# Localized Fault Tolerant Algorithm Based on Node Movement Freedom Degree in Flying Ad Hoc Networks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model and Problem Analysis

#### 2.1. Node Movement Freedom Degree Model

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

#### 2.2. Problem Analysis

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1.**

## 3. The Construction of Bi-Connected Fault-Tolerant Networks

#### 3.1. Cut-Point Detection Algorithm Based on k-Hop Local Topology Information

#### 3.2. Localized Fault-Tolerant Algorithm Based on Node Movement Freedom Degree (LFTMF)

- Move the non-cut points to connect the nodes except c based on k-hop local topology ${G}_{p}(t+\tau )$ predicted by k-hop cut-point c. Thus, the cut-point c is changed into non-cut point until all global cut points are changed into non-cut points to realize bi-connected fault-tolerant network.
- The value of k is greater than or equal to 3 and the cut-point c is kept static. To ensure the connectivity between the k-hop local topology and the external topology, the movement freedom degrees of the kth-hop nodes of c are 0, and they do not participate in the movement. The k-hop cut-point and $(k-1)$-hop cut-point of the cut-point c are regarded as non-cut points.
- The generalized leaf nodes do not participate in the calculation when calculating the degree of freedom of the cut-point.

- Case 1: The are no other cut-points in the 1-hop neighbor nodes of cut-point c.
- Case 2: There is only one other cut-point in the 1-hop neighbor nodes of cut-point c.
- Case 3: There are multiple other cut-points in the 1-hop neighbor nodes of cut-point c.

#### 3.2.1. No Other Cut-Points in the 1-Hop Neighbor Nodes of Cut-Point c

#### 3.2.2. Only One Other Cut-Point in the 1-Hop Neighbor Nodes of Cut-Point c

#### 3.2.3. Multiple Other Cut-Point in the 1-Hop Neighbor Nodes of Cut-Point c

#### 3.3. Complexity Analysis

## 4. Simulation Result

#### 4.1. Simulation Environment and Parameter Setting

#### 4.2. Evaluating Indicator

#### 4.3. Discussion of Simulation Results

#### 4.3.1. Experiment 1: Consistency of k-Hop Cut-Points and Global Cut-Points

#### 4.3.2. Experiment 2: With a Certain Number of UAV Nodes, Analyses of the Relationships among the Performances of LFTMF Algorithm, Global Block Movement Algorithm, Localized Movement Control Algorithm and the Network Node Density by Simulation

#### 4.3.3. Experiment 3: With a Certain Network Node Density, Analyses of the Relationships among the Performances of LFTMF Algorithm, Global Block Movement Algorithm, Localized Movement Control Algorithm and the Number of UAV Nodes by Simulation

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Gupta, L.; Jain, R.; Vaszkun, G. Survey of Important Issues in UAV Communication Networks. IEEE Commun. Surv. Tutor.
**2015**, 18, 1123–1152. [Google Scholar] [CrossRef] - İlker, B.; Sahingoz, O.K.; Şamil, T. Flying Ad-Hoc Networks (FANETs): A survey. Ad Hoc Netw.
**2015**, 11, 1254–1270. [Google Scholar] - Peng, W.; Dong, G.; Yang, K.; Su, J. A Random Road Network Model and Its Effects on Topological Characteristics of Mobile Delay-Tolerant Networks. IEEE Trans. Mob. Comput.
**2014**, 13, 2706–2718. [Google Scholar] [CrossRef] - Liu, X. Survivability-aware connectivity restoration for partitioned wireless sensor networks. IEEE Commun. Lett.
**2017**, 33, 2444–2447. [Google Scholar] [CrossRef] - Liu, H.; Yoo, S.-J.; Kwak, K.S. Opportunistic relaying for low-altitude UAV swarm secure communications with multiple eavesdroppers. IEEE Commun. Surv. Tutor.
**2018**, 20, 496–508. [Google Scholar] [CrossRef] - Ling, C.; Jiahong, L.; Zhiwei, H.; Wu, B. Movement control algorithm of fault-tolerant UAVs Ad Hoc networks. J. Natl. Univ. Def. Technol.
**2012**, 33, 58–62. [Google Scholar] - Shi, Y.; Sun, H.; Sheng, M.; Li, J.; Li, X. Constructing a Robust Topology for Reliable Communications in Multi-Channel Cognitive Radio Ad Hoc Networks. IEEE Commun. Mag.
**2018**, 56, 172–179. [Google Scholar] [CrossRef] - Chang, Y.; Yuan, X.; Al-Dhahir, N. A Joint Unsupervised Learning and Genetic Algorithm Approach for Topology Control in Energy-Efficient Ultra-Dense Wireless Sensor Networks. IEEE Commun. Lett.
**2018**, 22, 2370–2373. [Google Scholar] [CrossRef] - Koti, R.B.; Kakkasageri, M.S. Dynamic topology control in multiple clustered vehicular ad hoc networks. In Proceedings of the 2016 International Conference on Signal Processing, Communication, Power and Embedded System (SCOPES), Paralakhemundi, India, 3–5 October 2016; pp. 1371–1375. [Google Scholar]
- Aznar, F.; Pujol, M.; Aldeguer, R.R.; Pujol, F.A. Energy-Efficient Swarm Behavior for Indoor UAV Ad-Hoc Network Deployment. Symmetry
**2018**, 10, 632. [Google Scholar] [CrossRef] - Ramanathan, R.; Rosales-Hain, R. Topology control of multihop wireless networks using transmit power adjustment. IEEE Comput. Commun. Soc.
**2000**, 33, 404–413. [Google Scholar] - Ahmed, S.; Rahman, K.A.; Rubeaai, S.A. A delay-tolerant network architecture for challenged internets. In Proceedings of the 2003 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications, Karlsruhe, Germany, 25–29 August 2003; pp. 129–133. [Google Scholar]
- Mozaffari, M.; Saad, W.; Bennis, M.; Debbah, M. Unmanned Aerial Vehicle with Underlaid Device-to-Device Communications: Performance and Tradeoffs. IEEE Trans. Wirel. Commun.
**2016**, 15, 3949–3963. [Google Scholar] [CrossRef] - Lagum, F.; Bor-Yaliniz, I.; Yanikomeroglu, H. Strategic densification with UAV-BSs in cellular networks. IEEE Wirel. Commun. Lett.
**2018**, 7, 384–387. [Google Scholar] [CrossRef] - Zhang, Z.; Zhao, J. Relay route planning based on connectivity in airborne ad hoc networks. In Proceedings of the 2017 29th Chinese Control And Decision Conference (CCDC), Chongqing, China, 28–30 May 2017; pp. 1948–9447. [Google Scholar]
- Ling, C.; Jiahong, L.; Zhiwei, H. Fault tolerant relay node placement in UAVs Ad hoc networks. Syst. Eng. Electron.
**2012**, 34, 179–184. [Google Scholar] - Kashyap, A.; Khuller, S.; Shayman, M. Relay placement for fault tolerance in wireless networks in higher dimensions. Comput. Geom.
**2011**, 44, 206–215. [Google Scholar] [CrossRef] [Green Version] - Jie, L.I.; Gong, E.; Sun, Z. Relay speed control for realization of fault-tolerant aeronautical ad hoc networks. J. Natl. Univ. Def. Technol.
**2015**, 37, 158–164. [Google Scholar] - Song, X.; Zhou, L.; Zhao, H. Localized Fault Tolerant and Connectivity Restoration Algorithms in Mobile Wireless Ad Hoc Network. IEEE Access
**2018**, 6, 36469–36478. [Google Scholar] [CrossRef] - Prithwish, B.; Jason, R. Movement control algorithms for realization of fault tolerant Ad Hoc networks. IEEE Netw.
**2004**, 18, 36–44. [Google Scholar] - Shantanu, D.; Hai, L.; Amiya, N.; Stojmenović, I. A Localized algorithm for bi-connectivity of connected mobile robots. Telecommun. Syst.
**2009**, 40, 129–140. [Google Scholar] - Liu, H.; Chu, X.; Leung, Y.W. Simple movement control algorithm for bi-connectivity in robotic sensor networks. IEEE J. Sel. Areas Commun.
**2010**, 28, 994–1005. [Google Scholar] [CrossRef] [Green Version]

