W. Since G is the centroid of T, as well as W, the inscribed circle of T always coincides with the circumscribed circle of W. Then, the orientation of the two shapes is irrelevant. In addition, since W is the largest triangle that can be produced from the triangulation, any smaller triangles will always be inside the inscribed circle of T. In (

**b**), the general calculation case is shown for no normal or tangential quadrilateral FoVs. In order to draw the maximum incircle of the quadrilateral, all four expanded triangles ($a{c}_{2}b$, ${c}_{2}b{c}_{1}$, $b{c}_{1}a$, ${c}_{1}a{c}_{2}$) must be drawn and their incircles found. Afterwards, the largest circle that is also an incircle of the quadrilateral is chosen, in this case the inscribed circle that is adjacent to sides b, ${c}_{2}$ and a, and it is used for extracting the CDT constraint.

**Figure 6.**A CDT for a coastal region. In (

**a**), the outer region constraints in black form a complex non-concave polygon. Several no-fly zones inside the constrained area are denoted in red. In (

**b**) is depicted the CDT triangulation. The red dots represent the centroids of each cell. The shades of gray denote the Reverse Watershed Schema (RWS) formulation described later in Section 5.3.

**Figure 7.**A deadlock scenario. Four UAVs ${U}_{1}$, ${U}_{2}$, ${U}_{3}$ and ${U}_{4}$ after the baseline partition Algorithm 1. UAVs ${U}_{1}$, ${U}_{2}$ and ${U}_{4}$ have met their autonomy capability of ${Z}_{k}$ by covering ${Y}_{k}$ area. Nevertheless, ${U}_{3}$ was not able to overtake any more area, being “blocked” by the other UAVs and the borders of the whole region. Colored areas indicate the configuration space of each UAV, while the numbers inside the cells indicate the isotropic cost, as has been assigned by Algorithm 1. The free or non-allocated areas belong to virtual UAV ${U}_{-1}$.

**Figure 8.**Transition sequence selection. After the initial partition process, ${U}_{1}$, ${U}_{2}$ and ${U}_{4}$ have met their sub-area size constraint and blocked the growth of ${U}_{3}$. As a result, three areas are not allocated (${U}_{-1}$). The feasible transition sequences A(green), B(red) and C(blue) are used in order for ${U}_{3}$ to obtain the requested total area, by gradually exchanging cells in every pair of the sequence. Sequence D(black) does not lead to a partition that has an area shortfall, and thus, it is a not feasible sequence.

**Figure 9.**Selected areas for testing: (

**a**) Salamina area having narrow passages and complex shapes in shores; (

**b**) the Astipalea area is used for testing the suitability of the proposed algorithm; (

**c**) Sxoinousa area used for coverage planning. The red square shows the region where the simulated flights occurred.

**Figure 10.**UAV and sensor coordinate frames and their relation. Depending on the roll ($\gamma $), pitch ($\beta $) and yaw ($\alpha $) angles of the sensor with respect to the UAV fuselage, a rotation of the projected field of view occurs.

**Figure 11.**Software architecture with different libraries and components: the latest CGAL library (4.8.1) [19], ROS Indigo [1] components (the rviz package [21] for visualization and the mavros node [22] for the mavlink interface with the simulated UAV), an Arduplane instance [23] of the Ardupilot SITL [20], which uses the JSBSim flight dynamics model [24], and the qgroundcontrol control station [25].

**Figure 12.**The qTnP main application. The first tab echoes the ROS communication messages and logs. The main "UAV Manager" tab of the application includes the UAV management table, indicating the sensor type, the cell (FoV) size, autonomy percentages and initial positions. It also includes the visualization options for rviz, showing the cost values of each of the proposed algorithms, visualizing the partitioned configuration space, showing the borders of each UAV and the produced waypoints for coverage. Finally, the command panel on the right includes connection settings, CDT-specific configuration, the KML file of the area, as well as several command buttons for the different stages of the experiments.

