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Simulator based driver categorization and linear model identification*
14-th IFAC Symposium on Turkey Control in Transportation Systems May 18-20, 2016. Istanbul, 14-th18-20, IFAC Symposium Symposium on Turkey Control in in Transportation Transportation Systems Systems May 2016. Istanbul, 14-th IFAC on Control Available online at www.sciencedirect.com May May 18-20, 18-20, 2016. 2016. Istanbul, Istanbul, Turkey Turkey
ScienceDirect IFAC-PapersOnLine (2016) 255–260 Simulator based 49-3 driver categorization Simulator based driver categorization Simulator based driver categorization linear model identification Simulator based driver categorization linear model identification linear model identification linear model identification Andr´ as Mih´ aly ∗ P´ eter G´ asp´ ar ∗ ∗ ∗ ∗ ∗
and and and and
Andr´ as Mih´ aly ∗∗ P´ eter G´ asp´ ar ∗∗ ∗ P´ Andr´ a ss Mih´ a ly e ter G´ a sp´ a Andr´ a Mih´ a ly P´ e ter G´ a sp´ arr ∗ Institute for Computer Science and Control Hungarian Academy Institute Computer Science andEngineering Control Hungarian Sciencesfor and MTA-BME Control ResearchAcademy Group, Institute Computer Science and Control Sciencesfor and MTA-BME Control Engineering ResearchAcademy Group, Institute for Computer Science and Control Hungarian Hungarian Academy Budapest, Hungary Sciences Control Engineering Budapest, Sciences and and MTA-BME MTA-BME ControlHungary Engineering Research Research Group, Group, Budapest, Hungary Hungary Budapest,
of of of of
Abstract: Abstract: The paper proposes a classification method for different driver behaviors based on an identificaAbstract: The proposes a classification method for different driverout behaviors baseddriving on an identificaAbstract: tion paper method. The categorization and identification is carried on real-time simulator The paper proposes a classification method for different driver behaviors based on an tion method. The categorization and identification is carried out on real-time driving simulator The paper proposes a classification method for different driver behaviors based ondefine an identificaidentificaexperiments with several test drivers. The purpose of the identification is to typical tion method. The categorization and is carried out on driving simulator experiments with several test drivers. The purpose of theassistant identification is of tothe define typical tion method. The with categorization and identification identification carried out on real-time real-time driving simulator driving behaviors their identified models. The isdriving systems vehicle can experiments with with several test drivers.models. The purpose purposedriving of the theassistant identification is of tothe define typical driving behaviors their systems vehicle can experiments several test drivers. of identification is to define typical be adapted towith the behavior ofidentified the driverThe using The predefined driver models. driving behaviors their models. driving assistant systems be adapted to the with behavior the driver using The predefined models. driving behaviors with theirofidentified identified models. The drivingdriver assistant systems of of the the vehicle vehicle can can be adapted to the behavior of the driver using predefined driver models. be adapted to the behavior of the driver using predefined driver models. © 2016,1.IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. INTRODUCTION The paper deals with classification of drivers based on 1. INTRODUCTION The paper deals with classification of up drivers based on vehicle simulator experiments, setting typical driver 1. INTRODUCTION INTRODUCTION The paper deals with classification of drivers based on vehicle simulator experiments, setting up typical driver 1. The paper deals with classification of drivers based on Driver classification and modeling is in the focus of several categorizes. Then, using model identification methods linvehicle simulator experiments, setting up typical driver categorizes. Then, using model identification methods linDriver classification and modeling is in the focus of several vehicle simulator experiments, setting up typical driver automotive research. Since driver behavior can differ in ear driver models are set up for the predefined categorizes. Then, using methods linDriver classification classification and and modeling isbehavior in the the focus focus ofdiffer several ear set model up for identification the predefined categorizes. automotive Since driveris canof in categorizes. categorizes. Then,are using model identification methods linDriver modeling in several Thedriver modelmodels identification is founded on the previous work great extent,research. in the implementation of driver assistant ear driver models are set up for the predefined categorizes. automotive research. Since driver behavior can differ in The model identification is founded on the previous work great extent, in the implementation of driver assistant ear driver models are set up for the predefined categorizes. automotive driver and behavior candrivers differ for in presented in Mih´aly and G´asp´ar (2014), extended with systems it isresearch. importantSince to monitor classify model founded on previous work great extent, extent, in the the implementation implementation ofclassify driverdrivers assistant presented Mih´aof ly longitudinal andis asp´armotion. (2014), extended with systems it is important to vehicle monitorcontrol andof for The The modelinidentification identification isG´ founded on the theThe previous great in driver assistant the consideration aim ofwork the the interoperability of the systems Sentouh presented in Mih´ a ly and G´ a sp´ a r (2014), extended with systems it is important to monitor and classify drivers for the consideration of longitudinal motion. The aim of the the interoperability of the vehicle control systems Sentouh presented in Mih´ a ly and G´ a sp´ a r (2014), extended with systems it is important to monitor and classify drivers for extended model identification is to find such global driver et al. (2009); Saleh et al. (2013). consideration of longitudinal The aim of the theal. interoperability of the the vehicle control control systems systems Sentouh Sentouh the extended model identification tomotion. find such global driver et (2009); Saleh et al. (2013). the consideration of longitudinal motion. The aim of the the interoperability of vehicle models describing both lateral isand longitudinal dynamics, extended model identification identification isand to longitudinal find such such global global driver et al. al.this (2009); Salehthe et signals al. (2013). (2013). For purpose, describing the drivers has to extended models describing both lateral dynamics, model is to find driver et (2009); Saleh et al. that can be used for real-time applications. For this purpose, the can signals the drivers has to models both lateral and be examined, which be describing separated into three groups that candescribing be used for real-time describing both lateral applications. and longitudinal longitudinal dynamics, dynamics, Forexamined, this purpose, purpose, the can signals describing the drivers drivers has to to models be be describing separated into three For this the signals the has that can be used for real-time applications. structure of the paper is as follows. Section 2 presents Miyajima et al.which (2007): signals in connection with groups driver The that can be used for real-time applications. be examined, examined, which cansignals be separated separated into three three groups structure used of thefor paper as follows. Section 2 and presents Miyajima et al.which (2007): in connection withvehicle driver The be can be into groups the strategy theisdriver classification the action (steering, brake and throttle operation), The structure of the paper is as follows. Section 2 presents Miyajima et al. al. (2007): (2007): signals in connection with driver the strategy used for the driver classification and the action (steering, brake and throttle operation), vehicle The structure of the paper is as follows. Section 2 presents Miyajima et signals in connection with driver dynamic signals (acceleration, yaw rate, etc.) and signals driving simulator is also introduced. Section 3 introduces the strategy used for the driver classification and the action (steering, (steering, brake and throttle operation), vehicle driving simulator is also introduced. Section 3 introduces dynamic signals (acceleration, yaw rate, etc.) and signals the strategy used for the driver classification and the action brake and throttle operation), vehicle the linear driver model identification process. In Section in connection with the vehicle-environment (position in driving simulator is also introduced. Section 3 introduces dynamic signals (acceleration, yaw rate, etc.) and signals the driver model process. In Section in connection with the vehicle-environment in driving simulator is driver also identification introduced. Section 3 introduces dynamic signals (acceleration, yaw etc.). rate, etc.) (position and signals 4 thelinear results of the categorization experiments are lane, distance of preceding vehicle, linear driver model identification process. In Section Section in connection connection with the vehicle-environment vehicle-environment (position in in the 4the thelinear results of the driver categorization experiments are lane, distance of preceding vehicle, etc.). driver model identification process. In in with the (position detailed. Finally, a brief summary of the contribution of the results of the driver categorization experiments are lane, distance distance of vehicle, These signals need to be measured with different sensors. 