# Distributed Adaptive Neural Network Control Applied to a Formation Tracking of a Group of Low-Cost Underwater Drones in Hazardous Environments

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## Abstract

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## Featured Application

**These applications are suitable for missions, such as oceanic surveillance, undersea oil detection, submarine pipeline monitoring, and seabed explorations.**

## Abstract

## 1. Introduction

- We have proposed an incorporation of distributed adaptive neural networks control and collision-obstacle avoidance so that a group of the underwater drones is able to operate independently and autonomously in hazardous environments.
- The desired formation is proposed as a time-variant function, so that a group of UUVs can quickly change their shape between them to cross a narrow area.
- The implementation of algorithms is integrated on the Gazebo underwater drone models. The results show that the control framework can be applicable to low-cost UUVs.

## 2. Preliminaries and Problem Formulation

#### 2.1. Preliminaries

#### 2.1.1. Graph Theory

#### 2.1.2. Radial Basis Functions

#### 2.1.3. Low-Cost Underwater Drone Modeling

#### 2.2. Problem Formulation

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

**Remark**

**1.**

## 3. Incorporation of DANNC and Collision-Obstacle Avoidance for a Group of UUVs

#### 3.1. Leader-Follower Formation Tracking

#### 3.1.1. Formation Control Term

#### 3.1.2. Neural Network Control Term

**Lemma**

**1**

#### 3.1.3. Robust Control Term

**Remark**

**3.**

#### 3.2. Collision Avoidance for a Group of Multiple UUVs

#### 3.3. Obstacle Avoidance for a Group of Multiple UUVs

**Assumption**

**4.**

**Assumption**

**5.**

Algorithm 1: Propose to make a modified trajectory for obstacle avoidance. |

## 4. Experiments with a Group of Low-Cost UUVs

#### 4.1. Experimental Setup

#### 4.2. Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AUV | Autonomous Underwater Vehicle |

DANNC | Distributed Adaptive Neural Network Control |

LiDAR | Light Detection and Ranging |

NN | Neural Network |

ROS | Robot Operating System |

ROV | Remotely Operated Underwater Vehicle |

UUV | Unmanned Underwater Vehicle |

UWSim | UnderWater Simulator |

## Appendix A

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**Figure 1.**A proposal for submarine pipeline monitoring by using a low-cost unmanned underwater vehicle (UUV).

**Figure 2.**The overall distributed adaptive neural networks formation tracking control with collision and obstacle avoidance for the UUV follower.

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**MDPI and ACS Style**

Pham, H.A.; Soriano, T.; Ngo, V.H.; Gies, V.
Distributed Adaptive Neural Network Control Applied to a Formation Tracking of a Group of Low-Cost Underwater Drones in Hazardous Environments. *Appl. Sci.* **2020**, *10*, 1732.
https://doi.org/10.3390/app10051732

**AMA Style**

Pham HA, Soriano T, Ngo VH, Gies V.
Distributed Adaptive Neural Network Control Applied to a Formation Tracking of a Group of Low-Cost Underwater Drones in Hazardous Environments. *Applied Sciences*. 2020; 10(5):1732.
https://doi.org/10.3390/app10051732

**Chicago/Turabian Style**

Pham, Hoang Anh, Thierry Soriano, Van Hien Ngo, and Valentin Gies.
2020. "Distributed Adaptive Neural Network Control Applied to a Formation Tracking of a Group of Low-Cost Underwater Drones in Hazardous Environments" *Applied Sciences* 10, no. 5: 1732.
https://doi.org/10.3390/app10051732