# Path-Planning Strategy for Lane Changing Based on Adaptive-Grid Risk-Fields of Autonomous Vehicles

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## Abstract

**:**

## 1. Introduction

- The existing risk-field models are all continuous models, which are difficult to apply in spatially continuous traffic environments.
- In addition, most of the existing risk-field models do not consider the motion state of the obstacle vehicle.

## 2. Related Works

## 3. Risk-Field Modeling for Traffic Environments

#### 3.1. Road Divider Risk-Field

#### 3.2. Road Boundary Risk-Field

#### 3.3. Obstacle Vehicle Risk-Field

#### 3.4. Total Risk-Field Establishment

## 4. Adaptive-Grid Risk-Field Modeling

#### 4.1. Initial Gridding

#### 4.2. Triggering Rule of Grid Division

#### 4.3. Grid-Division Method

#### 4.4. Adaptive Dividing Risk-Field

## 5. Optimal Lane-Change Path Selection Based on Discretized Risk-Field

#### 5.1. Path Cluster Generation Based on Dynamic Programming

#### 5.2. Path Selecting

## 6. Algorithm Validation

#### 6.1. Simulation Verification

^{2}. The longitudinal distance between VE1 and EGO1 was 44 m. Figure 7b shows the idealized risk-field of the simulation scenario. The rear VE1 risk-field range is significantly larger than the front risk-field range because the acceleration of VE1 is less than 0.

#### 6.2. Actual Vehicle Verification

## 7. Conclusions

- The current risk-field model does not take into account the movement trend of the obstacle vehicle.
- Current risk-field models are not accurately modeled for specific vehicle types.
- Grid division rules need to be more detailed.

- Integrating obstacle vehicle trajectory prediction theory into risk-field models.
- Building more accurate risk-field models for common vehicles.
- Improving the rules of grid division.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Risk-field distribution of risk sources in traffic environment: (

**a**) road divider risk-field; (

**b**) road boundary risk-field; (

**c**) obstacle vehicle risk-field; (

**d**) total risk-field.

**Figure 7.**Adaptive grid risk-field generation for simulation scenario: (

**a**) simulation scene diagram; (

**b**)continuous spatial risk-field; (

**c**) fixed grid size risk field; (

**d**) adaptive grid size risk field.

**Figure 9.**Comparison of new and traditional paths in the simulation scenario: (

**a**) cost of smoothness of path; (

**b**) cost of lateral offset from road centerline; (

**c**) path risk cost; (

**d**) path cost.

**Figure 15.**Adaptive grid-based risk-field generation for actual vehicle scenario: (

**a**) schematic diagram of the actual vehicle scenario; (

**b**)continuous spatial risk-field; (

**c**) fixed grid size risk field; (

**d**) Adaptive grid size risk field;

**Figure 17.**Comparison of new and traditional paths in the actual vehicle scenario: (

**a**) cost of smoothness of path; (

**b**) cost of lateral offset from road centerline; (

**c**) path risk cost; (

**d**) path cost.

Range of Value at Risk | Name | Situation of Division |
---|---|---|

(−∞, L) | Low risk grid | No |

(L, H) | Medium risk grid | Yes |

(H, +∞) | High risk grid | No |

Xn | $\mathit{\lambda}$ | $\mathit{u}$ |
---|---|---|

0 | 1 | 1 |

1 | 2 | 1 |

2 | 1 | 2 |

3 | 2 | 2 |

Cost Function Parameter | Meaning |
---|---|

$k$ | Path point number of the i path |

${u}_{1}$ | Expectation weight coefficient |

${u}_{2}$ | Variance weight coefficient |

$\mathrm{cos}t\left(k\right)$ | Cost of the kth path point |

$COST\left(\mathrm{i}\right)$ | Cost of path(i) |

${p}_{c}\cdot {a}_{c}\left(k\right)$ | Cost of path smoothness |

${p}_{c}$ | Weight coefficient of path smoothness |

${p}_{\mathrm{d}}\cdot {a}_{d}\left(k\right)$ | Cost of lateral distance to road centerline |

${p}_{\mathrm{d}}$ | Weight coefficient of transverse distance to road centerline |

${p}_{\mathrm{s}}\cdot {a}_{s}\left(k\right)$ | Path risk cost |

${p}_{\mathrm{s}}$ | Path risk weight coefficient |

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

$L$ | 4 | ${A}_{V}$ | 20 | ${\mathsf{\Omega}}_{2}$ | 1 |

$H$ | 12.5 | ${\sigma}_{x}$ | 1.25 | ${u}_{1}$ | 1 |

${d}_{\mathrm{min}}$ | 0.2 m | ${\sigma}_{y}$ | 0.8 | ${u}_{2}$ | 0.7 |

${A}_{S}$ | 1 | ${k}_{r}$ | 1.2 | ${p}_{c}$ | 0.7 |

${\sigma}_{S}$ | 0.5 | ${w}_{1}$ | 1 | ${p}_{d}$ | 0.7 |

${A}_{B}$ | 20 | ${w}_{2}$ | 0.8 | ${p}_{s}$ | 1 |

${\sigma}_{B}$ | 1 | ${\mathsf{\Omega}}_{1}$ | 1.2 |

Serial Number | Equipment Name | Usage |
---|---|---|

(1) | dSPACE MicroAutoBoxII | 1. Collecting and Preprocessing Related Sensor Data |

2. Implementation of lane changing algorithm and strategy; building algorithm model; calculating, storing, searching and outputting calculation results. | ||

3. Send the torque magnitude for longitudinal control, steering wheel angle signal for lateral control, etc., to the wire control chassis in the form of CAN telegrams | ||

(2) | Millimeter wave radar ESR | Distance measuring sensors |

(3) | Binocular camera | Visual mapping, semantic segmentation and lane line recognition, etc. |

(4) | GPS positioning device SimPark982 | Positioning output of vehicle latitude and longitude coordinates |

(5) | Inertial navigation systems | Output of vehicle dynamics parameters |

(6) | Chassis communication protocols | CAN telegram signal |

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## Share and Cite

**MDPI and ACS Style**

Yang, Z.; Hu, Y.; Zhang, Y.
Path-Planning Strategy for Lane Changing Based on Adaptive-Grid Risk-Fields of Autonomous Vehicles. *World Electr. Veh. J.* **2022**, *13*, 175.
https://doi.org/10.3390/wevj13100175

**AMA Style**

Yang Z, Hu Y, Zhang Y.
Path-Planning Strategy for Lane Changing Based on Adaptive-Grid Risk-Fields of Autonomous Vehicles. *World Electric Vehicle Journal*. 2022; 13(10):175.
https://doi.org/10.3390/wevj13100175

**Chicago/Turabian Style**

Yang, Zhengcai, Yunzhong Hu, and Youbing Zhang.
2022. "Path-Planning Strategy for Lane Changing Based on Adaptive-Grid Risk-Fields of Autonomous Vehicles" *World Electric Vehicle Journal* 13, no. 10: 175.
https://doi.org/10.3390/wevj13100175