Fuzzy Logic-based Techniques for Human Driver Behavior Modelling during a Simple Lane-changing Task

IFAC PapersOnLine 58-9 (2024) 257–262 ScienceDirect ScienceDirect Available online at www.sciencedirect.com 2405-8963 Copyright © 2024 The Authors. This is an open access article under the CC BY-NC-ND license . Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2024.07.406 10.1016/j.ifacol.2024.07.406 2405-8963 Fuzzy Logic-based Techniques for Human Driver Behavior Modelling during a Simple Lane-changing Task M. Jirgl*, M. Mesarosova**, P. Fiedler***, J. Arm**** Department of Control and Instrumentation, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 616 00 Brno, Czech Republic *(e-mail: [email protected]), **(e-mail: [email protected]), ***(e-mail: [email protected]), ****(e-mail: [email protected]). Abstract: The paper presents an experiment with fuzzy-logic-based models for approximating data representing human driver behavior during a simple lane-changing task. Data are acquired via the selfdeveloped car driving simulator under defined conditions. Three fuzzy-logic-based models are considered: fuzzy Hammerstein model, fuzzy PD controller with a fixed structure (analogy to the linear PD controller) and fuzzy PD controller with an optimized structure. A comparison of the effectiveness of the individual approaches was evaluated using a criterion representing the fitness of the model output and the measured data. Although only one dataset was considered in the frame of this paper, the results indicate an investigative potential of the fuzzy models for this kind of task connected with the modelling of human behavior. Keywords: Human driver model, Hammerstein model, fuzzy logic, fuzzy controller, car driving simulator. 1. INTRODUCTION Human behavior assessment is still a current topic in many different areas. It is especially important in critical applications such as driving or piloting tasks. Most of the approaches are based on finding a suitable behavioral model (Mulder et al., 2018), (Xu, et al., 2017). Modelling of human behavior is a challenging task because a human being is a very versatile system and his/her decision processes defining the resulting control actions are dependent on many circumstances such as type of control task, controlled dynamics, current situation, or other influencing and environmental factors. Due to the listed factors, an effort to develop a general structure of the mathematical model valid for various situations is very difficult. In (Mulder et al., 2018), the authors summarized a state-of-theart and proposed an adaptive control model considering human adaptation based on learning and gaining experience. Such a general framework can be used for modelling human behavior during various tasks. Employing this model lies in analyzing cognitive processing on different levels of human control. However, most researches are focused on the description and modelling of human control actions as a whole. This process requires specifying the control task and definition of the testing conditions. Then, human behavior can be modelled via different approaches. Most of them concentrate on driver or pilot modelling during specific tasks. The most famous are McRuer’s models (McRuer and Krendel, 1974), Hess’ structural models (Hess, 2009), and Hossmanns’ models (Zaychik, 2006). These methods describe human control using linear systems in form of the transfer functions or multi-loop models based on state-space control. Recent literature focuses especially on the more advanced models in the form of statespace linear and non-linear controllers mostly employing MPC – Model Predictive Control), see (Nash and Cole 2018). . These advanced models can approximate human (driver) behavior with sufficient accuracy and are very effective in the prediction of human control actions. On the other hand, the disadvantages of such models are higher complexity, difficult interpretation of the parameters, and consuming optimization. Previous research of the authors was focused on finding a suitable structure for the pilot and driver behavioral model approximating human control actions during a simple task; this model should provide a set of parameters representing dynamical properties. The goal of the research was to develop a method for the evaluation of human performance based on measuring his/her responses to the desired input signal during specific tasks involving different controlled dynamics. For this purpose, the testing was carried out on drivingand flightsimulators. Description of the testing process and the results were published e.g. in (Jalovecky et al., 2021), (Jirgl et al., 2022). From this perspective, the simple McRuer’s models in the form of transfer functions were identified as an optimal structure for approximating human behavior in simple tasks, such as responses to the step changes of the desired value (when disturbances are excluded) during driving or piloting. Although the proposed McRuer’s models are able to provide satisfactory precision, the whole MMS (Man-Machine System) interaction is limited to approximation using pure linear behavior using linearization. This simplification could have a negative influence on the modelling process in some cases. On the other hand, complex non-linear models similar to those presented in (Nash and Cole, 2018) can be inefficient for our research activity. Mihalik (Mihalik and Fiedler, 2022) proposed and tested the Hammerstein model as an extension of the used linear model Fuzzy Logic-based Techniques for Human Driver Behavior Modelling during a Simple Lane-changing Task M. Jirgl*, M. Mesarosova**, P. Fiedler***, J. Arm**** Department of Control and Instrumentation, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 616 00 Brno, Czech Republic *(e-mail: [email protected]), **(e-mail: [email protected]), ***(e-mail: [email protected]), ****(e-mail: [email protected]). Abstract: The paper presents an experiment with fuzzy-logic-based models for approximating data representing human driver behavior during a simple lane-changing task. Data are acquired via the selfdeveloped car driving simulator under defined conditions. Three fuzzy-logic-based models are considered: fuzzy Hammerstein model, fuzzy PD controller with a fixed structure (analogy to the linear PD controller) and fuzzy PD controller with an optimized structure. A comparison of the effectiveness of the individual approaches was evaluated using a criterion representing the fitness of the model output and the measured data. Although only one dataset was considered in the frame of this paper, the results indicate an investigative potential of the fuzzy models for this kind of task connected with the modelling of human behavior. Keywords: Human driver model, Hammerstein model, fuzzy logic, fuzzy controller, car driving simulator. 