# Research on Path Planning and Tracking Control of Automatic Parking System

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## Abstract

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## 1. Introduction

## 2. Parking Path Planning

#### 2.1. Kinematic Model of Vehicle

_{f}is equivalent front wheel Angle $\left(\xb0/\mathrm{s}\right)$; l is wheelbase (m); v is rear axle midpoint velocity (km/h).

#### 2.2. Parking System Analysis

_{1min}(${x}_{{P}_{1min}}$,${y}_{{P}_{1min}}$) = (8.076, 3.335). The upper limit value is P

_{1max}(${x}_{{P}_{1max}}$,${y}_{{P}_{1max}}$) = (10.981,4.588). The upper limit value of P2 coordinate is P

_{2max}(${x}_{{P}_{2max}}$,${y}_{{P}_{2max}}$) = (9.246,$4.23$), and parking starting point area is as follows:

#### 2.3. Parallel Parking Path Planning Based on Quintic Polynomial

_{0}∼a

_{5}are the coefficients of a quintic polynomial, and changing the coefficients can change the shape of the polynomial.

## 3. Motion Control of Path Tracking Based on MPC

#### 3.1. Design of Parking Path Following Controller

#### 3.2. Mulation and Result Analysis of Parallel Parking

## 4. Parking Experiment of Intelligent Car

## 5. Conclusions

## 6. Future Research Directions

- Regarding parking conditions, this article only studies parallel parking conditions. For vertical parking conditions and parking with irregular parking spaces, further research is needed.
- Regarding the experiment, due to the lack of conditions, this article only uses the smart car to carry out the parking experiment. In the future, the designed controller needs to be verified on the actual vehicle.
- Regarding the development of automatic parking technology, automatic valet parking technology is an inevitable trend in the development of automatic parking technology in the future.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Hanafy, M.; Gomaa, M.M.; Taher, M.; Wahba, A.M. Development of a technology for car’s auto-parking using swarm search-based fuzzy control system. Int. J. Model. Identif. Control
**2012**, 17, 85. [Google Scholar] [CrossRef] - Zhang, C.R. Research on Automatic Parking Route Decision Planning and Vehicle Control Algorithm; North University of China: Taiyuan, China, 2019. [Google Scholar]
- Demirli, K.; Khoshnejad, M. Autonomous parallel parking of a car-like mobile robot by a neuro-fuzzy sensor-based controller. Fuzzy Sets Syst.
**2009**, 160, 2876–2891. [Google Scholar] [CrossRef] - Huang, S.-J.; Lin, G.-Y. Parallel auto-parking of a model vehicle using a self-organizing fuzzy controller. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2010**, 224, 997–1012. [Google Scholar] [CrossRef] - Kim, J.M.; Lim, K.I.; Kim, J.H. Auto parking path planning system using modified reeds-shepp curve algorithm. In Proceedings of the 2014 11th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), Kuala Lumpur, Malaysia, 12–15 November 2014; pp. 311–315. [Google Scholar]
- Ye, H.; Jiang, H.; Ma, S.; Tang, B.; Wahab, L. Linear model predictive control of automatic parking path tracking with soft constraints. Int. J. Adv. Robot. Syst.
**2019**, 16, 1729881419852201. [Google Scholar] [CrossRef] [Green Version] - Qin, S.; Badgwell, T.A. A survey of industrial model predictive control technology. Control Eng. Pract.
**2003**, 11, 733–764. [Google Scholar] [CrossRef] - Mayne, D.Q.; Rawlings, J.B.; Rao, C.V. Constrained model predictive control: Stability and optimality. Automatica
**2000**, 36, 789–814. [Google Scholar] [CrossRef] - Morari, M.; Barić, M. Recent developments in the control of constrained hybrid systems. Comput. Chem. Eng.
**2006**, 30, 1619–1631. [Google Scholar] [CrossRef] - Pearson, R. Selecting nonlinear model structures for computer control. J. Process. Control
**2003**, 13, 1–26. [Google Scholar] [CrossRef] - Wang, W.; Rivera, D.E.; Kempf, K.G. Model predictive control strategies for supply chain management in semiconductor manufacturing. Int. J. Prod. Econ.
**2007**, 107, 56–77. [Google Scholar] [CrossRef] - Dufour, P.; Michaud, D.J.; Touré, Y. A partial differential equation model predictive control strategy: Application to autoclave composite processing. Comput. Chem. Eng.
**2004**, 28, 545–556. [Google Scholar] [CrossRef] [Green Version] - Salsbury, T.; Mhaskar, P.; Qin, S.J. Predictive control methods to improve energy efficiency and reduce demand in buildings. Comput. Chem. Eng.
**2013**, 51, 77–85. [Google Scholar] [CrossRef] - Brdys, M.; Grochowski, M.; Gminski, T.; Konarczak, K.; Drewa, M. Hierarchical predictive control of integrated wastewater treatment systems. Control Eng. Pract.
**2008**, 16, 751–767. [Google Scholar] [CrossRef] - Keviczky, T.; Balas, G.J. Receding horizon control of an F-16 aircraft: A comparative study. Control Eng. Pract.
**2006**, 14, 1023–1033. [Google Scholar] [CrossRef] - Silani, E.; Lovera, M. Magnetic spacecraft attitude control: A survey and some new results. Control Eng. Pract.
**2005**, 13, 357–371. [Google Scholar] [CrossRef] - Jiang, M.G.; Lu, B. Ackerman principle and rectangular steering trapezoid design. Automob. Technol.
**1994**, 5, 16–19. [Google Scholar] - Gong, J.W.; Liu, K.; Qi, J.Y. Model Predictive Control for Self-Driving Vehicles; Beijing Institute of Technology: Beijing, China, 2020; pp. 82–84. [Google Scholar]
- He, P. Research on Path Planning and Tracking Control of Parallel Parking; Chongqing University of Technology: Chongqing, China, 2020. [Google Scholar]
- Wu, Z.W. Path Planning and Simulation Analysis of Automatic Parking System for Passenger Car; South China University of Technology: Guangzhou, China, 2018. [Google Scholar]
- Li, T. Path Planning and Tracking of Automatic Parking System; Harbin Institute of Technology: Harbin, China, 2017. [Google Scholar]
- Yang, S.B.; Liu, H.; Jiang, Z.L. Automatic parking control method based on MPC. J. Instrum. Autom. Syst.
**2019**, 34, 20–23. [Google Scholar] - Guo, Y.T. Research on Path Planning and Control System for Automatic Parallel Parking; Lanzhou Jiaotong University: Lanzhou, China, 2020. [Google Scholar]