**Figure 13.**Partitioned area for three UAVs (indicated by the white cells) and visualized by using the ROS rviz node. Each row represents the results for different relative capabilities: the first row is the 10% (red), 60% (blue), 30% (green) case; the second row depicts the 33% (red), 33% (blue), 34% (green) case; whereas the last row shows the 80% (red), 10% (blue), 10% (green) case. In each row, each pair of images indicates the comparison of the two algorithms. (

**a**,

**b**) show how the MoveAWP and MoveRWS algorithms have performed with the small (250 m) FoV, whereas (

**c**,

**d**) show the results for the large (2 km) FoV case. (

**a**) MoveAWP 250 m FoV; (

**b**) MoveRWS 250 m FoV; (

**c**) MoveAWP 2 km FoV; (

**d**) MoveRWS 2 km FoV; (

**e**) MoveAWP 250 m FoV; (

**f**) MoveRWS 250 m FoV; (

**g**) MoveAWP 2 km FoV; (

**h**) MoveRWS 2 km FoV; (

**i**) MoveAWP 250 m FoV; (

**j**) MoveRWS 250 m FoV; (

**k**) MoveAWP 2 km FoV; (

**l**) MoveRWS 2 km FoV.

**Figure 14.**Area of Figure 9b selected for the comparison of the two partitioning algorithms. (

**a**) is partitioned for three UAVs, whereas (

**b**) for five UAVs. The depicted FoV size is 30 m in both cases. Both figures are computed with the deadlock moveRWS handling of Algorithm 5.

**Figure 15.**Area partition after applying the baseline and the deadlock moveRWS handling algorithm. (

**a**) shows the area partitioned for four UAVs evenly distributed in the area and a FoV projection of 30 m. (

**b**) shows the results for a FoV projection of 15 m and four UAVs randomly located. The black triangles depict the initial positions in all of the cases.

**Figure 16.**A graphical representation of Table 3 and Table 4. Average difference after the baseline algorithm and after the deadlock moveRWS treatment algorithm. As expected, random initial positioning of UAVs creates more often deadlock scenarios for the baseline algorithm. The algorithm has been tested for 3–6 UAVs, evenly or randomly distributed in the area. FoV projections of 15 and 30 m have been tested, and in each case, a different Lloyd iteration setting (20, 30 and 60) has been set. The horizontal lines show the average difference.

**Figure 17.**Area partitioning for three UAVs on the same location as in Figure 9c. White areas indicate the no-fly zones, whereas the black triangles show the initial positions of the UAVs. In (

**a**), the FoV sized cell distribution is shown along with the centers of the triangles. Regarding waypoint generation for coverage, (

**b**) shows the produced coverage paths for all of the UAVs. The different shades of orange indicate the border-to-center cost computed by Algorithm 2.

**Figure 18.**Coverage trajectory computed in the simulation. (

**a**) shows a detailed view of the UAV 3 trajectory in Figure 17. Latitude and longitude information received during the simulated flight of that UAV is shown in (

**b**,

**c**) with the total sensor coverage considering a sensor working at a very slow rate of 1 Hz. Finally, (

**d**) shows a screenshot of the ground station visualization during the simulations.

**Table 1.**An even distribution of initial locations for three and five UAVs, with different relative capabilities.

FoV (15 m) | FoV (30 m) | ||||
---|---|---|---|---|---|

#UAVs | moveRWS | moveAWP | moveRWS | moveAWP | |

Metric F (m) | 3 | 333,861.84 | 333,909.67 | 82,768.44 | 84,979.76 |

Metric F (m) | 5 | 437,988.74 | 439,642.85 | 129,879.24 | 131,516.96 |

**Table 2.**Random initial position distribution for three and five UAVs, with different relative capabilities. Like before, Algorithm 5 has performed better than Algorithm 4.

