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

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## Abstract

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## 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

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**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.

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## 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