# Neuro-Sliding Control for Underwater ROV’s Subject to Unknown Disturbances

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

## 3. Control Design

#### 3.1. Second Order Sliding Mode Control (2nd-SMC)

#### 3.1.1. Nominal Reference

#### 3.1.2. Sliding Mode Control

#### 3.2. Self-Tuning Backpropagation Neural Network Control

_{k}

_{−1}, $\tilde{\eta}$

_{k}

_{−2}), respectively, were used by the input layer (X

_{1}, X

_{2}, X

_{3}). Additionally, a bias unit, B, was incorporated into the input X

_{4}, which stores the value of 1. The use of a bias unit in the neural network increases the capability of the network to adjust to the system.

_{j}based on the inputs X

_{i}with its weight coefficient W

_{ji}:

_{j}= Σ (X

_{i}· W

_{ji})

_{j}is calculated by the sigmoid function applied to the weighted sum S

_{j}:

_{j}and its weight coefficients V

_{j}were calculated:

_{j}· V

_{j})

## 4. Experimental Results

#### 4.1. Mini-ROV Architecture

#### 4.1.1. Mechanical Architecture

#### 4.1.2. Electronic Architecture

#### 4.2. Experiment Design

**Remark**

**1.**

- (a)
- Set-point. The mini-ROV was required to reach a desired fixed depth, ${z}_{d}=0.3\mathrm{m}$.
- (b)
- Trajectory tracking. The vehicle was required to follow a sinusoidal trajectory:$${z}_{d}=0.1\mathrm{sin}\left(t\right)+0.3m$$

#### 4.3. Results

#### 4.3.1. Position Regulation (${z}_{d}=0.3\text{}\mathrm{m}$)

#### 4.3.2. Tracking Trajectory (${z}_{d}=0.1\mathrm{sin}\left(t\right)+0.3\text{}\mathrm{m}$)

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Zhang, M.; Chu, Z. Adaptive sliding mode control based on local recurrent neural networks for underwater robot. Ocean Eng.
**2012**, 45, 56–62. [Google Scholar] [CrossRef] - Sun, B.; Zhu, D.; Ding, F.; Yang, S. A novel tracking control approach for unmanned underwater vehicles based on bio-inspired neurodynamics. J. Mar. Sci Technol.
**2013**, 18, 63–74. [Google Scholar] [CrossRef] - Gao, J.; Proctor, A.; Bradley, C. Adaptive neural network visual servo control for dynamic positioning of underwater vehicles. Neurocomput.
**2015**, 167, 604–613. [Google Scholar] [CrossRef] - Cui, R.; Zhang, X.; Cui, D. Adaptive sliding-mode attitude control for autonomous underwater vehicles with input nonlinearities. Ocean Eng.
**2016**, 123, 45–54. [Google Scholar] [CrossRef] - Yang, J.; Feng, J.; Qi, D.; Li, Y. Longitudinal motion control of underwater vehicle based on fast smooth second order sliding mode. Optik
**2016**, 127, 9118–9130. [Google Scholar] [CrossRef] - Guo, X.; Yan, W.; Cui, R. Neural network-based nonlinear sliding-mode control for an AUV without velocity measurements. Int. J. Control
**2017**, 92, 1–16. [Google Scholar] [CrossRef] - Gao, J.; Wu, P.; Yang, B.; Xia, F. Adaptive neural network control for visual servoing of underwater vehicles with pose estimation. J. Mar. Sci. Technol.
**2017**, 22, 470–478. [Google Scholar] [CrossRef] - Liu, S.; Liu, Y.; Wang, N. Robust adaptive self-organizing neuro-fuzzy tracking control of UUV with system uncertainties and unknown dead-zone nonlinearity. Nonlinear Dyn.
**2017**, 89, 1397–1414. [Google Scholar] [CrossRef] - Gao, J.; An, X.; Proctor, A.; Bradley, C. Sliding mode adaptive neural network control for hybrid visual servoing of underwater vehicles. Ocean. Eng.
**2017**, 142, 666–675. [Google Scholar] [CrossRef] - Elmokadem, T.; Zribi, M.; Youcef-Toumi, K. Terminal sliding mode control for the trajectory tracking of underactuated Autonomous Underwater Vehicles. Ocean. Eng.
**2017**, 129, 613–625. [Google Scholar] [CrossRef] - Londhe, P.S.; Dhadekar, D.D.; Patre, B.M.; Waghmare, L.M. Uncertainty and disturbance estimator based sliding mode control of an autonomous underwater vehicle. Int. J. Dyn. Control
**2017**, 5, 1122–1138. [Google Scholar] [CrossRef] - García-Valdovinos, L.; Salgado-Jiménez, T.; Bandala-Sánchez, M.; Nava-Balanzar, L.; Hernández-Alvarado, R.; Cruz-Ledesma, J. Modeling, Design and Robust Control of a Remotely Operated Underwater Vehicle. Int. J. Adv. Robot. Syst.
**2014**, 11, 1–16. [Google Scholar] [CrossRef] - Hernández-Alvarado, R.; García-Valdovinos, L.; Salgado-Jiménez, T.; Gómez-Espinosa, A.; Fonseca-Navarro, F. Neural Network-Based Self-Tuning PID Control for Underwater Vehicles. Sensors
**2016**, 16, 1429. [Google Scholar] [CrossRef] [PubMed] - García-Valdovinos, L.; Salgado-Jiménez, T. On the Dynamic Positioning Control of Underwater Vehicles subject to Ocean Currents. In Proceedings of the 2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control, Merida City, México, 26–28 October 2011. [Google Scholar]
- Fossen, T.I. Marine Control Systems: Guidance, Navigation and Control of Ships, Rigs and Underwater Vehicles; Marine Cybernetics: Trondheim, Norway, 2002. [Google Scholar]
- Cui, X.; Shih, K. Direct Control and Coordination Using Neural Networks. IEEE Trans.Syst. Man Cybern.
**1993**, 23, 686–697. [Google Scholar]

