# 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

## References

- Minh, V.T.; Katushin, N.; Pumwa, J. Motion tracking glove for augmented reality and virtual reality. Paladyn J. Behav. Robot.
**2019**, 10, 160–166. [Google Scholar] [CrossRef] - Zhao, P.; Chen, J.; Song, Y.; Tao, X.; Xu, T.; Mei, T. Design of a Control System for an Autonomous Vehicle Based on Adaptive-PID. Int. J. Adv. Robot. Syst.
**2012**, 9, 11. [Google Scholar] [CrossRef] - Taghavifar, H.; Rakheja, S. Path-tracking of autonomous vehicles using a novel adaptive robust exponential-like-sliding-mode fuzzy type-2 neural network controller. Mech. Syst. Signal Process.
**2019**, 130, 41–55. [Google Scholar] [CrossRef] - Hu, C.; Wang, Z.; Taghavifar, H.; Na, J.; Qin, Y.; Guo, J.; Wei, C. MME-EKF-Based Path-Tracking Control of Autonomous Vehicles Considering Input Saturation. IEEE Trans. Veh. Technol.
**2019**, 68, 5246–5259. [Google Scholar] [CrossRef][Green Version] - Wang, Y.; Gao, S.; Wang, Y.; Wang, P.; Zhou, Y.; Xu, Y. Robust trajectory tracking control for autonomous vehicle subject to velocity-varying and uncertain lateral disturbance. Arch. Transp.
**2021**, 57, 7–23. [Google Scholar] [CrossRef] - Calzolari, D.; Schurmann, B.; Althoff, M. Comparison of trajectory tracking controllers for autonomous vehicles. In Proceedings of the 2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC), Yokohama, Japan, 16–19 October 2017; pp. 1–8. [Google Scholar]
- Varma, B.; Swamy, N.; Mukherjee, S. Trajectory Tracking of Autonomous Vehicles Using Different Control Techniques (PID vs. LQR vs. MPC). In Proceedings of the 2020 International Conference on Smart Technologies in Computing, Electrical and Electronics (ICSTCEE), Bengaluru, India, 9–10 October 2020; pp. 84–89. [Google Scholar]
- Jezierski, A.; Mozaryn, J.; Suski, D. A Comparison of LQR and MPC Control Algorithms of an Inverted Pendulum. In 2017 Trends in Advanced Intelligent Control, Optimization and Automation; Springer: Kraków, Poland, 2017; pp. 65–76. [Google Scholar]
- Alcala, E.; Puig, V.; Quevedo, J.; Escobet, T.; Comasolivas, R. Autonomous vehicle control using a kinematic Lyapunov-based technique with LQR-LMI tuning. Control. Eng. Pract.
**2018**, 73, 1–12. [Google Scholar] [CrossRef] - Lee, K.; Jeon, S.; Kim, H.; Kum, D. Optimal Path Tracking Control of Autonomous Vehicle: Adaptive Full-State Linear Quadratic Gaussian (LQG) Control. IEEE Access
**2019**, 7, 109120–109133. [Google Scholar] [CrossRef] - Vu, T.M.; Nitin, A. Robust Model Predictive Control for Input Saturated and Softened State Constraints. Asian J. Control.
**2005**, 7, 319–325. [Google Scholar] - Minh, V.T. Nonlinear Model Predictive Controller and Feasible Path Planning for Autonomous Robots. Open Comput. Sci.
**2016**, 6, 178–186. [Google Scholar] [CrossRef] - Reda, A.; Bouzid, A.; Vásárhelyi, J. Model Predictive Control for Automated Vehicle Steering. Acta Polytech. Hung.
**2020**, 17, 163–182. [Google Scholar] [CrossRef] - Geng, K.; Liu, S. Robust Path Tracking Control for Autonomous Vehicle Based on a Novel Fault Tolerant Adaptive Model Predictive Control Algorithm. Appl. Sci.
**2020**, 10, 6249. [Google Scholar] [CrossRef] - Chen, S.; Chen, H.; Negrut, D. Implementation of MPC-Based Trajectory Tracking Considering Different Fidelity Vehicle Models. J. Beijing Inst. Technol.
**2020**, 29, 303–316. [Google Scholar] - Marcano, M.; Díaz, S.; Pérez, J.; Irigoyen, E. A Review of Shared Control for Automated Vehicles: Theory and Applications. IEEE Trans. Hum.-Mach. Syst.
**2020**, 50, 475–491. [Google Scholar] [CrossRef] - Chen, S.; Chen, H. MPC-based path tracking with PID speed control for autonomous vehicles. IOP Conf. Ser. Mater. Sci. Eng.
**2020**, 892, 3702–3720. [Google Scholar] [CrossRef] - Minh, V.T.; Moezzi, R.; Dhoska, K.; Pumwa, J. Model Predictive Control for Autonomous Vehicle Tracking. Int. J. Innov. Technol. Interdiscip. Sci.
**2021**, 4, 560–603. [Google Scholar] - Wang, J.; Teng, F.; Li, J.; Zang, L.; Fan, T.; Zhang, J.; Wang, X. Intelligent vehicle lane change trajectory control algorithm based on weight coefficient adaptive adjustment. Adv. Mech. Eng.
**2021**, 13, 1–16. [Google Scholar] [CrossRef] - Cao, H.; Zoldy, M. MPC Tracking Controller Parameters Impacts in Roundabouts. Mathematics
**2021**, 9, 1394. [Google Scholar] [CrossRef] - Vu, T.M.; Hashim, F. Tracking setpoint robust model predictive control for input saturated and softened state constraints. Int. J. Control. Autom. Syst.
**2011**, 9, 958–965. [Google Scholar] - Minh, V.T. Advanced Vehicle Dynamics; Universiti of Malaya Press: Kuala Lumpur, Malaysia, 2012; p. 265, ISBN: 9789831005446 9831005449. [Google Scholar]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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