44detailed. Finally, a brief summary of the contribution of the results of the driver categorization experiments are lane, of preceding preceding vehicle, etc.). etc.). the paper is given in Section 5. These signals on-board need to bedevice measured with different sensors. Finally, aainbrief summary of the contribution of One possible becoming more and more detailed. the paper is given Section 5. detailed. Finally, brief summary of the contribution of Thesepossible signals on-board need to to be bedevice measured with different different sensors. One becoming moreHuang and more These need measured with sensors. paper is given in Section 5. popularsignals in applications are video cameras and the the paper is given in Section 5. One possible on-board device becoming more and more popular in applications cameras Huang and One possible on-board becoming and more Trivedi (2004); Martin device etare al. video (2012). Themore movements of 2. DEFINING DRIVER BEHAVIOR CATEGORIZES popular (2004); in applications applications are video cameras Huang and and Trivedi Martin (2012). The movements of popular in video cameras the human body servesetare asal.the indication toHuang recognize 2. DEFINING DRIVER BEHAVIOR CATEGORIZES Trivedi (2004); Martin et al. (2012). The movements of the human body servessituation. indication to in recognize Trivedi (2004); Martin etasal.the (2012). The built movements of 2. certain cautious driving Recently sensors 2. DEFINING DEFINING DRIVER DRIVER BEHAVIOR BEHAVIOR CATEGORIZES CATEGORIZES the human body serves as the indication to recognize the paper, classification of drivers is founded on tracertain cautious driving situation. Recently built in sensors the human body serves asused the for indication toand recognize of smart phones are also detection driver In In the paper, classification of drivers is founded on tracertain cautious driving situation. Recently built in sensors jectory analysis, similar to the strategy introduced by of smart phones are also used for driver certain cautious situation. Recently builtand in classification, seedriving Sathyanarayana et detection al. (2012); Shisensors et al. In the paper, classification of drivers is founded on trajectory analysis, similar to the strategy introduced In the paper, classification of drivers is founded on traof smart phones are also used for detection and driver Carboni and Gogorny (2014). The classification is based on classification, see Sathyanarayana al. (2012);and Shi driver et al. jectory analysis, similar to the strategy introduced by of smart phones are also used foret detection (2011). by Carboni and Gogorny (2014). The classification is based on similar toofthe strategy introduced by classification, see Sathyanarayana et al. (2012); Shi et al. al. jectory detectinganalysis, abnormal motion the vehicle generated by the (2011). classification, see Sathyanarayana et al. (2012); Shi et Carboni and Gogorny (2014). The classification is based on detecting abnormal motion of the vehicle generated by the Carboni and Gogorny (2014). The classification is based on (2011). Vehicle data can also be gained via CAN bus and OBD- subject drivers. At the road section where the anomalous (2011). abnormal motion of the generated by Vehicle datainformation can also beabout gained CAN motion bus and(speed, OBD- detecting subject drivers. At the road where the anomalous detecting abnormal motion the vehicle vehicle generated by the the II, serving theviavehicle movement is detected, it isofsection further examined weather it Vehicle data can also be gained via CAN bus and OBDsubject drivers. At the road section where the anomalous II, serving information about the vehicle motion (speed, Vehicle data canand alsoitsbeactuators gained via CAN busangle, and OBDmovement isbydetected, it property is section furtherorwhere examined weather it drivers. At track the road the anomalous yaw rate, etc...) state (steer brake subject is induced the the drivers unique II, serving serving information about the thestate vehicle motion (speed, is weather it yaw rate, etc...) andetc..), its actuators (steer angle, brake movement II, information about vehicle motion is induced is the trackit the drivers unique movement isbydetected, detected, it property is further furtherorexamined examined weather it pressure, throttle, thus identification of (speed, driving behavior. yaw rate, etc...) and its actuators state (steer angle, brake is induced by the track property or the drivers unique pressure, throttle, etc..), thus identification of driving yaw rate, etc...) and its actuators state (steer angle, brake behavior. is induced by the track property or the drivers unique styles become viable. Several research has been conducted pressure, throttle, etc..), thus identification of driving Four behavior. driver categorizes are considered, which cover the styles become viable. Several research has been conducted pressure, throttle, etc..), identification of driving with different methods to thus classify drivers based on the behavior. Four driver categorizes are These considered, whichascover the styles different become viable. viable. Several research has been conducted typical attitudes of drivers. are defined follows: with methods to classify drivers based on the styles become Several research has been conducted CAN bus data Ly et al. (2013); Choi et al. (2007). In Four driver categorizes are considered, which cover the typical attitudes of drivers. These are defined as follows: Four driver categorizes are considered, which cover the with different methods to classify drivers based on the CAN bus Ly (2002) et al.todrivers (2013); Choi et al. (2007). In typical with different methods classifywere drivers based the Canale anddata Malan separated inonthree attitudes of drivers. These are defined as follows: • Beginner driver: Driver does not violate the speed typical attitudes of drivers. These are defined as follows: CAN bus data Ly et al. (2013); Choi et al. (2007). In Canale anddata Malan were in three CAN Ly (2002) et al. drivers (2013); Choiseparated et al. Jensen (2007). In • Beginner Driver does not violate the speed major bus groups (quit, normal, aggressive), while and limit over driver: 20 %, and produces abrupt movements at Canalegroups and Malan Malan (2002) (2002) drivers were separated separated in three three •• Beginner driver: Driver does not violate the major normal, aggressive), Jensen and Canale were in limit over 20 %, and produces abrupt movements at Beginner driver: Driver does not violate the speed speed Wagnerand (2011)(quit, defined five drivers classes for the while categorization in unique places. major groups groups (quit, normal, aggressive), while Jensen and and limit 20 produces abrupt movements at Wagner (2011) defined fiveused. classes for thedriving categorization in major (quit, aggressive), while Jensen uniqueover places. limit over 20 %, %, and and producesvehicle abruptmotion movements at which GPS data wasnormal, also Modern simulators • Defensive driver: Anomalous not deWagner (2011) defined fiveused. classes for the thedriving categorization in unique places. which GPS data was also Modern simulators Wagner (2011) defined five classes for categorization in • Defensive driver: Anomalous vehicle motion not deunique places. can also serve as an effective tool for studying driver tected and speed limit not violated over 20 %. whichalso GPS dataas was used. Modern simulators •• Defensive driver: Anomalous vehicle motion decan serve effective tool Ersal fordriving studying driver which GPS data wasanalso also Modern driving tected speedNolimit notlimit violated over 20 %.not driver: Anomalous vehicle motion not behavior, see Imamura et used. al. (2008); et al.simulators (2010). • Defensive Normaland driver: speed violation with the de20 can also serve as an effective tool for studying driver tected and speed limit not violated over 20 %. behavior, see Imamura et al. (2008); et al. (2010). can also serve as an effective tool Ersal for studying driver • tected Normal driver: Nolimit speed violation with the 20 and speed notlimit violated over 20 %. % margin, and abrupt motion only detected at places The research was supported by the National Research, Developbehavior, see see Imamura Imamura et et al. al. (2008); (2008); Ersal Ersal et et al. al. (2010). (2010). •• Normal driver: No speed limit violation with the 20 behavior, % margin, and abrupt motion only detected at places Normal driver: No speed limit violation with the 20 where other test drivers induce such movement. The research was supported by the National Research, Development and Innovation Fund through the project ”SEPPAC: Safety % margin, and abrupt motion only detected at places where other test drivers induce such movement. The research was supported by the National Research, Develop% margin, and abrupt motion only detected at places The ment and Innovation Fund through projectResearch, ”SEPPAC: Safety • Aggressive driver: Speed limit exceeded by more than research was supported by thethe National Developand Economic Platform for Partially Automated Commercial vehiother test such movement. ment and Fund through project • where Aggressive driver: Speed induce limit exceeded by more than where other test drivers drivers induce such and Platform for Partially Automated CommercialSafety vehiment and Innovation Innovation Fund through the the project ”SEPPAC: ”SEPPAC: Safety 20 % and abrupt motion detected at movement. unique places. cles”Economic (VKSZ 14-1-2015-0125). • Aggressive driver: Speed limit exceeded by than and Economic Platform for Partially Automated Commercial vehi20 % and abrupt detected at unique places. cles”Economic (VKSZ 14-1-2015-0125). • Aggressive driver:motion Speed limit exceeded by more more than and Platform for Partially Automated Commercial vehi20 % and abrupt motion detected at unique places. cles” (VKSZ 14-1-2015-0125). 20 % and abrupt motion detected at unique places. cles” (VKSZ 14-1-2015-0125).