1. INTRODUCTION Human behavior assessment is still a current topic in many different areas. It is especially important in critical applications such as driving or piloting tasks. Most of the approaches are based on finding a suitable behavioral model (Mulder et al., 2018), (Xu, et al., 2017). Modelling of human behavior is a challenging task because a human being is a very versatile system and his/her decision processes defining the resulting control actions are dependent on many circumstances such as type of control task, controlled dynamics, current situation, or other influencing and environmental factors. Due to the listed factors, an effort to develop a general structure of the mathematical model valid for various situations is very difficult. In (Mulder et al., 2018), the authors summarized a state-of-theart and proposed an adaptive control model considering human adaptation based on learning and gaining experience. Such a general framework can be used for modelling human behavior during various tasks. Employing this model lies in analyzing cognitive processing on different levels of human control. However, most researches are focused on the description and modelling of human control actions as a whole. This process requires specifying the control task and definition of the testing conditions. Then, human behavior can be modelled via different approaches. Most of them concentrate on driver or pilot modelling during specific tasks. The most famous are McRuer’s models (McRuer and Krendel, 1974), Hess’ structural models (Hess, 2009), and Hossmanns’ models (Zaychik, 2006). These methods describe human control using linear systems in form of the transfer functions or multi-loop models based on state-space control. Recent literature focuses especially on the more advanced models in the form of statespace linear and non-linear controllers mostly employing MPC – Model Predictive Control), see (Nash and Cole 2018). . These advanced models can approximate human (driver) behavior with sufficient accuracy and are very effective in the prediction of human control actions. On the other hand, the disadvantages of such models are higher complexity, difficult interpretation of the parameters, and consuming optimization. Previous research of the authors was focused on finding a suitable structure for the pilot and driver behavioral model approximating human control actions during a simple task; this model should provide a set of parameters representing dynamical properties. The goal of the research was to develop a method for the evaluation of human performance based on measuring his/her responses to the desired input signal during specific tasks involving different controlled dynamics. For this purpose, the testing was carried out on drivingand flightsimulators. Description of the testing process and the results were published e.g. in (Jalovecky et al., 2021), (Jirgl et al., 2022). From this perspective, the simple McRuer’s models in the form of transfer functions were identified as an optimal structure for approximating human behavior in simple tasks, such as responses to the step changes of the desired value (when disturbances are excluded) during driving or piloting. Although the proposed McRuer’s models are able to provide satisfactory precision, the whole MMS (Man-Machine System) interaction is limited to approximation using pure linear behavior using linearization. This simplification could have a negative influence on the modelling process in some cases. On the other hand, complex non-linear models similar to those presented in (Nash and Cole, 2018) can be inefficient for our research activity. Mihalik (Mihalik and Fiedler, 2022) proposed and tested the Hammerstein model as an extension of the used linear model Fuzzy Logic-based Techniques for Human Driver Behavior Modelling during a Simple Lane-changing Task M. Jirgl*, M. Mesarosova**, P. Fiedler***, J. Arm**** Department of Control and Instrumentation, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 616 00 Brno, Czech Republic *(e-mail: [email protected]), **(e-mail: [email protected]), ***(e-mail: [email protected]), ****(e-mail: [email protected]). Abstract: The paper presents an experiment with fuzzy-logic-based models for approximating data representing human driver behavior during a simple lane-changing task. Data are acquired via the selfdeveloped car driving simulator under defined conditions. Three fuzzy-logic-based models are considered: fuzzy Hammerstein model, fuzzy PD controller with a fixed structure (analogy to the linear PD controller) and fuzzy PD controller with an optimized structure. A comparison of the effectiveness of the individual approaches was evaluated using a criterion representing the fitness of the model output and the measured data. Although only one dataset was considered in the frame of this paper, the results indicate an investigative potential of the fuzzy models for this kind of task connected with the modelling of human behavior. Keywords: Human driver model, Hammerstein model, fuzzy logic, fuzzy controller, car driving simulator. 1. INTRODUCTION Human behavior assessment is still a current topic in many different areas. It is especially important in critical applications such as driving or piloting tasks. Most of the approaches are based on finding a suitable behavioral model (Mulder et al., 2018), (Xu, et al., 2017). Modelling of human behavior is a challenging task because a human being is a very versatile system and his/her decision processes defining the resulting control actions are dependent on many circumstances such as type of control task, controlled dynamics, current situation, or other influencing and environmental factors. Due to the listed factors, an effort to develop a general structure of the mathematical model valid for various situations is very difficult. In (Mulder et al., 2018), the authors summarized a state-of-theart and proposed an adaptive control model considering human adaptation based on learning and gaining experience. Such a general framework can be used for modelling human behavior during various tasks. Employing this model lies in analyzing cognitive processing on different levels of human control. However, most researches are focused on the description and modelling of human control actions as a whole. This process requires specifying the control task and definition of the testing conditions. Then, human behavior can be modelled via different approaches. Most of them concentrate on driver or pilot modelling during specific tasks. The most famous are McRuer’s models (McRuer and Krendel, 1974), Hess’ structural models (Hess, 2009), and Hossmanns’ models (Zaychik, 2006). These methods describe human control using linear systems in form of the transfer functions or multi-loop models based on state-space control. Recent literature focuses especially on the more advanced models in the form of statespace linear and non-linear controllers mostly employing MPC – Model Predictive Control), see (Nash and Cole 2018). . These advanced models can approximate human (driver) behavior with sufficient accuracy and are very effective in the prediction of human control actions. On the other hand, the disadvantages of such models are higher complexity, difficult interpretation of the parameters, and consuming optimization. Previous research of the authors was focused on finding a suitable structure for the pilot and driver behavioral model approximating human control actions during a simple task; this model should provide a set of parameters representing dynamical properties. The goal of the research was to develop a method for the evaluation of human performance based on measuring his/her responses to the desired input signal during specific tasks involving different controlled dynamics. For this purpose, the testing was carried