# Robust Control with Uncertain Disturbances for Vehicle Drift Motions
## 1 Introduction  
Professor drivers, including racing drivers, can drive cars to accomplish drifts and sharp turns in drift conditions, which means tire forces reach the maximum and tires are in high slip ratios and is very dangerous for ordinary drivers but can ensure maximum safety. The autonomous vehicle will be safer if it can realize drift motions. The paper studies how to control vehicles in drift motions. The studies of vehicle drift control are divided into two kinds based on analysis methods, one of which is experience-based and the other is theory-based. The experience-based is designed by artificial intelligence, including neural networks, based on the professor drivers' data. [PERSON] designed a PILCO (probabilistic inference for learning control) controller based on the combination of simulators and a real-world robot car to realize a steady-state drift motion by learning the optimal solutions of a simple model in [1]. [PERSON] proposed a hybrid structure formed by the MPC (model predictive controller) and NNs (neural networks) to achieve drift motions in which the NNs provided the motion references and tire parameters by learning in [2]. [PERSON] applied a feedforward-feedback controller based on the neural network to realize vehicle drift motions by learning experimental and simulated data in [3]. [PERSON] designed a controller based on the model-free deep reinforcement learning algorithm soft actor-critic to realize vehicle drift motions after being trained on tracks in [4]. Artificial intelligence is most often expressed in stochastic algorithms that often have no knowledge whatsoever of the underlying problem being learned(a considerable strength of the methods) in [5]. The theory-base is designed by control theories based on drift motion analyses. The drift circle motion is the first and important step of the vehicle drift study. [PERSON] obtained the main state parameters including the vehicle velocity and the sideslip angle and yaw rate by analyzing the steady-state cornering based on a three-state model in drift conditions in [6]. [PERSON] analyzed the drift equilibrium of the vehicle phase portrait based on the three-state bicycle model, presented a controller framework for autonomous drifting of a rear-wheel-drive vehicle, and achieved the drift motion in [7; 8]. [PERSON] analyzed vehicle stability properties and equilibrium point locations and movement to changing parameters and system inputs by phase portraits based on the bicycle model and applied phase portrait analysis to the controller design in drift motions in [9]. [PERSON] analyzed the vehicle equilibrium and designed an equilibrium condition calculator based on the pre-distribution of the longitudinal force of the rear tire of a four-wheel vehicle model in drift conditions in [10]. [PERSON] analyzed drift equilibrium states based on a three-state bicycle model and obtained the equilibrium status values of the body slip angle and yaw rate with low velocities when the vehicle rotated clockwise and counter-clockwise in [11]. Each of the two kinds of studies has its advantages and disadvantages. The experience-based option can be more human to achieve the drift motions than the theory-based one, but the theory-based option can have no need for operational data, which is different for various combinations of vehicles and roads and is difficult to obtain for most studies. Besides, the theory-based studies are mainly applied to vehicle planar models with the neglect of the large rolling motion which in drift conditions is possible regarding the vehicle behaviors controlled by drivers, and there are high risks of rollover with the large rolling. Therefore, this paper studies the vehicle drift control based on the drift motion analyses in consideration of rolling safety. Choosing an appropriate algorithm of the controller also is significant to achieve drift motions, which can be decided by the references of the existing vehicle drift control methods and vehicle path tracking methods.