# Enhancing Autonomous Vehicle Navigation with a Clothoid-Based Lateral Controller
## 2 Overview of the Clothoid-Based Lateral Control
By introducing tolerances, denoted as \(\delta_{x}\) and \(\delta_{y}\), it is acknowledged that achieving an exact endpoint match with the target point is not a prerequisite for the effectiveness of the proposed solution. This acknowledgment stems from the understanding that reaching the target point precisely in a single iteration is impractical. Therefore, the path from the current location to the target is formed using a single clothoid characterized by a constant curvature rate \(\Bigl{(}\kappa^{\prime}=\frac{\mathrm{d}x}{\mathrm{d}s}\Bigr{)}\). For a comprehensive mathematical explanation and details on the generation of the implemented clothoid, readers are encouraged to consult reference [3]. In such waypoint navigation control systems, lookahead distance determines how a vehicle anticipates and tracks its desired path. Lookahead distance represents the distance ahead of the vehicle along its current trajectory at which specific target points or waypoints are placed. The selection of an appropriate lookahead distance is a critical decision as it influences the vehicle's behavior [38; 39; 40]. A major novelty of the current work over the previously devised method is the development of a more robust and mathematically sensible way of evaluating this lookahead distance for the most commonly used heuristic approach as discussed in [3; 10]. This study employs a co-simulation framework, integrating TruckSim(r) (2017 edition) and Simulink(r) (Release 2022a) to create a simulated environment. Figure 2 illustrates the communication pathways for the closed-loop lateral control implemented within Simulink(r). As indicated in the block diagram, the kinematic quantities exported from TruckSim(r) closely align with real-world data obtained through GPS, rather than abstract state variables. It is important to note that, in this implementation, the complete reference path coordinates or waypoints are available in advance. The following steps summarize the working of the implemented clothoid controller:  
1. Global waypoints (_NWPs_ and _EWPs_) are established as the navigational path for the vehicle. 2. The clothoid controller receives the vehicle's current kinematic state \(\left(X,\ Y,\ V_{x},\ V_{y},\ \psi,\ \delta_{Ster}\right)\) and the desired path (_NWPs_, _EWPs_). 3. The clothoid controller computes the curvature rate \((\kappa^{\prime})\) required to steer the vehicle towards the target path. 4. The product block calculates the product of the curvature rate \((\kappa^{\prime})\) and vehicle's speed \((V)\) to determine the rate of change of the vehicle's curvature \((\mathrm{d}\kappa/\mathrm{d}s)\). 5. The Look-Up Table (LUT) or kinematic model utilizes the steering angle \((\delta_{Ster})\) to predict the vehicle's future state based on current steering dynamics. 6. The lead filter compensates for the vehicle's steering dynamics lag, ensuring the steering input is timely and accurate, preventing oscillatory behaviors. 7. The compensated steering angle is then fed into the TruckSim(r) vehicle model, which simulates the vehicle's response to the steering input. 8. TruckSim(r) provides a real-time simulation environment, updating the vehicle's kinematic state \(\left(X,\ Y,\ V_{x},\ V_{y},\ \psi,\ \delta_{Ster}\right)\) based on the provided steering inputs and vehicle dynamics. 9. The updated kinematic state of the vehicle is fed back into the clothoid controller, closing the loop for continuous real-time navigation control.