Copyright © 2016 IFAC 255 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 255 Hosting by Elsevier Ltd. All rights reserved. Copyright 2016 IFAC 255 Peer review© of International Federation of Automatic Copyright ©under 2016 responsibility IFAC 255Control. 10.1016/j.ifacol.2016.07.043
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The anomalous vehicle motion is defined with longitudinal and lateral acceleration thresholds. These values must be adapted to the environment and road conditions, as detailed in Carboni and Gogorny (2014); Xu et al. (2015). The structure of the classification and model identification is portrayed in Figure 1. The goal is to set up driver models for different driver behaviors. Thus, after the categorization of the drivers, a model identification is carried out as listed later in Section 3.
3. DRIVER MODEL IDENTIFICATION The driver maneuvers the vehicle in order to track the reference path and the speed limit defined by the geometry of the road and the regulations holding on the actual road section. Note, that the behavior of the driver affects considerably the performance of both longitudinal and lateral tracking task, as well as the disturbances acting on the vehicle (road slopes, wind, etc.). The aim of the driver model identification is to set up linear drivel models for different type of drivers. The behavior of the driver is represented by the parameters in the driver model discussed later. 3.1 Driver model measurement inputs
Fig. 1. Structure of the driver categorization
It is assumed, that the driver allocates the control input for the vehicle by perceiving certain information from both the vehicle motion and the environment. The former information connected to the dynamic state of the vehicle are gained by the vestibular perception of the human driver. These information sensed by the driver are the yaw rate ψ˙ vehicle of the vehicle along with the lateral and longitudinal acceleration ay and ax .
For the sake of measuring driver signals, a real-time HIL environment was built already introduced in Mih´ aly et al. (2012), thus here just a brief summary is given. The validated simulation environment CarSim works jointly with the real car, see in Figure 2. The vehicle signals are read through the CAN network using standard communication interface. Founded on the driver inputs, CarSim DS generates the vehicle signals, while real-time graphics is projected for visualization. With the vehicle noises (engine sound, wheel screech) and the working dashboard the driving involvement is close to that experienced in real life.
The visual perception of the driver accounts to gain information from the vehicle environment by detecting road sight-points, or by checking information of the dashboard and on-board electronic units. The vehicle velocity v is estimated by the relative speed difference from obstacles in the driver horizon, or by checking the speedometer of the vehicle. Note, that the reference velocity is also gained by the visual perception, reading the speed limit signs or the information message given by the on-board equipments such as GPS navigation system. The position of the vehicle in the lane is also detected by the visual perception of the driver, comparing the vehicle to a reference lateral position determined by the road geometry. In order to construct
A significant advantage of the simulator, is that all of the measurement signals used for the driver categorization is available, which is hard to gain in real life test conditions. In the course of the simulator experiment evaluated with the drivers, the important signals are measured for the categorization and identification process listed later.
Fig. 3. Reference trajectory for the driver appropriate measure signals for the characterization of the vehicle lateral deviation, it is necessary to define the reference road geometry in a word coordinate system described by Xgl and Ygl , as illustrated in Figure 3. In the calculation of the lateral deviation, another coordinate system (Xv and Yv ) rotating together with the vehicle needs to be introduced. Thus, the lateral position of the vehicle is calculated in both the word and the vehicle coordinate system, as illustrated in Figure 4. In order to calculate the difference between the reference lateral road position and the actual lateral position of the vehicle, the
Fig. 2. Driving simulator set-up
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Fig. 4. Single track bicycle model reference road has to be defined in the coordinate system of the vehicle as follows: yr = −sin(ψ)xgl,r + cos(ψ)ygl,r (1) where yr is the lateral position of the reference road geometry in the coordinate system of vehicle, xgl,r and ygl,r are the coordinates of the reference road geometry in the world coordinate system. In the simulation study described in Section 4, these global coordinates of the reference path are given in look-up tables for different roads as a function of the vehicle station. The lateral position of the vehicle in its own coordinate system is calculated as follows : yv = −sin(ψ)xgl,v + cos(ψ)ygl,v (2) where xgl,v and ygl,v defines the position of the vehicle in the global coordinate system. With zero initial conditions of x0 = 0 and y0 = 0 the global position of the vehicle can be calculated as in Rajamani (2005): (3) xgl = x0 + vx cos(ψ + β) − vy sin(ψ + β) ygl = y0 + vy cos(ψ + β) + vx sin(ψ + β)
where vx and vy are the longitudinal and lateral vehicle velocities, ψ is the yaw angle of the vehicle, while β is the side-slip angle (see Figure 4).
Thus, the lateral error of the vehicle from the reference path can be expressed by subtracting (2) from (1) as follows: ey = yr − yv (4) Note that the driver of the vehicle applies correction with the steering wheel to minimize the lateral error not by observing the actual error defined by (4). The lateral error is rather minimized on a certain preview distance, as illustrated in Figure 5. This preview distance is a function of the vehicle velocity, the driver mental state, the road type etc., however, in this paper the preview distance is assumed to depend on the velocity alone . For this purpose, a one second preview time is applied, thus the preview distance spreview is given as: spreview = vtpreview (5) where tpreview = 1s is the predefined preview time, and v is the vehicle velocity assumed to be constant on the preview time horizon. Thus, the lateral error on the preview distance determined by (5) is calculated as follows: 257
Fig. 5. Estimated lateral error for preview distance Edelmann et al. (2007)
yrprev
eprev = yrprev − yvprev y
(6)
yvprev
and is the estimated future vehicle and where reference road lateral position, assuming the vehicle states vx ,vy , ψ and β not to change on the preview time horizon. In the task of controlling the vehicle along the curves, the driver also relies on the sensing of the vehicle yaw rate, ψ˙ vehicle . This information along with the vehicle accelerations ax and ay gained by vestibular perception helps the driver to predict under or over steer vehicle behavior, and to match the vehicle yaw rate to that defined by the curvature of the road and the vehicle velocity. Thus, the reference yaw rate can be calculated straightforwardly as follows: v (7) ψ˙ ref = R where v = vx2 + vy2 is the velocity of the vehicle and R is the radius of the curve which can be calculated knowing the reference path of the vehicle. This calculation can be derived as follows. The reference path ahead of the vehicle can be divided into n number of section points. The global reference coordinates xgl,i and ygl,i i ∈ [1, n] are assumed to be known at each points using look-up tables. The trajectory of the vehicle can be regarded as an arc around each section point (see Figure 6), divided into k data points. Thus the curvature of the road Rj j ∈ [1, n] at each point can be calculated using geometrical considerations and Taylor series approximation by the following expression:
Fig. 6. The arc of the vehicle path
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Rj =
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s3j 24(sj − dj )
(8)
where dj = ((xk − x1 )2 + (yk − y1 )2 ) j ∈ [1, n] is the k length of the chord, sj = i=1 si j ∈ [1, n] is the length of the arc. Finally, the yaw rate error eψ˙ between the desired yaw rate determined by the geometry of the road and the measured vehicle yaw rate can be expressed as follows: (9) e ˙ = ψ˙ ref − ψ˙ v ψ
In order to describe the longitudinal dynamics of different drivers, the velocity error between the speed limit and the actual vehicle velocity has to be formulated as well with the following equation: (10) evel = vref − v where vref is the speed limit on the actual road sections. 3.2 Driver model identification The scheme of the identification is illustrated in Figure 7. The test drivers maneuver the vehicle simulator along a predefined track, while several input and output signals are measured with a sampling time of Tdt = 0.01 seconds. For the identification of combined driver models, both longitudinal and lateral dynamics have to be considered, as well as driver inputs affecting them. The input signals of the driver model described in Section 3.1 are the longitudinal and lateral accelerations ax and ay , the lateral preview error eprev defined by (6), the yaw rate error eψ˙ y defined by (9) and the velocity error evel defined by (10). These input measurement signals are formulated in the prev T eψ˙ ay evel ax . input vector u = ey The output of the driver model is the steering angle δ and the longitudinal force Fl , which are realized by the manipulation of the steering wheel and the accelerator and brake pedals of the simulator vehicle. These driver model outputs are the control inputs for the vehicle (see Figure T 7) and are given in the output vector y = [δ Fl ] .
