## 6 Conclusions  
The conducted research demonstrated that the low directional stability of articulated vehicles with hydraulic steering systems was mainly caused by limited driver perception in sensing angular yaw and the absence of mechanisms that straightened the twisted frame and prevented increasing lateral and angular deviation. In car steering systems, this task was performed by special steering knuckle geometry, which generate straightening torque. Hence, yaw was eliminated automatically and drivers had to mainly have to react to lateral displacement. In the case of articulated vehicles, in contrast to cars, angular deviations were dominant due to the limited possibility to detect and eliminate them. Unnoticed yaw could reach 0.5\({}^{\circ}\) and unnoticed lateral displacement was 0.1 m. The conducted tests showed that a hydraulic steering system, especially one operating in an LS system, could introduce a time lag of up to 0.4 s. This lowered the overall steering system efficiency and the vehicle's directional stability. The driver's location significantly influenced movement stability. Driver placement at the front of the vehicle accelerated sensing of lateral and angular deviations from the path. During the simulation, inert and anticipative driver models were used. The best results and higher simulation accuracy were obtained with the inert model. Simulations showed that limitation of the snaking phenomenon during movement of articulated vehicles with the driver-aid system was possible. The principles of their operation were verified using simulations. A limited flow rate in the driver-aid system did not cause lateral jerk and acceleration, and high dynamic reactions. The unique developed model of an articulated vehicle as a steered vehicle, exhibited full usefulness for such simulations and could be used in future work on developing the electronic control and the sensor systems necessary for stabilizing articulating vehicles. The proposed system could increase the productivity of articulated equipment, due to a significant reduction in driver activity. It lowered the necessary driver effort and concentration level. It, thus, enabled the development of higher travel speed during operations. As was mentioned above, a vehicle's velocity is crucial for its productivity and operation efficiency. The proposed system could also be used to improve the stability of robotized articulated vehicles--one of the main development direction  
Figure 13: Example of simulation for inert driver model, siting at the front of the vehicle—(**a**) hydraulic actuator displacement, (**b**) lateral displacement of front (1) and rear (2) axle, and (**c**) yaw angular driver deviation. of modern mining equipment. In automated or robotized equipment, it is strongly recommended to measure the frame twist and connect sensors of deviation to the front frame of vehicle. This paper only presented the concept and preliminary simulations of the new system. The simulations showed that it is possible to increase directional stability of the articulated vehicles. The results should be verified using wider simulations with different scenarios (on various types of terrain and with different slopes). Before the implementation of such a system on vehicles, risk assessments should be conducted and the implementation possibility of additional safety systems for the driver should be taken into consideration. Conceptualization: M.J.L. ; Methodology: M.J.L. ; Software: M.J.L. and A.R. ; Validation: A.R., Formal analysis: M.J.L. and A.R. ; Investigation: M.J.L. and A.R. ; Resources: M.J.L. ; Data curation: A.R. ; Writing--original draft preparation: M.J.L. ; Writing--review and editing: M.J.L. and A.R. ; Visualization: M.J.L. and A.R. ; Supervision: M.J.L. ; Project administration: M.J.L. and A.R. ; Funding acquisition: M.J.L. All authors have read and agreed to the published version of the manuscript.