# Hierarchical Model Predictive Control for Autonomous Collision Avoidance of Distributed Electric Drive Vehicle with Lateral Stability Analysis in Extreme Scenarios

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## Abstract

**:**

## 1. Introduction

## 2. Distributed Drive Vehicle Model

#### 2.1. Vehicle Kinematics Model

#### 2.2. Piecewise Affine Vehicle Lateral Dynamics Model

#### 2.3. Stability Region Analysis Based on Phase Portrait

## 3. Hierarchical Controller Design

#### 3.1. Path Planning Controller Based on Nonlinear MPC

#### 3.2. Path Tracking Controller Based on Hybrid MPC

## 4. Simulation and Results Analysis

#### 4.1. Simulation in a DLC Scenario

#### 4.2. Simulation in a collIsion Avoidance Scenario

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 4.**(

**a**–

**d**) shows the phase portrait with the front wheel steering angle of 0 rad, 0.1 rad, 0.25 rad, 0.35 rad, respectively. The red dotted line represents the boundary of different regions; the blue dotted line represents the position of saddle points.

**Figure 7.**Simulation results in low-adhesion DLC scenario. (

**a**) Path tracking performance; (

**b**) Yaw rate comparison; (

**c**) Steering angle comparison; (

**d**) Yaw moment comparison. (

**e**) State trajectories of sideslip angle and yaw rate.

**Figure 10.**Simulation results in the variable collision avoidance scenario. (

**a**) Path tracking performance; (

**b**) Yaw rate comparison; (

**c**) Steering angle comparison; (

**d**) Yaw moment comparison; (

**e**) State trajectories in low-adhesion condition; (

**f**) State trajectories in high-adhesion condition.

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

${l}_{f}$ | 1.015 | m | $m$ | 1270 | kg |

${l}_{r}$ | 1.885 | m | $g$ | 9.8 | m/s^{2} |

${v}_{x}$ | 15 | m/s | ${I}_{z}$ | 1536.7 | Kg·m^{2} |

Path Tracking Controller | RMSE of Tracking Errors | Computing Time Radio |
---|---|---|

Hybrid MPC | 0.20067 | 8.42104 |

Linear MPC | 1.36947 | 7.52817 |

Path Tracking Controller | RMSE of Tracking Error | Computing Time Radio |
---|---|---|

Hybrid MPC ($\mu =0.85$) | 0.44925 | 27.8171 |

Hybrid MPC ($\mu =0.2$) | 0.58644 | 25.2747 |

Linear MPC ($\mu =0.85$) | 0.49850 | 26.5447 |

Linear MPC ($\mu =0.2$) | 1.09053 | 23.4518 |

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**MDPI and ACS Style**

Wang, B.; Lin, C.; Liang, S.; Gong, X.; Tao, Z.
Hierarchical Model Predictive Control for Autonomous Collision Avoidance of Distributed Electric Drive Vehicle with Lateral Stability Analysis in Extreme Scenarios. *World Electr. Veh. J.* **2021**, *12*, 192.
https://doi.org/10.3390/wevj12040192

**AMA Style**

Wang B, Lin C, Liang S, Gong X, Tao Z.
Hierarchical Model Predictive Control for Autonomous Collision Avoidance of Distributed Electric Drive Vehicle with Lateral Stability Analysis in Extreme Scenarios. *World Electric Vehicle Journal*. 2021; 12(4):192.
https://doi.org/10.3390/wevj12040192

**Chicago/Turabian Style**

Wang, Bowen, Cheng Lin, Sheng Liang, Xinle Gong, and Zhenyi Tao.
2021. "Hierarchical Model Predictive Control for Autonomous Collision Avoidance of Distributed Electric Drive Vehicle with Lateral Stability Analysis in Extreme Scenarios" *World Electric Vehicle Journal* 12, no. 4: 192.
https://doi.org/10.3390/wevj12040192