# Hybrid Path Planning for Unmanned Surface Vehicles in Inland Rivers Based on Collision Avoidance Regulations

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Model of the USV

#### 2.2. Hybrid Path Planning of “Jinghai-I” USV

#### 2.2.1. Global Path Planning Based on Improved A*

#### Design of Evaluation Function

#### 2.2.2. Local Path Planning Based on the Model Predictive Control Algorithm

#### Collision Avoidance Regulations for Inland Rivers

#### Division of Encounter Situation

#### Design of Optimization Problem

## 3. Results

#### 3.1. Global Path Planning Based on Improved A* Algorithm

#### 3.1.1. Simulation Settings

- The green square represents the starting node and the yellow square represents the target node;
- The black area indicates the “Jinghai-I” USV’s inaccessible zones, including two static obstacles and the boundary of the channel;
- The white area indicates the “Jinghai-I” USV’s accessible zones.

#### 3.1.2. Simulation Results

#### Different Heuristic Functions $h\left(k\right)$

- The red circle line is the global optimal path planned by the improved A* algorithm;
- The yellow hexagon star represents the optimal path planned by the A* algorithm using the Manhattan method as the heuristic function;
- The green square represents the optimal path planned by the A* algorithm using the octave distance method as the heuristic function;
- The orange triangle represents the optimal path planned by the A* algorithm using the Euclidean method as the heuristic function.

#### Different Coefficients ${\mu}_{4}$

- The blue lower triangle shows the global optimal path planned by the improved A* algorithm when ${\mu}_{4}$ = 0.02;
- The red dot triangle represents the global optimal path planned by the improved A* algorithm when ${\mu}_{4}$ = 0.045;
- The blue upper triangle represents the global optimal path planned by the improved A* algorithm when ${\mu}_{4}$ = 0.6;
- The orange pentagram represents the global optimal path planned by the improved A* algorithm when ${\mu}_{4}$ = 6;
- The golden diamond represents the global optimal path planned by the improved A* algorithm when ${\mu}_{4}$ = 60;
- The green square represents the global optimal path planned by the improved A* algorithm when ${\mu}_{4}$ = 600;
- The sky-blue hexagram is the globally optimal path planned by the improved A* algorithm when ${\mu}_{4}$ = 6000.

#### Path Smoothing

#### 3.2. Local Path Planning Based on the MPC Algorithm

#### 3.2.1. Simulation Settings

- The yellow boat represents the “Jinghai-I” USV and the blue boat represents the obstacle boat;
- The golden dynamic area indicates the dynamic bumper domain of the “Jinghai-I” USV and the obstacle ship;
- The purple dotted line represents the reference path of the “Jinghai-I” USV;
- The blue dotted line represents the path planned after the cost function I;
- The green dotted line represents the path planned by the cost function II;
- The orange solid line represents the path planned by the cost function III;
- The dotted line in light blue indicates the navigation path of the obstacle ship.

#### 3.2.2. Simulation Result

#### Local Path planning Results without Water Flow

#### Local Path planning Results with Water Flow

## 4. Discussion

## 5. Conclusions

- Continuing to study more complex collision avoidance scenarios for the “Jinghai-I” USV in inland rivers, particularly when it encounters obstacles such as other ships, and further optimizing the collision avoidance behavior of the “Jinghai-I” USV in these scenarios;
- Conducting future research to improve the applicability of the current mathematical models used to differentiate between encounter scenarios, as they are not accurate for some of these scenarios; and
- Validating the research in this paper through practical testing on the “Jinghai-I” USV.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**The cost function. The left green box represents the start node and the right yellow box represents the target node.

**Figure 8.**Avoidance and maneuvering of the USV in accordance with regulations. The blue ship is the USV and the red ship is an obstacle ship. Where (

**a**) represents heading, (

**b**) represents overtaking, (

**c**) represents crossing from the port side, and (

**d**) represents crossing from the starboard side.

**Figure 12.**Simulation results before and after path smoothing. The red circular dots represent the smoothed path, while the blue lower triangle represents the original path.

