## 1 Introduction  
Wheel machines with an articulated frame due to rigid axles, large tires, and hydraulic steering systems have many unique features, such as high maneuverability, high cross-country mobility, high payload capacity, and high durability and reliability, with low manufacturing costs, as a result of the simplicity of construction and the serial, mass production of components. For these reasons, they are widely used with high efficiency in agriculture like heavy tractors; in forestry, as tree-harvesters and forwarders for transport tasks; in mining sites as transportation vehicles, and on construction and mining sites, as loaders for realization load and carry tasks, and as dumpers for hauling and transportation tasks. According to [PERSON] et al. [1], transportation productivity mainly depends on average speed. [PERSON] et al. [2] indicated that this speed for articulated vehicles is mainly limited by the snaking phenomenon--low direction stability of machine movement. According to [PERSON] et al. [3], the average speed of an articulated hauler on construction sites is about 25 km/h, with a top speed of 54 km/h. According to previous studies [2, 4, 5], low directional stability demands higher effort from drivers, increasing their concentration levels; additionally, cases of dynamic loads on bearings in joints and in the hydraulic cylinder are a serious problem. The robotization of such equipment is a main development trend, and according to [PERSON] et al. [6], the dynamics of vehicle steering systems are critical for path planning for articulated vehicles. Wider use of articulated vehicles in transport applications and increasing their productivity require improvements to their average speed, by limiting the snaking phenomenon at high speeds. The effective realization of transport tasks requires duplication of road speed and achieving about 60 km/h, during driving in good road conditions. The low lateral stability of articulated machines is a broadly known problem; for this reason, the international standard [7] was developed. It describes the method of dynamic testing of vehicle stability when moving at high speeds. Lateral stability of articulated vehicles is the subject of many studies. A general model of heavy articulated vehicles with hydraulic steering systems was presented [8]. It enabled investigating the influence of geometrical parameters on directional and roll-over lateral stability, and the influence of torsional joint stiffness on the front and rear parts of vehicles and their inertia. Additionally, the lateral and radial stiffness of tires were considered. [PERSON] et al. [9] described the handling behavior of articulated vehicles riding on smooth and rough surfaces at high speeds. The model used had three degrees of freedom (DOF) and was linear. Steering actuators were modeled as torsional springs and dampers at the articulation joints and were not actively controlled during riding. The main assumption for this investigation was that low directional stability is caused by mutual front and rear frame oscillation, due to low hydraulic cylinder stiffness. For the studied model, whose weight was 3000 kg, the authors found that with higher speed (12 m/s), folding instability could occur in addition to oscillation. The authors indicated that the most important parameter for stability is oil volume in the hydraulic steering system. [PERSON] et al. [10] added a model of a hydraulic steering system with linear directional valves. The authors showed the influence of cylinder dimensions and leakage in the hydraulic circuit and additional friction in the articulated joint, on the possibility of mutual frame oscillation damping and lateral vehicle stability improvements. The advanced model revealed that an oversteer mode is also possible. The authors concluded that the interaction between oversteering response and driver action is, in practice, the most likely cause for weaving oscillations, called the snaking phenomenon.