###### Abstract  
The article describes the application of a vehicle simulation model to assess the driving hazards that arise due to changes in the tyre-road adhesion during a lane change. An experimentally verified vehicle dynamics model was used. The typical single lane change maneuver, performed on dry concrete, wet concrete, and ice-covered roads, was simulated for three vehicle speeds. The disturbance was introduced as a changed tyre-road adhesion on the target lane. Typical sinusoidal (one-period) input was applied to the steering wheel. Adhesion change may lead to an accident when considering the driver's reaction time. An original control algorithm has been built. It is the driver assistance system with a double PID controller of the steering wheel angle. The system parameters were determined based on the principles recommended in the automatic control engineering monographs. The controller fulfils its tasks for motion at very high speeds on a homogeneous road surface and for the case where the tyre-road adhesion is changed during a maneuver. Thanks to this, the threat can be avoided.  
motor vehicle safety; lane change; change in the tyre-road adhesion; vehicle control systems; driver assistance system; vehicle dynamics and stability; simulation tests +
Footnote †: journal: Applied sciences  
straight-line braking with a possible lane change when the driver spots a sudden change in the tyre-road adhesion has been discussed and the process has been modeled in [11]. The simulation represented the pre-accident situation rather than the change in the vehicle behaviour during a normal lane change. A similar problem (but without an analysis of the impact of the tyre-road adhesion) was addressed in [15]. Publication [16] covered the examination of a PID controller within the scope of per-forming a double lane change on a homogeneous road surface. In [8], a collision avoidance assistance system was proposed, including lane changing as a defensive action. The work [17] reviews a two-axle autonomous vehicle's (AV) control methods (PID, MPC, SMC) to drive according to a given trajectory. An essential aspect of this work is to pay attention to the vehicle's motion on a low-friction surface. The examples focused on controlling the steering wheel angle will be discussed hereafter.  
This publication is to show the real threat that may arise in the road traffic from changes in the road surface condition, if the changes are encountered when the vehicle is driven without any influence of other vehicles or other road users. The single lane change on a straight road section has been described. Many simulations of the motion of a medium-class passenger car were carried out for a few typical speed values and different road surface conditions; the quantities that warn of the potential collision situation in question were pointed out when any intervention of the driver or the assistance systems is necessary.  
An algorithm has been proposed for the operation of the assistance system that is to perform the maneuvers of this kind in a safe way when the driver cannot avoid the danger of lane or road departure.  
The structure of the paper is organized as follows: Section 2 (Materials and Methods) presents a synthetic description of the vehicle simulation model and the reference trajectory model for the assistance system, while Section 3 (Scope and Parameters of the Tests) presents assumptions for the scope of calculations. The next section, Section 4 (Results and Discussion), presents the calculation results for the vehicle without the assistance system, followed by the model of the proposed assistance system and the results after its application, along with the analysis. Section 5 (Conclusions) summarises the authors' most important observations on the results.