# Autonomous Heading Planning and Control Method of Unmanned Underwater Vehicles for Tunnel Detection

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- The open-source underwater vehicle platform BlueROV is modified, and the control system is rebuilt. The ranging sonar and compass are added as the heading feedback sensor, which is used as the experimental platform for the heading planning method proposed;
- (2)
- Based on the principle of ultrasonic auto-receive ranging, a new heading planning method based on ranging sonar feedback control is proposed, and UUV’s autonomous heading planning control is realized.

## 2. Problem Description

#### 2.1. Mathematical Model

#### 2.1.1. Assumptions

- Mainly studying the heading control of UUV in the horizontal plane, ignoring the roll, trim, and snorkeling motions of UUV, and simplifying the model to a degree of freedom model;
- Due to the low advance velocity of UUV during tunnel detection, the impact of water flow speed on sonar ranging is not considered, and the effect of water quality in the simulation and test environment on sonar ranging is not considered;
- To better represent the heading in the algorithm design, this paper abstracts UUV into a straight line for mathematical modeling, ignoring the deviation angle between the theoretical model heading and the actual physical model heading;
- Do not consider the impact of gravity and buoyancy on UV motion in the vertical plane, and ignore the restoring force generated during their motion;
- The measurement range of a sonar ranging sensor is limited, and the maximum range constraint is considered in data feedback;
- The thrust that UUV thrusters can generate is limited, and the thrust distribution on the horizontal plane takes into account the constraint of thrust saturation.

#### 2.1.2. Kinematic and Dynamic Model

#### 2.1.3. Thrust Distribution Model

#### 2.2. Tunnel Autonomous Navigation

#### 2.3. UUV Test Platform

- The upper computer sends the target heading parameters to the lower computer through the interactive node. The heading planning node obtains the UUV’s relative position in the environment and plans a desired yaw angle based on the feedback data from the ranging sonar sensor.
- The heading control node utilizes a PID controller to adjust the heading angle by distributing the thrust of the required rotation torque based on the planned yaw angle.
- The thrust distribution node thus obtains the thrust value and direction of each horizontal thruster and controls the heading of UUV to change. This process continues until the vehicle’s forward heading is stabilized on the target heading.

Algorithm 1 Heading Planning and Control |

1: Set the initial parameters ${P}_{T}$ ^{1} and ${R}_{r}$ ^{2} of the heading planning method; |

2: Initialize target heading angle ${\phi}_{T}$; |

3: While the procedure is in progress: |

4: Calculate the yaw angle ${\alpha}_{3}$; |

5: Send the desired heading angle ${\phi}_{d}=\phi +{\alpha}_{3}$ to heading PID controller; |

6: If Current heading angle $\phi $ ! = ${\phi}_{T}$: |

7: Compute the control signal by heading PID controller; |

8: Thrust distribution; |

9: Send the control signal to the UUV; |

10: $t++$; |

11: End if |

12: End while |

^{1} Distance from target point to initial position. ^{2} Radius of the tunnel. |

## 3. Autonomous Heading Planning and Control Method

#### 3.1. Heading Planning Model

#### 3.2. Autonomous Heading Planning Method

## 4. Test and Analysis

#### 4.1. Heading Orientation Test Experiment

- First, use proportional control, starting from a larger proportionality $\delta $, and gradually reduce the proportional degree so that the system response to the step input can reach the critical oscillation state. The proportionality at this point is denoted as ${\delta}_{r}$, and the critical oscillation period is denoted as ${T}_{r}$;
- Determine the PID controller parameters according to the empirical formula of the critical proportionality method provided by Ziegler-Nichols (see Table 4); this method applies to the controlled object with self-balancing capability.

#### 4.2. Autonomous Heading Planning Simulation and Verification

- Case I: The starting position of UUV is located at about 1 m to the left of the tunnel central axis, and the heading is left relative to the target heading;
- Case II: The starting position of UUV is located about 1 m to the right of the tunnel central axis, and the heading is right relative to the target heading;
- Case III: The starting position of UUV is near the central axis of the tunnel.