**Figure 5.**Parallel parking path planning simulation results. (

**a**) Vehicle rear axle midpoint trajectory. (

**b**) The curvature of the path curve. (

**c**) The derivative of the path curve. (

**d**) Equivalent front wheel angle. (

**e**) Equivalent front wheel rotation speed.

**Figure 7.**Parallel parking path tracking simulation results. (

**a**) Path tracking. (

**b**) Ordinate tracking error curve. (

**c**) Variation of yaw angle of vehicle. (

**d**) Tracking error of vehicle yaw angle.

Parameter | Symbol | Numerical Value | Unit |
---|---|---|---|

Vehicle length | L | 4.7 | m |

Vehicle width | W | 1.86 | m |

Wheelbase | l | 2.71 | m |

Front overhang | l_{f} | 0.89 | m |

Rear overhang | l_{r} | 1.1 | m |

Maximum front wheel angle | ${\delta}_{{f}_{max}}$ | 0.482 | rad |

Front wheel angle maximum speed | ${\omega}_{{f}_{max}}$ | 0.482 | rad/m |

Path Curve Type | Advantage | Disadvantages |
---|---|---|

Double arc combination Arc-straight arc combination | The path structure is simple, easy to implement, and the size of the required parking space is appropriate | The curvature is discontinuous and it is difficult to track; there are higher requirements for the parking starting point |

B-spline curve Cloth curve | Continuous curvature, easy to track | The path structure and expression are complex, and the amount of calculation is large; |

Arctangent function curve | The curve expression is easy to calculate, the curvature is continuous and the curvature change rate is continuous | The curvature of the starting point and ending point of the path is not zero, which does not meet the pose requirements |

Quintic polynomial curve | The curve expression is simple, the curvature is continuous and the curvature change rate is continuous, and the calculation amount is small | Properly increase the length of the parking space to ensure that the end point of the path has zero curvature |

Prediction Horizon $\left({\mathit{N}}_{\mathit{P}}\right)$ | Control Horizon $\left({\mathit{N}}_{\mathit{C}}\right)$ | Sampling Period | Simulation Time | Relaxation Factor (Row) | Weight Matrix (Q) | Weight Matrix (R) |
---|---|---|---|---|---|---|

60 s | 30 s | 0.1 s | 40 s | 10 | 100 | 5 |

Control Algorithm | $\mathbf{\u2206}{\mathit{y}}_{\mathit{e}}\left(\mathbf{m}\right)$ | $\mathbf{\u2206}\mathit{y}\mathit{a}{\mathit{w}}_{\mathit{e}}\left(\mathbf{r}\mathbf{a}\mathbf{d}\right)$ | ${\mathit{y}}_{\mathit{m}\mathit{a}\mathit{x}}$ | $\mathit{y}\mathit{a}{\mathit{w}}_{\mathit{m}\mathit{a}\mathit{x}}$ |
---|---|---|---|---|

MPC controller | −0.018 | 0.0053 | 0.09638 | 0.02527 |

Preview controller | 0.039 | 0.0072 | 0.08602 | 0.026 |

_{e}: the average of ordinate error; ∆yaw

_{e}: the average of yaw error; y

_{max}: the maximum ordinate error; yaw

_{max}: the maximum yaw error.

Parameters | Numerical Value (mm) |
---|---|

Vehicle length | 495 |

Vehicle width | 290 |

Front overhang | 115 |

Rear overhang | 40 |

Wheelbase | 340 |

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**MDPI and ACS Style**

Zhang, B.; Li, Z.; Ni, Y.; Li, Y.
Research on Path Planning and Tracking Control of Automatic Parking System. *World Electr. Veh. J.* **2022**, *13*, 14.
https://doi.org/10.3390/wevj13010014

**AMA Style**

Zhang B, Li Z, Ni Y, Li Y.
Research on Path Planning and Tracking Control of Automatic Parking System. *World Electric Vehicle Journal*. 2022; 13(1):14.
https://doi.org/10.3390/wevj13010014

**Chicago/Turabian Style**

Zhang, Bingzhan, Zhiyuan Li, Yaoyao Ni, and Yujie Li.
2022. "Research on Path Planning and Tracking Control of Automatic Parking System" *World Electric Vehicle Journal* 13, no. 1: 14.
https://doi.org/10.3390/wevj13010014