# Model Predictive Control for Autonomous Driving Vehicles

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Vehicle Modeling and Constraints

_{0}, y

_{0}, θ

_{0}, ϕ

_{0}] at the time t = 0, and move to the destination at the end of a trajectory [x

_{T}, y

_{T}, θ

_{T}, ϕ

_{T}] at the time t = T.

## 3. NMPC with Hard Constraints

## 4. NMPC with Softened Constraints

## 5. NMPC Tracking Trajectory Performance

_{0}, y

_{0}of [0, 0] to x

_{T}, y

_{T}of [10, 10]. The vehicle is starting from an initial condition at $\left[{x}_{0},{y}_{0},{\theta}_{0},{\varphi}_{0}\right]={\left[0,-0.5,\text{}0,\text{}0\right]}^{\prime}$, and arriving at the destination condition at $\left[{x}_{T},{y}_{T},{\theta}_{T},{\varphi}_{T}\right]={\left[10,\text{}10,\text{}0,\text{}0\right]}^{\prime}$ The prediction horizon is set with ${N}_{u}={N}_{y}=10$; the penalty matrices for states and inputs are set with $Q=diag\left\{1,\text{}1,\text{}1,\text{}1\right\}$ and $R=diag\left\{1,\text{}1\right\}$. The vehicle speed vs. the steering angular velocity is fully controlled. The performance of the two schemes is shown in Figure 7.

## 6. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**MDPI and ACS Style**

Vu, T.M.; Moezzi, R.; Cyrus, J.; Hlava, J.
Model Predictive Control for Autonomous Driving Vehicles. *Electronics* **2021**, *10*, 2593.
https://doi.org/10.3390/electronics10212593

**AMA Style**

Vu TM, Moezzi R, Cyrus J, Hlava J.
Model Predictive Control for Autonomous Driving Vehicles. *Electronics*. 2021; 10(21):2593.
https://doi.org/10.3390/electronics10212593

**Chicago/Turabian Style**

Vu, Trieu Minh, Reza Moezzi, Jindrich Cyrus, and Jaroslav Hlava.
2021. "Model Predictive Control for Autonomous Driving Vehicles" *Electronics* 10, no. 21: 2593.
https://doi.org/10.3390/electronics10212593