#### 4.3. Autonomous Heading Planning Experiment and Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Xie, X. Analysis on construction technology of water conveyance tunnel of water conservancy project. Pearl River Water Transp.
**2016**, 2, 84–85. [Google Scholar] - Alattas, K.A.; Vu, M.T.; Mofid, O. Adaptive nonsingular terminal sliding mode control for performance improvement of perturbed nonlinear systems. Mathematics
**2022**, 10, 1064. [Google Scholar] [CrossRef] - Karimi, H.R.; Lu, Y. Guidance and control methodologies for marine vehicles: A survey. Control Eng. Pract.
**2021**, 111, 104785. [Google Scholar] [CrossRef] - Wan, C.; Zhou, H.; Liu, G. Research on Heading Motion of Remotely Operated Underwater Vehicle Based on PID Controller. Mech. Electr. Eng. Technol.
**2022**, 51, 109–111. [Google Scholar] - Liu, S.; Wang, Y.; Fu, H. Variable universe fuzzy—Least squares support-vector-machine compound control for ship course-keeping. Control Theory Appl.
**2011**, 28, 485–490. [Google Scholar] - Zhu, D.; Ma, N.; Gu, X. Adaptive fuzzy compensation control for nonlinear ship course-keeping. J. Shanghai JiaoTong Univ.
**2015**, 49, 250–261. [Google Scholar] - Vu, M.T.; Thanh, H.L.N.N.; Huynh, T.T. Station-keeping control of a hovering over-actuated autonomous underwater vehicle under ocean current effects and model uncertainties in horizontal plane. IEEE Access
**2021**, 9, 6855–6867. [Google Scholar] [CrossRef] - Luo, W.; Zou, Z.; Li, T. Robust tracking control of nonlinear ship steering. Control Theory Appl.
**2009**, 26, 893–895. [Google Scholar] - Xiao, Y. Research on Motion Control Method of Underwater Robot in Tunnel Based on Fuzzy Sliding Mode Control. Master’s Thesis, Shenyang University of Technology, Shenyang, China, 2022. [Google Scholar]
- Thanh, H.N.; Vu, M.T.; Mung, N.X. Perturbation observer-based robust control using a multiple sliding surfaces for nonlinear systems with influences of matched and unmatched uncertainties. Mathematics
**2020**, 8, 1371. [Google Scholar] [CrossRef] - Alattas, K.A.; Mobayen, S.; Din, S.U. Design of a non-singular adaptive integral-type finite time tracking control for nonlinear systems with external disturbances. IEEE Access
**2020**, 8, 102091–102103. [Google Scholar] [CrossRef] - Mofid, O.; Amirkhani, S.; Din, S.U. Finite-time convergence of perturbed nonlinear systems using adaptive barrier-function nonsingular sliding mode control with experimental validation. J. Vib. Control
**2022**, 1–14. [Google Scholar] [CrossRef] - Rojsiraphisal, T.; Mobayen, S.; Asad, J.H. Fast terminal sliding control of underactuated robotic systems based on disturbance observer with experimental validation. Mathematics
**2021**, 9, 1935. [Google Scholar] [CrossRef] - Kurniawan, E.; Wang, H.; Sirenden, B.H. Discrete-time modified repetitive sliding mode control for uncertain linear systems. Int. J. Adapt. Control Signal Process.
**2021**, 35, 2245–2258. [Google Scholar] [CrossRef] - Mashhad, A.M.; Mashhadi, S.K. H infinity robust controller comparison with PD like fuzzy logic controller for an AUV control. In Proceedings of the 4th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS), Zahedan, Iran, 9–11 September 2015; pp. 1–4. [Google Scholar]
- Zhang, Q.; Zhang, X.K.; Im, N.K. Ship Nonlinear-Feedback Course Keeping Algorithm Based on Mmg Model Driven by Bipolar Sigmoid Function for Berthing. Int. J. Nav. Archit. Ocean. Eng.
**2017**, 9, 525–536. [Google Scholar] [CrossRef] - Guan, W.; Sun, J.; Li, X.; Ren, Z. Unmanned Surface Vessel Steering L2 Gain Robust Control Based on Closed-Loop Shaping Filter. J. Northwest. Polytech. Univ.
**2019**, 37, 1018–1019. [Google Scholar] [CrossRef] [Green Version] - Chu, Z.; Wang, F.; Lei, T.; Luo, C. Path Planning based on Deep Reinforcement Learning for Autonomous Underwater Vehicles under Ocean Current Disturbance. IEEE Trans. Intell. Veh.
**2022**, 8, 1. [Google Scholar] [CrossRef] - Vu, M.T.; Le, T.H.; Thanh, H.N. Robust position control of an over-actuated underwater vehicle under model uncertainties and ocean current effects using dynamic sliding mode surface and optimal allocation control. Sensors
**2021**, 21, 747. [Google Scholar] [CrossRef] - Chu, Z.Z.; Wang, D.; Meng, F. An Adaptive RBF-NMPC Architecture for Trajectory Tracking Control of Underwater Vehicles. Machines
**2021**, 9, 105. [Google Scholar] [CrossRef] - Zhang, H.; Wang, P.; Zhang, Y. A Novel Dynamic Path Re-Planning Algorithm with Heading Constraints for Human Following Robots. IEEE Access
**2020**, 8, 49329–49337. [Google Scholar] [CrossRef] - Vu, M.T.; Van, M.; Bui, D.H.P. Study on dynamic behavior of unmanned surface vehicle-linked unmanned underwater vehicle system for underwater exploration. Sensors
**2020**, 20, 1329. [Google Scholar] [CrossRef] [Green Version] - Chu, Z.Z.; Li, Z.Q.; Zhang, M.J. A fault diagnosis method for underwater thruster based on RFR-SVM. Inst. Mech. Eng.
**2022**, 1–11. [Google Scholar] [CrossRef] - D’Angelo, V.; Folino, P. A ROS-Based GNC Architecture for Autonomous Surface Vehicle Based on a New Multimission Management Paradigm. Drones
**2022**, 6, 382. [Google Scholar] [CrossRef] - Ashhar, K.; Noor-A-Rahim, M.; Khyam, M.O.; Soh, C.B. A Narrowband Ultrasonic Ranging Method for Multiple Moving Sensor Nodes. IEEE Sens. J.
**2019**, 19, 6289–6297. [Google Scholar] [CrossRef]