The goal of the identification procedure is to estimate linear dynamic models of different driver behaviors from the observation data. Black-box identification methods, in which both the model structure and its parameters are unknown, have been well elaborated, see Ljung (1987); Kon et al. (2013). One of the biggest advantage of ARX model estimation compared to other techniques lies in the numerical efficiency, giving a unique solution satisfying the global minimum of the loss function. An AutoRegressive with Exogeneous part (ARX) model is estimated in the following form: p q Ai yt−i + Bj ut−j + et (11) yt = − i=1
j=0
where p is the AR order of the system and q is the input order of the system, while e(t) is white noise disturbance. Here, coefficients A1 ...Ap are ny × ny matrices, while B0 ...Bq are ny × nu matrices.
After defining the model structure described in (11) it is possible to search for the best fitting model for each driver. In the analysis the number of previous inputs and outputs q and p has to be determined such way, that the relation between the input and output variables are also considered. Both structure and parameter estimation methods the System Identification Toolbox of the Matlab is applied, see Ljung (1987). The identified driver model is validated by comparing the outputs of the driver model (vector y with the measurement vehicle inputs data gained as a result of the driving simulator experiment. Note, that the excitations of the driver model (vector u) are that gained by the simulator study. The outputs of the driver model (steering angle δ and longitudinal force Fl ) are compared to the measurement results by analyzing the results of the model fitting. The smaller the error between the simulated and measured values, the more punctual the driver model is. The analysis of the model fitting is as follows. First, the model output signals are put on the same scale before further analysis. The normalized data are calculated with the following equation: yi (t) y (t) − i yinorm (t) = , i = [1, 2] (12) n yi (t) 2 (yi (t)− n
n
)
where y1 = δ, y2 = Fl are the simulated output signals, n is the number of sampled data on the simulation time.
The normalization of the measurement signals are evaluated identically. For example for the steering angle the normalization is the following: δexp (t) δ (t) − exp norm δexp (t) = (13) n δexp (t) 2 (δexp (t)− n
Fig. 7. Scheme of the driver model identification The identification method is based on the experimental data of the test drivers maneuvering the simulator vehicle in the real-time simulation environment with the input and output signals measured and saved. The driver model is set up with nu = 5 model inputs and ny = 2 outputs. 258
n
)
For the sake of analysis, three error functions are introduced to compare the measured and the simulated normalized signals. These are the root mean square (RMS), the standard deviation (STD) and the mean squared error (MSE). The error values are calculated for the different variations of parameter values in matrix na and nb . The
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4. SIMULATION RESULTS The vehicle parameters used in the simulator are calibrated to represent an A-class small car, propelled with a 75 kW engine driving the front axle of the car.
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Fig. 8. Simulation environment
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The geometry of the track is illustrated in Figure 8 is based on the Waterford Michigan Race Track, and contains several types of curves. The subject drivers were chosen such way to represent a broad range of behavior, and were asked to operate the simulator around the racetrack. Note, that in present study only 10 drivers have been taken into the test process to demonstrate the operation of the proposed classification and identification method, however, a much bigger number of subject drivers are needed to gain results for real-life applications. The signals were measured and saved for post processing. The classification was then evaluated, using the acceleration/deceleration and velocity data collected. These are shown in Figure 9 along with the threshold values. It can be seen at glance in Figure 9 (a), that Driver 8 exceeds the speed limit the most time and the longitudinal and lateral acceleration threshold values in Figure 9 (b) and Figure 9 (c) are also violated several times. Since the vehicle brake system is always designed to be much stronger than the engine, the longitudinal acceleration threshold value has been separated for acceleration (3 m/s2 (minA)) and deceleration (6 m/s2 (minD)), as it can be seen in 9 (b). It can be observed, that these longitudinal acceleration threshold values are only violated at racetrack parts with speed limit sign or at the entrance of sharp corners. The lateral acceleration threshold value is chosen to be 6 m/s2 (minC), and is only violated at high speed cornering for few drivers (including Driver 8). Note, that in most cases there is a link between the speed limit violation and the violation of the lateral acceleration limit. The classification calculation has been evaluated offline, working with the vehicle records and threshold values 259
Fig. 9. Results of test drivers listed above. The cumulative value of time duration when the vehicle exceeds the threshold values during the lap serves as the basis for the driver categorization. By this mean, the categorization algorithm in Matlab identifies the speed limit violations for each driver, along with the abrupt motions and their station on the track. In the proposed algorithm, the comparison of the detected abrupt motions are evaluated with 0.1 meter margin for the station on the track, i.e detected threshold violations for different drivers with smaller distance margin than 0.1 meter are considered as mutual, not unique violation. Next, the most typical drivers for each category has been selected to identify a benchmark model. Thus, Driver 8 represents the aggressive driver with most of the abrupt motions (even at unique places) and speed limit violations, Driver 1 stands for the defensive driver with no speed limit violation and abrupt movement at all, while Driver 5 represents the normal category with few abrupt movements at some common places where others also violate the acceleration/deceleration limits. Note, that none of the chosen test drivers fall in the beginner category, since abrupt motions at unique places without speed limit violation has not been detected. For each of these listed driver types (defensive, normal, aggressive) a linear model has been set up with using ARX identification method, and these models are chosen as benchmark models to represent the category type. It has been proven by error analysis that the gained models represent well other drivers falling in the same category. For example, Driver 4 categorized as defensive driver can be modeled with the benchmark model for defensive
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driver (Driver 1). By applying its measured inputs for the different benchmark models and comparing the model outputs with signals gained by the simulator study, the results shown in Figure 10 validate that behavior of Driver 4 is closest to the defensive benchmark model.
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Fig. 10. Error signals of Driver 4 with benchmark models 5. CONCLUSION The paper presented an off-line driver classification method based on trajectory analysis of several test drivers. A linear model identification procedure has also been introduced, considering both lateral and longitudinal behavior of the drivers. The categorization and identification method was underlined with a simulator experiment conducted by ten drivers with different attitude and driving experience. The result have shown that the presented offline algorithm serves as powerful tool for driver classification. With the presented model identification, benchmark driver models have been set up and validated for the different categorizes. Future work will focus on applying the proposed method with bigger number of subject drivers and different test tracks, in order to gain a more punctual model for each driver category. REFERENCES Canale, M. and Malan, S. (2002). Analysis and classification of human driving behaviour in an urban environment. Cognition, Technology & Work, 4, 197–206. Carboni, E.M. and Gogorny, V. (2014). Inferring drivers behavior through trajectory analysis. Intelligent Systems, 13, 837–848.
