# A Novel Data-Driven Modeling and Control Design Method for Autonomous Vehicles

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## Abstract

**:**

## 1. Introduction and Motivation

## 2. Formulation of the Control-Oriented LPV Model Using Data-Driven Approach

#### 2.1. Acquisition of Data from Simulations

- (1)
- longitudinal velocity (${v}_{x}$)
- (2)
- angular velocity of the wheels (${\omega}_{x,y}$), $x\in \{front,rear\}$, $y\in \{left,right\}$
- (3)
- steering angle ($\delta $)
- (4)
- yaw-rate ($\dot{\psi}$)
- (5)
- accelerations (${a}_{x}$, ${a}_{y}$)
- (6)
- lateral velocity (${v}_{y}$).
- (7)
- side-slips of the wheels (${\alpha}_{x}$), $x\in \{front,rear\}$.

#### 2.2. Categorization of Instances

## 3. Parameters Optimization and Determination of Scheduling Parameters

#### 3.1. Fundamentals of the Applied Machine-Learning-Based Method

#### 3.2. Parameter Selection of the Control-Oriented Model

#### 3.3. Evaluation of the Data-Driven LPV Models

## 4. Path Following LPV Control Design Using the Data-Driven Model

- Minimization of the lateral error: As mentioned, the goal of the control design is to guarantee the trajectory tracking of the vehicle thus the error between the measured and the reference lateral positions must be minimized:$$\begin{array}{c}\hfill {z}_{2}={y}_{ref}-y,\phantom{\rule{28.45274pt}{0ex}}\left|{z}_{2}\right|\to min,\end{array}$$

- Minimization of the yaw-rate error: In order to achieve smooth trajectory tracking, a reference yaw-rate is also prescribed, which also must be tracked by the vehicle:$$\begin{array}{c}\hfill {z}_{1}={\dot{\psi}}_{ref}-\dot{\psi},\phantom{\rule{28.45274pt}{0ex}}\left|{z}_{1}\right|\to min,\end{array}$$

- Minimization of the interventions: Due to the energy consumption, the interventions also must be minimized during the operation of the vehicle:$$\begin{array}{cc}\hfill {z}_{3}& =\delta ,\phantom{\rule{34.14322pt}{0ex}}|{z}_{3}|\to min.\hfill \end{array}$$$$\begin{array}{cc}\hfill {z}_{4}& ={M}_{d},\phantom{\rule{25.6073pt}{0ex}}\left|{z}_{4}\right|\to min.\hfill \end{array}$$

## 5. Simulation Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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

Mass of the car | m | 1690 | kg |

Yaw-inertia | J | 4192 | kg/m${}^{2}$ |

Location of front axis from COG | ${l}_{1}$ | 1.11 | m |

Cornering stiffness of front wheels | ${C}_{1}$ | 155,160 | N/rad |

Location of rear axis from COG | ${l}_{2}$ | 1.66 | m |

Cornering stiffness of rear wheels | ${C}_{2}$ | 114,659 | N/rad |

Front drag area of the car | A | 1.8 | m${}^{2}$ |

Height of COG | h | 0.56 | m |

Type of front suspensions | - | Independent | - |

Mass of front suspensions | ${m}_{s,f}$ | 85 | kg |

Type of rear suspensions | - | Independent | - |

Mass of rear suspensions | ${m}_{s,r}$ | 85 | kg |

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**MDPI and ACS Style**

Fényes, D.; Németh, B.; Gáspár, P. A Novel Data-Driven Modeling and Control Design Method for Autonomous Vehicles. *Energies* **2021**, *14*, 517.
https://doi.org/10.3390/en14020517

**AMA Style**

Fényes D, Németh B, Gáspár P. A Novel Data-Driven Modeling and Control Design Method for Autonomous Vehicles. *Energies*. 2021; 14(2):517.
https://doi.org/10.3390/en14020517

**Chicago/Turabian Style**

Fényes, Dániel, Balázs Németh, and Péter Gáspár. 2021. "A Novel Data-Driven Modeling and Control Design Method for Autonomous Vehicles" *Energies* 14, no. 2: 517.
https://doi.org/10.3390/en14020517