# A Path Planning Method for Underground Intelligent Vehicles Based on an Improved RRT* Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

#### 2.1. Underground Intelligent Vehicles

#### 2.2. Path Planning Methods

## 3. Constraints Formulation

#### 3.1. Drift Environment Formulation

#### 3.2. Kinematics of Vehicles

## 4. Improved RRT* Algorithm for Intelligent Vehicles

- (1)
- The underground drift is long and narrow, and the available area of the entire map is small. The RRT* algorithm uses fixed-step full-map sampling, which results in low sampling efficiency in the scene of the drift map;
- (2)
- Drifts are usually constructed by a drilling and blasting method, and their surface will inevitably be irregular. As a result, the map of drifts cannot be as smooth as a regular road map, which will affect the smoothness of the solution path;
- (3)
- Underground vehicles are usually large in size, and the steering radius should be strictly controlled during their driving. Due to the randomness of the expansion, the RRT* algorithm cannot guarantee a path that meets the steering radius of the vehicles.

- (1)
- Dynamic step size

- (2)
- Steering angle constraints

- (3)
- Optimal tree reconnection

Algorithm 1 Improved RRT* Algorithm | |

Input: ${x}_{start}$, ${x}_{goal}$, MapOutput: A path T from ${x}_{start}$ to ${x}_{goal}$ | |

1 | T.initalize(); |

2 | for i = 1 to n do |

3 | while true do |

4 | ${x}_{rand}$←Sample(Map); |

5 | ${x}_{near}$←Near(${x}_{rand}$, T); |

6 | DynamicSize←CollisionCheck(${x}_{near}$, Map); |

7 | ${x}_{new}$←Steer(${x}_{rand}$,${x}_{near}$,DynamicSize); |

8 | if CollisionFree(${x}_{new}$, Map) and Turnable(${x}_{new}$, ${x}_{near}$, ${x}_{parent}$) then |

9 | break; |

10 | end |

11 | end |

12 | ${X}_{near\_neighbours}$←NearNeighbour(${x}_{new}$, T) |

13 | foreach ${x}_{near\_neighbour}\in {X}_{near\_neighbours}$ do |

14 | Test_dis←Cost(${x}_{new}$) + Distance(${x}_{new}$, ${x}_{near\_neighbour}$) |

15 | if CollisionFree(${x}_{new}$, ${x}_{near\_neighbour}$, Map) and Test_dis < Cost(${x}_{near\_neighbour}$)then |

16 | ${x}_{parent}$←Parent(${x}_{near\_neighbour}$); |

17 | Update(T); |

18 | end |

19 | end |

20 | if ${x}_{new}$ = ${x}_{goal}$ then |

21 | T←OptimalTreeReconnection(T); |

22 | success(); |

23 | end |

24 | end |

## 5. Simulation Analysis

#### 5.1. Simulation Environment

#### 5.2. Simulation Results

#### 5.3. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Comparison of the rasterized map and vectorized map. (

**a**) The rasterized map; (

**b**) the vectorized map.

**Figure 8.**Comparison of fixed step size and dynamic step size. (

**a**) Fixed step size; (

**b**) dynamic step size.

**Figure 15.**The simulation result with known obstacles. (

**a**) With avoidable obstacles; (

**b**) with unavoidable obstacles.

**Figure 16.**The simulation result for the kidnapping problem. (

**a**) With turnable kidnapping; (

**b**) with unturnable kidnapping.

Research | Algorithms | Scenarios | Path Type | Map Type | Equipment |
---|---|---|---|---|---|

[32] | Dijkstra, Ant colony | Rescue | Global | Rasterized | Mine robots |

[33] | Scanning algorithms | Dangerous environment in coal mines | Local | Real-time sensing | Multi-robot systems |

[34] | Optimized multimodal sensor fusion approach | Navigation, mapping | Navigation | Real-time sensing | Aerial robots |

[35] | Enumeration algorithm | Production | Global | Topological | Underground vehicles |

[36] | Feature detection algorithm | Production | Navigation | Real-time sensing | Underground articulated vehicles |

[37] | Artificial potential field | Rescue | Global | Rasterized | Mine robots and UAVs |

[38] | A* algorithm | Production | Global and local | Rasterized | Underground four-wheeled vehicles |

[39] | Graph-based exploration path planning | Exploration, mapping | Global and local | Real-time sensing | UAVs |

[40] | Ant colony algorithm | Not mentioned | Global | Rasterized | Mine robots |

[41] | Genetic algorithm | Rescue | Navigation | Real-time sensing | Rescue snake robot |

[42] | D* algorithm | Not mentioned | Global | Rasterized | Mine robots |

This paper | Improved RRT* algorithm | Production | Global | Vectorized | Underground articulated vehicles |

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

Max steering angle | 42.5° |

Width | 2120 mm |

Front body length | 4130 mm |

Rear body length | 4330 mm |

Parameters | Classic RRT | Classic RRT* | Improved RRT* |
---|---|---|---|

Average path length (m) | 211.11 | 189.86 | 189.54 |

Average search time (s) | 168.94 | 44.16 | 86.12 |

Average of search node count | 561.60 | 267.30 | 360.00 |

Average of path node count | 32.00 | 28.80 | 16.20 |

Effective ratio of steering angle | 81.87% | 92.71% | 100.00% |

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**MDPI and ACS Style**

Wang, H.; Li, G.; Hou, J.; Chen, L.; Hu, N.
A Path Planning Method for Underground Intelligent Vehicles Based on an Improved RRT* Algorithm. *Electronics* **2022**, *11*, 294.
https://doi.org/10.3390/electronics11030294

**AMA Style**

Wang H, Li G, Hou J, Chen L, Hu N.
A Path Planning Method for Underground Intelligent Vehicles Based on an Improved RRT* Algorithm. *Electronics*. 2022; 11(3):294.
https://doi.org/10.3390/electronics11030294

**Chicago/Turabian Style**

Wang, Hao, Guoqing Li, Jie Hou, Lianyun Chen, and Nailian Hu.
2022. "A Path Planning Method for Underground Intelligent Vehicles Based on an Improved RRT* Algorithm" *Electronics* 11, no. 3: 294.
https://doi.org/10.3390/electronics11030294