# Collective Perception Using UAVs: Autonomous Aerial Reconnaissance in a Complex Urban Environment

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## Abstract

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## 1. Introduction

#### 1.1. Motivation

#### 1.2. Contributions

- The problem of autonomous aerial reconnaissance in complex environments via a swarm of unmanned aerial vehicles is formulated. The monitoring is performed from a number of waypoints deployed in the area of operations; each waypoint is defined in the three-dimensional space by its coordinates and altitude.
- The approach to effectively evaluate the coverage (monitored area) from a number of deployed waypoints is proposed. Terrain and obstacles, which may occlude the objects of interest are taken into consideration as well as the parameters of the sensors used.
- The algorithm to estimate a minimum number of waypoints needed to explore a required portion of the area of interest is proposed.
- The metaheuristic algorithm based on the simulated annealing principles is proposed to deploy waypoints in the area of operations (in three dimensions).
- A set of experiments is designed to assess the proposed algorithms. The results are compared to the optimal solutions.
- A set of scenarios is designed based on the parameters and features of the real typical reconnaissance operations, and the behavior and results are discussed. The real geographic data is used in these experiments.

## 2. Literature Review

## 3. Problem Definition

- Angular field of view (${\alpha}_{fov}$).
- Maximum distance from monitored objects (${d}_{max}$).

- Minimum height of flight above the ground level (${h}_{min}$).
- Maximum height of flight above the ground level (${h}_{max}$).

- Geographical data: the terrain and database of obstacles in the area of operations ($E$, $O$).
- Size, shape and position of the area of interest ($AoI$).
- Number and basic positions of available UAVs, parameters of their sensors ($M$, $U$, ${\alpha}_{fov}$, ${d}_{max}$).
- Minimum and maximum permitted height of flight above the ground level (${h}_{min}$, ${h}_{max}$).
- Minimum requested coverage (${C}_{min}$).

- Number of waypoints ($N$).
- Positions of waypoints (coordinates ${x}_{i}$ and ${y}_{i}$ for all ${W}_{i}\in W$).
- Heights above the ground level of the UAVs at waypoints (${h}_{i}$ for all ${W}_{i}\in W$).

## 4. Solution Algorithms

#### 4.1. Evaluation of a Solution

Algorithm 1 Evaluation of a solution in pseudocode |

Algorithm 2 Visibility evaluation between a point and a waypoint in pseudocode |

#### 4.2. Optimization of Waypoint Deployment

- Maximum temperature ${T}_{max}$: the initial value of temperature used in the first iteration.
- Minimum temperature ${T}_{min}$: the threshold value of temperature (the algorithm ends when the temperature drops below this threshold).
- Cooling coefficient λ: it controls the speed of temperature reduction by cooling in successive iterations.
- Maximum number of transformations in iteration ${n}_{1max}$: it controls the higher limit of transformations performed per iteration.
- Maximum number of replacements in iteration ${n}_{2max}$: it controls the higher limit of replacements (accepting the transformed solution and replacing the original) per iteration.

Algorithm 3 Optimization of waypoint deployment in pseudocode |

Algorithm 4 Generation of a random solution in pseudocode |

Algorithm 5 Transformation of a solution in pseudocode |

#### 4.3. Optimizing the Number of Waypoints

Algorithm 6 Optimizing the number of waypoints in pseudocode |

#### 4.4. Planning of Routes

## 5. Experiments and Results

#### 5.1. Evaluation of a Solution

#### 5.2. Optimizing the Waypoint Deployment

- The area of interest is assembled by joining a number of hexagons with the circumradius 100 m.
- The terrain is absolutely flat (the altitude does not change within the area of operations).
- There are no obstacles in the area of operations.
- Parameters of sensors are ${d}_{max}=\sqrt{2}\xb7100$, ${\alpha}_{fov}=90\xb0$.
- The number of waypoints to be deployed are the same as the number of hexagons.

- The waypoints (coordinates ${x}_{i}$, ${y}_{i}$) lie in the centers of the hexagons (see Figure 10).
- The monitoring height is exactly 100 m above the ground level (${h}_{i}=100\mathrm{m}$).

