## 1 Introduction
Such models are used, inter alia, in the development of driver assistance systems, autonomous vehicles [20; 21], or accident reconstruction programs [22; 23; 24; 25]. These programs very often do not take into account the impact of the driver during the road accident and the defensive reactions undertaken by the driver at that time. In the paper [26], the authors described a model of driver behaviour using the information obtained from the vehicle motion sensors. In the study [27], the authors proposed a method for the real-time identification of a driver model. This method requires the calculation of simple motion parameters: yaw rate, steering angle, and velocity. In the paper [28], the analysis of the driver behaviour in semi-autonomous driving was described. The authors determined how the message accompanying the car's autonomous driving affects the driver's behaviour. Various driver models are used to analyse the driver-vehicle-road (surroundings) relationship. These models describe typical driver behaviour without taking into account the abundance of possible driver reactions in different road situations. It is very difficult to build a complete driver model that takes into account most of the driver's psychophysical characteristics, even with the use of computerised calculation techniques. The cooperation of specialists from various fields of science, such as medicine, psychology, and technology, still does not entail the creation of a full description of driver's behaviour. Yet, such a model should cover the full spectrum of the driver's actions. In modelling the driver's behaviour, the aim is to ensure that the results of the analyses and modelling accurately reflect the drivers' reactions and are consistent with the real world. Driver behaviour research is often based on the observation of the way drivers act in road traffic, during research conducted according to certain formulated tests in staged situations on separate test sections or special simulators. This paper analyses many of the driver models related to the driver's actions in critical situations. The first created driver models are currently referred to as compensatory models [29]. Their operation was based on the driver's ongoing compensation for the vehicle position error concerning the assumed traffic path. However, due to their simplicity, such models could not be used to simulate many manoeuvres. They were not intended to take into account the fact that a driver, when observing the road ahead of the vehicle, tries to define a strategy for further action. In the anticipation models [30; 31; 32; 33], the driver acted by compensating for the position error based on the expected position of the vehicle at a certain distance from it. Despite this action from the driver, the simulated motion path of a car could still be different from the real one. Therefore, further predictive models were developed [34], in which a driver was able to anticipate the future position of the car at a certain anticipation distance [35; 36; 37; 38; 39]. In other models, both anticipatory and compensatory activities were taken into account. An example of such a model can be, e.g., the Dong model [40; 41]. In his work [42; 43], [PERSON] assumed a simple process of processing the image seen by a driver, the so-called optical flow, as the basis for driving a car. In this process, the driver reacted to a change in the position of two borderlines (two road edges or lines limiting a given lane). Many models, based on visible information reaching the driver, were created [44]. The proposed model also uses such information, and many methods of determining the position of other objects can be used, e.g., radars, ultrasonic sensors, or laser sensors. In the study described in the paper [45], the authors proposed a speed model of the vehicle motion on the curve. That model uses driving styles and other factors related to vehicle and road. The authors proposed a model that reflects, e.g., the speed preferences determined for three different types of drivers.