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Choi, S., Kim, J.H., Kwak, D.G., Angkititrakul, P., and Hansen, J.H.L. (2007). Analysis and classification of driver behavior using in-vehicle can-bus information. Biennial Workshop on DSP for In-Vehicle and Mobile Systems. Edelmann, J., Plochl, M., Reinalter, W., and Tieber, W. (2007). A passenger car driver model for higher lateral acceleration. Vehicle System Dynamics, 45, 1117–1129. Ersal, T., Fuller, H., Tsimhoni, O., Stein, J., and Fathy, H. (2010). Model-based analysis and classification of driver distraction under secondary tasks. IEEE Transactions on Intelligent Transportation Systems, 11, 692–701. Huang, K.S. and Trivedi, M.M. (2004). Robust real-time detection, tracking, and pose estimation of faces in video streams. 17th IEEE International Conference on Pattern Recognition, 3, 965–968. Imamura, T., Yamashita, H., Zhang, Z., Othman, R., and Miyake, T. (2008). A study of classification for driver conditions using driving behaviors. IEEE International Conference on Systems, Man, and Cybernetics (SMC), 1506–1511. Jensen, M. and Wagner, J. (2011). Analysis of in-vehicle driver behaviour data for improved safety. International Journal of Vehicle Safety, 5, 197–212. Kon, J., Yamashita, Y., Tanaka, T., Tashiro, A., and Daiguji, M. (2013). Practical application of model identification based on arx models with transfer functions. Control Engineering Practice, 21, 195–203. Ljung, L. (1987). System identification: Theory for the user. Prentice-Hall, Inc., Englewood Cliffs, New Jersey. Ly, M.V., Martin, S., and Trivedi, M.M. (2013). Driver classification and driving style recognition using inertial sensors. IEEE Intelligent Vehicles Symposium,Gold Coast, Australia, 1040–1045. Martin, S., Tran, C., Tawari, A., Kwan, J., and Trivedi, M.M. (2012). Optical flow based head movement and gesture analysis in automotive environment. 15th IEEE International Conference on Intelligent Transportation Systems (ITSC), 882–887. Mih´ aly, A. and G´ asp´ ar, P. (2014). Identification of a linear driver model based on simulator experiments. 9th IEEE International Symposium on Applied Computational Intelligence and Informatics, Timisoara, Romania, 13–18. Mih´ aly, A., N´ emeth, B., and G´ asp´ ar, P. (2012). Analysis of driver behavior related to look-ahead control. 13th IFAC Symposium on Control in Transportation Systems, Bulgaria, Sofia, 13, 268–273. Miyajima, C., Nishiwaki, Y., Ozawa, K., Wakita, T., Itou, K., Takeda, K., and Itakura, F. (2007). Driver modeling based on driving behavior and its evaluation in driver identification. Proceedings of the IEEE, 95, 427–437. Rajamani, R. (2005). Vehicle dynamics and control. Springer. Saleh, L., Chevrel, P., Claveau, F., Lafay, J.F., and F.Mars (2013). Shared steering control between a driver and an automation: Stability in the presence of driver behavior uncertainty. IEEE Transactions on Intelligent Transportation Systems, 2462–2467. Sathyanarayana, A., Sadjadi, S.O., and Hansen, J.H. (2012). Leveraging sensor information from portable devices towards automatic driving maneuver recognition. 15th IEEE International Conference on Intelligent Transportation Systems (ITSC), 660–665. Sentouh, C., Chevrel, P., Mars, F., and Claveau, F. (2009). A sensorimotor driver model for steering control. IEEE International Conference on Systems, Man, and Cybernetics, 2462–2467. Shi, W., Yang, J., Jiang, Y., Yang, F., and Xiong, Y. (2011). Passive user identification on smartphones using multiple sensors. 7th IEEE International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob), 141–148. Xu, J., Yang, K., Shao, Y., and Lu, G. (2015). An experimental study on lateral acceleration of cars in different environments in sichuan, southwest china. Discrete Dynamics in Nature and Society, 2015, 1–16.
ScienceDirect IFAC-PapersOnLine (2016) 255–260 Simulator based 49-3 driver categorization Simulator based driver categorization Simulator based driver categorization linear model identification Simulator based driver categorization linear model identification linear model identification linear model identification Andr´ as Mih´ aly ∗ P´ eter G´ asp´ ar ∗ ∗ ∗ ∗ ∗
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Andr´ as Mih´ aly ∗∗ P´ eter G´ asp´ ar ∗∗ ∗ P´ Andr´ a ss Mih´ a ly e ter G´ a sp´ a Andr´ a Mih´ a ly P´ e ter G´ a sp´ arr ∗ Institute for Computer Science and Control Hungarian Academy Institute Computer Science andEngineering Control Hungarian Sciencesfor and MTA-BME Control ResearchAcademy Group, Institute Computer Science and Control Sciencesfor and MTA-BME Control Engineering ResearchAcademy Group, Institute for Computer Science and Control Hungarian Hungarian Academy Budapest, Hungary Sciences Control Engineering Budapest, Sciences and and MTA-BME MTA-BME ControlHungary Engineering Research Research Group, Group, Budapest, Hungary Hungary Budapest,
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Abstract: Abstract: The paper proposes a classification method for different driver behaviors based on an identificaAbstract: The proposes a classification method for different driverout behaviors baseddriving on an identificaAbstract: tion paper method. The categorization and identification is carried on real-time simulator The paper proposes a classification method for different driver behaviors based on an tion method. The categorization and identification is carried out on real-time driving simulator The paper proposes a classification method for different driver behaviors based ondefine an identificaidentificaexperiments with several test drivers. The purpose of the identification is to typical tion method. The categorization and is carried out on driving simulator experiments with several test drivers. The purpose of theassistant identification is of tothe define typical tion method. The with categorization and identification identification carried out on real-time real-time driving simulator driving behaviors their identified models. The isdriving systems vehicle can experiments with with several test drivers.models. The purpose purposedriving of the theassistant identification is of tothe define typical driving behaviors their systems vehicle can experiments several test drivers. of identification is to define typical be adapted towith the behavior ofidentified the driverThe using The predefined driver models. driving behaviors their models. driving assistant systems be adapted to the with behavior the driver using The predefined models. driving behaviors with theirofidentified identified models. The drivingdriver assistant systems of of the the vehicle vehicle can can be adapted to the behavior of the driver using predefined driver models. be adapted to the behavior of the driver using predefined driver models. © 2016,1.IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. INTRODUCTION The paper deals with classification of drivers based on 1. INTRODUCTION The paper deals with classification of up drivers based on vehicle simulator experiments, setting typical driver 1. INTRODUCTION INTRODUCTION The paper deals with classification of drivers based on vehicle simulator experiments, setting up typical driver 1. The paper deals with classification of drivers based on Driver classification and modeling is in the focus of several categorizes. Then, using model identification methods linvehicle simulator experiments, setting up typical driver categorizes. Then, using model identification methods linDriver classification and modeling is in the focus of several vehicle simulator experiments, setting up typical driver automotive research. Since driver behavior can differ in ear driver models are set up for the predefined categorizes. Then, using methods linDriver classification classification and and modeling isbehavior in the the focus focus ofdiffer several ear set model up for identification the predefined categorizes. automotive Since driveris canof in categorizes. categorizes. Then,are using model identification methods linDriver modeling in several Thedriver modelmodels identification is founded on the previous work great extent,research. in the implementation of driver assistant ear driver models are set up for the predefined categorizes. automotive research. Since driver behavior can differ in The model identification is founded on the previous work great extent, in the implementation of driver assistant ear driver models are set up for the predefined categorizes. automotive driver and behavior candrivers differ for in presented in Mih´aly and G´asp´ar (2014), extended with systems it isresearch. importantSince to monitor classify model founded on previous work great extent, extent, in the the implementation implementation ofclassify driverdrivers assistant presented Mih´aof ly longitudinal andis asp´armotion. (2014), extended with systems it is important to vehicle monitorcontrol andof for The The modelinidentification identification isG´ founded on the theThe previous great in driver assistant the consideration aim ofwork the the interoperability of the systems Sentouh presented in Mih´ a ly and G´ a sp´ a r (2014), extended with systems it is important to monitor and classify drivers for the consideration of longitudinal motion. The aim of the the interoperability of the vehicle control systems Sentouh presented in Mih´ a ly and G´ a sp´ a r (2014), extended with systems it is important to monitor and classify drivers for extended model identification is to find such global driver et al. (2009); Saleh et al. (2013). consideration of longitudinal The aim of the theal. interoperability of the the vehicle control control systems systems Sentouh Sentouh the extended model identification tomotion. find such global driver et (2009); Saleh et al. (2013). the consideration of longitudinal motion. The aim of the the interoperability of vehicle models describing both lateral isand longitudinal dynamics, extended model identification identification isand to longitudinal find such such global global driver et al. al.this (2009); Salehthe et signals al. (2013). (2013). For purpose, describing the drivers has to extended models describing both lateral dynamics, model is to find driver et (2009); Saleh et al. that can be used for real-time applications. For this purpose, the can signals the drivers has to models both lateral and be examined, which be describing separated into three groups that candescribing be used for real-time describing both lateral applications. and longitudinal longitudinal dynamics, dynamics, Forexamined, this purpose, purpose, the can signals describing the drivers drivers has to to models be be describing separated into three For this the signals the has that can be used for real-time applications. structure of the paper is as follows. Section 2 presents Miyajima et al.which (2007): signals in connection with groups driver The that can be used for real-time applications. be examined, examined, which cansignals be separated separated into three three groups structure used of thefor paper as follows. Section 2 and presents Miyajima et al.which (2007): in connection withvehicle driver The be can be into groups the strategy theisdriver classification the action (steering, brake and throttle operation), The structure of the paper is as follows. Section 2 presents Miyajima et al. al. (2007): (2007): signals in connection with driver the strategy used for the driver classification and the action (steering, brake and throttle operation), vehicle The structure of the paper is as follows. Section 2 presents Miyajima et signals in connection with driver dynamic signals (acceleration, yaw rate, etc.) and signals driving simulator is also introduced. Section 3 introduces the strategy used for the driver classification and the action (steering, (steering, brake and throttle operation), vehicle driving simulator is also introduced. Section 3 introduces dynamic signals (acceleration, yaw rate, etc.) and signals the strategy used for the driver classification and the action brake and throttle operation), vehicle the linear driver model identification process. In Section in connection with the vehicle-environment (position in driving simulator is also introduced. Section 3 introduces dynamic signals (acceleration, yaw rate, etc.) and signals the driver model process. In Section in connection with the vehicle-environment in driving simulator is driver also identification introduced. Section 3 introduces dynamic signals (acceleration, yaw etc.). rate, etc.) (position and signals 4 thelinear results of the categorization experiments are lane, distance of preceding vehicle, linear driver model identification process. In Section Section in connection connection with the vehicle-environment vehicle-environment (position in in the 4the thelinear results of the driver categorization experiments are lane, distance of preceding vehicle, etc.). driver model identification process. In in with the (position detailed. Finally, a brief summary of the contribution of the results of the driver categorization experiments are lane, distance distance of vehicle, These signals need to be measured with different sensors. 