# Obstacle-Avoidance Path-Planning Algorithm for Autonomous Vehicles Based on B-Spline Algorithm

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Risk-Identification Model Based on SVM

_{i}value, the standard value can be set to one. For other types of objects, the T value is the ratio of the average loss of this type of object to the average loss of the standard type. When collisions are unavoidable, the types of obstacles that collide with autonomous vehicles can be generally divided into three types [17]. Additionally, according to the types, the risky level can be divided into three levels.

## 3. B-Spline Algorithm

_{i}(i = 0, 1, 2, …, n) is the control point, and n + 1 control points are fused with B-spline curve baseline. The k-order B-spline is:

_{0}and m

_{0}, respectively. The length of the road is L and the width is 2r. During normal driving, the vehicle body shall be in the lane, and it will not cross the road boundary except during lane changes. Then, the selection range of B-spline control point position (x, y) is:

_{0}, −$\frac{r}{2}$), and the first control point is set as P

_{0}= (x

_{0}− minD, −$\frac{r}{2}$). Meanwhile, in order to satisfy that the yaw of autonomous vehicle at the initial time is zero without sudden change, set P

_{2}= (x

_{0}+ h

_{0}− minD, −$\frac{r}{2}$). To further strengthen this constraint, set the control point P

_{1}= (x

_{0}$+\frac{{h}_{0}}{2}$ − minD, −$\frac{r}{2}$). Assuming that the vehicle is driving at the original speed, when the distance from the obstacle vehicle to the collision-free critical position is minD. At this time, the displacement of the obstacle vehicle can be expressed as:

_{0}+ x

_{1}. If the head abscissa of the autonomous vehicle is located at x

_{0}+ x

_{1}, the vehicle can cross the lane line to the target lane. This ensures that the ego-vehicle has enough safety space from the obstacle vehicle and the roadside. In addition, the lateral displacement of the ego-vehicle is small in this period, which ensures that the lateral acceleration takes place within a reasonable range. Therefore, the control point is P

_{3}= (x

_{0}+ x

_{1}, $\frac{r}{2}$).

_{0}is the length of the ego-vehicle; h

_{1}is the length of the obstacle vehicle.

_{4}= ($x$

_{0}+$\text{}x$

_{1}$+\frac{{X}_{\mathrm{obs}}^{\u2019}t}{2}{+h}_{0}$, $\frac{r}{2}$), $P$

_{5}= ($x$

_{2}, $\frac{r}{2}$) is selected. The path back to the original lane is set to be symmetrical with the obstacle avoidance path. Additionally, the control point $P$

_{6}= (minD + $x$

_{2}− $h$

_{0}, −$\frac{r}{2}$), $P$

_{7}= (min$D+x$

_{2}− $\frac{{h}_{0}}{2}$, −$\frac{r}{2}$), P

_{8}= (minD$+$x

_{2}, −$\frac{r}{2}$) is selected, respectively.

## 4. Simulation Analysis

## 5. Path Tracking Method Based on LQR

^{2}. In this simulation scenario, the vehicle is running on a dry asphalt road. In order to ensure that the vehicle tires are in a linear working area, the maximum lateral acceleration should be less than 3.92 m/s