**Figure 2.**Horizontal thrust distribution diagram of UUV: (

**a**) force direction of UUV three degrees of freedom; (

**b**) thrust distribution diagram of UUV.

**Figure 3.**Single degree of freedom thrust distribution result: (

**a**) thrust distribution result of surge direction; (

**b**) thrust distribution result of sway direction; (

**c**) thrust distribution result of yaw direction.

**Figure 9.**Model diagram of heading planning: (

**a**) simulation process of autonomous navigation of UUV in tunnel; (

**b**) mathematical model of autonomous navigation coordinate system.

**Figure 12.**Path curve graph of UUV in simulation environment: (

**a**) path curve of UUV in case I; (

**b**) path curve of UUV in case II; and (

**c**) path curve of UUV in case III.

**Figure 14.**Process of UUV heading change in heading planning experiment: (

**a**) UUV starts from the starting position; (

**b**) UUV starts to deviate from the target heading; (

**c**) UUV approaches the target heading; and (

**d**) UUV steadily advances on the target heading.

Degree of Freedom of UUV | Position/Posture (E) ^{1} | Velocity (O) ^{2} |
---|---|---|

Movement-X ^{3} | $x$ | $u$ |

Movement-Y ^{3} | $y$ | $v$ |

Movement-Z ^{3} | $z$ | $r$ |

Rotation-X ^{4} | $\phi $ | $p$ |

Rotatio-Y ^{4} | $\theta $ | $q$ |

Rotation-Z ^{4} | $\psi $ | $r$ |

^{1}Position and posture of UUV in geodetic coordinate system;

^{2}the velocity of UUV in the carrier coordinate system;

^{3}movement of UUV in the X, Y, and Z directions;

^{4}and rotation of UUV around X, Y, Z directions.