44detailed. Finally, a brief summary of the contribution of the results of the driver categorization experiments are lane, of preceding preceding vehicle, etc.). etc.). the paper is given in Section 5. These signals on-board need to bedevice measured with different sensors. Finally, aainbrief summary of the contribution of One possible becoming more and more detailed. the paper is given Section 5. detailed. Finally, brief summary of the contribution of Thesepossible signals on-board need to to be bedevice measured with different different sensors. One becoming moreHuang and more These need measured with sensors. paper is given in Section 5. popularsignals in applications are video cameras and the the paper is given in Section 5. One possible on-board device becoming more and more popular in applications cameras Huang and One possible on-board becoming and more Trivedi (2004); Martin device etare al. video (2012). Themore movements of 2. DEFINING DRIVER BEHAVIOR CATEGORIZES popular (2004); in applications applications are video cameras Huang and and Trivedi Martin (2012). The movements of popular in video cameras the human body servesetare asal.the indication toHuang recognize 2. DEFINING DRIVER BEHAVIOR CATEGORIZES Trivedi (2004); Martin et al. (2012). The movements of the human body servessituation. indication to in recognize Trivedi (2004); Martin etasal.the (2012). The built movements of 2. certain cautious driving Recently sensors 2. DEFINING DEFINING DRIVER DRIVER BEHAVIOR BEHAVIOR CATEGORIZES CATEGORIZES the human body serves as the indication to recognize the paper, classification of drivers is founded on tracertain cautious driving situation. Recently built in sensors the human body serves asused the for indication toand recognize of smart phones are also detection driver In In the paper, classification of drivers is founded on tracertain cautious driving situation. Recently built in sensors jectory analysis, similar to the strategy introduced by of smart phones are also used for driver certain cautious situation. Recently builtand in classification, seedriving Sathyanarayana et detection al. (2012); Shisensors et al. In the paper, classification of drivers is founded on trajectory analysis, similar to the strategy introduced In the paper, classification of drivers is founded on traof smart phones are also used for detection and driver Carboni and Gogorny (2014). The classification is based on classification, see Sathyanarayana al. (2012);and Shi driver et al. jectory analysis, similar to the strategy introduced by of smart phones are also used foret detection (2011). by Carboni and Gogorny (2014). The classification is based on similar toofthe strategy introduced by classification, see Sathyanarayana et al. (2012); Shi et al. al. jectory detectinganalysis, abnormal motion the vehicle generated by the (2011). classification, see Sathyanarayana et al. (2012); Shi et Carboni and Gogorny (2014). The classification is based on detecting abnormal motion of the vehicle generated by the Carboni and Gogorny (2014). The classification is based on (2011). Vehicle data can also be gained via CAN bus and OBD- subject drivers. At the road section where the anomalous (2011). abnormal motion of the generated by Vehicle datainformation can also beabout gained CAN motion bus and(speed, OBD- detecting subject drivers. At the road where the anomalous detecting abnormal motion the vehicle vehicle generated by the the II, serving theviavehicle movement is detected, it isofsection further examined weather it Vehicle data can also be gained via CAN bus and OBDsubject drivers. At the road section where the anomalous II, serving information about the vehicle motion (speed, Vehicle data canand alsoitsbeactuators gained via CAN busangle, and OBDmovement isbydetected, it property is section furtherorwhere examined weather it drivers. At track the road the anomalous yaw rate, etc...) state (steer brake subject is induced the the drivers unique II, serving serving information about the thestate vehicle motion (speed, is weather it yaw rate, etc...) andetc..), its actuators (steer angle, brake movement II, information about vehicle motion is induced is the trackit the drivers unique movement isbydetected, detected, it property is further furtherorexamined examined weather it pressure, throttle, thus identification of (speed, driving behavior. yaw rate, etc...) and its actuators state (steer angle, brake is induced by the track property or the drivers unique pressure, throttle, etc..), thus identification of driving yaw rate, etc...) and its actuators state (steer angle, brake behavior. is induced by the track property or the drivers unique styles become viable. Several research has been conducted pressure, throttle, etc..), thus identification of driving Four behavior. driver categorizes are considered, which cover the styles become viable. Several research has been conducted pressure, throttle, etc..), identification of driving with different methods to thus classify drivers based on the behavior. Four driver categorizes are These considered, whichascover the styles different become viable. viable. Several research has been conducted typical attitudes of drivers. are defined follows: with methods to classify drivers based on the styles become Several research has been conducted CAN bus data Ly et al. (2013); Choi et al. (2007). In Four driver categorizes are considered, which cover the typical attitudes of drivers. These are defined as follows: Four driver categorizes are considered, which cover the with different methods to classify drivers based on the CAN bus Ly (2002) et al.todrivers (2013); Choi et al. (2007). In typical with different methods classifywere drivers based the Canale anddata Malan separated inonthree attitudes of drivers. These are defined as follows: • Beginner driver: Driver does not violate the speed typical attitudes of drivers. These are defined as follows: CAN bus data Ly et al. (2013); Choi et al. (2007). In Canale anddata Malan were in three CAN Ly (2002) et al. drivers (2013); Choiseparated et al. Jensen (2007). In • Beginner Driver does not violate the speed major bus groups (quit, normal, aggressive), while and limit over driver: 20 %, and produces abrupt movements at Canalegroups and Malan Malan (2002) (2002) drivers were separated separated in three three •• Beginner driver: Driver does not violate the major normal, aggressive), Jensen and Canale were in limit over 20 %, and produces abrupt movements at Beginner driver: Driver does not violate the speed speed Wagnerand (2011)(quit, defined five drivers classes for the while categorization in unique places. major groups groups (quit, normal, aggressive), while Jensen and and limit 20 produces abrupt movements at Wagner (2011) defined fiveused. classes for thedriving categorization in major (quit, aggressive), while Jensen uniqueover places. limit over 20 %, %, and and producesvehicle abruptmotion movements at which GPS data wasnormal, also Modern simulators • Defensive driver: Anomalous not deWagner (2011) defined fiveused. classes for the thedriving categorization in unique places. which GPS data was also Modern simulators Wagner (2011) defined five classes for categorization in • Defensive driver: Anomalous vehicle motion not deunique places. can also serve as an effective tool for studying driver tected and speed limit not violated over 20 %. whichalso GPS dataas was used. Modern simulators •• Defensive driver: Anomalous vehicle motion decan serve effective tool Ersal fordriving studying driver which GPS data wasanalso also Modern driving tected speedNolimit notlimit violated over 20 %.not driver: Anomalous vehicle motion not behavior, see Imamura et used. al. (2008); et al.simulators (2010). • Defensive Normaland driver: speed violation with the de20 can also serve as an effective tool for studying driver tected and speed limit not violated over 20 %. behavior, see Imamura et al. (2008); et al. (2010). can also serve as an effective tool Ersal for studying driver • tected Normal driver: Nolimit speed violation with the 20 and speed notlimit violated over 20 %. % margin, and abrupt motion only detected at places The research was supported by the National Research, Developbehavior, see see Imamura Imamura et et al. al. (2008); (2008); Ersal Ersal et et al. al. (2010). (2010). •• Normal driver: No speed limit violation with the 20 behavior, % margin, and abrupt motion only detected at places Normal driver: No speed limit violation with the 20 where other test drivers induce such movement. The research was supported by the National Research, Development and Innovation Fund through the project ”SEPPAC: Safety % margin, and abrupt motion only detected at places where other test drivers induce such movement. The research was supported by the National Research, Develop% margin, and abrupt motion only detected at places The ment and Innovation Fund through projectResearch, ”SEPPAC: Safety • Aggressive driver: Speed limit exceeded by more than research was supported by thethe National Developand Economic Platform for Partially Automated Commercial vehiother test such movement. ment and Fund through project • where Aggressive driver: Speed induce limit exceeded by more than where other test drivers drivers induce such and Platform for Partially Automated CommercialSafety vehiment and Innovation Innovation Fund through the the project ”SEPPAC: ”SEPPAC: Safety 20 % and abrupt motion detected at movement. unique places. cles”Economic (VKSZ 14-1-2015-0125). • Aggressive driver: Speed limit exceeded by than and Economic Platform for Partially Automated Commercial vehi20 % and abrupt detected at unique places. cles”Economic (VKSZ 14-1-2015-0125). • Aggressive driver:motion Speed limit exceeded by more more than and Platform for Partially Automated Commercial vehi20 % and abrupt motion detected at unique places. cles” (VKSZ 14-1-2015-0125). 20 % and abrupt motion detected at unique places. cles” (VKSZ 14-1-2015-0125).