^{2}(0.4 times of the gravitational acceleration). The small lateral acceleration ensures the stability and comfort of the vehicle and proves the availability of the path.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Min, H.; Xiong, X.; Wang, P.; Yu, Y. Autonomous driving path planning algorithm based on improved A* algorithm in unstructured environment. Proc. Inst. Mech. Eng.
**2021**, 235, 513–526. [Google Scholar] [CrossRef] - Lim, W.; Lee, S.; Sunwoo, M.; Jo, K. Hybrid trajectory planning for autonomous driving in on-road dynamic scenarios. IEEE Trans. Intell. Transp. Syst.
**2019**, 22, 341–355. [Google Scholar] [CrossRef] - Li, Y.; Ibanez-Guzman, J. Lidar for autonomous driving: The principles, challenges, and trends for automotive lidar and perception systems. IEEE Signal Processing Mag.
**2020**, 37, 50–61. [Google Scholar] [CrossRef] - Xu, C.; Zhao, W.; Wang, C. An integrated threat assessment algorithm for decision-making of autonomous driving vehicles. IEEE Trans. Intell. Transp. Syst.
**2019**, 21, 2510–2521. [Google Scholar] [CrossRef] - Cui, J. An overview of unmanned vehicle path planning algorithms. J. Phys. Conf. Ser. IOP Publ.
**2019**, 1345, 042092. [Google Scholar] [CrossRef] - Wu, J.; Zhang, J.; Nie, B.; Liu, Y.; He, X. Adaptive control of PMSM servo system for steering-by-wire system with disturbances observation. IEEE Trans. Transp. Electrif.
**2021**, 8, 2015–2028. [Google Scholar] [CrossRef] - Wu, J.; Tian, Y.; Walker, P.; Li, Y. Attenuation reference model based adaptive speed control tactic for automatic steering system. Mech. Syst. Signal Processing
**2021**, 156, 107631. [Google Scholar] [CrossRef] - Wu, J.; Zhang, J.; Tian, Y.; Li, L. A novel adaptive steering torque control approach for human–machine cooperation autonomous vehicles. IEEE Trans. Transp. Electrif.
**2021**, 7, 2516–2529. [Google Scholar] [CrossRef] - Wu, J.; Kong, Q.; Yang, K.; Liu, Y.; Cao, D.; Li, Z. Research on the Steering Torque Control for Intelligent Vehicles Co-Driving With the Penalty Factor of Human-Machine Intervention. IEEE Trans. Syst. Man Cybern. Syst.
**2022**, 1–12. [Google Scholar] [CrossRef] - Ji, J.; Khajepour, A.; Melek, W.W.; Huang, Y. Path Planning and Tracking for Vehicle Collision Avoidance Based on Model Predictive Control with Multiconstraints. IEEE Trans. Veh. Technol.
**2017**, 66, 952–964. [Google Scholar] [CrossRef] - Luo, Y.; Xiang, Y.; Cao, K.; Li, K. A dynamic automated lane change maneuver based on vehicle-to-vehicle communication. Transp. Res. Part C
**2016**, 62, 87–102. [Google Scholar] [CrossRef] - Chen, Y.; Peng, H.; Grizzle, J. Obstacle Avoidance for Low-Speed Autonomous Vehicles With Barrier Function. IEEE Trans. Control Syst. Technol.
**2018**, 99, 1–13. [Google Scholar] [CrossRef] - Wang, B. Intelligent vehicle obstacle avoidance risk assessment and trajectory planning. Automot. Technol.
**2018**, 32–37. [Google Scholar] - Paleti, R.; Eluru, N.; Bhat, C.R. Examining the influence of aggressive driving behavior on driver injury severity in traffic crashes. Accid. Anal. Prev.
**2010**, 42, 1839–1854. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wang, J.; Wu, J.; Li, Y. Concept, Principle and Modeling of Driving Risk Field Based on Driver-vehicle-road Interaction. China J. Highw. Transp.
**2016**, 29, 105–114. [Google Scholar] - Liu, Z.; Han, J.; Ni, J. A Research on Adaptive Lane Change Warning Algorithm Based on Driver Characteristics. Automot. Eng.
**2019**, 41, 440–446. [Google Scholar] - Yu, S.; Shu, X.; Chen, W.; Xu, G. Predictive Control of Active Obstacle Avoidance for Autonomous Vehicles Based on Risk Assessment. J. Zhejiang Univ. Technol.
**2022**, 50, 1–8. [Google Scholar] - Wang, Z.; Peng, R.; Gong, Z. B-spline curve generation principle and implementation. J. Shihezi Univ. (Nat. Sci. Ed.)
**2009**, 27, 118–121. [Google Scholar] - Sun, Z. Research on Local Path Planning and Tracking Control of Driverless Vehicles. Master’s Thesis, Northeastern Forestry University, Harbin, China, 2021. [Google Scholar]

**Figure 5.**The vehicle has a constant speed of 35 km/h and 70 km/h to avoid small stationary obstacles.

**Figure 6.**The vehicle has a constant speed of 35 km/h and 70 km/h to avoid large stationary obstacles.

**Figure 7.**The vehicle has a constant speed of 35 km/h and 70 km/h to avoid small low-speed obstacles.

**Figure 8.**The vehicle has a constant speed of 35 km/h and 70 km/h to avoid large low-speed obstacles.

**Figure 12.**Variation curve of vehicle yaw angle and yaw rate. (

**a**) is the yaw angle, (

**b**) is the yaw rate.

Model Parameters | Numerical Value/(Unit) |
---|---|

Vehicle mass | 1270/(kg) |

Vehicle length | 4.79/(m) |

Vehicle width | 2/(m) |

Inertia | 1536.7/(kg·m^{2}) |

Distance from barycenter to front axle | 0.907/(m) |

Distance from barycenter to rear axle | 1.693/(m) |

Friction coefficient road surfaces | 0.85 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, P.; Yang, J.; Zhang, Y.; Wang, Q.; Sun, B.; Guo, D.
Obstacle-Avoidance Path-Planning Algorithm for Autonomous Vehicles Based on B-Spline Algorithm. *World Electr. Veh. J.* **2022**, *13*, 233.
https://doi.org/10.3390/wevj13120233

**AMA Style**

Wang P, Yang J, Zhang Y, Wang Q, Sun B, Guo D.
Obstacle-Avoidance Path-Planning Algorithm for Autonomous Vehicles Based on B-Spline Algorithm. *World Electric Vehicle Journal*. 2022; 13(12):233.
https://doi.org/10.3390/wevj13120233

**Chicago/Turabian Style**

Wang, Pengwei, Jinshan Yang, Yulong Zhang, Qinwei Wang, Binbin Sun, and Dong Guo.
2022. "Obstacle-Avoidance Path-Planning Algorithm for Autonomous Vehicles Based on B-Spline Algorithm" *World Electric Vehicle Journal* 13, no. 12: 233.
https://doi.org/10.3390/wevj13120233