## 3 Scope and Parameters of the Tests  
The vehicle data adopted for the tests corresponded to a fully loaded KIA Seed car (1890 kg) with \"symmetrical\" specifications, i.e., a car where its centre of mass is situated in the car symmetry plane and the parameters of setting the left and right steerable wheels are identical to each other. The scope of the tests included the following, in succession:  
* simulation tests of the single lane change maneuver (1 LCM) for the vehicle with no driver assistance system, on homogeneous and heterogeneous road surfaces;
* verification of the vehicle trajectory model for the driver assistance system;
* simulation tests of the single lane change maneuver (1 LCM) for the vehicle with a driver assistance system, on homogeneous and heterogeneous road surface. The simulation tests were carried out for three initial vehicle speeds, i.e., 50, 90, and 140 km/h (the last is the speed limit on motorways in Poland). These values were adopted as the typical speed limits that occur in the road traffic. Initially, the vehicle was moving in the centre of the right lane (R) and then it changed the lane to the left one (L) (see Figure 2). Three types of the road surface condition were adopted for the tests: dry concrete, wet concrete, and ice. In the case of homogeneous road surface, the surface condition was identical for both the left (L) and right (R) lanes (see Figure 2). For the case with the heterogeneous road surface (also referred to as being of the \(\mu\) split type), six combinations were considered, as shown in Table 1.  
The maneuver was forced by changing the steering wheel angle. For the vehicle with no driver assistance system, the input to be applied was adopted as a single period of a sinusoid with a duration time of T\({}_{\rm w}\) = 3 s. The amplitude of changes in the steering wheel angle for the homogeneous road surface was selected by iteration so that the lateral vehicle \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Road Surface** & **R (Right Lane)** & **L (Left Lane)** & **Notation** \\ \hline \multirow{3}{*}{homogeneous} & Dry concrete & Dry concrete & Dry \\  & Wet concrete & Wet concrete & Wet \\  & Ice-covered surface & Ice-covered surface & Ice \\ \hline \multirow{3}{*}{heterogeneous (\(\mu\)-split)} & Dry concrete & Wet concrete & Dry\(\rightarrow\)Wet \\  & Wet concrete & Dry concrete & Wet\(\rightarrow\)Dry \\ \cline{1-1}  & Dry concrete & Ice-covered surface & Dry\(\rightarrow\)Ice \\ \cline{1-1}  & Ice-covered surface & Dry concrete & Ice\(\rightarrow\)Dry \\ \cline{1-1}  & Wet concrete & Ice-covered surface & Wet\(\rightarrow\)Ice \\ \cline{1-1}  & Ice-covered surface & Wet concrete & Ice\(\rightarrow\)Wet \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The road lane surface combinations adopted. displacement (in the y direction, see Figure 2) was about 3.5 m. For the heterogeneous road surface, it was assumed that the driver performed the maneuver by applying an input identical (as regards its period and amplitude) to that used for the surface of the right lane (R) in the case of the homogeneous road surface (dry concrete, wet concrete, or ice), keeping this input unchanged in spite of entering the other lane, i.e., the left one (L) with a different surface. For the vehicle with a driver assistance system, the input applied to the steering wheel was as determined by the system. As mentioned, the HSRI-UMTRI model [25; 26], together with the IPG-Tire model of transient states of tyres [23; 27], was used for the description of the forces and moments of forces. Table 2 shows the values of the main coefficients of the model, which is also referred to as the Dugoff-Fancher-Segel model [25; 26], for the three road surface types adopted.