Copyright © 2016 IFAC 255 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 255 Hosting by Elsevier Ltd. All rights reserved. Copyright 2016 IFAC 255 Peer review© of International Federation of Automatic Copyright ©under 2016 responsibility IFAC 255Control. 10.1016/j.ifacol.2016.07.043
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The anomalous vehicle motion is defined with longitudinal and lateral acceleration thresholds. These values must be adapted to the environment and road conditions, as detailed in Carboni and Gogorny (2014); Xu et al. (2015). The structure of the classification and model identification is portrayed in Figure 1. The goal is to set up driver models for different driver behaviors. Thus, after the categorization of the drivers, a model identification is carried out as listed later in Section 3.
3. DRIVER MODEL IDENTIFICATION The driver maneuvers the vehicle in order to track the reference path and the speed limit defined by the geometry of the road and the regulations holding on the actual road section. Note, that the behavior of the driver affects considerably the performance of both longitudinal and lateral tracking task, as well as the disturbances acting on the vehicle (road slopes, wind, etc.). The aim of the driver model identification is to set up linear drivel models for different type of drivers. The behavior of the driver is represented by the parameters in the driver model discussed later. 3.1 Driver model measurement inputs
Fig. 1. Structure of the driver categorization
It is assumed, that the driver allocates the control input for the vehicle by perceiving certain information from both the vehicle motion and the environment. The former information connected to the dynamic state of the vehicle are gained by the vestibular perception of the human driver. These information sensed by the driver are the yaw rate ψ˙ vehicle of the vehicle along with the lateral and longitudinal acceleration ay and ax .
For the sake of measuring driver signals, a real-time HIL environment was built already introduced in Mih´ aly et al. (2012), thus here just a brief summary is given. The validated simulation environment CarSim works jointly with the real car, see in Figure 2. The vehicle signals are read through the CAN network using standard communication interface. Founded on the driver inputs, CarSim DS generates the vehicle signals, while real-time graphics is projected for visualization. With the vehicle noises (engine sound, wheel screech) and the working dashboard the driving involvement is close to that experienced in real life.
The visual perception of the driver accounts to gain information from the vehicle environment by detecting road sight-points, or by checking information of the dashboard and on-board electronic units. The vehicle velocity v is estimated by the relative speed difference from obstacles in the driver horizon, or by checking the speedometer of the vehicle. Note, that the reference velocity is also gained by the visual perception, reading the speed limit signs or the information message given by the on-board equipments such as GPS navigation system. The position of the vehicle in the lane is also detected by the visual perception of the driver, comparing the vehicle to a reference lateral position determined by the road geometry. In order to construct
A significant advantage of the simulator, is that all of the measurement signals used for the driver categorization is available, which is hard to gain in real life test conditions. In the course of the simulator experiment evaluated with the drivers, the important signals are measured for the categorization and identification process listed later.
Fig. 3. Reference trajectory for the driver appropriate measure signals for the characterization of the vehicle lateral deviation, it is necessary to define the reference road geometry in a word coordinate system described by Xgl and Ygl , as illustrated in Figure 3. In the calculation of the lateral deviation, another coordinate system (Xv and Yv ) rotating together with the vehicle needs to be introduced. Thus, the lateral position of the vehicle is calculated in both the word and the vehicle coordinate system, as illustrated in Figure 4. In order to calculate the difference between the reference lateral road position and the actual lateral position of the vehicle, the
Fig. 2. Driving simulator set-up
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257
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Fig. 4. Single track bicycle model reference road has to be defined in the coordinate system of the vehicle as follows: yr = −sin(ψ)xgl,r + cos(ψ)ygl,r (1) where yr is the lateral position of the reference road geometry in the coordinate system of vehicle, xgl,r and ygl,r are the coordinates of the reference road geometry in the world coordinate system. In the simulation study described in Section 4, these global coordinates of the reference path are given in look-up tables for different roads as a function of the vehicle station. The lateral position of the vehicle in its own coordinate system is calculated as follows : yv = −sin(ψ)xgl,v + cos(ψ)ygl,v (2) where xgl,v and ygl,v defines the position of the vehicle in the global coordinate system. With zero initial conditions of x0 = 0 and y0 = 0 the global position of the vehicle can be calculated as in Rajamani (2005): (3) xgl = x0 + vx cos(ψ + β) − vy sin(ψ + β) ygl = y0 + vy cos(ψ + β) + vx sin(ψ + β)
where vx and vy are the longitudinal and lateral vehicle velocities, ψ is the yaw angle of the vehicle, while β is the side-slip angle (see Figure 4).
