# Research on Vehicle Adaptive Cruise Control Method Based on Fuzzy Model Predictive Control

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fuzzy-MPC Based Vehicle Multi-Target Upper Controller

#### 2.1. Longitudinal Kinematics Modelling of Two Vehicles

_{0}the minimum safe spacing greater than the length of the vehicle.

#### 2.2. Scrolling Optimization

#### 2.3. Variable Weight Coefficient Design Based on Fuzzy Control

#### 2.4. Numerical Simulation Verification

#### 2.4.1. Normal Condition

#### 2.4.2. Emergency Conditions

^{2}. The initial relative distance between the two vehicles is 25 m. The simulation results are shown in Figure 4.

## 3. Lower Controller Design

#### 3.1. Throttle/Brake Switching Strategy

#### 3.2. Throttle Control

#### 3.3. Brake Control

#### 3.4. Design of Lower Controller Based on PID

## 4. Co-Simulation Verification and Analysis

#### 4.1. Follow the Vehicle Smoothly

#### 4.2. Target Vehicle Insertion

#### 4.3. Emergency Braking

^{2}at the 20th second and continues for 5 s and then maintains a constant speed. The simulation results are shown in Figure 10.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of longitudinal kinematics. where ${x}_{p}$ is the target vehicle position, ${x}_{f}$ is the ACC vehicle position, and $d$ is the actual relative distance between the two vehicles.

**Figure 2.**Membership function of each variable: (

**a**) relative distance $d$; (

**b**) relative speed ${v}_{rel}$; (

**c**) the weight coefficient ${c}_{f}$.

**Figure 3.**Stable follow: (

**a**) speed; (

**b**) relative distance; (

**c**) acceleration; (

**d**) acceleration change rate.

**Figure 4.**Emergency brake: (

**a**) speed; (

**b**) relative distance; (

**c**) acceleration; (

**d**) acceleration change rate.

**Figure 8.**Acceleration conditions: (

**a**) speed; (

**b**) relative distance; (

**c**) throttle opening/brake pressure; (

**d**) weight coefficient ${\varsigma}_{f}$.

**Figure 9.**Target vehicle insertion: (

**a**) speed; (

**b**) relative distance; (

**c**) throttle opening/brake pressure; (

**d**) weight coefficient ${\varsigma}_{f}$.

**Figure 10.**Emergency braking: (

**a**) speed; (

**b**) relative distance; (

**c**) throttle opening/brake pressure; (

**d**) weight coefficient ${\varsigma}_{f}$.

d | HE | HC | GD | FC | FE | |
---|---|---|---|---|---|---|

v_{ref} | ||||||

HE | FE | FE | FW | FC | FC | |

HC | FE | FE | FW | FC | FE | |

GD | FE | FE | FC | GD | GD | |

FC | FE | FW | FC | GD | GD | |

FE | FW | FC | GD | GD | GD |

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

T_{s} | 0.2 | s | u_{min} | −5.5 | m/s^{2} |

${\tau}_{h}$ | 1 | s | ${\xi}_{\mathrm{max}}^{d}$ | 1 | - |

$\tau $ | 0.5 | m | ${\xi}_{\mathrm{min}}^{d}$ | 0 | - |

d_{0} | 5 | m | ${\xi}_{\mathrm{max}}^{{v}_{f}}$ | 1 | - |

N_{p} | 16 | - | ${\xi}_{\mathrm{min}}^{{v}_{f}}$ | −1 | - |

N_{c} | 5 | - | ${\xi}_{\mathrm{max}}^{{a}_{f}}$ | 0.1 | - |

v_{fmax} | 35 | m/s | ${\xi}_{\mathrm{min}}^{{a}_{f}}$ | −0.1 | - |

v_{fmin} | 0 | m/s | ${\xi}_{\mathrm{max}}^{jerk}$ | 0 | - |

a_{fmax} | −5.5 | m/s^{2} | ${\xi}_{\mathrm{min}}^{jerk}$ | 0 | - |

a_{fmin} | 2.5 | m/s^{2} | ${\xi}_{\mathrm{max}}^{u}$ | 0.1 | - |

jerk_{max} | 2.5 | m/s^{3} | ${\xi}_{\mathrm{min}}^{u}$ | −0.1 | - |

jerk_{min} | −2.5 | m/s^{3} | p_{1}, p_{2}, p_{3}, p_{4}, p_{5} | 3 | - |

u_{max} | 2.5 | m/s^{2} | w_{1}, w_{2}, w_{3}, w_{4}, w_{5} | 0.5 | - |

$\mathit{a}(\mathbf{m}/{\mathbf{s}}^{2})$ | |||||||||
---|---|---|---|---|---|---|---|---|---|

v(km/h) | −1 | 0 | 1 | 1.5 | 2 | 2.5 | 3 | 4 | |

0 | 0 | 0 | 0.05 | 0.1 | 0.12 | 0.12 | 0.15 | 4 | |

10 | 0 | 0.1 | 0.12 | 0.12 | 0.13 | 0.15 | 0.18 | 0.2 | |

20 | 0 | 0.12 | 0.14 | 0.18 | 0.2 | 0.2 | 0.25 | 0.4 | |

30 | 0 | 0.12 | 0.17 | 0.2 | 0.25 | 0.3 | 0.35 | 0.5 | |

40 | 0 | 0.13 | 0.2 | 0.25 | 0.3 | 0.35 | 0.45 | 0.7 | |

80 | 0 | 0.15 | 0.3 | 0.45 | 0.5 | 0.7 | 1 | 1 | |

120 | 0 | 0.2 | 0.45 | 0.7 | 1 | 1 | 1 | 1 |

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**MDPI and ACS Style**

Mao, J.; Yang, L.; Hu, Y.; Liu, K.; Du, J.
Research on Vehicle Adaptive Cruise Control Method Based on Fuzzy Model Predictive Control. *Machines* **2021**, *9*, 160.
https://doi.org/10.3390/machines9080160

**AMA Style**

Mao J, Yang L, Hu Y, Liu K, Du J.
Research on Vehicle Adaptive Cruise Control Method Based on Fuzzy Model Predictive Control. *Machines*. 2021; 9(8):160.
https://doi.org/10.3390/machines9080160

**Chicago/Turabian Style**

Mao, Jin, Lei Yang, Yuanbo Hu, Kai Liu, and Jinfu Du.
2021. "Research on Vehicle Adaptive Cruise Control Method Based on Fuzzy Model Predictive Control" *Machines* 9, no. 8: 160.
https://doi.org/10.3390/machines9080160