Parameter | Unit Symbol | Description |
---|---|---|

$m$ | $kg$ | Mass |

${X}_{u}$ | $N\xb7s/m$ | Linear resistance in $u$ direction |

${Y}_{v}$ | $N\xb7s/m$ | Linear resistance in $v$ direction |

${N}_{r}$ | $N\xb7s/m$ | Linear resistance in $r$ direction |

${X}_{\dot{u}}$ | $kg$ | Additional mass in the $u$ direction |

${Y}_{\dot{v}}$ | $kg$ | Additional mass in the $v$ direction |

${N}_{\dot{r}}$ | $N\xb7m\xb7{s}^{2}$ | Additional rotational inertia in $r$ direction |

${D}_{u}$ | $N\xb7{s}^{2}/{m}^{2}$ | Secondary resistance in $u$ direction |

${D}_{v}$ | $N\xb7{s}^{2}/{m}^{2}$ | Secondary resistance in $v$ direction |

${D}_{r}$ | $N\xb7{s}^{2}/{m}^{2}$ | Secondary resistance in $r$ direction |

${I}_{Z}$ | $N\xb7m\xb7{s}^{2}$ | Rotational inertia |

Case | Offset Direction of UUV Heading ^{1} | Direction of ^{2} |
---|---|---|

${l}_{1}>{l}_{2}$ | Left | ${\alpha}_{3}>0$ |

${l}_{1}={l}_{2}$ | Right, $\{\begin{array}{l}{\alpha}_{2}>{\alpha}_{1}\\ {\alpha}_{2}<{\alpha}_{1}\end{array}$ | $\begin{array}{l}{\alpha}_{3}>0\\ {\alpha}_{3}<0\end{array}$ |

${l}_{1}<{l}_{2}$ | Level, $\{\begin{array}{l}{l}_{1}>{l}_{3}\\ {l}_{1}<{l}_{3}\end{array}$ | $\begin{array}{l}{\alpha}_{3}>0\\ {\alpha}_{3}<0\end{array}$ |

^{1}The heading of UUV deviates from the direction of the central axis;

^{2}direction of heading planning angle.

Controller Type | Proportionality $\mathit{\delta}\mathbf{\%}$ | Integral Time ${T}_{I}$ | Differential Time ${T}_{D}$ |
---|---|---|---|

P | 2${\delta}_{r}$ | ||

PI | 2.2${\delta}_{r}$ | 0.85${T}_{r}$ | |

PID | 1.7${\delta}_{r}$ | 0.5${T}_{r}$ | 0.13${T}_{r}$ |

Parameters | ${k}_{p}$ | ${k}_{i}$ | ${k}_{d}$ |
---|---|---|---|

Value | 0.530 | 0.400 | 0.175 |

Test | Max Deviation ^{1} (°) | Mean Deviation ^{2} (°) | Standard Deviation ^{3} (°) |
---|---|---|---|

Case I | 5.925 | 1.049 | 1.829 |

Case II | 4.428 | 1.688 | 1.512 |

Case III | 4.583 | −1.081 | 1.249 |

^{1}Absolute value of the maximum heading deviation from the target heading;

^{2}mean deviation from target heading;

^{3}and standard deviation from target heading.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xia, T.; Cui, D.; Chu, Z.; Yu, X.
Autonomous Heading Planning and Control Method of Unmanned Underwater Vehicles for Tunnel Detection. *J. Mar. Sci. Eng.* **2023**, *11*, 740.
https://doi.org/10.3390/jmse11040740

**AMA Style**

Xia T, Cui D, Chu Z, Yu X.
Autonomous Heading Planning and Control Method of Unmanned Underwater Vehicles for Tunnel Detection. *Journal of Marine Science and Engineering*. 2023; 11(4):740.
https://doi.org/10.3390/jmse11040740

**Chicago/Turabian Style**

Xia, Tianxing, Dehao Cui, Zhenzhong Chu, and Xing Yu.
2023. "Autonomous Heading Planning and Control Method of Unmanned Underwater Vehicles for Tunnel Detection" *Journal of Marine Science and Engineering* 11, no. 4: 740.
https://doi.org/10.3390/jmse11040740