Thus, the lateral error of the vehicle from the reference path can be expressed by subtracting (2) from (1) as follows: ey = yr − yv (4) Note that the driver of the vehicle applies correction with the steering wheel to minimize the lateral error not by observing the actual error defined by (4). The lateral error is rather minimized on a certain preview distance, as illustrated in Figure 5. This preview distance is a function of the vehicle velocity, the driver mental state, the road type etc., however, in this paper the preview distance is assumed to depend on the velocity alone . For this purpose, a one second preview time is applied, thus the preview distance spreview is given as: spreview = vtpreview (5) where tpreview = 1s is the predefined preview time, and v is the vehicle velocity assumed to be constant on the preview time horizon. Thus, the lateral error on the preview distance determined by (5) is calculated as follows: 257
Fig. 5. Estimated lateral error for preview distance Edelmann et al. (2007)
yrprev
eprev = yrprev − yvprev y
(6)
yvprev
and is the estimated future vehicle and where reference road lateral position, assuming the vehicle states vx ,vy , ψ and β not to change on the preview time horizon. In the task of controlling the vehicle along the curves, the driver also relies on the sensing of the vehicle yaw rate, ψ˙ vehicle . This information along with the vehicle accelerations ax and ay gained by vestibular perception helps the driver to predict under or over steer vehicle behavior, and to match the vehicle yaw rate to that defined by the curvature of the road and the vehicle velocity. Thus, the reference yaw rate can be calculated straightforwardly as follows: v (7) ψ˙ ref = R where v = vx2 + vy2 is the velocity of the vehicle and R is the radius of the curve which can be calculated knowing the reference path of the vehicle. This calculation can be derived as follows. The reference path ahead of the vehicle can be divided into n number of section points. The global reference coordinates xgl,i and ygl,i i ∈ [1, n] are assumed to be known at each points using look-up tables. The trajectory of the vehicle can be regarded as an arc around each section point (see Figure 6), divided into k data points. Thus the curvature of the road Rj j ∈ [1, n] at each point can be calculated using geometrical considerations and Taylor series approximation by the following expression:
Fig. 6. The arc of the vehicle path
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Rj =
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s3j 24(sj − dj )
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where dj = ((xk − x1 )2 + (yk − y1 )2 ) j ∈ [1, n] is the k length of the chord, sj = i=1 si j ∈ [1, n] is the length of the arc. Finally, the yaw rate error eψ˙ between the desired yaw rate determined by the geometry of the road and the measured vehicle yaw rate can be expressed as follows: (9) e ˙ = ψ˙ ref − ψ˙ v ψ
In order to describe the longitudinal dynamics of different drivers, the velocity error between the speed limit and the actual vehicle velocity has to be formulated as well with the following equation: (10) evel = vref − v where vref is the speed limit on the actual road sections. 3.2 Driver model identification The scheme of the identification is illustrated in Figure 7. The test drivers maneuver the vehicle simulator along a predefined track, while several input and output signals are measured with a sampling time of Tdt = 0.01 seconds. For the identification of combined driver models, both longitudinal and lateral dynamics have to be considered, as well as driver inputs affecting them. The input signals of the driver model described in Section 3.1 are the longitudinal and lateral accelerations ax and ay , the lateral preview error eprev defined by (6), the yaw rate error eψ˙ y defined by (9) and the velocity error evel defined by (10). These input measurement signals are formulated in the prev T eψ˙ ay evel ax . input vector u = ey The output of the driver model is the steering angle δ and the longitudinal force Fl , which are realized by the manipulation of the steering wheel and the accelerator and brake pedals of the simulator vehicle. These driver model outputs are the control inputs for the vehicle (see Figure T 7) and are given in the output vector y = [δ Fl ] .
The goal of the identification procedure is to estimate linear dynamic models of different driver behaviors from the observation data. Black-box identification methods, in which both the model structure and its parameters are unknown, have been well elaborated, see Ljung (1987); Kon et al. (2013). One of the biggest advantage of ARX model estimation compared to other techniques lies in the numerical efficiency, giving a unique solution satisfying the global minimum of the loss function. An AutoRegressive with Exogeneous part (ARX) model is estimated in the following form: p q Ai yt−i + Bj ut−j + et (11) yt = − i=1
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After defining the model structure described in (11) it is possible to search for the best fitting model for each driver. In the analysis the number of previous inputs and outputs q and p has to be determined such way, that the relation between the input and output variables are also considered. Both structure and parameter estimation methods the System Identification Toolbox of the Matlab is applied, see Ljung (1987). The identified driver model is validated by comparing the outputs of the driver model (vector y with the measurement vehicle inputs data gained as a result of the driving simulator experiment. Note, that the excitations of the driver model (vector u) are that gained by the simulator study. The outputs of the driver model (steering angle δ and longitudinal force Fl ) are compared to the measurement results by analyzing the results of the model fitting. The smaller the error between the simulated and measured values, the more punctual the driver model is. The analysis of the model fitting is as follows. First, the model output signals are put on the same scale before further analysis. The normalized data are calculated with the following equation: yi (t) y (t) − i yinorm (t) = , i = [1, 2] (12) n yi (t) 2 (yi (t)− n
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The normalization of the measurement signals are evaluated identically. For example for the steering angle the normalization is the following: δexp (t) δ (t) − exp norm δexp (t) = (13) n δexp (t) 2 (δexp (t)− n
Fig. 7. Scheme of the driver model identification The identification method is based on the experimental data of the test drivers maneuvering the simulator vehicle in the real-time simulation environment with the input and output signals measured and saved. The driver model is set up with nu = 5 model inputs and ny = 2 outputs. 258
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For the sake of analysis, three error functions are introduced to compare the measured and the simulated normalized signals. These are the root mean square (RMS), the standard deviation (STD) and the mean squared error (MSE). The error values are calculated for the different variations of parameter values in matrix na and nb . The
IFAC CTS 2016 May 18-20, 2016. Istanbul, Turkey
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4. SIMULATION RESULTS The vehicle parameters used in the simulator are calibrated to represent an A-class small car, propelled with a 75 kW engine driving the front axle of the car.
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The geometry of the track is illustrated in Figure 8 is based on the Waterford Michigan Race Track, and contains several types of curves. The subject drivers were chosen such way to represent a broad range of behavior, and were asked to operate the simulator around the racetrack. Note, that in present study only 10 drivers have been taken into the test process to demonstrate the operation of the proposed classification and identification method, however, a much bigger number of subject drivers are needed to gain results for real-life applications. The signals were measured and saved for post processing. The classification was then evaluated, using the acceleration/deceleration and velocity data collected. These are shown in Figure 9 along with the threshold values. It can be seen at glance in Figure 9 (a), that Driver 8 exceeds the speed limit the most time and the longitudinal and lateral acceleration threshold values in Figure 9 (b) and Figure 9 (c) are also violated several times. Since the vehicle brake system is always designed to be much stronger than the engine, the longitudinal acceleration threshold value has been separated for acceleration (3 m/s2 (minA)) and deceleration (6 m/s2 (minD)), as it can be seen in 9 (b). It can be observed, that these longitudinal acceleration threshold values are only violated at racetrack parts with speed limit sign or at the entrance of sharp corners. The lateral acceleration threshold value is chosen to be 6 m/s2 (minC), and is only violated at high speed cornering for few drivers (including Driver 8). Note, that in most cases there is a link between the speed limit violation and the violation of the lateral acceleration limit. The classification calculation has been evaluated offline, working with the vehicle records and threshold values 259
Fig. 9. Results of test drivers listed above. The cumulative value of time duration when the vehicle exceeds the threshold values during the lap serves as the basis for the driver categorization. By this mean, the categorization algorithm in Matlab identifies the speed limit violations for each driver, along with the abrupt motions and their station on the track. In the proposed algorithm, the comparison of the detected abrupt motions are evaluated with 0.1 meter margin for the station on the track, i.e detected threshold violations for different drivers with smaller distance margin than 0.1 meter are considered as mutual, not unique violation. Next, the most typical drivers for each category has been selected to identify a benchmark model. Thus, Driver 8 represents the aggressive driver with most of the abrupt motions (even at unique places) and speed limit violations, Driver 1 stands for the defensive driver with no speed limit violation and abrupt movement at all, while Driver 5 represents the normal category with few abrupt movements at some common places where others also violate the acceleration/deceleration limits. Note, that none of the chosen test drivers fall in the beginner category, since abrupt motions at unique places without speed limit violation has not been detected. For each of these listed driver types (defensive, normal, aggressive) a linear model has been set up with using ARX identification method, and these models are chosen as benchmark models to represent the category type. It has been proven by error analysis that the gained models represent well other drivers falling in the same category. For example, Driver 4 categorized as defensive driver can be modeled with the benchmark model for defensive
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driver (Driver 1). By applying its measured inputs for the different benchmark models and comparing the model outputs with signals gained by the simulator study, the results shown in Figure 10 validate that behavior of Driver 4 is closest to the defensive benchmark model.
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Fig. 10. Error signals of Driver 4 with benchmark models 5. CONCLUSION The paper presented an off-line driver classification method based on trajectory analysis of several test drivers. A linear model identification procedure has also been introduced, considering both lateral and longitudinal behavior of the drivers. The categorization and identification method was underlined with a simulator experiment conducted by ten drivers with different attitude and driving experience. The result have shown that the presented offline algorithm serves as powerful tool for driver classification. With the presented model identification, benchmark driver models have been set up and validated for the different categorizes. Future work will focus on applying the proposed method with bigger number of subject drivers and different test tracks, in order to gain a more punctual model for each driver category. REFERENCES Canale, M. and Malan, S. (2002). Analysis and classification of human driving behaviour in an urban environment. Cognition, Technology & Work, 4, 197–206. Carboni, E.M. and Gogorny, V. (2014). Inferring drivers behavior through trajectory analysis. Intelligent Systems, 13, 837–848.
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