## 3 Simulation Results  
For the road situation presented in Figure 4, a computer simulation of the obstacle avoidance manoeuvre and the obtained values of the potential hazard and then the steering wheel angle was carried out. The simulation verified how the assumed shapes of the safety zone around the analysed objects affect the obtained parameters of potential hazards and the driver's response. The following parameters were used in the simulation:  
* The beginning of the \(x\), \(y\) coordinate system is situated on the border of the road and sidewalk;
* The vehicle in its initial position moves in the middle of the right lane--initial position of the vehicle: \(x_{o}=0\) m, \(y_{o}=1.5\) m;
* Vehicle dimensions: length--4.1 m, width--1.8 m;
* The initial longitudinal speed of the vehicle is assumed to be \(V_{Lg}=40\) km/h, with the vehicle running parallel to the edge of the roadway, so the lateral speed is assumed to be \(V_{Lt}=0\) km/h;
* The obstacle (pedestrian) speed is assumed as follows: longitudinal \(V_{Lg}=0\) km/h, lateral \(V_{Lt}=0\dots\) 3 km/h;
* The obstacle (pedestrian) at the initial moment is in the middle of the sidewalk, at a specified distance from the vehicle \(x_{o}=30\) m. The width of the sidewalk is 1 m; hence, the initial position \(y_{o}=-0.5\) m;
* The width of the roadway is 6 m, and the width of the lane is 3 m.  
Examples of dimensions of safety zones around the vehicle and obstacle (e.g., man, dog) are shown in Figure 5.  
Figure 6 shows how the value of the radius \(R_{V}\) (see the scheme from Figure 4) changes during a simulated drive for the two selected safety zone shapes around the vehicle. As can be seen from the presented scheme, when we are dealing with a safety zone in the form of a rectangle, there are visible sharp refractions of the obtained characteristics, caused by the occurrence of \"corners\" of the rectangular safety zone. The use of an elliptical-shaped vehicle zone eliminates these. Figure 7 shows how the value of the distance \(p^{\prime}{}_{O}\) (see Figure 4) changes during a simulated drive for different shapes of the vehicles and obstacle safety zones. Four different configurations of safety zone shapes were analysed. It was observed that the shape of the obstacle safety zone (when it is small in relation to the vehicle) has a very slight influence on the change of the \(p^{\prime}{}_{O}\) parameter. Figure 5: Size of the safety zone dimensions used in the simulation; (**a**) vehicle rectangular, (**b**) vehicle elliptical, (**c**) pedestrian circular, (**d**) pedestrian elliptical. Figure 6: \(R_{V}\) parameter change depending on the shape of the safety zone around the vehicle: (**a**) rectangle, (**b**) ellipse. Figure 8 shows the results of simulations which show how the distance between the safety zones of the vehicle change in the \(y\)-axis direction for different zone shapes and different speeds of the lateral movement of the obstacle. Figure 8: Distance in \(y\)-axis direction between safety zones for different lateral speeds (km/h) of the obstacle: (**a**) vehicle—rectangle, obstacle—circle; (**b**) vehicle—rectangle, obstacle—ellipse; (**c**) vehicle—ellipse, obstacle—circle; (**d**) vehicle—ellipse, obstacle—ellipse. Figure 7: Change of \(p^{\prime}o\) values, depending on the shape of the safety zone around the vehicle and the obstacle: (**a**) vehicle—rectangle, obstacle—circle; (**b**) vehicle—rectangle, obstacle—ellipse; (**c**) vehicle—ellipse, obstacle—circle; (**d**) vehicle—ellipse, obstacle—ellipse. The analysed distance changes in a similar manner, where on schemes from Figure 8, slight refractions, originating in the rectangular shape of the safety zone of the vehicle, are visible. Assuming no change in the vehicle's position in the \(y\)-axis direction, the distance between safety zones is reduced with the increase in obstacle speed. In this specific case, there is a maximum speed at which the safety zones will come into contact with each other and, if exceeded, they will interfere with each other.