# A Probabilistic Target Search Algorithm Based on Hierarchical Collaboration for Improving Rapidity of Drones

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## Abstract

**:**

## 1. Introduction

- First, an improved hierarchical probabilistic target search algorithm based on the collaboration of drones at different altitudes is proposed. This is a method for reducing the search time and search distance by improving the information transfer methods between high-altitude and low-altitude drones. Specifically, to improve the speed of target detection, a high-altitude drone performs a preliminary search of a wide area.
- Second, this study suggests a method of using thresholds for information transfer between high altitude and low altitude to improve the efficiency of a search, i.e., to reduce the search time and search travel distance. In this method, when the probability of the existence of a target at a high altitude is higher than a certain threshold, the search information is transmitted to a low-altitude drone.
- Third, several drone collaboration scenarios that can be performed by two drones at different altitudes are introduced and compared to the proposed algorithm. These methods are hierarchical cooperation methods of drones that can be used in an actual search. Through simulations, it is demonstrated that methods utilizing hierarchical searches with drones are comparatively excellent and that the proposed algorithm has better performance compared to other scenarios.

## 2. Related Works

#### 2.1. Target Detection Method

#### 2.2. Target Detection Based on Probabilistic Search

^{t}becomes a set of observations up to time t as {d

^{1}, …, d

^{t}}, and x

_{T}= a indicates that a target exists in cell a. Therefore, Pr(x

_{T}= a|D

^{t}) is the probability of a target being present in cell ‘a’ for the time step t. Pr(x

_{T}= a|D

^{t−1}) is the probability for the previous time step. Pr(${d}_{a}^{t}$|D

^{t}

^{−1}) is the marginalization of the measurement as Equation (2). In Equation (2), H is a binary variable indicating whether a target exists in the search area. Pr(${d}_{a}^{t}$|x

_{T}= a, D

^{t}) is the search result of cell ‘a’ at time t and is obtained from the search model of Equation (3):

_{T}indicates whether the actual target exists in cell a, α is the false alarm probability, and β is the missed detection probability. That is, α denotes that the target does not actually exist in cell ‘a’ but the observed value denotes that there is a target, and β denotes the case where the target actually exists in cell ‘a’ but the observed value denotes that there is no target.

^{t}is one, then the probability value of the cell is calculated utilizing the upper expression in Equation (4). If the value of d

^{t}is zero, the lower expression is utilized.

#### 2.3. Altitude Control Strategies

## 3. Advanced Hierarchical Probabilistic Search Algorithm

#### 3.1. Improvement of the Probabilistic Search

^{b}is the threshold value for target detection success, Max

^{b}is the highest belief value at the current altitude, Area

^{h}is the area having the highest belief value, and Th

^{n}is the threshold of reliability for transmitting information from a higher drone to a lower drone. Checking this value to change the search altitude is one of the most important aspects of our algorithm.

^{n}, then the high-altitude drone transmits the search information to the low-level drone. This initial search is performed to obtain the advantages of a high altitude, namely search efficiency as a result of covering a wide search area by a small travel distance and continuously searching at as high an altitude as possible. This is an important part of the proposed algorithm. The low-altitude drone performs a more specific search based on the search information from the high-altitude drone. When the highest probability value is greater than or equal to the threshold value, target searching stops and the target is considered to be found.

Algorithm 1 Basic Outline of Proposed Algorithm | |

1: | while Max^{b} < Th^{b} |

2: | //high-altitude search |

3: | high-altitude drone searches for the target sequentially in four search areas |

4: | and computes a belief value for each cell in the search areas, |

5: | it then selects an Area^{h} |

6: | if Max^{b} > Th^{n} then |

7: | //low-altitude search |

8: | send search information to the low-altitude drone, |

9: | low-altitude drone searches for the target sequentially in the Area^{h} |

10: | and computes Max^{b} |

11: | end |

12: | end |

13: | stop searching |

#### 3.2. Altitude Control Strategy

#### 3.3. Advanced Hierarchical Probabilistic Search Algorithm

^{sp}for search success and threshold value Th

^{lp}for low-altitude movement, are utilized. The main goal of this algorithm is to reduce the time spent searching at low altitude as much as possible and to increase the probability of finding a target by searching at a high altitude utilizing the conditional query in line 16 of the algorithm. Table 1 lists the definitions of the variables utilized in the proposed algorithm.

