## 4 Simulation Results  
The developed sliding mode controller (SMC) for path tracking is assessed through simulation using a challenging path signal containing sharp turns representing difficult scenarios. This path was constructed from a series of multiple sinusoidal waves, each with varying frequencies, sequentially linked in order of increasing frequency. Supplementary path details, including curvature and heading angle, are inferred by fitting a quadratic function to the waypoints within a limited distance horizon. Initially, we tested the controller during forward motion, and the outcomes are illustrated in Figure 3. Notably, despite the fact that the controller parameters are not finely tuned, we observed effortless path tracking. This is attributed to the system's inherent stability during forward motion. In reverse motion, the challenge escalates due to the potential for jackknifing if errors accumulate. This phenomenon, where the trailer pushes the towing vehicle from behind, causes it to spin around, leading to hazardous situations. Figure 4 displays the outcome when driving backward from an off-path starting position. This visualization offers a clear picture of how the vehicle behaves under various conditions. The demonstrated  
Figure 2: Block diagram of proposed control law. path-tracking outcomes primarily focus on evaluating the trailer vehicle's tracking accuracy. Accurate tracking ensures that the trailer stays on course, reducing the risk of accidents and enhancing overall safety. We measure this performance using multiple metrics, as shown in Figure 5.  
Firstly, we consider the Trailer Lateral Distance Tracking Error. Here, the controller managed to sustain an error below 0.5 m for the initial three turns. This is a significant achievement considering the complexity of the motion. Even in the more challenging turns, the controller exhibited commendable performance, keeping the error within a range of \(\pm\)2 m. Secondly, the Trailer Heading Angle Tracking Error is examined. Maintaining a consistent heading angle is crucial for the stability of both the towing vehicle and the trailer. For the first three turns, the controller effectively maintained a heading error within \(\pm\)10\({}^{\circ}\). For tougher turns, the error stayed within \(\pm\)20\({}^{\circ}\). Focusing exclusively on the trailer vehicle's tracking, the distance tracking error remains consistently low. This precision speaks volumes about the system's robustness. This is notable even when the SMC control gain and look-ahead distance are not finely  
Figure 4: Simulation results illustrating the backward motion scenario. The red square represents the tractor, while the blue square represents the trailer. Figure 3: Simulation results illustrating the forward motion scenario. The red square represents the tractor, while the blue square represents the trailer. calibrated. Furthermore, the steering control makes out at \(\psi_{max}\) for roughly 2 s, leading to sporadic peaks in error accumulation. Adjusting these parameters could potentially further refine the system's performance in the future. Additionally, we compare the developed controller with an Evolving Neural Network (NN)-based controller, similar to the one described in ref. [12]. The NN controller design was refined using a genetic algorithm, adjusting the weights of a pre-defined neural network structure. Evolving Neural network controllers, often praised for their adaptability and capability to learn complex representations, can sometimes falter when faced with unseen data or if they are not adequately trained. They are particularly proficient at managing systems with complex, nonlinear dynamics due to their architecture's ability to approximate any function. However, they may be vulnerable to over-fitting and might not generalize well in scenarios that diverge from their training data, making them less reliable in certain unpredictable real-world applications.