**Figure 8.**Performance of the 2nd-SMC scheme. The SME and the RMS values remained constant during the whole experiment.

**Figure 9.**Performance of the BP-NN control. As time went by the neural network updated its weights online in order to drive the position error to zero. In the same fashion, the energy required to achieve a smaller SME increased.

**Figure 10.**Performance of the NSC scheme (2nd-SMC 20%/BP-NN 80%). The BP-NN scheme appeared as the predominant control with a contribution of 80%. As the neural network adjusted its weights online, the SME decreased in time. The RMS voltage remained practically unchanged.

**Figure 11.**Performance of the NSC scheme (2nd-SMC 50%/BP-NN 50%). The overshoot showed a reduction and the BP-NN gradually reduced the SME value.

**Figure 12.**Performance of the NSC scheme (2nd-SMC 80%/BP-NN 20%). The 2nd-SMC scheme was the predominant control with a contribution of 80%. The SME exhibited a reduced value since the beginning; however, due to the low contribution of the BP-NN control, the SME value did not reflect a significant reduction by the end of the experiment. The RMS voltage remained practically unchanged throughout the experiment.

Gain | Value | Gain | Value |
---|---|---|---|

$\alpha $ | 15 | ${K}_{i}$ | 43 |

$\kappa $ | 43 | ${K}_{d}$ | 0.7 |

**Table 2.**Square mean error (SME) and effective value (RMS) comparison for a set-point of ${z}_{d}=0.3\mathrm{m}$.

Control Law | Control Signal (%) | Test #1 | Test #5 | |||
---|---|---|---|---|---|---|

2nd-SMC | NN | SME [cm] | RMS [volts] | SME [cm] | RMS [volts] | |

2nd-SMC | 100 | - | 2.7 | 8.51 | 2.6 | 8.5 |

BP-NN | - | 100 | 10.28 | 7.8 | 4.09 | 8.19 |

NSC | 20 | 80 | 10.32 | 8.18 | 2.59 | 8.05 |

NSC | 50 | 50 | 7.09 | 8.31 | 4.5 | 8.09 |

NSC | 80 | 20 | 3.75 | 8.27 | 3.42 | 8.57 |

**Table 3.**Square mean error (SME) and effective value (RMS) comparison for a trajectory of ${z}_{d}=0.1\mathrm{sin}\left(t\right)+0.3\mathrm{m}$.

Control Law | Control Signal (%) | Test #1 | Test #5 | |||
---|---|---|---|---|---|---|

SMC | NN | SME [cm] | RMS [volts] | SME [cm] | RMS [volts] | |

2nd-SMC | 100 | - | 2.51 | 8.36 | 2.51 | 8.36 |

BP-NN | - | 100 | 10.78 | 7.56 | 1.82 | 8.0 |

NSC | 20 | 80 | 10.22 | 7.83 | 2.2 | 8.15 |

NSC | 50 | 50 | 8.0 | 8.52 | 5.34 | 8.69 |

NSC | 80 | 20 | 7.0 | 8.45 | 3.53 | 8.6 |

© 2019 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/).

## Share and Cite

**MDPI and ACS Style**

García-Valdovinos, L.G.; Fonseca-Navarro, F.; Aizpuru-Zinkunegi, J.; Salgado-Jiménez, T.; Gómez-Espinosa, A.; Cruz-Ledesma, J.A.
Neuro-Sliding Control for Underwater ROV’s Subject to Unknown Disturbances. *Sensors* **2019**, *19*, 2943.
https://doi.org/10.3390/s19132943

**AMA Style**

García-Valdovinos LG, Fonseca-Navarro F, Aizpuru-Zinkunegi J, Salgado-Jiménez T, Gómez-Espinosa A, Cruz-Ledesma JA.
Neuro-Sliding Control for Underwater ROV’s Subject to Unknown Disturbances. *Sensors*. 2019; 19(13):2943.
https://doi.org/10.3390/s19132943

**Chicago/Turabian Style**

García-Valdovinos, Luis Govinda, Fernando Fonseca-Navarro, Joanes Aizpuru-Zinkunegi, Tomas Salgado-Jiménez, Alfonso Gómez-Espinosa, and José Antonio Cruz-Ledesma.
2019. "Neuro-Sliding Control for Underwater ROV’s Subject to Unknown Disturbances" *Sensors* 19, no. 13: 2943.
https://doi.org/10.3390/s19132943