out on drivingand flightsimulators. Description of the testing process and the results were published e.g. in (Jalovecky et al., 2021), (Jirgl et al., 2022). From this perspective, the simple McRuer’s models in the form of transfer functions were identified as an optimal structure for approximating human behavior in simple tasks, such as responses to the step changes of the desired value (when disturbances are excluded) during driving or piloting. Although the proposed McRuer’s models are able to provide satisfactory precision, the whole MMS (Man-Machine System) interaction is limited to approximation using pure linear behavior using linearization. This simplification could have a negative influence on the modelling process in some cases. On the other hand, complex non-linear models similar to those presented in (Nash and Cole, 2018) can be inefficient for our research activity. Mihalik (Mihalik and Fiedler, 2022) proposed and tested the Hammerstein model as an extension of the used linear model Fuzzy Logic-based Techniques for Human Driver Behavior Modelling during a Simple Lane-changing Task M. Jirgl*, M. Mesarosova**, P. Fiedler***, J. Arm**** Department of Control and Instrumentation, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 616 00 Brno, Czech Republic *(e-mail: [email protected]), **(e-mail: [email protected]), ***(e-mail: fied[email protected]), ****(e-mail: a[email protected]). Abstract: The paper presents an experiment with fuzzy-logic-based models for approximating data representing human driver behavior during a simple lane-changing task. Data are acquired via the selfdeveloped car driving simulator under defined conditions. Three fuzzy-logic-based models are considered: fuzzy Hammerstein model, fuzzy PD controller with a fixed structure (analogy to the linear PD controller) and fuzzy PD controller with an optimized structure. A comparison of the effectiveness of the individual approaches was evaluated using a criterion representing the fitness of the model output and the measured data. Although only one dataset was considered in the frame of this paper, the results indicate an investigative potential of the fuzzy models for this kind of task connected with the modelling of human behavior. Keywords: Human driver model, Hammerstein model, fuzzy logic, fuzzy controller, car driving simulator. 1. INTRODUCTION Human behavior assessment is still a current topic in many different areas. It is especially important in critical applications such as driving or piloting tasks. Most of the approaches are based on finding a suitable behavioral model (Mulder et al., 2018), (Xu, et al., 2017). Modelling of human behavior is a challenging task because a human being is a very versatile system and his/her decision processes defining the resulting control actions are dependent on many circumstances such as type of control task, controlled dynamics, current situation, or other influencing and environmental factors. Due to the listed factors, an effort to develop a general structure of the mathematical model valid for various situations is very difficult. In (Mulder et al., 2018), the authors summarized a state-of-theart and proposed an adaptive control model considering human adaptation based on learning and gaining experience. Such a general framework can be used for modelling human behavior during various tasks. Employing this model lies in analyzing cognitive processing on different levels of human control. However, most researches are focused on the description and modelling of human control actions as a whole. This process requires specifying the control task and definition of the testing conditions. Then, human behavior can be modelled via different approaches. Most of them concentrate on driver or pilot modelling during specific tasks. The most famous are McRuer’s models (McRuer and Krendel, 1974), Hess’ structural models (Hess, 2009), and Hossmanns’ models (Zaychik, 2006). These methods describe human control using linear systems in form of the transfer functions or multi-loop models based on state-space control. Recent literature focuses especially on the more advanced models in the form of statespace linear and non-linear controllers mostly employing MPC – Model Predictive Control), see (Nash and Cole 2018). . These advanced models can approximate human (driver) behavior with sufficient accuracy and are very effective in the prediction of human control actions. On the other hand, the disadvantages of such models are higher complexity, difficult interpretation of the parameters, and consuming optimization. Previous research of the authors was focused on finding a suitable structure for the pilot and driver behavioral model approximating human control actions during a simple task; this model should provide a set of parameters representing dynamical properties. The goal of the research was to develop a method for the evaluation of human performance based on measuring his/her responses to the desired input signal during specific tasks involving different controlled dynamics. For this purpose, the testing was carried out on drivingand flightsimulators. Description of the testing process and the results were published e.g. in (Jalovecky et al., 2021), (Jirgl et al., 2022). From this perspective, the simple McRuer’s models in the form of transfer functions were identified as an optimal structure for approximating human behavior in simple tasks, such as responses to the step changes of the desired value (when disturbances are excluded) during driving or piloting. Although the proposed McRuer’s models are able to provide satisfactory precision, the whole MMS (Man-Machine System) interaction is limited to approximation using pure linear behavior using linearization. This simplification could have a negative influence on the modelling process in some cases. On the other hand, complex non-linear models similar to those presented in (Nash and Cole, 2018) can be inefficient for our research activity. Mihalik (Mihalik and Fiedler, 2022) proposed and tested the Hammerstein model as an extension of the used linear model Fuzzy Logic-based Techniques for Human Driver Behavior Modelling during a Simple Lane-changing Task M. Jirgl*, M. Mesarosova**, P. Fiedler***, J. Arm**** Department of Control and Instrumentation, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 616 00 Brno, Czech Republic *(e-mail: [email protected]), **(e-mail: [email protected]), ***(e-mail: [email protected]), ****(e-mail: [email protected]). Abstract: The paper presents an experiment with fuzzy-logic-based models for approximating data representing human driver behavior during a simple lane-changing task. Data are acquired via the selfdeveloped car driving simulator under defined conditions. Three fuzzy-logic-based models are considered: fuzzy Hammerstein model, fuzzy PD controller with a fixed structure (analogy to the linear PD controller) and fuzzy PD controller with an optimized structure. A comparison of the effectiveness of the individual approaches was evaluated using a criterion representing the fitness of the model output and the measured data. Although only one dataset was considered in the frame of this paper, the results indicate an investigative potential of the fuzzy models for this kind of task connected with the modelling of human behavior. Keywords: Human driver model, Hammerstein model, fuzzy logic, fuzzy controller, car driving simulator. 