#### 5.3. Optimizing the Number of Waypoints

#### 5.4. Experiments on Real Scenarios

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$AoO$ | Area of operations. |

$AoI$ | Area of interest to be explored. |

$U$ | Set of available unmanned aerial vehicles: $U=\left\{{U}_{1},{U}_{2},\dots ,{U}_{M}\right\}$. |

${U}_{i}$ | An available UAV. |

$M$ | Number of available unmanned aerial vehicles. |

$W$ | Set of waypoints deployed in the area of operations: $W=\left\{{W}_{1},{W}_{2},\dots ,{W}_{N}\right\}$. |

${W}_{i}$ | A waypoint deployed in the area of operations. |

${x}_{i}$,${y}_{i}$ | Coordinates of waypoint ${W}_{i}$ in the area of operations. |

$N$ | Number of waypoints deployed in the area of operations. |

${\alpha}_{fov}$ | Angular field of view of sensors of the UAVs. |

${d}_{max}$ | Maximum distance from a sensor to an object of interest. |

${h}_{alt}^{i}$ | Altitude of an UAV at waypoint ${W}_{i}\in W$. |

${h}_{i}$ | Height of flight of an UAV above the ground level at waypoint ${W}_{i}\in W$. |

${h}_{min}$ | Minimum allowed height of flight of UAVs. |

${h}_{max}$ | Maximum allowed height of flight of UAVs. |

$P$ | Set of points on the ground in the area of operations: $P=\left\{{P}_{1},{P}_{2},\dots \right\}$. |

$E$ | Function to determine the terrain elevation in any point in the $AoO$. |

$O$ | Set of obstacles in the area of interest: $O=\left\{{O}_{1},{O}_{2},\dots ,{O}_{L}\right\}$. |

${O}_{k}$ | An obstacle in the area of interest. |

$L$ | Number of obstacles in the area of interest. |

${V}_{i}$ | Set of points in the area of interest visible from waypoint ${W}_{i}\in W$. |

$V$ | Set of points in the area of interest monitored from all the waypoints. |

${d}_{rast}$ | Size of the rasterization step. |

${N}_{P}$ | Total number of points in the rasterized area of interest. |

${N}_{V}$ | Number of visible points in the rasterized area of interest. |

${X}^{N}$ | Solution in the state space (particular deployment of waypoints). |

$C$,${C}^{N}$ | Coverage of the area of interest from all the waypoints. |

${C}_{min}$ | Minimum required coverage of the area of interest. |

$R$ | Routes of UAVs: $R=\left\{{R}_{1},{R}_{2},\dots ,{R}_{M}\right\}$. |

${R}_{j}$ | A route of UAV ${U}_{j}$. (order of nodes to be visited): ${R}_{j}=\left\{{R}_{j}^{0},{R}_{j}^{1},{R}_{j}^{2},\dots ,{R}_{j}^{{K}_{j}},{R}_{j}^{{K}_{j}+1}\right\}$. |

${K}_{j}$ | Number of waypoints to be visited en route ${R}_{j}$. |

${T}_{j}$ | Time to perform route ${R}_{j}$ by ${U}_{j}$. |

$T$ | Duration of the reconnaissance operation. |

${T}_{max}$ | Initial temperature (simulated annealing parameter). |

${T}_{min}$ | Minimum temperature threshold (simulated annealing parameter). |

${T}_{cur}$ | Current temperature (variable used in the simulated annealing algorithm). |

$\gamma $ | Cooling coefficient (simulated annealing parameter). |

${n}_{1max}$ | Number of transformations (simulated annealing parameter). |

${n}_{2max}$ | Number of replacements (simulated annealing parameter). |

$\tau $ | Constant used when estimating the necessary number of waypoints. |

$\mu $ | Mean. |

$\sigma $ | Standard deviation. |

$\epsilon $ | Constant used in the solution transformation process. |

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**Figure 5.**Rasterization of the area of interest: (

