## 2 Materials and Methods
### Model of the Desired Vehicle Trajectory During the Single Lane Change Maneuver  
In publications [32; 33; 34; 35], the following models to describe the vehicle trajectory (represented by the trajectory of vehicle's centre of mass) during the single lane change maneuver (1 LCM) have been proposed: model 1 by [PERSON] et al. [33] and [PERSON] [32], model 2 by [PERSON] [35], model 3 by [PERSON] [34], model 4 by [PERSON], [PERSON] and [PERSON] [33], and model 5 by [PERSON] [33]. They have trigonometrical forms based on sin/cos functions or circular/polynomial functions. As a result, they show very similar shapes. Authors of this paper decided to apply model 3 by [PERSON] [34] presented in the paper by [PERSON] et al. [33]--see Equation (1). The reason was the closest (in the mean square sense) distance of this analytical description to the motion trajectory of the simulated vehicle during the lane change maneuver (1 LCM).  
\[\mathrm{y}(\mathrm{x})=\mathrm{H}\cdot\left[\frac{\mathrm{x}}{\mathrm{L_{m} }}-\frac{1}{2\pi}\mathrm{sin}\left(\frac{2\pi}{\mathrm{L_{m}}}\cdot\mathrm{x} \right)\right], \tag{1}\]  
where x--longitudinal vehicle displacement, [m]; y--lateral vehicle displacement, [m]; H--planned maximum lateral vehicle displacement, [m]; L\({}_{\mathrm{m}}\)--longitudinal vehicle displacement during the performing of the single lane change maneuver, [m].  
In this case, the vehicle yaw angle during the maneuver can be expressed as below:  
\[\mathrm{\psi}(\mathrm{x})=\mathrm{arctg}\left\{\frac{\mathrm{H}}{\mathrm{L_{ m}}}\cdot\left[1-\mathrm{cos}\left(\frac{2\pi}{\mathrm{L_{m}}}\cdot\mathrm{x} \right)\right]\right\}. \tag{2}\]  
If the vehicle speed (v [m/s] or V [km/h]) is constant during the 1 LCM (single lane change maneuver), then Equations (1) and (2) may be transformed into the time domain t [s] thanks to the relation:  
\[\mathrm{t}=\frac{\mathrm{x}}{\mathrm{v}} \tag{3}\]  
The parameter of the 1 LCM is the maneuver duration time T [s]:  
\[\mathrm{T}=\frac{\mathrm{L_{m}}}{\mathrm{v}}. \tag{4}\]  
The 1 LCM duration time T is estimated based on experimental tests. In publication [3], this time is 2-7 s. In [36], its full range, i.e., 1-13.3 s, is considered, but particular attention is paid (based on a statistical analysis) to the range of 2.54-6.28 s. In [37], the range of 1.0-2.6 s is covered by the analysis. In the normative act withdrawn by ISO [28], the value of 2 s was adopted. In the simulation tests reported herein, the authors adopted a value of T = 3 s, thus emphasizing the low dynamics of the maneuver under analysis, which corresponds to the normal smooth driving on a straight road section. This is usually connected with  
Figure 2: Straight section of a two-lane road, where the right and left lanes, separated from each other by a broken line, are labelled R and L, respectively (the latter being intended for the oncoming traffic). Oxyz is an inertial reference system, attached to the road.  
an identical steering wheel input duration time T\({}_{\rm w}\) = 3 s (a single period of the sinusoidal input). In [36], attention is directed to the fact that the 1 LCM duration time T does not depend on the vehicle speed.  
The final lateral vehicle displacement H during the 1 LCM depends on the lane width. In the normative act [38], values from the range of 2.5-3.75 m were specified; actually, the value of H = 3.5 m often occurs on higher-class roads and this value was adopted in the simulation tests reported herein.  
In [39], the range of the maximums of the lateral acceleration values recorded during the overtaking maneuvers in the real traffic has been specified as 0.3-3.2 m/s\({}^{2}\). The averaged values of these maximums were in the range of 0.99-2.01 m/s\({}^{2}\).