Algorithm 2 Downward Delay Search | |

1: | //Initialize |

2: | found = 0; |

3: | round = 0;_{h} |

4: | round = 0; _{l} |

5: | while found ! = 1 |

6: | //High-altitude search |

7: | if round < round_limit ^{h}then |

8: | the drone searches four Areas at high altitude^{h} |

9: | select the Area containing the cell with the highest probability^{h} |

10: | if HP ≥ ^{h}Th^{sp} then |

11: | found = 1 |

12: | stop searching |

13: | break |

14: | else |

15: | if HP > ^{h}Th^{lp} then |

16: | //Low-altitude search |

17: | if round < round_limit ^{l}then |

18: | send information to low-altitude drone |

19: | low-altitude drone searches four Areas at low altitude^{l} |

20: | if HP ≥ ^{l}Th^{sp} then |

21: | found = 1 |

22: | break |

23: | end |

24: | else |

25: | change altitude upward |

26: | end |

27: | end |

28: | end |

29: | else |

30: | move to the next area for another high-altitude search |

31: | end |

32: | round = ^{h}round + 1^{h} |

33: | end |

## 4. Simulation

#### 4.1. Simulation Environment

_{t−1}.

#### 4.2. Search Scenarios

- Scenario 1This scenario is the initial version of the proposed algorithm. In this method, the first drone searches four high-altitude search areas for quick navigation. Then, the area with the highest probability is selected and searched more precisely by a drone at a low altitude. In this method, control is transferred from the high-altitude drone to the low-altitude drone without verifying control transfer. This method operates based on a hierarchical control of drones.
- Scenario 2In the second scenario, a low-altitude drone performs a linear probability search. Specifically, the drone searches each low-altitude search area linearly. The low-altitude drone moves linearly in the direction in which the values of x and y increase and searches for the target. The values of α and β of the low-altitude drone are applied to obtain the target existence probability. The low-altitude drone continues searching based on the α and β values. The probability of the existence of a target in each cell is calculated recursively utilizing Equation (4).
- Scenario 3The third scenario utilizes another altitude-control strategy to detect a target in the search area. The search scenario is as follows. Unlike Scenario 1, the drone searches only one high-altitude search area. The drone selects a low-altitude search area (2 × 2) within the high-altitude search area and sends the search information to the low-altitude drone for more precise searching of the low-altitude search area. This drone then searches the low-altitude search area in detail.
- Scenario 4In this scenario, a high-altitude drone performs a linear probability search. This scenario is very similar to the second scenario. The only difference is that the drone is at a high altitude. In addition, since it has a higher altitude, different α and β values for high altitude are utilized to calculate the probability of each cell.
- Scenario 5This scenario represents the full method proposed in this study. The high-altitude drone sequentially searches an area corresponding to four times its search range from a high altitude. The search range containing the cell with the highest probability of existence of the target is selected. The drone then checks if the highest probability of target existence is greater than or equal to a threshold value to determine if the search control should be transferred to the low-altitude drone. If the value is above the threshold, the search information is transmitted to the low-altitude drone, which then performs a more precise search at a low altitude.

#### 4.3. Simulation Results and Analysis

_{m}is the number of units moved, tan a

_{hb}is the tangent angle of the hypotenuse and base, and h is the altitude height of a drone.

_{s}is the search time, S

_{d}is the search distance, and V

_{d}is the drone velocity. As shown in Figure 6, the drone required a relatively small amount of time to perform the search utilizing the methods of Scenarios 1 and 5.

## 5. Conclusions

- This study proposed an improved hierarchical probabilistic target search algorithm based on the collaboration of drones at different altitudes. This method reduced the search time and search travel distance by improving the information transfer between high-altitude and low-altitude drones. In addition, the information transfer method increased the efficiency of the proposed algorithm by using thresholds in the information transmission process.
- This study introduced several drone collaboration scenarios performed by two drones at different altitudes and compared the scenarios to the proposed algorithm. Through simulations, the performance of the proposed algorithm and the cooperation scenarios were analyzed. It was demonstrated that methods utilizing hierarchical searches with drones are comparatively excellent and that the proposed algorithm is approximately 13% more effective than a previous method with much better performance compared to other scenarios.

