# Practical Approach for Developing Lateral Motion Control of Autonomous Lane Change System  
[PERSON]  
1 Agency for Defense Development (ADD), The 1 st R&D Institute-5 th Directorate, Daejeon 34186, Korea; [EMAIL_ADDRESS]  
[PERSON]  
2 Department of Electrical and Engineering, Incheon National University (INU), Incheon 22012, Korea  
or high-precision light detection and ranging (LIDAR). When the lane following method is used, the autonomous vehicle tracks the detected lane [10; 11; 12; 13; 14; 15]. Generally, the state with respect to the road is obtained via various parameters, such as lateral offset and heading errors, and a control objective for the lane keeping system (LKS) is maintaining this error at zero [16]. Meanwhile, for lane change, the autonomous vehicle tracks the desired lateral offset that increases or decreases the lateral offset error from the original lane, while the front camera obtains the original lane information. In this situation, the vehicle crosses over between the original and target lanes for lane change, and the camera vision sensor starts obtaining the target lane information instead of that of the original lane. Consequently, an inevitable jumped lane information is obtained as shown in Figure 1. This discrete change in lane information, i.e., the state jump, may deteriorate the lateral control performance. Moreover, the ALCS can cause serious accidents because of sudden changes in the control input. Thus, these discrete changes in the lane information should be considered while implementing the ALCS. To overcome the state jump problem, adding and subtracting the lane width might be a solution at the moment the vehicle changes the lane. However, it is dangerous if the detection time of the camera vision sensor and the calculation time of the system are different when the vehicle is controlled for the lane change because of the unmatched state information, as shown in Figure 1. This figure shows that a sudden control input is generated becuase of the unmatched state information with respect to time in our real-vehicle experiment. The reason is that the camera vision sensor usually has a hysteresis to reduce the detection error when driving near the lane. Therefore, it is difficult to detect a state jump and provide the control system with synchronized lane change information. In this study, we proposed a linear parameter varying (LPV) lateral motion controller using the cylinder domain to overcome the state jump problem. First, the lateral motion of vehicle dynamics in a plane is reformulated in the cylinder domain. Gluing the edges of the plane road creates the cylindrical domain. Further, the state jump does not occur due to a lane change in this cylinder domain means that the vehicle come back to the original position by maintaining its continuous state. Second, to solve the nonlinear term caused by domain gluing, the procedure of the LPV design method is proposed. The lateral movement of the vehicle in the new cylinder domain is nonlinear; however, the proposed method allows the designing of linear controllers without considering complicated nonlinear controllers. By considering the nonlinear bounded varying term as a system parameter using the trigonometric function constraint, the overall control design procedure changes into linear parameter dependent gain-scheduling problem. To the best of our knowledge, the proposed method is the first algorithm in literature to avoid state jump during lane changes as applicable to the automotive industry. The contributions of this study can be summarized as follows:  
Figure 1: Example of jumped lane information during the lane change toward left. * A new lateral motion model for a lane change system is introduced in the cylinder domain. In addition, the overall lateral motion controller design procedure for autonomous lane change system is presented in the cylinder domain. * State jump in lateral offset does not appear in the proposed cylinder domain due to its gluing characteristics.