## 5 Results and Discussion  
The goal of the simulation was to select the best driver model, then to verify the acting efficiency of the proposed driver-aid system and finally to investigate the possibility of increasing vehicle velocity. For these reasons, the simulation of straight-line riding with a speed of 30 km/h was made. To compare simulation results with experimental results, a simulation was conducted for both anticipative and inert driver models. Apart from the two driver positions, sitting at the front and above the articulated joint were taken into consideration. In the beginning, the linear model of drivers without a dead zone of sensing was used. For both driver models (anticipative and inert), the snacking phenomenon did not occur. The system was stable without any oscillation. After adding dead zones of driver perception, oscillation appeared in both models. This confirmed that limited driver perception was crucial for the occurrence of the snaking phenomenon. For these reasons, the non-linear driver model was used for the following simulation. The conducted simulations confirmed the high quality of the used models and the coherence of the results. For the anticipative driver model, results for sitting at the front of the vehicle are shown together with long low driver activity periods (Figure 11a). The length of the hydraulic actuator changed by about \(\pm\)15 mm. The lateral axle displacement reached 70 mm and the driver yaw angular deviation was about 0.65\({}^{\circ}\) (Figure 11b,c, respectively). The oscillation period was about 5.2 s. In the case of the driver sitting above the joint and connected with the rear frame, there was no low driver activity period (Figure 11d) and the length of the actuator changed by up to \(\pm\)50 mm. The driver was constantly active and the oscillation period was about  
The simulation performed for the same assumption but with an inert driver model produced slightly different results. For a driver model sitting at the front of the vehicle, similar long low driver activity periods arose (Figure 12a), but the oscillation period was shorter, at about 4.5 s, and the hydraulic actuator length changed by about \(\pm\)12 mm. The lateral axle displacement reached 51 mm and driver yaw angular deviation was about 0.52\({}^{\circ}\) (Figure 12b,c, respectively). In the case of the driver sitting above the joint and connected with the rear frame, there was no low driver activity period (Figure 12d) but the length of the hydraulic actuator changed by only up to \(\pm\)10 mm. The oscillation period was shorter, at about 3.4 s. Despite this, the lateral axle displacement reached 170 mm and driver yaw angular deviation was about 2.3\({}^{\circ}\) (Figure 12e,f, respectively). Comparisons of experimental and simulated results showed that the inert model produced much better results. The period of oscillation and lateral displacement was reflected better. It was particularly visible in the simulation with the driver sitting over the articulating joint and connected with the rear frame of vehicle. For these reasons, the inert model was selected as a better driver model for future simulations. As the driver was sitting at the front of the vehicle in transport applications, such as articulated dump trucks and forwarders, and given the possibility of the speed increasing, it was crucial for these applications that the following simulation for higher vehicle velocity was made for this configuration. The results showed (Table 4) that the system could be stable up to 60 km/h but the driver must adapt their behavior. The period of oscillation caused by the snaking phenomenon for varied vehicle velocity was at similar level and the driver had to introduce corrections to the steering system at intervals of approximately 2 s. This indicated a demand for high driver concentration level and heavy physical effort during driving. The proposed driver-aid system should reduce this effort. To evaluate the efficiency of the driver-aid system, its operation was simulated.