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Bekmezci, I.; Sahingoz, O.K.; Temel, Ş. Flying ad-hoc Networks (FANETs): A survey. Ad Hoc Netw.
**2013**, 11, 1254–1270. [Google Scholar] [CrossRef] - Sahingoz, O.K. Networking models in flying ad-hoc networks (FANETs): Concepts and Challenges. J. Intell. Robot. Syst.
**2014**, 74, 513–527. [Google Scholar] [CrossRef] - Ha, I.-K. Analysis of importance of search altitude control for rapid target detection of drones. J. Inf. Commun. Converg. Eng.
**2018**, 16, 78–83. [Google Scholar] - Chung, T.H.; Burdick, J.W. A decision-making framework for control strategies in probabilistic search. In Proceedings of the 2007 IEEE International Conference on Robotics and Automation (ICRA 2007), Roma, Italy, 10–14 April 2007; pp. 4386–4393. [Google Scholar]
- Liu, Y.; Dai, Q. A survey of computer vision applied in aerial robotic vehicles. In Proceedings of the 2010 International Conference on Optics, Photonics and Energy Engineering (OPEE 2010), Wuhan, China, 10–12 May 2010; pp. 277–280. [Google Scholar]
- Wang, X.; Zhu, H.; Zhang, D.; Zhou, D.; Wang, X. Vision-based detection and tracking of a mobile ground target using a fixed-wing UAV. Int. J. Adv. Robot. Syst.
**2014**, 11, 1–10. [Google Scholar] [CrossRef] - Mejias, L.; Mcnamara, S.; Lai, J.; Ford, J. Vision-based detection and tracking of aerial targets for UAV collision avoidance. In Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2010), Taibei, Taiwan, 18–22 October 2010; pp. 87–92. [Google Scholar]
- Minaeian, S.; Liu, J.; Son, Y. Vision-based target detection and localization via a team of cooperative UAV and UGVs. IEEE Trans. Syst. Man Cybern. Syst.
**2016**, 46, 1005–1016. [Google Scholar] [CrossRef] - Arora, A.; Dutta, P.; Bapat, S.; Kulathumani, V.; Zhang, H.; Naik, V.; Mittal, V.; Cao, H.; Demirbas, M.; Gouda, M.; et al. A line in the sand: A wireless sensor network for target detection, classification, and tracking. Comput. Netw.
**2004**, 46, 605–634. [Google Scholar] [CrossRef] - Costa, F.G.; Ueyama, J.; Braun, T.; Pessin, G.; Osorio, F.S.; Vargas, P.A. The use of unmanned aerial vehicles and wireless sensor network in agricultural applications. In Proceedings of the 2012 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2012), Munich, Germany, 22–27 July 2012; pp. 5045–5048. [Google Scholar]
- Jawhar, I.; Mohamed, N.; Al-Jaroodi, J.; Zhang, S. Data communication in linear wireless sensor networks using unmanned aerial vehicles. In Proceedings of the 2013 International Conference on Unmanned Aircraft Systems (ICUAS 2013), Atlanta, GA, USA, 28–31 May 2013; pp. 492–499. [Google Scholar]
- Chung, T.H.; Burdick, J.W. Analysis of search decision making using probabilistic search strategies. IEEE Trans. Robot.
**2012**, 28, 132–144. [Google Scholar] [CrossRef] - Washburn, A.R. Search and Detection (Topics in Operations Research Series), 4th ed.; Institute for Operations Research and the Management Sciences: Linthicum, MD, USA, 2002. [Google Scholar]
- Choset, H. Coverage for robotics—A survey of recent results. Ann. Math. Artif. Intell.
**2001**, 31, 113–126. [Google Scholar] [CrossRef] - Robie, A.A. Multimodal Sensory Control of Exploration by Walking Drosophila Melanogaster. Ph.D. Thesis, California Institute of Technology, Pasadena, CA, USA, 2010. [Google Scholar]
- Itti, L.; Koch, C. A saliency-based search mechanism for overt and covert shifts of visual attention. Vis. Res.
**2000**, 40, 1489–1506. [Google Scholar] [CrossRef] [Green Version] - Waharte, S.; Trigoni, N. Supporting search and rescue operations with UAVs. In Proceedings of the 2010 International Conference on Emerging Security Technologies (EST 2010), Canterbury, UK, 6–7 September 2010; pp. 142–147. [Google Scholar]
- Symington, A.; Waharte, S.; Julier, S.; Trigoni, N. Probabilistic target detection by camera-equipped UAVs. In Proceedings of the 2010 IEEE International Conference on Robotics and Automation (ICRA 2010), Anchorage, AK, USA, 3–8 May 2010; pp. 4076–4082. [Google Scholar]
- Morse, B.S.; Engh, C.H.; Goodrich, M.A. UAV video coverage quality maps and prioritized indexing for wilderness search and rescue. In Proceedings of the 5th ACM/IEEE International Conference on Human-Robot Interaction (HRI 2010), Osaka, Japan, 2–5 March 2010; pp. 227–234. [Google Scholar]
- Waharte, S.; Symington, A.; Trigoni, N. Probabilistic search with agile UAVs. In Proceedings of the 2010 IEEE International Conference on Robotics and Automation (ICRA 2010), Anchorage, AK, USA, 3–8 May 2010; pp. 2840–2845. [Google Scholar]
- Zarco-Tejada, P.J.; Diaz-Varela, R.; Angileria, V.; Loudjani, P. Tree height quantification using very high resolution imagery acquired from an unmanned aerial vehicle (UAV) and automatic 3D photo-reconstruction methods. Eur. J. Agron.
**2014**, 55, 89–99. [Google Scholar] [CrossRef] [Green Version] - Lin, Y.; Hyyppa, J.; Jaakkola, A. Mini-UAV-borne LIDAR for fine-scale mapping. IEEE Geosci. Remote Sens. Lett.
**2011**, 8, 426–430. [Google Scholar] [CrossRef] - Waharte, S.; Trigoni, N.; Julier, S.J. Coordinated search with a swarm of UAVs. In Proceedings of the 6th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks Workshops (SECON 2009), Rome, Italy, 22–26 June 2009; pp. 1–3. [Google Scholar]
- Deisenroth, M.P.; Fox, D.; Rasmussen, C.E. Gaussian processes for data-efficient learning in robotics and control. IEEE Trans. Pattern Anal. Mach. Intell.
**2015**, 37, 408–423. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Smaragdis, P.; Fevotte, C.; Mysore, G.J.; Mohammadiha, N.; Hoffman, M. Static and dynamic source separation using nonnegative factorizations: A unified view. IEEE Signal Process. Mag.
**2014**, 31, 66–75. [Google Scholar] [CrossRef] - Schneider, N.; Gavrila, D.M. Pedestrian path prediction with recursive Bayesian filters: A comparative study. In Proceedings of the 35th German Conference on Pattern Recognition (GCPR 2013), Saarbrücken, Germany, 3–6 September 2013; pp. 174–183. [Google Scholar]
- Kim, D.H.; Lee, J.S.; Choi, J.D.; Kim, K.E. A POMDP framework for dynamic task allocation and reconnaissance of multiple unmanned aerial vehicles. J. KIISE Softw. Appl.
**2012**, 39, 453–463. [Google Scholar]

