# Study on Path Planning Method for Imitating the Lane-Changing Operation of Excellent Drivers

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## Abstract

**:**

## 1. Introduction

## 2. Acquisition of Ideal Path

#### 2.1. Lane-Changing Test

#### 2.2. Data Processing

_{g}axis, Y

_{g}axis and Z

_{g}axis are the east, north and sky directions, respectively, of the carrier’s location. To accurately describe the travel path, it is necessary to transform the coordinates of the geodetic coordinate system into the geographic coordinate system. However, a direct conversion of coordinates between the geodetic coordinate system and the geographic coordinate system is hard to process. Therefore, the Earth Cartesian coordinate system is introduced into the transformation. The relationships between the geodetic coordinate system, the geographic coordinate system and the Earth Cartesian coordinate system are shown in Figure 3.

_{e}, y

_{e}, z

_{e}) in the Cartesian coordinate system can be obtained from Equation (1).

_{N}is the radius of curvature of the ellipsoid, R

_{N}= R

_{e}(1 + esin2L). e is eccentricity of ellipsoid, e = (R

_{e}− R

_{p})/R

_{e}. R

_{e}is the long radius of the ellipse and R

_{p}is the short radius of the ellipsoid.

_{g}− y

_{g}plane in the geographic coordinate system. To facilitate the analysis of the driving path, the coordinate origin of the geographical coordinate system is set at the initial record point of the driving track. Thus, the coordinates of each sampling point in the Earth Cartesian coordinate system needs to be transformed by Equation (2).

_{g}, y

_{g}).

## 3. Fitting of the Test Path

_{i}, y

_{i}). According to above process, the coordinates of the ideal path in the geographical coordinate system have been obtained. For the convenience of calculation, only the two-dimensional coordinate (x

_{g}, y

_{g}) is needed to be fitted without considering the vertical motion. Figure 4 is a schematic diagram of the lane-changing path.

_{f}, y

_{f}) and y

_{f}is the lane width of the current driving road. Thus, the position of the vehicle is at the middle of the lane when lane-changing is completed. While the initial and final positions of lane-changing are determined, the trajectory selected by different types of drivers will also be different, which has impact on the riding comfort of the lane-changing process. Therefore, it is necessary to consider the intermediate state of the vehicle during lane-changing path planning. It is noticed that the entire lane-changing process can be divided into three phases: collision avoidance, rotation and adjustment [30]. It can be seen that the steering wheel angular speed during the obstacle avoidance and the rotation phase are faster than that during the adjustment phase by analyzing the steering wheel angular speed during the lane-changing process. Therefore, the vehicle position state (x

_{m}, y

_{m}) at the end of the rotation phase is adopted as the intermediate state constraint of the lane-changing operation. By substituting the state constraint of the initial point, final point and intermediate point into Equation (4), Equation (6) can be obtained as follows:

_{0}= y

_{0}= 0 and y

_{f}= D into Equation (6), Equation (7) is as follows:

## 4. Path Planning Method Based on Excellent Driver Lane-Changing Model

#### 4.1. GA-BP Neural Networks

_{1}, X

_{2}, …, X

_{p})

^{T}, is randomly generated. The individual code, X

_{i}= (x

_{1}, x

_{2}, …, x

_{s}), utilizes the real number coding method. The length coding is as follows:

_{j}is the expected output. o

_{j}is the actual output based on the weights and thresholds generated in Step 1. k is compensation factor.

_{min}and x

_{max}are the minimum and maximum values of the x

_{ij}, respectively. r is a random number in [0, 1]. r

_{2}is a random number. g represents the current number of iterations and G

_{max}is the maximum number of evolutions.

#### 4.2. Excellent Driver Lane-Changing Model

_{m}, y

_{m}) and the final distance x

_{f}of lane-changing are determined. Thus, the model proposed in the paper has three outputs: x

_{m}, y

_{m}, and x

_{f}.

## 5. Simulation and Analysis

#### 5.1. Obstacle Avoidance Simulation

#### 5.2. Free Lane-Changing Simulation

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**The framework of the path planning method for imitating the lane-changing operation of excellent drivers.

**Figure 12.**The simulation results at the speed of 30 km/h under the obstacle avoidance conditions of the conservative driver: (

**a**) simulation trajectory and actual trajectory; and (

**b**) lateral deviations between the simulated and real trajectories.

**Figure 13.**The simulation results at the speed of 30 km/h under the obstacle avoidance conditions of the aggressive driver: (

**a**) simulation trajectory and actual trajectory; and (

**b**) lateral deviations between the simulated and real trajectories.

**Figure 14.**The simulation results at the speed of 40 km/h under the obstacle avoidance conditions of the conservative driver: (

**a**) simulation trajectory and actual trajectory; and (

**b**) lateral deviations between the simulated and real trajectories.

**Figure 15.**The simulation results at the speed of 30 km/h under the obstacle avoidance conditions of the aggressive driver: (

**a**) simulation trajectory and actual trajectory; and (

**b**) lateral deviations between the simulated and real trajectories.

**Figure 16.**The simulation results at the speed of 30 km/h under the free lane-changing conditions of the aggressive driver: (

**a**) simulation trajectory and actual trajectory; and (

**b**) lateral deviations between the simulated and real trajectories.

**Figure 17.**The simulation results at the speed of 30 km/h under the free lane-changing conditions of the conservative driver: (

**a**) simulation trajectory and actual trajectory; and (

**b**) lateral deviations between the simulated and real trajectories.

**Figure 18.**The simulation results at the speed of 40 km/h under the free lane-changing conditions of the aggressive driver: (

**a**) simulation trajectory and actual trajectory; and (

**b**) lateral deviations between the simulated and real trajectories.

**Figure 19.**The simulation results at the speed of 40 km/h under the free lane-changing conditions of the conservative driver: (

**a**) simulation trajectory and actual trajectory; and (

**b**) lateral deviations between the simulated and real trajectories.

Driver Number | Gender | Age | Driving Age (Years) |
---|---|---|---|

Driver 1 | Female | 55 | 33 |

Driver 2 | Male | 28 | 10 |

Driver 3 | Male | 53 | 31 |

Driver 4 | Male | 46 | 22 |

Driver 5 | Male | 53 | 21 |

Classification | Information |
---|---|

Number of drivers | 5 |

Velocity (km/h) | 30, 35, 40, 45, 50 |

Distance from obstacle (m) | 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 100 (no obstacle) |

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**MDPI and ACS Style**

Geng, G.; Wu, Z.; Jiang, H.; Sun, L.; Duan, C.
Study on Path Planning Method for Imitating the Lane-Changing Operation of Excellent Drivers. *Appl. Sci.* **2018**, *8*, 814.
https://doi.org/10.3390/app8050814

**AMA Style**

Geng G, Wu Z, Jiang H, Sun L, Duan C.
Study on Path Planning Method for Imitating the Lane-Changing Operation of Excellent Drivers. *Applied Sciences*. 2018; 8(5):814.
https://doi.org/10.3390/app8050814

**Chicago/Turabian Style**

Geng, Guoqing, Zhen Wu, Haobin Jiang, Liqin Sun, and Chen Duan.
2018. "Study on Path Planning Method for Imitating the Lane-Changing Operation of Excellent Drivers" *Applied Sciences* 8, no. 5: 814.
https://doi.org/10.3390/app8050814