# Practical Approach for Developing Lateral Motion Control of Autonomous Lane Change System
## 3 Simulation Results
### Scenario 2: Human Driver-Based Trajectory  
As discussed earlier, the steering angle obtained when a human driver changes lanes does not follow the sine and cosine trend perfectly. Therefore, in scenario 2, we performed a simulation to determine if the proposed controller exhibits reasonable performance even with this nonsinusoidal reference trajectory. In scenario 2, after 3 s the vehicle started changing lanes for about 3 s. To generate  
Figure 5: Result of ALCS using formal sine and cosine trajectory. (**a**) Reference and measured states in the cylinder domain; (**b**) Trajectory of vehicle in global, local and cylinder domain, respectively; (**c**) Convex interpolation parameter and the control input.  
a human driver-based reference for the second scenario, we make a several lane changes using the driver model, which is already implemented in the CarSim. During several lane changes using the human driver model, we logged both \(\xi_{1}\) and \(\xi_{2}\). Further, we used the logged signals \(\xi_{1}\) and \(\xi_{2}\) as reference inputs for the proposed ALCS.  
Figure 6a shows the reference trajectory and measured state in the cylinder domain. As shown in Figure 6a, the given reference trajectories of \(\xi_{1}\) and \(\xi_{2}\) are similar but not exactly matched to the sine function. However, unlike scenario 1, the derivative of the reference is continuous; thus the control input changes smoothly during lane change, as shown in Figure 6c In addition, the other states in the cylinder domain, (\(\xi_{3}\), \(\xi_{4}\) and \(\xi_{5}\)), which are affected by the control input, have similar patterns. Furthermore, it can be seen that a constant value is not maintained in each state. We can infer that the change in the yawrate, which affects the ride quality, is smooth and not abrupt when a human driver changes lanes, as shown in Figure 6a. It is observed that when the lane change begins, the slope of the control input value is smaller than the slope of the moment when crossing the lane, as shown in Figure 6c.  
To change lanes to the left, the desired lateral position of the vehicle is set to 3.4 m, as shown by the green line in Figure 6b. Furthermore, using the inverse gluing function in (10), the human characteristics-based trajectories \(\xi_{1}\) and \(\xi_{2}\) are merged with the reference trajectory, as shown by the red  
Figure 6: Result of ALCS using human driver characteristics-based trajectory. (**a**) Reference and measured states in the cylinder domain; (**b**) Trajectory of vehicle in global, local and cylinder domain, respectively; (**c**) Convex interpolation parameter and the control input.  
dashed line in Figure 5b. It is observed that when the vehicle crosses the boundary between the original and target lanes at about 5 s, the position of the vehicle in the cylinder domain is \((\xi_{1},\xi_{2})=(0,-1)\).  
The controller uses sub-obtimal gain, which is obtained by interpolation of the optimized gain for each vertex, as shown in Figure 5c; however, the proposed method provides a reasonable performance. In addition to the significant advantages in terms of computation time, the control performance is remarkable despite the simple linear controller. We expect the proposed method to be suitable for low-cost electronic control units, which cannot handle heavy computations. Furthermore, if necessary, advanced lane change controllers can be applied to improve the control performance, such as model predictive control.