# Robust Control with Uncertain Disturbances for Vehicle Drift Motions
## 5 Conclusions  
This paper analyzes drift motion mechanisms in steady and transient states based on the theory-based method with the reference of the human operation by considering longitudinal, lateral, roll, and yaw motions and the rolling safety with the nonlinear tire model UniTire. It obtains the velocity limitation and main statue parameters including the side-slip angle and the yaw rate, and the drift motion characteristics are analyzed and described. With the consideration of uncertain disturbances in practice, the state-feedback robust controller is designed based on LMIs and proposed to realize drift circle motions and to improve the driving safety of autonomous vehicles, and the robustness of the control system is verified by simulations in MATLAB/Simulink on the pavement whose friction coefficient equals 0.7 in the proposed study. The results show that vehicles that can drive in drift conditions are safer and the designed controller can realize drift circle motions as well as stability with robustness.  
Conceptualization, [PERSON] and D.X.; methodology, software, validation, and writing--original draft preparation, [PERSON]; writing--review and editing, supervision, and project administration, [PERSON]; investigation, [PERSON], [PERSON] and C.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, Grant Number 51775548.  
Not applicable.  
Data Availability Statement: Data is contained within the article. All data in this study can be obtained by calculation as shown.  
The author(s) would like to thank to all the students taking part in the experiment from College of Engineering, China Agricultural University. [PERSON] and [PERSON] conceived motion mechanism analysis, control algorithm, performed the simulations, and finished the manuscript. [PERSON] and [PERSON] revised the paper. And the authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (No. 51775548).  
The authors declare no conflict of interest.  
The following abbreviations are basic parameters that is used in this manuscript:  
\begin{tabular}{l l} DOF & degree of freedom \\ LQR & linear quadratic regulator \\ index \(i=f,r\) & to denote the front and rear axle respectively \\ \(R\) & trajectory radius around mass center \\ \(m\) & vehicle mass \\ \(m_{b}\) & vehicle body mass (sprung mass) \\ \(\delta_{f}\) & front-wheel steering angle \\ \(v\) & vehicle velocity \\ \(v_{x}\) & vehicle longitudinal velocity \\ \(v_{y}\) & vehicle lateral velocity \\ \(\beta\) & vehicle sideslip angle \\ \(\gamma\) & vehicle yaw rate \\ \(\phi\) & vehicle roll angle \\ \(l_{i}\) & distance from gravity center to front or rear axle \\ \(h_{b}\) & height of gravity center from the roll axis \\ \(h_{g}\) & height of gravity center \\ \(F_{d}\) & aerodynamic drag force \\ \(\rho_{a}\) & air density \\ \(C_{d}\) & aerodynamic drag coefficient \\ \(A_{f}\) & frontal area of vehicle \\ \(C_{\phi}\) & combined roll damping coefficient \\ \(K_{\phi}\) & combined roll stiffness coefficient \\ \(I_{x}\) & moment of inertia with respect to roll axis \\ \(I_{z}\) & moment of inertia with respect to yaw axis \\ \(I_{xz}\) & moment of inertia with respect to roll and yaw axis \\ \(I_{x\phi}\) & moment of inertia with respect to roll axis after wheel lift-off \\ \end{tabular}