# Model Predictive Stabilization Control of High-Speed Autonomous Ground Vehicles Considering the Effect of Road Topography

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## Abstract

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## Featured Application

**This work presents an MPC scheme for stabilization control of high-speed autonomous ground vehicles (AGVs) considering the effect of road topography. Accounting for the road curvature and bank angle, this scheme is able to maintain handling stability by preventing excessive sideslip and rollover while ensuring collision-free trajectories. Such an MPC scheme can not only contribute to the performance of AGVs, but also be used as an advanced safety technique in advanced driver-assistance systems (ADAS) and intelligent transportation systems (ITS)**.

## Abstract

## 1. Introduction

## 2. Preliminaries of MPC and Framework Overview

#### 2.1. Preliminaries of MPC

#### 2.2. Framework Overview

## 3. Vehicle Dynamics Modeling and Discretization

#### 3.1. Dynamics Modeling

- ${e}_{\psi}$, ${\delta}_{f}$ and $\varphi $ satisfy the small angle assumption;
- The vehicle pitch/actuators dynamics can be neglected, and the steering system is rigid;
- The disturbances such as wind lateral thrust are not considered.

#### 3.2. Model Discretization

## 4. MPC Scheme Design

#### 4.1. Sideslip Constraints

#### 4.2. Rollover Constraints

#### 4.3. Lateral Safety Corridor

#### 4.4. MPC Problem Formulation

## 5. Simulations and Discussions

#### 5.1. Simulation Settings

#### 5.2. Performance Evaluation Considering Road Topography

- The MPC controller considers both road curvature and bank angle, as proposed in this work, denoted as Controller I;
- The MPC controller without consideration of road topography, i.e., setting ${\mathit{u}}_{2}={[0,0]}^{T}$, denoted as Controller II;
- The MPC controller only considers the effect of road bank angle, i.e., setting the second term of ${\mathit{u}}_{2}$ as zero, denoted as Controller III;
- The MPC controller only considers the effect of road curvature, i.e., setting the first term of ${\mathit{u}}_{2}$ as, denoted as Controller IV.

#### 5.3. Performance Evaluation Considering Feedback Corrections

- MPC controller without feedback corrections, setting ${k}_{1}=0,{k}_{2}=0$, denoted as Controller V;
- MPC controller with feedback corrections, as proposed in this work, denoted as Controller VI.

#### 5.4. Real-Time Ability

## 6. Conclusions

- A vehicle model with roll dynamics is developed to account for the road curvature and bank angle. Variable time steps are utilized for model discretization, leading to long enough prediction for obstacle avoidance without compromising the prediction accuracy;
- The handling stability constraints, expressed as sideslip envelope and zero-moment-point, can be used to prevent excessive sideslip and rollover;
- An MPC control scheme is designed to generate the optimal steering sequence while satisfying the handling stability constraints. Comparative simulation results validate the effectiveness and real-time ability of the proposed control scheme.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Parameters | Values (Unit) | Parameters | Values (Unit) | Parameters | Values (Unit) |
---|---|---|---|---|---|

m | 1600 (kg) | ${\overline{C}}_{\alpha f}$ | −110,000 (N/rad) | ${t}_{s}$ | 0.05 (s) |

${m}_{s}$ | 1430 (kg) | ${\overline{C}}_{\alpha r}$ | −92,000 (N/rad) | ${t}_{l}$ | 0.5 (s) |

${I}_{x}$ | 700. 7 (kg· m^{2}) | ${K}_{\varphi}$ | 145,330 (N· m/rad) | ${N}_{s}$ | 10 |

${I}_{z}$ | 2059.2 (kg· m^{2}) | ${D}_{\varphi}$ | 4500 (N· m· s/rad) | ${N}_{p}$ | 20 |

${l}_{f}$ | 1.12 (m) | g | 9.81 (m/s^{2}) | ${W}_{ey},{W}_{e\psi}$ | 500 |

${l}_{r}$ | 1.48 (m) | ${\delta}_{f,max}$ | 0.4 (rad) | ${W}_{sh}$ | 50 |

${T}_{r}$ | 1.565 (m) | $\Delta {\delta}_{f,max}$ | 0.08 (rad/s) | ${W}_{\delta f}$ | 5 |

${h}_{sr}$ | 0.68 (m) | ${\alpha}_{r,lim}$ | 0.1 (rad) | ${k}_{1}$ | 0.5 |

${d}_{s}$ | 0.5 (m) | ${\overline{y}}_{ZMP,max}$ | 0.7 | ${k}_{2}$ | 0.6 |

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## Share and Cite

**MDPI and ACS Style**

Liu, K.; Gong, J.; Chen, S.; Zhang, Y.; Chen, H.
Model Predictive Stabilization Control of High-Speed Autonomous Ground Vehicles Considering the Effect of Road Topography. *Appl. Sci.* **2018**, *8*, 822.
https://doi.org/10.3390/app8050822

**AMA Style**

Liu K, Gong J, Chen S, Zhang Y, Chen H.
Model Predictive Stabilization Control of High-Speed Autonomous Ground Vehicles Considering the Effect of Road Topography. *Applied Sciences*. 2018; 8(5):822.
https://doi.org/10.3390/app8050822

**Chicago/Turabian Style**

Liu, Kai, Jianwei Gong, Shuping Chen, Yu Zhang, and Huiyan Chen.
2018. "Model Predictive Stabilization Control of High-Speed Autonomous Ground Vehicles Considering the Effect of Road Topography" *Applied Sciences* 8, no. 5: 822.
https://doi.org/10.3390/app8050822