# Hierarchical Synchronization Control Strategy of Active Rear Axle Independent Steering System
## 1 Introduction
Therefore, to obtain a desired steering angle control performance, a robust controller with higher response speed and control accuracy is required. This is very important to the driving performance of the vehicle. In addition, not only should the steering angle tracking control be realized, but also the steering kinematics characteristics of the vehicle should be considered to ensure steering angle synchronized control of the left and right of the rear axle wheels [16]. In this paper, we define the process of realizing the steering angle between left and right rear wheels to satisfy the Ackerman principle as synchronized control. So, we mainly focus on the high-precision tracking control and synchronized control of the steering angle of the ARIS system in this paper. In the four-wheel steering system of vehicles, the traditional control method is often used. The single wheel tracking controller is designed by decoupling multiple steering wheels through motion planning. Proportional-integral-derivative (PID) control, adaptive control, sliding mode control, fuzzy control and other methods are used in steering angle controller. The adaptive control method was used to realize the steering wheel angle tracking control in [17; 18], but its prediction and estimation method for the road disturbance is based on the tire characteristics in a better linear region. Neither the nonlinearity of tires nor the uncertainty of road conditions in the actual situation are taken into account. Aiming at the nonlinearity of the steering system, sliding mode control (SMC) was adopted to realize the tracking control of the steering angle in [19; 20; 21], which improves the robustness of the controller. SMC can solve the nonlinearity of a control system and has strong robustness, but the chattering phenomenon at the balance point is still a problem to be overcome in practical application. Moreover, even if the expected tracking performance of each independent steering wheel tracking controller is achieved, it cannot guarantee that the synchronization error between wheels can be reduced. A master-slave control strategy based on disturbance sliding mode control was proposed for a two motor coupled steer by wire system in [22]. However, when the slave steering wheel is disturbed by external disturbance, the master steering wheel will not respond. The master-slave control method is suitable for the system with an obvious master-slave relationship, but not for the system with a mutual coupling relationship. In Reference [23], the contour error model for the four-wheel independent steering system (4 WIS) mobile robot system was established and the synchronization control was designed based on the cross coupling algorithm, which can reduce the synchronization error between wheels and improve the accuracy of the tracking trajectory. But complex sensors are needed to acquire the vehicle's attitude and position information to calculate the trajectory error. It is not suitable for general vehicles without navigation sensors. In Reference [24], [PERSON] proposed the concept of virtual shaft control applied to the synchronization control of a multi-axis machine. The virtual shaft control and improved electronic line-shafting are widely applied in multi-axis machine systems [25; 26]. In [27], fault diagnosis and fault-tolerant control techniques were proposed for an over-actuated electric vehicle to deal with the controller reconfiguration in the presence of system faults and structured and unstructured uncertainties. In this study, firstly, we will establish the model of the dynamics and kinematics of the ARIS system. Then, considering the coupling between wheels, a hierarchical synchronization control strategy will be designed to reduce the synchronization error between rear wheels. The upper controller adopts the virtual synchronization controller based on the dynamic model of the virtual rear wheel steering mechanism, while the lower controller is designed based on the linear active disturbance rejection control (LADRC) algorithm.