1. INTRODUCTION Human behavior assessment is still a current topic in many different areas. It is especially important in critical applications such as driving or piloting tasks. Most of the approaches are based on finding a suitable behavioral model (Mulder et al., 2018), (Xu, et al., 2017). Modelling of human behavior is a challenging task because a human being is a very versatile system and his/her decision processes defining the resulting control actions are dependent on many circumstances such as type of control task, controlled dynamics, current situation, or other influencing and environmental factors. Due to the listed factors, an effort to develop a general structure of the mathematical model valid for various situations is very difficult. In (Mulder et al., 2018), the authors summarized a state-of-theart and proposed an adaptive control model considering human adaptation based on learning and gaining experience. Such a general framework can be used for modelling human behavior during various tasks. Employing this model lies in analyzing cognitive processing on different levels of human control. However, most researches are focused on the description and modelling of human control actions as a whole. This process requires specifying the control task and definition of the testing conditions. Then, human behavior can be modelled via different approaches. Most of them concentrate on driver or pilot modelling during specific tasks. The most famous are McRuer’s models (McRuer and Krendel, 1974), Hess’ structural models (Hess, 2009), and Hossmanns’ models (Zaychik, 2006). These methods describe human control using linear systems in form of the transfer functions or multi-loop models based on state-space control. Recent literature focuses especially on the more advanced models in the form of statespace linear and non-linear controllers mostly employing MPC – Model Predictive Control), see (Nash and Cole 2018). . These advanced models can approximate human (driver) behavior with sufficient accuracy and are very effective in the prediction of human control actions. On the other hand, the disadvantages of such models are higher complexity, difficult interpretation of the parameters, and consuming optimization. Previous research of the authors was focused on finding a suitable structure for the pilot and driver behavioral model approximating human control actions during a simple task; this model should provide a set of parameters representing dynamical properties. The goal of the research was to develop a method for the evaluation of human performance based on measuring his/her responses to the desired input signal during specific tasks involving different controlled dynamics. For this purpose, the testing was carried out on drivingand flightsimulators. Description of the testing process and the results were published e.g. in (Jalovecky et al., 2021), (Jirgl et al., 2022). From this perspective, the simple McRuer’s models in the form of transfer functions were identified as an optimal structure for approximating human behavior in simple tasks, such as responses to the step changes of the desired value (when disturbances are excluded) during driving or piloting. Although the proposed McRuer’s models are able to provide satisfactory precision, the whole MMS (Man-Machine System) interaction is limited to approximation using pure linear behavior using linearization. This simplification could have a negative influence on the modelling process in some cases. On the other hand, complex non-linear models similar to those presented in (Nash and Cole, 2018) can be inefficient for our research activity. Mihalik (Mihalik and Fiedler, 2022) proposed and tested the Hammerstein model as an extension of the used linear model Fuzzy Logic-based Techniques for Human Driver Behavior Modelling during a Simple Lane-changing Task M. Jirgl*, M. Mesarosova**, P. Fiedler***, J. Arm**** Department of Control and Instrumentation, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 616 00 Brno, Czech Republic *(e-mail: [email protected]), **(e-mail: [email protected]), ***(e-mail: [email protected]), ****(e-mail: [email protected]). Abstract: The paper presents an experiment with fuzzy-logic-based models for approximating data representing human driver behavior during a simple lane-changing task. Data are acquired via the selfdeveloped car driving simulator under defined conditions. Three fuzzy-logic-based models are considered: fuzzy Hammerstein model, fuzzy PD controller with a fixed structure (analogy to the linear PD controller) and fuzzy PD controller with an optimized structure. A comparison of the effectiveness of the individual approaches was evaluated using a criterion representing the fitness of the model output and the measured data. Although only one dataset was considered in the frame of this paper, the results indicate an investigative potential of the fuzzy models for this kind of task connected with the modelling of human behavior. Keywords: Human driver model, Hammerstein model, fuzzy logic, fuzzy controller, car driving simulator. 1. INTRODUCTION Human behavior assessment is still a current topic in many different areas. It is especially important in critical applications such as driving or piloting tasks. Most of the approaches are based on finding a suitable behavioral model (Mulder et al., 2018), (Xu, et al., 2017). Modelling of human behavior is a challenging task because a human being is a very versatile system and his/her decision processes defining the resulting control actions are dependent on many circumstances such as type of control task, controlled dynamics, current situation, or other influencing and environmental factors. Due to the listed factors, an effort to develop a general structure of the mathematical model valid for various situations is very difficult. In (Mulder et al., 2018), the authors summarized a state-of-theart and proposed an adaptive control model considering human adaptation based on learning and gaining experience. Such a general framework can be used for modelling human behavior during various tasks. Employing this model lies in analyzing cognitive processing on different levels of human control. However, most researches are focused on the description and modelling of human control actions as a whole. This process requires specifying the control task and definition of the testing conditions. Then, human behavior can be modelled via different approaches. Most of them concentrate on driver or pilot modelling during specific tasks. The most famous are McRuer’s models (McRuer and Krendel, 1974), Hess’ structural models (Hess, 2009), and Hossmanns’ models (Zaychik, 2006). These methods describe human control using linear systems in form of the transfer functions or multi-loop models based on state-space control. Recent literature focuses especially on the more advanced models in the form of statespace linear and non-linear controllers mostly employing MPC – Model Predictive Control), see (Nash and Cole 2018). . These advanced models can approximate human (driver) behavior with sufficient accuracy and are very effective in the prediction of human control actions. On the other hand, the disadvantages of such models are