FoV (15 m) | FoV (30 m) | ||||
---|---|---|---|---|---|

#UAVs | moveRWS | moveAWP | moveRWS | moveAWP | |

Metric F (m) | 3 | 508,801.74 | 508,751.513 | 211,395 | 214,945.82 |

Metric F (m) | 5 | 566,971.55 | 568,819.45 | 151,389.621 | 155,269.99 |

**Table 3.**For each UAV, the difference from its given capability is shown after the initial baseline algorithm and after the moveRWS deadlock treatment algorithm. An average for all UAVs, as well as the total difference is shown below each experimental setup, where G is the metric defined in Equation 2 and $\mathrm{area}\left(R\right)$ is the area in ${m}^{2}$ of the whole region R. The UAVs have evenly distributed initial positions. Setups for 3, 4, 5 and 6 UAVs have been tested, with different relative capabilities and FoV values. Different Lloyd iterations on the mesh have been tested, ranging between 20 and 60.

UAV Capability % | FoV (15 m) | FoV (30 m) | ||||
---|---|---|---|---|---|---|

Lloyd Iterations | Lloyd Iterations | |||||

20 | 30 | 60 | 20 | 30 | 60 | |

50% | 0.5/0.92 | 0/0.62 | 0/0.92 | 0.35/0.3 | 0.35/0.18 | 0.05/0.3 |

30% | 6.74/0.14 | 6.74/0.89 | 6.88/1.21 | 6.95/0.21 | 7.19/0.65 | 6.86/0.25 |

20% | 0.01/1.04 | 0.01/0.26 | 0.01/0.28 | 0/0.49 | 0.03/0.82 | 0.05/0.54 |

Average% | 2.41/0.69 | 2.25/0.59 | 2.29/0.80 | 2.43/0.32 | 2.52/0.55 | 2.32/0.36 |

$\mathit{G}/\mathbf{area}\left(\mathit{R}\right)$% | 7.25/2.1 | 6.75/1.78 | 6.89/2.42 | 7.3/0.99 | 7.57/1.66 | 6.96/1.09 |

20% | 0.02/0.02 | 0.02/0.08 | 0.02/0.06 | 0/0.41 | 0.05/0.12 | 0.05/0.45 |

40% | 0/0.06 | 0/0.11 | 0/0.05 | 3.89/0.28 | 3.91/0.59 | 3.6/0.49 |

20% | 0.96/0 | 1.11/0 | 0.78/0.06 | 0.48/0.17 | 0.48/0 | 0.62/0.12 |

20% | 0/0.02 | 0/0.17 | 0/0.03 | 0/0.29 | 0/0.48 | 0/0.07 |

Average% | 0.25/0.03 | 0.28/0.09 | 0.2/0.05 | 1.09/0.37 | 1.11/0.3 | 1.07/0.28 |

$\mathit{G}/\mathbf{area}\left(\mathit{R}\right)$% | 0.98/0.12 | 1.13/0.35 | 0.8/0.2 | 4.37/1.11 | 4.44/1.18 | 4.27/1.13 |

20% | 0.15/0.38 | 0.15/0.6 | 0.18/0.01 | 0.15/0.11 | 0.11/0.59 | 0.11/1.36 |

30% | 13.73/0.34 | 13.75/0.31 | 13.72/0.15 | 13.1/0.24 | 12.98/0.76 | 12.63/1.64 |

20% | 0/0.31 | 0/0.42 | 0/0.08 | 0/1.6 | 0.3/0.81 | 0/0.66 |

10% | 0/0.41 | 0/0.86 | 0/0.41 | 0/0.71 | 0/0.3 | 0/1.21 |

20% | 0.21/0.65 | 0.05/0.14 | 0.21/0.36 | 0/1.01 | 0/0.36 | 0/1.61 |

Average% | 2.81/0.42 | 2.79/0.47 | 2.28/0.35 | 2.65/0.92 | 2.68/0.56 | 2.55/0.9 |

$\mathit{G}/\mathbf{area}\left(\mathit{R}\right)$% | 14.09/2.1 | 13.95/2.33 | 14.11/1.01 | 13.25/3.69 | 13.39/2.81 | 12.74/4.5 |

