# Dynamic Decoupling and Trajectory Tracking for Automated Vehicles Based on the Inverse System
## 1 Introduction  
Automated vehicles (AVs) provide safe, cheap, and efficient travel as well as attracting widespread research interest in industry and academia [1, 2]. The trajectory tracking module manipulates vehicle chassis actuators to reach the target position at the right time, which is a core part of AVs and directly affects driving safety and comfort [3]. According to the different control structures, the existing trajectory tracking control can be divided into a decentralized control method and centralized control method. The decentralized control method decomposes the trajectory tracking problem into longitudinal velocity control issue and lateral position tracking issue, and the corresponding control laws of these subsystems need to be designed, respectively. In the past few decades, the problem of lateral position tracking has always been the core issue. In order to improve tracking accuracy or control stability, many lateral position tracking methods have been proposed, such as preview [4], pure-pursuit (PP) [5], Stanley [6], linear quadratic regulator (LQR) [7] and model predictive control (MPC) [8]. After being integrated with longitudinal controllers, these methods could realize accurate tracking under most scenarios [9, 10, 11, 12]. However,due to the interaction between the motion directions, the motion tracking error of the decentralized control method will increase under the coupling condition, i.e., lane changing with varying speed. To solve the problem, some centralized control methods which designed the recompense law between the longitudinal and lateral controller were developed. [PERSON] (2016) designed the lateral controller considering the time-varying velocity, which can eliminate the lateral disturbance caused by longitudinal control. [PERSON] et al. (2018) proposed the nonlinear model predictive control (NMPC) considering the characteristics of vehicle body motion coupling and tire force coupling, which can effectively solve the problem of motion interference between different directions. Besides the lateral control compensation, [PERSON] (2018) applied the Lyapunov method to solve the integrated longitudinal and lateral tracking problem. [PERSON] (2018) used the differential flatness theory to design the control laws of longitudinal and lateral directions, which realized the dynamic trade-off. In the architecture of MPC, the longitudinal and lateral control could be transformed into one constrained optimization problem with full consideration of the coupling effect of vehicle motion ([PERSON] et al., 2019; [PERSON] et al., 2020). However, since the weighted optimization is still a compromise rather than a real decoupling, the improvement in tracking accuracy is not obvious. Therefore, in trajectory tracking, dynamic decoupling is an effective method to eliminate the interactions of various vehicle motion directions. To decouple the lateral and the yaw motion of the vehicle, [PERSON] (2018) calculated eigenvalues of the optimal control system by minimizing the weighted sum of the cross-transfer function. Then, referring to the target sideslip angle and yaw rate obtained from the nonlinear vehicle model, the zero-yaw rate maneuver and the zero lateral speed maneuver were guaranteed to improve vehicle handling performance. [PERSON] (2018) derived an analytical method to decouple the motion control on vehicles' longitudinal and lateral directions. The responses of the ideal bicycle model were followed to improve the driving safety and handling performance of the vehicle. [PERSON] (2018) adopted the inverse system to decouple lateral, yaw, and roll motions. The decoupling method can transform the coupled vehicle dynamics system into multiple parallel single input single output (SISO) sub-systems. Then, by tracking the ideal vehicle motion states, e.g., yaw rate, longitudinal acceleration and sideslip angle, the vehicle handling performance is enhanced.