higher complexity, difficult interpretation of the parameters, and consuming optimization. Previous research of the authors was focused on finding a suitable structure for the pilot and driver behavioral model approximating human control actions during a simple task; this model should provide a set of parameters representing dynamical properties. The goal of the research was to develop a method for the evaluation of human performance based on measuring his/her responses to the desired input signal during specific tasks involving different controlled dynamics. For this purpose, the testing was carried out on drivingand flightsimulators. Description of the testing process and the results were published e.g. in (Jalovecky et al., 2021), (Jirgl et al., 2022). From this perspective, the simple McRuer’s models in the form of transfer functions were identified as an optimal structure for approximating human behavior in simple tasks, such as responses to the step changes of the desired value (when disturbances are excluded) during driving or piloting. Although the proposed McRuer’s models are able to provide satisfactory precision, the whole MMS (Man-Machine System) interaction is limited to approximation using pure linear behavior using linearization. This simplification could have a negative influence on the modelling process in some cases. On the other hand, complex non-linear models similar to those presented in (Nash and Cole, 2018) can be inefficient for our research activity. Mihalik (Mihalik and Fiedler, 2022) proposed and tested the Hammerstein model as an extension of the used linear model Copyright © 2024 The Authors. This is an open access article under the CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4.0/ ) 258 M. Jirgl et al. / IFAC PapersOnLine 58-9 (2024) 257–262 by identifying static non-linearity; this non-linearity was modelled via a fuzzy system. The idea of modelling based on fuzzy logic is investigated in more detail also in the frame of this paper. The field of fuzzy logic was introduced as early as 1965 by Lotfi A. Zadeh of the University of California, Berkeley, and has been intensively researched ever since. The expansion and development of computer technology enabled the implementation of systems using fuzzy elements, thanks to which it was possible to further investigate the applicability of this theory in various scientific fields (Ross, 2004). The main reason for the origination of fuzzy logic was an effort to get closer to human reasoning. Such an idea makes this tool effective also for the modelling of human behavior during specific tasks (Kolarik and Slanina, 2017). The goal of the paper is to investigate and compare the fuzzy logic-based techniques for modelling human behavior during a lane-changing task implemented on the self-developed driving simulator. 2. DATA ACQUISITION Modelling human driver behavior is based on the model structure proposal and identifying the parameters. Acquiring data characterizing human behavior during an investigated task is a vital part of the whole experiment. This data generated during a given activity can provide comprehensive information about the habits and learned routines of the human operator (driver). However, the data collection process also has certain limitations that prevent the examination of various situations under defined conditions. These limitations consist on the one hand of the costs incurred and on the other hand of the safety of the performed measurements, or tests. A suitable alternative is employing simulators or simulation technologies (Roesener, 2018). In this experiment, the drivers’ testing was carried out on the in-house developed car driving simulator (CDS), see Fig. 1. Figure 1. The workstation with developed CDS for driver testing. The simulator software was developed in Unreal Engine 4 (UE4) and enables the definition of custom testing scenarios, or storing measured and virtual data (under sufficient sampling rate) in a .csv file. The car model is built on NVIDIA PhysX. The implemented testing scenarios represent different driving situations under specific conditions. More detailed information about the CDS as well as the reasons leading to the development of this solution can be found in (Michalik et al., 2021). The Step response scenario was employed in this research. This scenario provides a simple lane-changing task under a defined car speed (here 90 km/h) kept by the speed limiter. The demand to change a lane is visualized by a green arrow in front of the driver’s view, as well as by an implemented lane assistant. The whole testing process is described in (Jirgl et al., 2022) in more detail. The measured data are logged for the individual drivers under a unique ID into a .csv file and include e.g. time vector – t, distance from the center of the desired lane – e(t), and steering wheel rotation (the driver’s control actions) – u(t). An example of the measured data (applied for the presented experiments) for a selected driver no.69 is in Fig. 2. Figure 2. Data representing the distance from the center of the desired lane – e(t), and corresponding control actions u(t) of driver no.69 as a response to the lane-change demands. 3. FUZZY HAMMERSTEIN MODEL A traditional Hammerstein's (or Wiener's) non-linear dynamical model can be used provided that the non-linear behavior of the system can be easily identified and separated from the linear dynamic part. This idea results in a model containing a static non-linearity at the input of the model, followed by a linear dynamical part – H(s), see Fig. 3. Figure 3. Structure of the Hammerstein model. In the context of this paper, the linear part can be modelled by a model in the form of the transfer function (1): 𝐻𝐻(𝑠𝑠)=𝐾𝐾𝑠𝑠 (𝑇𝑇2𝑠𝑠2+2𝜉𝜉𝑇𝑇𝑠𝑠+1) 𝑒𝑒−𝑠𝑠𝑠𝑠 , (1) where 𝐾𝐾 – driver’s gain, 𝑇𝑇− time constant [s], 𝜉𝜉 – damping, 𝜏𝜏 – reaction delay [s], 𝑠𝑠 – the Laplace operator. Linear system 𝑒𝑒 𝐻𝐻(𝑠𝑠) Non-linear part 𝑓𝑓(𝑒𝑒) 𝑢𝑢 M. Jirgl et al. / IFAC PapersOnLine 58-9 (2024) 257–262 259 by identifying static non-linearity; this non-linearity was modelled via a fuzzy system. The idea of modelling based on fuzzy logic is investigated in more detail also in the frame of this paper. The field of fuzzy logic was introduced as early as 1965 by Lotfi A. Zadeh of the University of California, Berkeley, and has been intensively researched ever since. The expansion and development of computer technology enabled the implementation of systems using fuzzy elements, thanks to which it was possible to further investigate the applicability of this theory in various scientific fields (Ross, 2004). The main reason for the origination of fuzzy logic was an effort to get closer to human reasoning. Such an idea makes this tool effective also for the modelling of human behavior during specific tasks (Kolarik and Slanina, 2017). The goal of the paper is to investigate and compare the fuzzy logic-based techniques for modelling human behavior during a lane-changing task implemented on the self-developed driving simulator. 