# Lateral Control Calibration and Testing in a Co-Simulation Framework for Automated Vehicles
## 1 Introduction  
The advancement of highly automated vehicles holds a critical position in the field of automotive engineering. The key advantages of highly automated driving include improving road safety, particularly by minimizing driver errors and making efficient use of commuters' travel time [1, 2]. Perception, trajectory planning, and control are three main parts in the structure of automated vehicles, where the control part allows the car to follow the trajectory, which has been determined in the trajectory planning parts. Because of the complex interconnections between the vehicle's lateral and longitudinal dynamics, designing a controller needs to be considered carefully [3] and it continues to remain a challenge. There are various control techniques that have been used for trajectory tracking in automated vehicles, such as: PID [4, 5], linear quadratic regulator (LQR) [6, 7, 8, 9], the sliding mode control (SMC) [10, 11], robust control [12], model predictive control (MPC) [8, 13, 14, 15, 16] and reinforcement learning [17, 18]. However, most of them are used to control longitudinal and lateral dynamics separately. Recently, controlling both longitudinal and lateral dynamics has been applied [4, 19, 20, 21, 22, 23]. [PERSON] et al. [21] designed a multi-input-multi-output (MIMO) linear MPC with some constraints in the vehicle dynamics, in which the reference path is tracked based on the steering angle and angular velocity. In [4], [PERSON] et al. adopted the MPC and nonlinear model predictive control (NMPC) method to cope with the nonlinear MIMO problem for the vehicle's lateral stability. Although the MPC controller can use nonlinear dynamics to solve the constraints, MPCprevents having to conduct an experiment on a real-time system because of the increase in the model complexity and constraints as well as the huge amount of computation. The SMC technique is proposed to control by combining the lateral and longitudinal dynamic [22]. However, when applying the SMC technique, the chattering phenomenon often appears when acquiring robustness. To overcome this obstacle, in [23], the authors applied a new sliding mode that reduces chattering and makes state variables converge faster. However, rough road surfaces can lead to compromised path tracking accuracy and overall system stability. The LQR approach is popularly used in automated vehicle controllers because of algorithmic simplicity, high-precision performance, and satisfaction with dynamic constraints. [PERSON] [24] compared the robust controller with LQR and MPC in terms of performance as well as computation. In the parking scenario, the LQR controller has a better performance. Regarding computation, the LQR requires less in comparison with MPC while it has the same performance indicators in some cases. However, LQR methods usually do not consider disturbances which can contribute to system errors. To cope with this problem, [PERSON] et al. [25] designed a controller by combining feedback and feedforward steering. The aim is to keep the stability of the vehicle under hard maneuvering conditions as well as minimize path deviation. However, the steady-state path deviation drastically increases at high velocity. In [26], the authors also proposed an LQR controller using feedforward and predictive steering for lateral dynamics, which helps vehicle driving under complex conditions. Although LQR controllers were widely applied to automated vehicles, most LQRs choose weight factors based on empirical consideration. To dispose of empiricism, some studies added algorithms to optimize the LQR controller in order to improve performance. In [27; 28; 29], the authors used GA, fuzzy control, and PSO to choose the optimized weight factors for the LQR controller. The results showed the effectiveness of these algorithms regarding the tracking accuracy and the stability of the vehicle. Although promising results are shown in these studies, there is still potential for further improvement in the accuracy of the controller.