**a**) points in the area of interest; (

**b**) visible points.

**Figure 6.**Scenario for the evaluation of a solution: (

**a**) area of interest and the layout of obstacles; (

**b**) deployment of waypoints for $N=5$; (

**c**) deployment of waypoints for $N=10$.

**Figure 7.**Coverage errors for the original and optimized versions of the algorithm for the solution evaluation: (

**a**) number of waypoints $N=5$; (

**b**) number of waypoints $N=10$.

**Figure 8.**Influence of the size of the rasterization step on the solution evaluation: (

**a**) rasterization step ${d}_{rast}=1$; (

**b**) rasterization step ${d}_{rast}=10$; (

**c**) rasterization step ${d}_{rast}=50$.

**Figure 9.**Dependence of the execution time on the number of points: (

**a**) original algorithm; (

**b**) optimized algorithm.

**Figure 11.**Comparison of the continuous and discrete versions of the algorithm: (

**a**) error of the best solutions; (

**b**) error of the average values.

**Figure 13.**The progress in optimizing the number of waypoints, for instance d04: (

**a**) first estimation ($N=28$); (

**b**) first update ($N=30$); (

**c**) second update ($N=31$).

$\mathbf{Number}\text{}\mathbf{of}\text{}\mathbf{Waypoints}\text{}\mathit{N}$ | $\mathbf{Rasterization}\text{}\mathbf{Step}\text{}{\mathit{d}}_{\mathit{r}\mathit{a}\mathit{s}\mathit{t}}\left(\mathbf{m}\right)$ | $\mathbf{Number}\text{}\mathbf{of}\text{}\mathbf{Points}\text{}{\mathit{N}}_{\mathit{P}}$ | $\mathbf{Coverage}\text{}{\mathit{C}}^{\mathit{N}}$ | Coverage Error | Execution Time (ms) ^{1} |
---|---|---|---|---|---|

5 | 1 | 678,953 | 59.49% | Benchmark | 1347 |

5 | 2 | 169,740 | 59.49% | 0.00% | 378 |

5 | 5 | 27,160 | 59.54% | 0.08% | 74 |

5 | 10 | 6786 | 59.43% | 0.10% | 15 |

5 | 20 | 1696 | 60.26% | 1.29% | 4.4 |

5 | 50 | 271 | 59.04% | 0.76% | 0.7 |

10 | 1 | 678,953 | 93.98% | Benchmark | 1859 |

10 | 2 | 169,740 | 93.98% | 0.00% | 465 |

10 | 5 | 27,160 | 93.97% | 0.01% | 75 |

10 | 10 | 6786 | 93.78% | 0.21% | 18 |

10 | 20 | 1696 | 94.81% | 0.88% | 5.1 |

10 | 50 | 271 | 95.20% | 1.30% | 1.3 |

^{1}Each experiment was performed 1000 times and results were averaged.

$\mathbf{Number}\text{}\mathbf{of}\text{}\mathbf{Waypoints}\text{}\mathit{N}$ | $\mathbf{Rasterization}\text{}\mathbf{Step}\text{}{\mathit{d}}_{\mathit{r}\mathit{a}\mathit{s}\mathit{t}}\text{}\left(\mathbf{m}\right)$ | $\mathbf{Number}\text{}\mathbf{of}\text{}\mathbf{Points}\text{}{\mathit{N}}_{\mathit{P}}$ | $\mathbf{Coverage}\text{}{\mathit{C}}^{\mathit{N}}$ | Coverage Error | Execution Time (ms) ^{1} |
---|---|---|---|---|---|

5 | 1 | 678,953 | 59.50% | 0.02% | 22.02 |

5 | 2 | 169,740 | 59.74% | 0.42% | 5.53 |

5 | 5 | 27,160 | 60.08% | 0.99% | 0.92 |

5 | 10 | 6786 | 59.77% | 0.47% | 0.28 |

5 | 20 | 1696 | 59.37% | 0.20% | 0.11 |

5 | 50 | 271 | 56.52% | 4.99% | 0.06 |

10 | 1 | 678,953 | 94.19% | 0.22% | 33.58 |

10 | 2 | 169,740 | 94.54% | 0.60% | 8.56 |

10 | 5 | 27,160 | 95.42% | 1.53% | 1.45 |

10 | 10 | 6786 | 95.38% | 1.49% | 0.47 |

10 | 20 | 1696 | 94.53% | 0.59% | 0.19 |

10 | 50 | 271 | 91.97% | 2.14% | 0.11 |

^{1}Each experiment was performed 1000 times and results were averaged.