2. DATA ACQUISITION Modelling human driver behavior is based on the model structure proposal and identifying the parameters. Acquiring data characterizing human behavior during an investigated task is a vital part of the whole experiment. This data generated during a given activity can provide comprehensive information about the habits and learned routines of the human operator (driver). However, the data collection process also has certain limitations that prevent the examination of various situations under defined conditions. These limitations consist on the one hand of the costs incurred and on the other hand of the safety of the performed measurements, or tests. A suitable alternative is employing simulators or simulation technologies (Roesener, 2018). In this experiment, the drivers’ testing was carried out on the in-house developed car driving simulator (CDS), see Fig. 1. Figure 1. The workstation with developed CDS for driver testing. The simulator software was developed in Unreal Engine 4 (UE4) and enables the definition of custom testing scenarios, or storing measured and virtual data (under sufficient sampling rate) in a .csv file. The car model is built on NVIDIA PhysX. The implemented testing scenarios represent different driving situations under specific conditions. More detailed information about the CDS as well as the reasons leading to the development of this solution can be found in (Michalik et al., 2021). The Step response scenario was employed in this research. This scenario provides a simple lane-changing task under a defined car speed (here 90 km/h) kept by the speed limiter. The demand to change a lane is visualized by a green arrow in front of the driver’s view, as well as by an implemented lane assistant. The whole testing process is described in (Jirgl et al., 2022) in more detail. The measured data are logged for the individual drivers under a unique ID into a .csv file and include e.g. time vector – t, distance from the center of the desired lane – e(t), and steering wheel rotation (the driver’s control actions) – u(t). An example of the measured data (applied for the presented experiments) for a selected driver no.69 is in Fig. 2. Figure 2. Data representing the distance from the center of the desired lane – e(t), and corresponding control actions u(t) of driver no.69 as a response to the lane-change demands. 3. FUZZY HAMMERSTEIN MODEL A traditional Hammerstein's (or Wiener's) non-linear dynamical model can be used provided that the non-linear behavior of the system can be easily identified and separated from the linear dynamic part. This idea results in a model containing a static non-linearity at the input of the model, followed by a linear dynamical part – H(s), see Fig. 3. Figure 3. Structure of the Hammerstein model. In the context of this paper, the linear part can be modelled by a model in the form of the transfer function (1): 𝐻𝐻(𝑠𝑠)=𝐾𝐾𝑠𝑠 (𝑇𝑇2𝑠𝑠2+2𝜉𝜉𝑇𝑇𝑠𝑠+1) 𝑒𝑒−𝑠𝑠𝑠𝑠 , (1) where 𝐾𝐾 – driver’s gain, 𝑇𝑇− time constant [s], 𝜉𝜉 – damping, 𝜏𝜏 – reaction delay [s], 𝑠𝑠 – the Laplace operator. Linear system 𝑒𝑒 𝐻𝐻(𝑠𝑠) Non-linear part 𝑓𝑓(𝑒𝑒) 𝑢𝑢 The structure of the linear model was selected based on the discussion in (Jirgl et al., 2022). Subsequently, the type of static non-linearity needs to be identified as an input part of the Hammerstein model. 3.1 Experimental approach to non-linearity identification Because the common approaches for identifying non-linearity could not be applied due to the testing environment setup, the non-linearity had to be identified experimentally. The approach is based on applying a general n-th order polynomial of an input variable 𝑒𝑒 and with coefficients 𝑎𝑎𝑖𝑖 in the form of (2): 𝑓𝑓𝑛𝑛(𝑒𝑒)= ∑ 𝑎𝑎𝑖𝑖𝑒𝑒𝑖𝑖 𝑛𝑛 𝑖𝑖=0 , (2) Parameters of the Hammerstein model, consisting of a polynomial model of the non-linearity and transfer function model (1) as a linear part, were identified via the Hammerstein-Wiener Models tool from MATLAB System Identification Toolbox (SIT). The effectiveness of the polynomial application within the range from 3rd to 10th order (see Tab. 1) was evaluated via the Best fit parameter which is a percentual value of a complement to the Normalized Root Mean Square Error (NRMSE) (Ljung, 2022). The result labelled as zero polynomial order represents a pure linear model for possible comparison. Table 1. Comparison of Polynomial Degree Effectiveness. Polynomial order 0 3 4 5 Best fit [%] 49.50 51.98 52.92 56.59 The results indicate that polynomials with a higher order than 5th have a negligible effect on the accuracy of the model. Then, the identified 5th-order polynomial is: 𝑓𝑓5(𝑒𝑒)= −0.0065𝑒𝑒5−0.0033𝑒𝑒4+0.1461𝑒𝑒3+0.0323𝑒𝑒2 +0.2303𝑒𝑒+0.0716 . (3) The mentioned polynomial approximates the non-linearity in the perception of the deviation from the center of the desired lane e(t) in the interval 〈−4.5;4.5〉 m. The dependence of the non-linear function f(e) defined by the identified polynomial (3) on the deviation e from the indicated interval is shown in Fig. 5. Except for the extreme values, the trend of the characteristic indicates a decreased sensitivity near the zero value of the control error e; this may correspond to the given nature of the task connected with human perception. The parameters of the linear part were identified as 𝐾𝐾 = 0.005, 𝑇𝑇 = 0.52 s, 𝜉𝜉 =0.4, and 𝜏𝜏 = 0.35 s. 3.2 Fuzzy model of the non-linearity Because the purpose of this paper is to present employing fuzzy approaches to modelling human behavior during a simple driving task, the identified non-linearity is modelled via a fuzzy system. The Takagi-Sugeno models are often used for efficient approximation of a non-linear function (Abonyi, 2003). The polynomial function in Fig. 5 can be easily divided into 5 basic areas. Then, the implementation of the Takagi-Sugeno system consists of replacing the non-linear function with several (here 5) linear functions or constants, and subsequent tuning of the system consisting mainly of changing the position and overlapping of the input membership functions. Thus, the input variable, i.e. the deviation e(t) was mapped within the universe 𝑈𝑈𝑒𝑒 in the interval 𝑈𝑈𝑒𝑒=〈−4.5;4.5〉 m using a symmetric distribution of 5 triangular membership functions denoted as: - NB (negative big), - NS (negative small), - Z (zero), - PS (positive small), - PB (positive big). The rules were defined in the Takagi-Sugeno form, i.e.> - IF 𝑒𝑒 = NB THEN 𝑓𝑓𝑒𝑒 = 𝑓𝑓1(𝑒𝑒)= −2𝑒𝑒−10, - IF 𝑒𝑒 = NS THEN 𝑓𝑓𝑒𝑒 =𝑓𝑓2(𝑒𝑒) =1.5𝑒𝑒+1.7, - IF 𝑒𝑒 = Z THEN 𝑓𝑓𝑒𝑒 = 𝑓𝑓3(𝑒𝑒)= 0, - IF 𝑒𝑒 = PS THEN 𝑓𝑓𝑒𝑒 = 𝑓𝑓4(𝑒𝑒)=1.6𝑒𝑒−1.7, - IF 𝑒𝑒 = PB THEN 𝑓𝑓𝑒𝑒 = 𝑓𝑓5(𝑒𝑒)=−2𝑒𝑒+10, where 𝑓𝑓𝑖𝑖(𝑒𝑒) are the output linear (constant) functions. The initial fuzzy system was optimized via built-in functions in the Fuzzy Logic Designer toolbox in MATLAB (R2023a) employing a genetic algorithm with default settings. Twentyfour parameters were optimized in sum, involving the position of the input membership functions (see results in Fig. 4) and coefficients of the output linear functions 𝑓𝑓𝑖𝑖(𝑒𝑒). The resulting output functions were optimized as: 𝑓𝑓1(𝑒𝑒)=−0.2𝑒𝑒−4.2, 𝑓𝑓2(𝑒𝑒) =1.9𝑒𝑒+2.4, 𝑓𝑓3(𝑒𝑒) = 0.3, 𝑓𝑓4(𝑒𝑒)=2.6𝑒𝑒−3.3, and 𝑓𝑓5(𝑒𝑒)=0.3e+0.5. Figure 4. Optimized input membership functions. The Best fit value evaluating a matching of the non-linearity modelled as a polynomial and as the fuzzy system (see Fig. 5) was 89 %. 4. FUZZY PD CONTROLLER Another domain of the use of fuzzy logic for modelling dynamic systems is their use as fuzzy controllers, where the fuzzy system is a sole model of the whole system (without a linear part). The application of fuzzy controllers as an analogy to the standard linear PI/PD/PID controllers is discussed e.g. in (Ross, 2004). 