**Figure 13.**The local optimal paths planned by the three cost functions under the condition of no water flow.

**Figure 14.**The speed of the “Jinghai-I” USV planned by the three cost functions under the condition of no water flow.

**Figure 16.**The speed of the “Jinghai-I” USV planned by the three cost functions under the condition of water flow.

Parameter | Value | Parameter | Value |
---|---|---|---|

length | $5\mathrm{m}$ | maximum speed | $6\mathrm{k}\mathrm{n}$ |

wide | $2\mathrm{m}$ | cruise speed | $3~4\mathrm{k}\mathrm{n}$ |

height | $1.5\mathrm{m}$ | acceleration | $0.3\mathrm{m}/{\mathrm{s}}^{2}$ |

full load draft | $\le 0.5\mathrm{m}$ | maximum yaw rate | $15\xb0/{\mathrm{s}}^{2}$ |

full load displacement | $\ge 1150\mathrm{k}\mathrm{g}$ | average yaw rate | $5~10\xb0/{\mathrm{s}}^{2}$ |

Parameter | Value |
---|---|

${\delta}_{1}$ | $40\xb0$ |

${\delta}_{2}$ | $7.5\xb0$ |

${\delta}_{3}$ | $68.5\xb0$ |

${\delta}_{4}$ | $68.5\xb0$ |

Parameter | Value | Parameter | Value |
---|---|---|---|

The size of the grid | 5 × 5 m | ${\mu}_{3}$ | $10$ |

${\mu}_{1}$ | 0.1 | ${\epsilon}_{1}$ | $0.5$ |

${\mu}_{2}$ | $1$ | ${\epsilon}_{2}$ | $0.7$ |

$\mathit{h}\left(\mathit{k}\right)$ | Average Time/s |
---|---|

Manhattan distance method | 0.0786 |

Octave distance method | 0.0812 |

Euclidean distance method | 0.2239 |

Dynamic-adjustment heuristic method | 0.1552 |

Parameter | Value | Parameter | Value |
---|---|---|---|

L | 5 m | $[{u}_{min},{u}_{max}]$ | $[0.5,3]\mathrm{m}/\mathrm{s}$ |

N | 20 | $[{r}_{min},{r}_{max}]$ | $\left[-10,10\right]\xb0/\mathrm{s}$ |

T | $0.1\mathrm{s}$ | $[{\dot{u}}_{min},{\dot{u}}_{max}]$ | $\left[-0.05,0.3\right]\mathrm{m}/{\mathrm{s}}^{2}$ |

${d}_{close\_d\_min}$ | $25\mathrm{m}$ | $[{\dot{r}}_{min},{\dot{r}}_{max}]$ | $[-0.6,0.6]\xb0/{\mathrm{s}}^{2}$ |

${d}_{close\_s\_min}$ | 15 m | ${\sigma}_{4}$ | 0.2 |

${d}_{close\_s\_pre}$ | 20 m | ${\sigma}_{5}$ | 10 |

${d}_{close\_d\_pre}$ | 30 m | ${\sigma}_{6}$ | 10 |

$|\chi {|}_{max}$ | (2$\mathsf{\pi}/9$) rad | ${\sigma}_{7}$ | 0.5 |

${u}_{ref}$ | $2\mathrm{m}/\mathrm{s}$ | ${\sigma}_{8}$ | 0.5 |

Encounter Scenarios | ${\mathit{\sigma}}_{1}$ | ${\mathit{\sigma}}_{2}$ | ${\mathit{\sigma}}_{3}$ | ${\mathit{\sigma}}_{\mathit{h}\mathit{e}\mathit{a}\mathit{d}\mathit{i}\mathit{n}\mathit{g}}$ | ${\mathit{\sigma}}_{\mathit{c}\mathit{r}\mathit{o}\mathit{s}\mathit{s}\mathit{i}\mathit{n}\mathit{g}}$ | ${\mathit{\sigma}}_{\mathit{o}\mathit{v}\mathit{e}\mathit{r}\mathit{t}\mathit{a}\mathit{k}\mathit{i}\mathit{n}\mathit{g}}$ | ${\mathit{i}}_{\mathit{o}\mathit{w}\_\mathit{s}\_\mathit{i}}$ |
---|---|---|---|---|---|---|---|