Benchmark Instance | $\mathbf{Minimum}\text{}\mathbf{Height}\text{}{\mathit{h}}_{\mathit{m}\mathit{i}\mathit{n}}$ | $\mathbf{Maximum}\text{}\mathbf{Height}\text{}{\mathit{h}}_{\mathit{m}\mathit{a}\mathit{x}}$ | Degree | $\mathbf{Number}\text{}\mathbf{of}\text{}\mathbf{Waypoints}\text{}\mathit{N}$ | $\mathbf{Number}\text{}\mathbf{of}\text{}\mathbf{Variables}\text{}\mathbf{in}\text{}{\mathit{X}}^{\mathit{N}}$ |
---|---|---|---|---|---|

d01 | 50 m | 150 m | 1 | 1 | 3 |

d02 | 50 m | 150 m | 3 | 7 | 21 |

d03 | 50 m | 150 m | 5 | 17 | 51 |

d04 | 50 m | 150 m | 7 | 31 | 93 |

d05 | 50 m | 150 m | 9 | 49 | 147 |

d06 | 50 m | 150 m | 11 | 71 | 213 |

Instance | $\mathbf{Rast}.\text{}\mathbf{Step}\text{}{\mathit{d}}_{\mathit{r}\mathit{a}\mathit{s}\mathit{t}}\left(\mathbf{m}\right)$ | Optimal Solution | Solution Found ^{1} | Error ^{2} | Execution Time (s) ^{1} | ||
---|---|---|---|---|---|---|---|

Best | Mean | Stdev | |||||

d01 | 2 | 100% | 100% | 100% | 0.00% | 0.00% | 2.9 |

d02 | 2 | 100% | 100% | 100% | 0.00% | 0.00% | 31.4 |

d03 | 5 | 100% | 99.99% | 99.87% | 0.51% | 0.01% | 16.8 |

d04 | 5 | 100% | 99.91% | 98.95% | 0.84% | 0.09% | 32.4 |

d05 | 10 | 100% | 99.46% | 98.00% | 0.58% | 0.54% | 19.6 |

d06 | 10 | 100% | 98.26% | 97.25% | 0.46% | 1.74% | 28.1 |

^{1}50 trials.

^{2}Difference between the best and optimal solution.

Instance | $\mathbf{Rast}.\text{}\mathbf{Step}\text{}{\mathit{d}}_{\mathit{r}\mathit{a}\mathit{s}\mathit{t}}\left(\mathbf{m}\right)$ | Optimal Solution | Solution Found ^{1} | Error ^{2} | Execution Time (s) ^{1} | ||
---|---|---|---|---|---|---|---|

Best | Mean | Stdev | |||||

d01 | 2 | 100% | 100% | 100% | 0.00% | 0.00% | 3.2 |

d02 | 2 | 100% | 100% | 100% | 0.00% | 0.00% | 32.1 |

d03 | 5 | 100% | 100% | 99.96% | 0.02% | 0.00% | 18.2 |

d04 | 5 | 100% | 99.96% | 99.14% | 0.67% | 0.04% | 34.5 |

d05 | 10 | 100% | 99.51% | 98.55% | 0.43% | 0.49% | 21.0 |

d06 | 10 | 100% | 99.30% | 98.06% | 0.45% | 0.70% | 31.0 |

^{1}50 trials.

^{2}Difference between the best and optimal solution.

Instance | $\mathbf{Optimal}\text{}\mathit{N}$ | First Estimation | First Update | Second Update | |||
---|---|---|---|---|---|---|---|

${\mathit{N}}_{1}$ | ${\mathit{C}}_{\%}^{{\mathit{N}}_{1}}$ | ${\mathit{N}}_{2}$ | ${\mathit{C}}_{\%}^{{\mathit{N}}_{2}}$ | ${\mathit{N}}_{3}$ | ${\mathit{C}}_{\%}^{{\mathit{N}}_{3}}$ | ||

d01 | 1 | 1 | 100% | – | – | – | – |

d02 | 7 | 7 | 100% | – | – | – | – |

d03 | 17 | 16 | 96.90% | 17 | 99.96% | – | – |

d04 | 31 | 28 | 94.77% | 30 | 97.72% | 31 | 99.88% |

d05 | 49 | 45 | 95.67% | 48 | 98.35% | 49 | 99.13% |

d06 | 71 | 65 | 95.68% | 68 | 96.98% | 71 | 99.03% |

Scenario | Area of Interest | Elevation Difference | Obstacles | |||
---|---|---|---|---|---|---|