10% | 0.15/0.21 | 0.15/0.73 | 0.15/0.41 | 0.11/0.72 | 0/0.18 | 0.11/0.29 |

20% | 0.3/1.04 | 0.3/1.37 | 0.3/1.35 | 0/1.83 | 0/1.37 | 0/0.43 |

10% | 0.15/0.23 | 0.15/0.16 | 0.15/0.23 | 0.11/0.14 | 0/0.97 | 0.11/0.39 |

30% | 11.26/0.38 | 11.45/0.69 | 11.2/0.53 | 11.94/0.84 | 12.64/0.83 | 10.75/0.96 |

20% | 0.3/0.51 | 0.3/0.36 | 0.3/0.33 | 0.24/0.8 | 0/0.98 | 0.24/0.55 |

10% | 0.15/0.19 | 0.15/0.47 | 0.15/0.15 | 0.11/1.04 | 0.11/1.25 | 0.11/0.98 |

Average% | 2.05/0.41 | 2.08/0.63 | 2.04/0.5 | 2.09/0.9 | 2.13/0.93 | 1.89/0.6 |

$\mathit{G}/\mathbf{area}\left(\mathit{R}\right)$% | 12.32/2.47 | 12.5/3.78 | 12.25/3.01 | 12.51/5.36 | 12.75/5.58 | 11.32/3.59 |

**Table 4.**For each UAV, the difference from its given capability is shown after the initial baseline algorithm and after the moveRWS deadlock treatment algorithm. An average for all UAVs, as well as the total difference is shown below each experimental setup, where G is the metric defined in Equation 2 and $\mathrm{area}\left(R\right)$ is the area in ${m}^{2}$ of the whole region R. The UAVs have randomly distributed initial positions. Setups for 3, 4, 5 and 6 UAVs have been tested, with different relative capabilities and FoV values. Different Lloyd iterations on the mesh have been tested, ranging between 20 and 60.

UAV Capability % | FoV (15 m) | FoV (30 m) | ||||
---|---|---|---|---|---|---|

Lloyd Iterations | Lloyd Iterations | |||||

20 | 30 | 60 | 20 | 30 | 60 | |

50% | 0/0.1 | 0/0 | 30.8/0.27 | 0/0 | 0/1.49 | 29.81/0.5 |

30% | 1.19/0.02 | 0.08/0.02 | 0.01/0.16 | 0.024/0.024 | 20.9/0.65 | 0.01/0.57 |

20% | 0.01/0.09 | 0.01/0.01 | 0.01/0.11 | 0.024/0.024 | 0.024/0.84 | 0.05/1.1 |

Average% | 0.4/0.07 | 0.03/0.01 | 10.27/0.18 | 0.02/0.02 | 6.97/0.99 | 9.95/0.72 |

$\mathit{G}/\mathbf{area}\left(\mathit{R}\right)$% | 1.2/0.21 | 0.09/0.03 | 30.82/0.54 | 0.05/0.05 | 20.92/2.98 | 29.87/2.17 |

20% | 0/0.43 | 15.37/0.22 | 2.19/0.49 | 0/0.730 | 14.2/1.66 | 0.62/0.05 |

40% | 13.1/0.33 | 0/0.53 | 0/0.22 | 14/0.43 | 0/1.89 | 0.07/0.14 |

20% | 6.48/0.31 | 0/0.06 | 2.64/0.35 | 6.24/0.56 | 0/0.12 | 1.8/0.16 |

20% | 0/0.42 | 0/0.69 | 0/0.35 | 0/0.26 | 0/0.12 | 0.02/0.07 |

Average% | 4.9/0.37 | 3.84/0.38 | 1.21/0.36 | 5.06/0.5 | 3.55/0.95 | 0.67/0.11 |

$\mathit{G}/\mathbf{area}\left(\mathit{R}\right)$% | 19.58/1.48 | 15.37/1.5 | 4.83/1.43 | 20.24/1.98 | 14.2/3.79 | 2.67/0.42 |