No obstacles | 2.5 | 1.1 | 7 | 0 | 0 | 0 | 0 |

Crossing | 0.7 | 0.2 | 7 | 0 | 1 | 0 | 0 |

Overtaking | 0.5 | 0.1 | 5 | 0 | 0 | 1 | 0 |

Heading | 0.7 | 0.2 | 5 | 1 | 0 | 0 | 0 |

Only static obstacles | 0.25 | 0.1 | 7 | 0 | 0 | 0 | 1 |

**Table 7.**Path and yaw angle errors of three cost functions. Here, ${error}_{max\_A}$ represents the maximum path deviation for Region A.

Cost Function | ${\mathit{v}}_{\mathit{c}}$ | ${\mathit{e}\mathit{r}\mathit{r}\mathit{o}\mathit{r}}_{\mathit{t}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\_\mathit{p}}$ | ${\mathit{e}\mathit{r}\mathit{r}\mathit{o}\mathit{r}}_{\mathit{m}\mathit{a}\mathit{x}\_\mathit{A}}$ | ${\mathit{e}\mathit{r}\mathit{r}\mathit{o}\mathit{r}}_{\mathit{m}\mathit{a}\mathit{x}\_\mathit{B}}$ | ${\mathit{e}\mathit{r}\mathit{r}\mathit{o}\mathit{r}}_{\mathit{m}\mathit{a}\mathit{x}\_\mathit{C}}$ | ${\mathit{e}\mathit{r}\mathit{r}\mathit{o}\mathit{r}}_{\mathit{m}\mathit{a}\mathit{x}\_\mathit{D}}$ | ${\mathit{e}\mathit{r}\mathit{r}\mathit{o}\mathit{r}}_{\mathit{t}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\_\mathit{r}}$ |
---|---|---|---|---|---|---|---|

$I$ | $\times $ | 99.0318 m | 2.9882 m | 5.7263 m | 2.6925 m | 3.9568 m | 17.3502 rad |

$\mathit{II}$ | $\times $ | 91.1743 m | 1.8611 m | 5.9423 m | 6.8505 m | 3.0001 m | 10.5379 rad |

$\mathit{III}$ | $\times $ | 90.9654 m | 2.1878 m | 5.3729 m | 2.6234 m | 2.8795 m | 11.4376 rad |

$\mathit{I}$ | $\surd $ | 93.4238 m | 3.4382 m | 4.5093 m | 2.5324 m | 4.3987 m | 16.7966 rad |

$\mathit{II}$ | $\surd $ | 77.4369 m | 3.2110 m | 4.3026 m | 2.8485 m | 4.8261 m | 10.0409 rad |

$\mathit{III}$ | $\surd $ | 79.1045 m | 3.2743 m | 4.0516 m | 3.0425 m | 4.5786 m | 11.0247 rad |

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**MDPI and ACS Style**

Gao, P.; Xu, P.; Cheng, H.; Zhou, X.; Zhu, D.
Hybrid Path Planning for Unmanned Surface Vehicles in Inland Rivers Based on Collision Avoidance Regulations. *Sensors* **2023**, *23*, 8326.
https://doi.org/10.3390/s23198326

**AMA Style**

Gao P, Xu P, Cheng H, Zhou X, Zhu D.
Hybrid Path Planning for Unmanned Surface Vehicles in Inland Rivers Based on Collision Avoidance Regulations. *Sensors*. 2023; 23(19):8326.
https://doi.org/10.3390/s23198326

**Chicago/Turabian Style**

Gao, Pengcheng, Pengfei Xu, Hongxia Cheng, Xiaoguo Zhou, and Daqi Zhu.
2023. "Hybrid Path Planning for Unmanned Surface Vehicles in Inland Rivers Based on Collision Avoidance Regulations" *Sensors* 23, no. 19: 8326.
https://doi.org/10.3390/s23198326