6 7 8 9 10 56.61 56.61 56.62 56.61 56.62 260 M. Jirgl et al. / IFAC PapersOnLine 58-9 (2024) 257–262 Figure 5. Identified static non-linearity modelled as 5th order polynomial and as a fuzzy system. Due to the investigated driving task, where the controlled element behaves as an integrative system – double integrator (Jirgl et al., 2022), a human controller needs to adjust his/her control actions to accomplish similar behavior as a PD controller. In the case of the fuzzy PD implementation, the general difference equation is: 𝑢𝑢(𝑘𝑘)=𝐾𝐾3∙𝐃𝐃{𝐅𝐅{(𝐾𝐾1𝑒𝑒(𝑘𝑘)+𝐾𝐾2∆𝑒𝑒(𝑘𝑘))}} , (4) where 𝐾𝐾1,𝐾𝐾2,𝐾𝐾3− fuzzy PD controller parameters (scales), 𝑢𝑢(𝑘𝑘)− control action in the k-step, 𝑒𝑒(𝑘𝑘)− control error in the k-step, ∆𝑒𝑒(𝑘𝑘)− difference of a control error in the k-step. The F and D symbols represent the fuzzification and the defuzzification process respectively. The linear PD controller equation considers a control error and its derivative, or difference. Since the calculation of the difference inside the fuzzy system does not make much sense, the derivation/difference is implemented outside the fuzzy system and fed to the controller as a second input, see Fig. 6. Figure 6. Structure of a fuzzy PD controller. There are two basic ways to implement a fuzzy PD controller investigated in this paper. In the first case, a standardized structure of the fuzzy controller remains fixed, i.e. the tuning of the controller runs only based on the optimization of 𝐾𝐾1,𝐾𝐾2,𝐾𝐾3 scales. With a sufficient amount and a suitable overlap of the membership functions, we essentially get a more general replacement for the standard linear controller. This option is simpler, as the parameters can be optimized via standard optimization methods. The second option consists of tuning the internal structure of the fuzzy controller, i.e. positioning and overlaying membership functions. This form is relatively efficient. However, it is also much more demanding to optimize, as it contains a relatively large number of optimized parameters and the optimization is non-linear in this case. Therefore, it is necessary to choose non-linear optimization algorithms or other forms of machine learning, such as genetic algorithms. 4.1 Fuzzy PD controller with a fixed structure This implementation lies in mapping the input variables (weighted deviation – e and its difference – de) and the output variable (control action – u) into the standardized universe in the range <-1;1>. In the frame of the universe, all of the fuzzy variables were mapped using 7 triangular, symmetrically distributed membership functions (see Fig. 7): - NB (negative big), - NM (negative medium), - NS (negative small), - ZO (zero), - PS (positive small), - PM (positive medium), - PB (positive big). Variables “e”, “de”, “u” Figure 7. Membership functions for the input and the output variables of the fuzzy PD controller with a fixed structure. The rules were defined in the standard form, representing a logical functionality of the controller according to (Ross, 2004), see Fig. 8. Figure 8. Fuzzy PD controller rules. The resulting control surface of the fuzzy PD controller with the AND method implemented as MIN, the OR method as MAX, the Implication as MIN (the Mamdani implication), the Aggregation as MAX, and the defuzzification method as Centroid (i.e. center of gravity method) is in Fig. 9. M. Jirgl et al. / IFAC PapersOnLine 58-9 (2024) 257–262 261 Figure 5. Identified static non-linearity modelled as 5th order polynomial and as a fuzzy system. Due to the investigated driving task, where the controlled element behaves as an integrative system – double integrator (Jirgl et al., 2022), a human controller needs to adjust his/her control actions to accomplish similar behavior as a PD controller. In the case of the fuzzy PD implementation, the general difference equation is: 𝑢𝑢(𝑘𝑘)=𝐾𝐾3∙𝐃𝐃{𝐅𝐅{(𝐾𝐾1𝑒𝑒(𝑘𝑘)+𝐾𝐾2∆𝑒𝑒(𝑘𝑘))}} , (4) where 𝐾𝐾1,𝐾𝐾2,𝐾𝐾3− fuzzy PD controller parameters (scales), 𝑢𝑢(𝑘𝑘)− control action in the k-step, 𝑒𝑒(𝑘𝑘)− control error in the k-step, ∆𝑒𝑒(𝑘𝑘)− difference of a control error in the k-step. The F and D symbols represent the fuzzification and the defuzzification process respectively. The linear PD controller equation considers a control error and its derivative, or difference. Since the calculation of the difference inside the fuzzy system does not make much sense, the derivation/difference is implemented outside the fuzzy system and fed to the controller as a second input, see Fig. 6. Figure 6. Structure of a fuzzy PD controller. There are two basic ways to implement a fuzzy PD controller investigated in this paper. In the first case, a standardized structure of the fuzzy controller remains fixed, i.e. the tuning of the controller runs only based on the optimization of 𝐾𝐾1,𝐾𝐾2,𝐾𝐾3 scales. With a sufficient amount and a suitable overlap of the membership functions, we essentially get a more general replacement for the standard linear controller. This option is simpler, as the parameters can be optimized via standard optimization methods. The second option consists of tuning the internal structure of the fuzzy controller, i.e. positioning and overlaying membership functions. This form is relatively efficient. However, it is also much more demanding to optimize, as it contains a relatively large number of optimized parameters and the optimization is non-linear in this case. Therefore, it is necessary to choose non-linear optimization algorithms or other forms of machine learning, such as genetic algorithms. 4.1 Fuzzy PD controller with a fixed structure This implementation lies in mapping the input variables (weighted deviation – e and its difference – de) and the output variable (control action – u) into the standardized universe in the range <-1;1>. In the frame of the universe, all of the fuzzy variables were mapped using 7 triangular, symmetrically distributed membership functions (see Fig. 7): - NB (negative big), - NM (negative medium), - NS (negative small), - ZO (zero), - PS (positive small), - PM (positive medium), - PB (positive big). Variables “e”, “de”, “u” Figure 7. Membership functions for the input and the output variables of the fuzzy PD controller with a fixed structure. The rules were defined in the standard form, representing a logical functionality of the controller according to (Ross, 2004), see Fig. 8. Figure 8. Fuzzy PD controller rules. The resulting control surface of the fuzzy PD controller with the AND method implemented as MIN, the OR method as MAX, the Implication as MIN (the Mamdani implication), the Aggregation as MAX, and the defuzzification method as Centroid (i.e. center of gravity method) is in Fig. 9. The identified values of the 𝐾𝐾1,𝐾𝐾2,𝐾𝐾3 scales were: 𝐾𝐾1= 0.123,𝐾𝐾 2 =0.323, 𝐾𝐾 3 = 0.042. These scales shape the resulting control surface of the fuzzy PD controller. The input of the fuzzy controller was delayed by τ = 0.35 s which represents an evaluated average value of the driver’s reaction delay. Figure 9. A default control surface of the fuzzy PD controller with a fixed structure. 