Variable | Definition |
---|---|

Area^{h} | search area of drone at high altitude |

Area^{l} | search area of drone at low altitude |

Th^{sp} | threshold probability value for search success |

Th^{lp} | threshold probability value for low-altitude search |

HP^{h} | highest probability among cells at high altitude |

HP^{l} | highest probability among cells at low altitude |

found | binary variable for found alarm |

round^{h} | number of rounds executed at high altitude |

round^{l} | number of rounds executed at low altitude |

Category | Value |
---|---|

Size of search area | 8 × 8 units |

Number of drones | 2 |

Average drone speed | 15 km/h |

High-altitude search area of drone | 4 × 4 units (altitude: 20 m) |

Low-altitude search area of drone | 2 × 2 units (altitude: 10 m) |

Threshold probability1 (TH^{sp}) | 0.95 |

Threshold probability2 (TH^{lp}) | 0.75 |

Length of a side of one unit | 7.592 m |

Probability variables for high-altitude drone | α = 0.00130, β = 0.34593 [17] |

Probability variables for low-altitude drone | α = 0.06286, β = 0.20000 [17] |

Algorithm | Search Method | Total Time (sec) | Total Distance (m) | Comparison (%) |
---|---|---|---|---|

High + Low | After high-altitude search, low-altitude search | 1,099,028 | 4,579,283 | 100 |

Low Linear | Search linearly at low altitude | 2,893,980 | 12,058,251 | 263 |

High + Low2 | After high-altitude search, low-altitude search (search by one high-altitude area) | 1,673,795 | 6,974,146 | 152 |

High Linear | Search linearly at high altitude | 1,139,097 | 4,746,240 | 104 |

High + Low3 (Proposed) | After high-altitude search with threshold value, low-altitude search | 959,327 | 3,997,199 | 87 |

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**MDPI and ACS Style**

Ha, I.-K.; Cho, Y.-Z.
A Probabilistic Target Search Algorithm Based on Hierarchical Collaboration for Improving Rapidity of Drones. *Sensors* **2018**, *18*, 2535.
https://doi.org/10.3390/s18082535

**AMA Style**

Ha I-K, Cho Y-Z.
A Probabilistic Target Search Algorithm Based on Hierarchical Collaboration for Improving Rapidity of Drones. *Sensors*. 2018; 18(8):2535.
https://doi.org/10.3390/s18082535

**Chicago/Turabian Style**

Ha, Il-Kyu, and You-Ze Cho.
2018. "A Probabilistic Target Search Algorithm Based on Hierarchical Collaboration for Improving Rapidity of Drones" *Sensors* 18, no. 8: 2535.
https://doi.org/10.3390/s18082535