**Figure 4.**Realization of bi-connected fault-tolerant networks by adjusting the movement directions of some nodes.

**Figure 8.**The relationship between the consistency of k-hop cut-points and global cut-points and network node density with different values of k.

**Figure 9.**This figure shows the the relationship between the performance of different algorithms and the network node density when the number of UAV nodes is certain: (

**a**) the success rate of the achievement of bi-connected fault-tolerant network, RAFN; (

**b**) the adjustment period, AAP; (

**c**) the ratio of UAV nodes participating in cascade movement, RCM; and (

**d**) average offset distance, ADDO.

**Figure 10.**This figure shows the the relationship between the performance of different algorithms and the number of UAV nodes when the the network node density is certain: (

**a**) The success rate of the achievement of bi-connected fault-tolerant network, RAFN; (

**b**) the adjustment period, AAP; (

**c**) the ratio of UAV nodes participating in cascade movement, RCM; and (

**d**) average offset distance, ADDO.

Symbols | Definitions |
---|---|

$\tau $ | The time for each adjustment period. |

${\mathit{x}}_{i}\left(t\right)$ | Location of UAV Node ${v}_{i}$ at time t. |

${\mathit{x}}_{\mathit{p}i}(t+\tau )$ | Predictive Location of UAV ${v}_{i}$ at time $t+\tau $ in k-hop local topology. |

${\mathit{x}}_{i}^{\prime}(t+\tau )$ | The calculated Location of UAV ${v}_{i}$ in k-hop local topology at time $t+\tau $. |

${l}_{ij}$ | Distance between UAV Nodes ${v}_{i}$ and ${v}_{j}$. |

$N\left({v}_{i}\right)$ | The set of neighbor nodes of UAV ${v}_{i}$. |

${N}_{k}\left({v}_{i}\right)$ | Set of k-hop neighbor nodes of UAV ${v}_{i}$. |

$N\left[{v}_{i}\right]$ | Closed set of neighbors of UAV ${v}_{i}$, $N\left[{v}_{i}\right]=N\left({v}_{i}\right)\cup {v}_{i}$. |

${D}_{mean}$ | Network node density. |

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**MDPI and ACS Style**

Guo, Q.; Yan, J.; Xu, W.
Localized Fault Tolerant Algorithm Based on Node Movement Freedom Degree in Flying Ad Hoc Networks. *Symmetry* **2019**, *11*, 106.
https://doi.org/10.3390/sym11010106

**AMA Style**

Guo Q, Yan J, Xu W.
Localized Fault Tolerant Algorithm Based on Node Movement Freedom Degree in Flying Ad Hoc Networks. *Symmetry*. 2019; 11(1):106.
https://doi.org/10.3390/sym11010106

**Chicago/Turabian Style**

Guo, Qiang, Jichen Yan, and Wei Xu.
2019. "Localized Fault Tolerant Algorithm Based on Node Movement Freedom Degree in Flying Ad Hoc Networks" *Symmetry* 11, no. 1: 106.
https://doi.org/10.3390/sym11010106