# Enhancing Autonomous Vehicle Navigation with a Clothoid-Based Lateral Controller
## 6 Results and Discussion  
This section delves into the comprehensive results obtained from the implementation of a clothoid-based lateral controller featuring an adaptive Frechet distance-driven lookahead adjustment mechanism. The objective here is to assess the controller's ability to maintain accurate lateral tracking across a diverse range of challenging curves. Additionally, the controller's effort and aggressive behavior will be scrutinized through steering wheel angle (control effort) versus time plots, shedding light on its effectiveness and stability under various simulated scenarios.  
Notably, the lateral control simulations incorporated a speed controller to follow a reference velocity along the waypoints, crucial for realistic simulation in maintaining safe lateral acceleration, especially for a semi-tractor trailer. For this reason, the reference path dataset not only contains the northing and easting coordinates, but also the velocity/speed data at each of these waypoints (spatial velocity data). These velocity data were evaluated using \"Smart velocity waypoint generation\" which is a method for intelligently computing a batch of velocity waypoints based on given northing and easting waypoints. It emphasizes maintaining acceleration and velocity limits, ensuring the computed velocities are within a specified range and subject to constraints like lateral and longitudinal accelerations. This method uses quadratic polynomials to estimate curvature, heading, and path distance at each waypoint and adjusts velocities to optimize speed while adhering to the set constraints.  
Figure 10: Frequency response of the plant (estimated lag transfer function), cascaded dynamics, and compensator (lead filter) (**a**) Magnitude and (**b**) Phase plot.  
Figure 9: Time-domain validation of lead filter. (**a**) Dual-lane-change maneuver. (**b**) Step series maneuver.  
The lateral acceleration constraint was set at 0.3 g's which is a conservative threshold for preventing rollover (refer [44; 45]).  
_Tracking Performance Assessment_  
Precise lateral control is crucial for autonomous vehicles to adhere to their designated paths with minimal errors. The primary metric for evaluating the lateral controller's tracking performance is the cross-track error (CTE) plot. CTE quantifies the deviation of the ego vehicle (in this case, tractor's rear axle center) from their reference path and serves as a key indicator of how effectively the clothoid controller manages the lateral position.  
The efficacy of the clothoid-based lateral controller is evident from tests conducted on various complex paths, including the dual-lane change and figure-eight maneuvers. The CTE plots for all the trajectories reveal low lateral deviations throughout the platooning maneuvers. This result underscores the effectiveness of the adaptive Frechet distance-based lookahead distance mechanism in guiding the ego vehicle precisely along their reference paths.  
_Controller Effort and Aggressiveness_  
In addition to tracking accuracy, understanding the controller's effort and aggressiveness is crucial for assessing its stability and real-world applicability. One way to gauge these aspects is through the steering angle versus time plots, which provide insights into how smoothly the controller adjusts the steering inputs.  
The steering angle versus time plots illustrate the dynamic response of the clothoid controller under various driving scenarios. It is essential to balance between aggressive maneuvers and maintaining the driver's comfort. Across all tested tracks, the controller consistently exhibited a well-behaved response, keeping the curvature changes within reasonable limits. This ensures that the steering inputs are smooth and gradual, minimizing abrupt changes that could potentially lead to discomfort for drivers and reduce the overall stability of the vehicle.