Width | Height | Area | Count | Height | ||

sc01 | 0.40 km | 0.25 km | 0.1 km^{2} | 44 m | 14 | 14.6 m |

sc02 | 0.95 km | 1.14 km | 0.7 km^{2} | 79 m | 266 | 6.4 m |

sc03 | 3.75 km | 3.04 km | 2.8 km^{2} | 129 m | 533 | 5.1 m |

sc04 | 2.99 km | 3.24 km | 5.3 km^{2} | 47 m | 936 | 10.6 m |

sc05 | 4.00 km | 2.10 km | 6.8 km^{2} | 654 m | 8 | 9.4 |

Scenario | Number of UAVs | Minimum Coverage | Sensors | Minimum Height | Maximum Height | |
---|---|---|---|---|---|---|

${\mathit{d}}_{\mathit{m}\mathit{a}\mathit{x}}$ | ${\mathit{\alpha}}_{\mathit{f}\mathit{o}\mathit{v}}$ | |||||

sc01 | 1 | 99% | 80 m | 75° | 20 m | 120 m |

sc02 | 2 | 98% | 150 m | 75° | 20 m | 180 m |

sc03 | 5 | 99% | 200 m | 90° | 50 m | 300 m |

sc04 | 3 | 95% | 200 m | 90° | 50 m | 300 m |

sc05 | 4 | 99% | 500 m | 120° | 50 m | 400 m |

Scenario | $\mathbf{Rast}.\text{}\mathbf{Step}\text{}{\mathit{d}}_{\mathit{r}\mathit{a}\mathit{s}\mathit{t}}\left(\mathbf{m}\right)$ | Number of Waypoints | Solution Found ^{1} | Execution Time (s) ^{1} | ||
---|---|---|---|---|---|---|

Best | Mean | Stdev | ||||

sc01 | 2 | 23 | 99.19% | 98.09% | 1.06% | 22.9 |

sc02 | 3 | 37 | 98.58% | 98.05% | 0.28% | 83.1 |

sc03 | 5 | 70 | 99.26% | 98.68% | 0.41% | 770.4 |

sc04 | 5 | 111 | 95.47% | 94.88% | 0.26% | 772.8 |

sc05 | 10 | 22 | 99.03% | 98.21% | 0.38% | 66.7 |

^{1}50 trials.

Scenario | Number of UAVs | Number of Waypoints | Coverage | Routes | |
---|---|---|---|---|---|

Distance (km) | $\mathbf{Time}\text{}\mathit{T}$ (min) | ||||

sc01 | 1 | 23 | 99.19% | 1.515 | 2:31 |

sc02 | 2 | 37 | 98.58% | 6.823 | 5:41 |

sc03 | 5 | 70 | 99.26% | 25.756 | 8:41 |

sc04 | 3 | 111 | 95.47% | 25.234 | 14:07 |

sc05 | 4 | 22 | 99.03% | 16.067 | 7:11 |

Scenario | Number of UAVs | Number of Waypoints | Waypoints Coverage | Continuous Coverage | Improvement |
---|---|---|---|---|---|

sc01 | 1 | 23 | 99.19% | 99.71% | 0.52% |

sc02 | 2 | 37 | 98.58% | 99.50% | 0.92% |

sc03 | 5 | 70 | 99.26% | 99.66% | 0.40% |

sc04 | 3 | 111 | 95.47% | 97.82% | 2.35% |

sc05 | 4 | 22 | 99.03% | 99.70% | 0.67% |

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**MDPI and ACS Style**

Stodola, P.; Drozd, J.; Šilinger, K.; Hodický, J.; Procházka, D.
Collective Perception Using UAVs: Autonomous Aerial Reconnaissance in a Complex Urban Environment. *Sensors* **2020**, *20*, 2926.
https://doi.org/10.3390/s20102926

**AMA Style**

Stodola P, Drozd J, Šilinger K, Hodický J, Procházka D.
Collective Perception Using UAVs: Autonomous Aerial Reconnaissance in a Complex Urban Environment. *Sensors*. 2020; 20(10):2926.
https://doi.org/10.3390/s20102926

**Chicago/Turabian Style**

Stodola, Petr, Jan Drozd, Karel Šilinger, Jan Hodický, and Dalibor Procházka.
2020. "Collective Perception Using UAVs: Autonomous Aerial Reconnaissance in a Complex Urban Environment" *Sensors* 20, no. 10: 2926.
https://doi.org/10.3390/s20102926