20% | 0.01/0.03 | 0.01/0.21 | 11.23/0.77 | 0/1.8 | 0.02/1.43 | 10.78/0.4 |

30% | 0.53/0.02 | 12.85/0.24 | 0.02/0.68 | 0/0.27 | 13.45/0.42 | 0.02/1.4 |

20% | 0.01/0.03 | 0.01/0.11 | 11.59/2.65 | 6.24/0.57 | 6.88/0.44 | 10.78/0.64 |

10% | 0.01/0.07 | 0.01/0.19 | 3.382/1.19 | 0/0.46 | 0.04/0.21 | 3.97/0.04 |

20% | 0.01/0.14 | 0.01/0.14 | 0.01/1.36 | 0/1.03 | 0.02/0.37 | 0.02/0.4 |

Average% | 0.11/0.05 | 2.58/0.18 | 5.25/1.33 | 1.25/0.82 | 4.12/0.57 | 5.11/0.58 |

$\mathit{G}/\mathbf{area}\left(\mathit{R}\right)$% | 0.57/0.27 | 12.89/0.89 | 26.24/6.64 | 6.24/4.12 | 20.59/2.87 | 25.57/2.88 |

10% | 0.02/0.46 | 4.36/0.05 | 4.2/0.26 | 0.04/0.36 | 0.04/0.18 | 0.04/0.09 |

20% | 0.02/1.02 | 4.23/0.26 | 0.01/0.06 | 0.05/0.3 | 0.05/0.36 | 0.05/1.49 |

10% | 0.02/0.42 | 0.01/0.47 | 0.01/0.01 | 0.04/1.2 | 0/0.41 | 0.04/0.25 |

30% | 19.04/0.5 | 0.01/1.22 | 0.01/0.01 | 20.32/0.74 | 20/1.48 | 19.85/0.31 |

20% | 0.01/0.9 | 0.02/0.04 | 0.01/0.02 | 10.32/0.49 | 10.32/0.24 | 10.08/0.65 |

10% | 0.02/0.66 | 0.01/0.58 | 0.01/0.2 | 0.04/0.028 | 0/1.01 | 0.04/0.22 |

Average% | 3.18/0.66 | 1.44/0.43 | 0.71/0.09 | 5.13/0.52 | 5.07/0.61 | 5.02/0.5 |

$\mathit{G}/\mathbf{area}\left(\mathit{R}\right)$% | 19.13/3.96 | 8.64/2.62 | 4.25/0.56 | 30.81/3.12 | 30.41/3.68 | 30.1/3.01 |

**Table 5.**Values of the parameters considered for the UAVs in the simulations. The FoV projection size is the maximum cell side size of the triangulation. Angle $\gamma $ is the on-board sensor pitch angle with respect to the horizontal plane. The relative capability percentages represent the capability of each UAV related to the whole area for covering purposes.

UAV | FoV Projection Size (m) | $\mathit{\gamma}$ (deg) | Altitude (m) | Relative Capability |
---|---|---|---|---|

UAV 1 | 30 | −45 | 100 | 20% |

UAV 2 | 40 | −45 | 80 | 30% |

UAV 3 | 55 | −45 | 120 | 50% |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Balampanis, F.; Maza, I.; Ollero, A.
Coastal Areas Division and Coverage with Multiple UAVs for Remote Sensing. *Sensors* **2017**, *17*, 808.
https://doi.org/10.3390/s17040808

**AMA Style**

Balampanis F, Maza I, Ollero A.
Coastal Areas Division and Coverage with Multiple UAVs for Remote Sensing. *Sensors*. 2017; 17(4):808.
https://doi.org/10.3390/s17040808

**Chicago/Turabian Style**

Balampanis, Fotios, Iván Maza, and Aníbal Ollero.
2017. "Coastal Areas Division and Coverage with Multiple UAVs for Remote Sensing" *Sensors* 17, no. 4: 808.
https://doi.org/10.3390/s17040808