## 2 Description of the Assumption of the Driver Model  
The new driver model proposed in this publication uses a modified potential field method. The use of some elements from the potential field method [70; 71; 72; 73] used in robotics has created the possibility of a new approach for determining the algorithm of driver behaviour in road emergency situations. This method is widely used due to its ease of physical interpretation. Possible obstacles may arise in the course of traffic, and the situation changes dynamically, although in this respect the vehicle is characterised by a slightly different specificity. This is all the more important in emergencies [74; 75; 76; 77; 78]. A similar method, described in the paper [79], was used for the mobile robot path planning. The artificial potential field method was used to find the parameters to determine a safe path of motion. The paper [80] described a path planning method for an autonomous mobile robot, called the discrete artificial potential field (DAPF). The DAPF algorithm is capable of finding a collision-free path for a mobile robot in static and dynamic environments. The authors of the cited paper proposed the path optimisation algorithm (POA), which should modify the collision-free path to obtain a smoother and shorter path. A driver, while driving, reacts to visible information and chooses the planned position of the vehicle, which has been defined as the target point, but also takes into account the existence of the obstacle and the edge of the roadway. A similar situation should be taken into account in the accident reconstruction process. The position of the vehicle and any obstacles in the space around the vehicle are known. The aim is to keep the vehicle in the lane for safety reasons. When modelling the driver's behaviour in a specific traffic situation (Figure 2), the effect on point \(q(x_{v}\), \(y_{v})\), which is the centre of the vehicle's mass, of artificial potential fields from an obstacle, from both sides of the road and the target point, was taken into account. In this paper, an analysis of a similar obstacle avoidance process that uses one obstacle was described [81]. The value of the potential field \(U(q)\) and affecting point \(q(x_{v},y_{v})\) in a fixed coordinate system \((x,y)\) was determined. The field consists of the interactions from the above-mentioned factors: target point, obstacle, and edge of the road. The value of the potential field is expressed with the following Equation (4):  
\[U(q)=U_{T}(q)+U_{O}(q)+\sum_{j=1}^{2}U_{Bj}(q) \tag{4}\]  
where  
\(U_{T}(q)\)--potential field to the target point;  
\(U_{O}(q)\)--potential field from the obstacle;  
\(U_{Bj}(q)\)--potential field from the left and right edge of the roadway. In many papers describing in particular the research on the creation and verification of anticipation (prediction) models, the authors determine the location of the traffic destination point. It is \"set\" by the driver on the road, at a certain distance in front of the car--often called the anticipation section. In the model, we will refer to this car destination point as the target point. The potential of the field \(U_{T}\) being attracted to the target point can be defined as follows:  
\[U_{T}(q)=\frac{1}{2}k_{T}L^{2}(q) \tag{5}\]  
where  
\(L(q)\)--distance to the target points;  
\(k_{T}\)--scaling coefficient of the potential. In developing the model concept, it was assumed that the target point is not a fixed point but is at a certain distance \(L\) in front of the vehicle. The concept of the observation section was used (similar to the anticipation models). The distance to the target point depends not only on the psychophysical capabilities and perception of the driver (e.g., eyesight condition) but also on the way the road is shaped. In the case of straight road sections and low traffic volumes, this distance can be assumed to be greater because the driver can \"look\" further ahead and \"set\" the assumed target point at a greater distance.