**6. Conclusions**

In this article, the authors highlighted the importance of vehicle motion control at handling limits and automated drifting as one of the critical developments of fully autonomous vehicles of the future, aiming at improved road safety. Vehicle automated drifting capabilities were demonstrated during different operating conditions with a systematic controller development process, as outlined below. The handling of changing road conditions and vehicle model nonlinearities is among the key advantages of the proposed adaptive MPC control framework. In Section 2, a nonlinear dynamic vehicle model and a nonlinear tire model were introduced for control-oriented purposes, and the parameter identification was carried out. In Sections 3 and 4, the control scheme and the updating strategy were explained in detail.

In Section 5.1, the weight matrices were determined using a single equilibrium for testing. It was shown that a linear MPC is capable of driving the nonlinear system into the desired drifting equilibrium, keeping it there with the appropriate tuning.

Linear MPC is a simpler control methodology compared to nonlinear MPC, but it performs poorly if the change in vehicle dynamic behavior is far from the design point due to nonlinearities or when it faces parameter variations (road surface changes). According to the proposed idea, these drawbacks can be eliminated by updating the discrete model of the vehicle, reformulating the MPC in an adaptive way, and utilizing measured or estimated model parameter values. This allows using the same MPC structure by updating it instead of using a more different linear MPC and a decision controller for drifting in multiple equilibria as a gain scheduling.

Another advantage of this method in vehicle motion control is directly handling changes in the road surface. A slight or abrupt variation in friction is a common occurrence in real-life driving scenarios. This paper showed that the controller could handle not only various transitions between multiple equilibria but also a simultaneous change in the road grip.

A reasonable next step of the work is to extend the proposed framework with trajectory-planning and -tracking capabilities and possibly online road surface estimation to demonstrate advantages in critical road safety scenarios.

**Author Contributions:** Conceptualization, Á.B., Sz.Cz., Á.D. and Zs.Sz.; methodology, Á.B., Sz.Cz., Á.D. and Zs.Sz.; software, Á.B., Sz.Cz., Á.D. and Zs.Sz.; validation, Á.B., Sz.Cz., Á.D. and Zs.Sz.; formal analysis, Á.B., Sz.Cz., Á.D. and Zs.Sz.; investigation, Á.B., Sz.Cz., Á.D. and Zs.Sz.; resources, Á.B., Sz.Cz., Á.D. and Zs.Sz.; data curation, Á.B., Sz.Cz., Á.D. and Zs.Sz.; writing—original draft preparation, Á.B., Sz.Cz., Á.D. and Zs.Sz.; writing—review and editing, Á.B., Sz.Cz., Á.D. and Zs.Sz.; visualization, Á.B., Sz.Cz., Á.D. and Zs.Sz.; supervision, Á.B., Sz.Cz., Á.D. and Zs.Sz.; project administration, Á.B., Sz.Cz., Á.D. and Zs.Sz.; funding acquisition, Á.B., Sz.Cz., Á.D. and Zs.Sz. All authors have read and agreed to the published version of the manuscript.

**Funding:** TKP2020 Institution Excellence Subprogram, Grant No. BME-IE-MIFM, Autonomous Systems National Laboratory Program Ministry of Innovation and Technology NRDI Office.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The research reported in this paper and carried out at the Budapest University of Technology and Economics was supported by the National Research Development and Innovation Fund (TKP2020 Institution Excellence Subprogram, Grant No. BME-IE-MIFM) based on the charter of bolster issued by the National Research Development and Innovation Office under the auspices of the Ministry for Innovation and Technology. In addition, the research was supported by the Ministry of Innovation and Technology NRDI Office within the framework of the Autonomous Systems National Laboratory Program.

**Conflicts of Interest:** The authors declare no conflict of interest.