4.2 Fuzzy PD controller with an optimized structure This approach enables us to optimize the input and output membership functions (shape, position, overlap), rules, and other parameters defining the fuzzy controller. Although it would be appropriate to reduce the number of optimized parameters (due to the effectiveness of the optimization), the initial structure of the fuzzy system was left the same as in the previous part, for the sake of comparability and the possibility of evaluating the effectiveness. Thus, the fuzzy PD controller has 2 input variables (control error - e and its difference - de) and one output variable (control action - u), see Fig. 7. Given that the selected optimization algorithm is intended for tuning the internal structure of the fuzzy system, the scales 𝐾𝐾1,𝐾𝐾2,𝐾𝐾3 were set to 1 and the universes were scaled in the ranges of the measured data, i.e. 𝑈𝑈𝑒𝑒= 〈−4.5;4.5〉, 𝑈𝑈𝑑𝑑𝑒𝑒 =〈−5;5〉, and 𝑈𝑈𝑢𝑢=〈−0.04;0.04〉. All of the universes were covered by 7 triangular membership functions (NB, NM, NS, ZO, PS, PM, PB) with symmetrical distribution. Therefore, the inference runs on 49 rules initialized according to the Fig. 8. The model was optimized via library functions of the Fuzzy Logic Designer toolbox in MATLAB, employing a genetic algorithm with default settings. This process reduced rules of the system to 34 rules which fully describe the input-output data relation. The result can be demonstrated via the optimized control surface of the fuzzy PD controller, see Fig. 10. 5. RESULTS Measured control actions – 𝑢𝑢(𝑡𝑡), see Fig. 2, was approximated via the above-described fuzzy approaches. A comparison of the modelled control actions – 𝑢𝑢𝑚𝑚(𝑡𝑡) employing the different fuzzy systems is summarized in Fig. 11. Due to the clarity of the presented results, two selected responses representing a driver's response to left-hand, and a right-hand request to lane change are zoomed in. The response of the linear model (1) with the identified parameters 𝐾𝐾 =0.005, 𝑇𝑇 = 0.52 s, 𝜉𝜉 = 0.33 , and 𝜏𝜏 = 0.35 is presented too because it enables to evaluate the effectivity of the fuzzy approach in contrast to the pure linear solution. Figure 10. The control surface of the fuzzy PD controller with an optimized structure. Figure 11. A comparison of the modelled control actions – um(t) employing the different (fuzzy) approaches. Table 2 presents the achieved accuracy, or fitness, of the individual models evaluated via the Best fit parameter. 262 M. Jirgl et al. / IFAC PapersOnLine 58-9 (2024) 257–262 Table 2. Comparison of the approximation fitness. Model Best fit [%] Fuzzy Hammerstein model 56.6 Fuzzy PD – fixed structure 54.9 Fuzzy PD – optimized structure 62.1 Linear model 49.5 Although the Best fit values seem to be relatively low, they reflect the whole – multi-experiment dataset, upon which they were evaluated. In the case of fitness evaluation of the individual responses, the values are higher, e.g. in the case of the first zoomed response in Fig. 11, the Best fit values are [79.4, 71.8, 81.8, 64.3] % and in the second zoomed response [74.7, 73.4, 77.6, 71.2] % - sorted according to the items in Tab. 2. 6. CONCLUSIONS The goal of the paper was to investigate and compare the fuzzy logic-based techniques for approximation of the input-output data relation which represents human control action during a simple lane-changing task. The data was acquired on the self-developed car driving simulator which is briefly described in the second chapter, together with the data acquisition process. The experiment lied in measuring driver’s response to the requirement on the step change of the driving lane. From the cybernetic point of view, the input data in form of the deviation from the center of the desired driving lane represents the control error and the steering-wheel angle is a corresponding control action of a human (driver) controller. Then, three fuzzy-logic based approaches were employed as a model representing driver's behavior during the specified control (or driving) task. The considered models were: fuzzy Hammerstein model, fuzzy PD controller with a fixed structure (analogy to the linear PD controller) and fuzzy PD controller with an optimized structure. The models’ structures and results of the parameters identification procedure are described in sections 3 and 4. The final section summarizes the achieved results. One multiexperiment dataset corresponding to measurement with one selected driver was evaluated using the mentioned models. The best reached accuracy expressed using Best fit criterion was in the case of the fuzzy PD controller with an optimized structure. Its advantage is ability to non-linearly adjust the shape of the control surface. On the other hand, the optimization of this structure is very demanding and the results cannot be briefly summarized as a set of the evaluated parameters in contrast e.g. to the (fuzzy) Hammerstein model which accuracy was very near to the mentioned structure. Future work will be focused on experiments with reducing the complexity (number of the optimized parameters) of the fuzzy PD controller and validation of the presented results on the broader, statistically significant, dataset. ACKNOWLEDGMENT This work was supported by the Internal science fund of Brno University of Technology under Grant No. FEKT-S-23-8451. REFERENCES Abonyi, J. (2003). Fuzzy Model Identification for Control, Boston: Birkhauser. Hess, R.A. (2009). Candidate Structure for Modeling Pilot Control Behavior with Sudden Changes in Vehicle Dynamics. In AIAA Atmospheric Flight Mechanics Conference. Illinois. Jalovecky, R., Boril, J. and Jirgl, M. (2021). Testing Pilots' Responses on Flight Simulators - Current Status. In 2021 New Trends in Aviation Development (NTAD). IEEE, pp. 59-65, Kosice. Jirgl, M., Fiedler, P. and Bradac, Z. (2022). Human Driver Performance Assessment based on HiLCPS Concept. In IFAC-PapersOnLine. pp. 345-350. Ljung, L. (2022). System identification toolbox: Reference. Natick, MathWorks; 2022. Kolarik, J., and Slanina, Z. (2017). Fuzzy control application in swarm robotics cars. 18th International Carpathian Control Conference (ICCC), Sinaia, Romania. McRuer, D.T. and Krendel, E.S. (1974). Mathematical Models of Human Pilot Behavior, London: AGARD AG-188. Michalik, D., Jirgl, M., Arm, J., Fiedler, P. (2021). An Unreal Engine 4-Based Vehicle Driving Simulator and its Application in Driver Behavior Analysis. Safety, 7 (2), 1-15. Mihálik, O. and Fiedler, P. (2022). Means of Obtaining Mamdani Fuzzy Model of Car Driver’s Dynamics. In Proceedings of the 28th Conference STUDENT EEICT 2022: Selected papers, pp. 243-247, Brno. Mulder, M., Pool, D. M., et al. (2017). Manual Control Cybernetics: State-of-the-Art and Current Trends. IEEE Transactions on Human-Machine Systems, 48(5), pp. 118. Nash, C.J. and Cole D.J (2018). Modelling the influence of sensory dynamics on linear and nonlinear driver steering control. Vehicle system dynamics, 56(5), pp. 689–718. Roesener, C. et al. (2018). Modelling Human Driver Performance for Safety Assessment of Road Vehicle Automation. In: 21st International Conference on Intelligent Transportation Systems (ITSC). IEEE, pp. 735-741. Ross, T.J. (2004). Fuzzy logic with engineering applications 2nd ed., Chichester: Wiley. Xu, S. et al. (2017). Review of control models for human pilot behavior: State-of-the-Art and Current Trends. Annual Reviews in Control, 44(5), pp.274-291. Zaychik, K., Cardullo, F. and George, G. (2006). A Conspectus on Operator Modeling: Past, Present and Future. In AIAA Modeling and Simulation Technologies Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics.