research article design of an integrated vehicle chassis ...carsim virtual scene dspace real-time...

Research ArticleDesign of an Integrated Vehicle Chassis Control System withDriver Behavior Identification

Bing Zhu12 Yizhou Chen1 Jian Zhao1 and Yunfu Su1

1State Key Laboratory of Automotive Simulation and Control Jilin University Changchun 130022 China2Key Laboratory of Bionic Engineering of Ministry of Education Jilin University Changchun 130022 China

Correspondence should be addressed to Jian Zhao zhaojianjlueducn

Received 27 April 2015 Accepted 18 August 2015

Academic Editor Yannis Dimakopoulos

Copyright copy 2015 Bing Zhu et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

An integrated vehicle chassis control strategy with driver behavior identification is introduced in this paper In order to identifythe different types of driver behavior characteristics a driver behavior signals acquisition systemwas established using the dSPACEreal-time simulation platform and the driver inputs of 30 test drivers were collected under the double lane change test conditionThen driver behavior characteristics were analyzed and identified based on the preview optimal curvature model through geneticalgorithm and neural networkmethod Using it as a base an integrated chassis control strategy with active front steering (AFS) anddirect yaw moment control (DYC) considering driver characteristics was established by model predictive control (MPC) methodFinally simulations were carried out to verify the control strategy by CarSim and MATLABSimulink The results show that theproposed method enables the control system to adjust its parameters according to the driver behavior identification results and thevehicle handling and stability performance are significantly improved

1 Introduction

In recent years improving the active safety performance ofvehicles is what researchers have been working on Withthe development of electronic control technology manyactive safety systems such as antilock braking system (ABS)traction control system (TCS) electronic stability control(ESC) active front steering (AFS) and four-wheel steering(4WS) have been widely equipped on vehicles to ensure saferand more stable driving experience However the potentialconflicts among the active control systems increase whenthey are combined without coordination [1ndash3] Thus therehave been plenty of attempts to integrate the chassis controlsubsystems for instance the Integrated Chassis Control(ICC) Unified Chassis Control (UCC) and Vehicle Dynam-ics Management (VDM) [4ndash6] With the implementationof integrated control systems the interference and couplingamong dynamic subsystems are effectively eliminated andthe stability performance of vehicle is significantly improvedNevertheless integrated control systems nowadays are gener-ally designed in the uniformmode lacking the consideration

of the influence that drivers exert on control systems As amatter of fact the driver and the active control system havestrong coupling on each other while controlling the vehicleAccording to a survey sponsored byNational Highway TrafficSafety Administration (NHTSA) of USA driverrsquos mistakeaccounts for 90 or more of all the crashes recorded [7]Therefore human driverrsquos characteristics should be involvedin the process where the integrated control system is devel-oped

As the primary control element within the traditionaldriver-vehicle system the role of human driver has beenstudied by a plenty of scientists and researchers The driverbehavior includes driverrsquos sensing judging reasoning decid-ing and finally operating the vehicle to turn accelerateand brake with strong randomicity adaptivity discretenessand variability Currently research is mainly carried out inthe aspects of driver behavior modeling the identificationof fatigue intelligent traffic control and advanced driverassistance systems (ADAS) [8]

Koh et al present a tire slip-angle based speed con-trol race driver model through analyzing the vehicle-driver

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 954514 12 pageshttpdxdoiorg1011552015954514

2 Mathematical Problems in Engineering

interaction at limit handling [9] Miyajima et al modeleddriverrsquos behavior such as turning the steering wheel orhitting the pedal with Gaussian mixture model (GMM)to identify different kinds of drivers Compared with themethod using raw pedal operation signals spectral analysismethod proposed shows a far better accuracy [10] Bolia et alproposed a two-level preview driver steering control modelThe outer loop focuses on path following while the inner onetries to capture driverrsquos physical behavior [11] Lin et al usedseveral sophisticated artificial neural network architecturesto develop driver models in a Driver-Vehicle-Environment(DVE) system [12] Sathyanarayana et al proposed a ldquocontextand driver awarerdquo (CDA) active vehicle system combiningGMM universal background model and likelihood max-imization based on information fusion to identify driverstatus and predict driverrsquos distracted behavior [13] Profoundand enlightening works above endeavored to explain whatkind of a role driver is playing in a driver-vehicle closed-loop system With further research early efforts have beenmade to design the active control system on the basis ofdriverrsquos characteristics Macadam studied the physiologicallimits and physical characteristics of drivers in detail and thenestablished the lateral and longitudinal manipulating modelof drivers [14] Hoult and Cole built a neuromuscular linearmodel which considers the coactivation of neuromuscularsystem muscle body and vehicle [15] Chai et al describeda method to adjust the parameters of steer-by-wire (SBW)system according to the driverrsquos steer characteristics whichcould be estimated from experimental data based on thegeneral driverrsquos model [16] Raksincharoensak et al Japaneseresearchers designed the direct yaw moment control systembased on the identification of driverrsquos intention and theperformance of the vehicle is significantly improved [17] Inthe literature [18] a driver behavior signal capturing systemwas introduced based onwhich the riding comfort and safetyof the vehicle are enhanced Fu et al integrated a drivermodelwith a run-off-road recovery controller considering driverrsquostarget planning pursuit behavior compensate behavior andphysical limitations [19] Keen and Cole proposed a steeringcontroller based on linear model predictive control A formalsystem identification procedure is applied to avoid bias fromthe closed-loop operation of the driver-vehicle system [20]Although the driver behavior identification methods havemade remarkable progress in practical applications thedriver behavior observation equipment mentioned above isseldom used due to its disadvantages in prize and portability

The active chassis control systems and the driver havemutual influence for vehicle control with strong couplingsDue to the complexity polytrope and uncertainty of driverbehavior it is extremely essential to fully understand thecharacteristics of drivers and control systems build thecollaborative optimization mechanism and optimize theperformance of the Driver-Vehicle-Environment system

To design the personalized vehicle control system one ofthe most important prerequisites is identifying the driverrsquosindividualities On the basis of the literature [14] ProfessorGuo proposed a ldquoPreview-Followingrdquo system theory whichdefines the decision procedure of drivers as preview andcompensation According to this theory Preview Optimal

Driver

Torquewheel

ADC

CAN

ADC

Brakepedal

Accelerationpedal

CarSimvirtualscene

dSPACE real-timesimulation

system

Figure 1 Structure of the driver behavior data acquisition system

Curvature Model is established As it demonstrates clearly arelationship between the vehicle stability and driverrsquos charac-teristics this theory has been widely used in the research ofvehicle stability control and adaptive cruise control due to itshigh precision and independence of special equipment [21]Simulation and test results show that this theory preciselydepicts driverrsquos steering procedure The key to applying thistheory is the identification of driverrsquos steering characteristics

In this paper an integrated chassis control strategy basedon the identification of driver characteristics is proposedFirst a real-time driver operation signal acquisition systembased on dSPACE is built Using this system 10 skilled10 normal and 10 novice driversrsquo manipulation signals onthe same path are collected Then genetic algorithm isapplied to analyzing the steering characteristics of differentkinds of drivers based on the Preview Optimal CurvatureModel An online driver behavior identification method isestablished using BP neural network An integrated chas-sis control (ICC) system with active front steering (AFS)and direct yaw moment control (DYC) is designed usingmodel predictive control (MPC) and considering the driverbehavior characteristics Finally simulations are carried outto validate the proposed method through the cosimulationof MATLABSimulink and CarSim Test results show thatthe proposed method enables the control system to adjustits parameters according to the driver behavior identificationresults and the vehicle stability is effectively enhanced

2 Driver Behavior Data Acquisition

21 Driver Behavior Data Acquisition System In order toprecisely analyze the driver behavior the driver behaviordata acquisition system is designed and established basedon dSPACE real-time simulation platform as shown inFigure 1 The dSPACE real-time simulation system couldrealize the seamless connection to MatlabSimulink throughthe automatic code generation and downloading Real-timeInterface (RTI) And with the test software ControlDeskthe dSPACE can accomplish the visual management andautomatic control of the tests

In this system dSPACE DS1006 is used as real-time sim-ulation processor which collects the opening of accelerator

Mathematical Problems in Engineering 3

Lane line 1 Lane line 3Lane line 2

1m

12m 135m 11m 125m 12m

3m

Figure 2 Working condition used in driver behavior data acquisi-tion

pedal and brake pedal along with the steering wheel angel inreal-time andmeanwhile feeds back the signals to the CarSimvehiclemodel which runs on an industrial personal computer(IPC) CarSim generates a virtual scene projected to a largescreen according to which the driver perceives the drivingenvironment and operates the vehicle

In order to enhance the immersion the torque steeringwheel made by SENSODRIVE is adopted in the system Thesteering wheel possessing adjustable variables of damp andfriction can simulate the torque feedback of the real roadand greatly enhances the driving experience The steeringwheel is connected to dSPACE DS1006 through CAN busThe linear potentiometer displacement sensors are used forthe acquisition of the accelerator pedal and the brake pedalsignals through the AD ports

22 Driver Behavior Data Acquisition In order to identifythe characteristics of different drivers the usage modes ofdifferent kinds of drivers are analyzed In normal workingconditions the usage modes of different drivers tend tobe similar and difficult to distinguish Thus driving dataacquisition experiments are carried out under the double lanechange (DLC) working conditions The target path is shownin Figure 2

In the experiments to guarantee the validation of the testdata 20 male drivers and 10 female drivers are chosen as thetest samples Among the drivers 10 are skilled drivers 10 arenormal ones and the last 10 are novice in driving Before theexperiment started all drivers are trained to be acquaintedwith the experiment process and the data collection systemWhen the data collection begins the driver accelerates fromthe same start point to the speed of 60Kmh 80Kmh100Kmh 110 Kmh and 120Kmh respectively at the endof lane line 1 Then the lane change is carried out accordingto the target path When the car passes lane line 3 the driverdecelerates the car to stop

Typical collection signals of three different kinds ofdrivers are shown in Figure 3 It is seen that facing the paniclane change the skilled driver shows shorter response timeand could implement lane change smoothly In contrast thenovice driver tends to operate the vehicle sharply and thevehicle may lose its stability

3 Analysis of Driver Behavior Characteristics

31 Preview Optimal Curvature Model As is shown inFigure 3 among the driversrsquo operating signals the steering

wheel angles show the most significant difference amongthree kinds of drivers Thus in this research steering wheelangle is chosen to identify behavior characteristics of differentkinds of drivers Preview optimal curvature model which iswidely used in driver-vehicle closed-loop system research asmentioned above is introduced here to analyze the driversteering behavior [22]

It is widely believed that the driver plans for the desiredpathwhen heshe is driving a vehicle Assume that the desiredpath is119884 = 119891(119883) and the preview time of driver is a constantas is shown in Figure 4 At time 119905 the state of the vehicle is

119910 = 119910 (119905)

119910 = 119910 (119905)

(1)

On the condition that the preview distance is 119889 namelythe driver always gazes at preview point which is 119889 away infront of the vehicle the preview time could be defined as

119879 =119889

119881119909

(2)

where 119881119909is the longitudinal velocity of the vehicle

The lateral coordinate of the preview point is 119891(119905 + 119879) Ifthe driver operates a steering angel 120575sw in accordance withwhich the curvature of the vehicle is 1119877 and the lateralacceleration is 119910(119905) in time 119879 the lateral displacement of thevehicle is

119891 (119905 + 119879) = 119910 (119905) + 119879 sdot 119910 (119905) +1198792

2119910 (119905) (3)

Considering

119910 =1198812

119909

119877=120575sw1198941198711198812

119909 (4)

among which 119871 is the wheel base and 119894 is the steering ratioWe get the optimal steering wheel angle

120575sw =2119894119871

1198892(119891 (119905 + 119879) minus 119910 (119905) minus 119879 sdot 119910 (119905)) (5)

Drivers always intend to operate a steering wheel angle120575sw under which the displacement of the vehicle could fitthe desired path in time 119879 Considering the lag of driverrsquosperception and action together with the dynamic response ofthe vehicle under a sharp steering the steering wheel angle120575sw that the driver is supposed to operate to track the targetpath 119891 is

120575sw119891(119904)

=21198620(1 + 119879

119888119904) 119890minus1199051198891199041199042

1198792119901(1 + 119879

ℎ119904) 1199042 + 2119862

0(1 + 119879

119888119904) (1 + 119879

119901119904) 119890minus119905119889119904 (119886

119910120575sw)

(6)

where 119879119901is the driverrsquos preview time 119905

119889is the driverrsquos neural

delay time 119879ℎis the driverrsquos muscle delay time 119879

119888is the

correction parameter of steering and 1198620is the proportional


Skilled driverNormal driverNovice driver

020406080

100

Ope

ning

of a

ccel

erat

or

peda

l (

)

2 4 6 8 10 12 14 16 18 200Time (s)

(a) Accelerator pedal input


020406080

100

Ope

ning

of b

rake

pe

dal (

)

2 4 6 8 10 12 14 16 18 200Time (s)

(b) Brake pedal input


minus200

minus100

0

100

200

Stee

ring

whe

el an

gle (

rad)

2 4 6 8 10 12 14 16 18 200Time (s)

(c) Steering wheel input


020406080

100120

Spee

d (k

m hminus1)

2 4 6 8 10 12 14 16 18 200Time (s)

(d) Vehicle speed

Figure 3 Typical signals of different kinds of drivers

f(t)

y(t)

t

f(t + T) minus y(t) minus T middot y(t)

t + T

T middot y(t)

Figure 4 Frame of driverrsquos steering decision

gain correction parameter The relationships among theparameters are

119879119888= 119905119889+ 119879ℎ+ 119879119886minus

119886119879119901

3

1198620=1

119866119886119910

(7)

where 119879119886is a parameter of the vehicle and 119886 is the following

order 119866119886119910

is the steady-state gain of lateral acceleration of119886119910to 120575sw whose dynamic response is defined as the vehicle

model 119881(119904) which will be described in the next section

Driver modelVehiclemodel

f(X)

1y

minus

minus

+V(s)

yTp

eTps2C0(1 + Tcs)e

minustds

T2p(1 + Ths)

1

s

1

s

120575sw ay

Figure 5 Driver preview optimal curvature model

Therefore the frame of driver preview optimal curvaturemodel could be demonstrated as in Figure 5 from whichit is clearly seen that the parameters 119879

119901 119905119889 and 119879

ℎcould

characterize different kinds of driversrsquo behavior and namelythe task of identification of different kinds of driversrsquo steeringbehavior is confirming the three parameters

32 Identification of Driver BehaviorCharacteristics Parameters

321 Identification of the Parameters of Vehicle Model Asshown in Figure 5 before identifying the driverrsquos parametersthe characteristics of the vehicle should be specified


Output of ARX model

minus25

minus2

minus15

minus1

minus05

005

115

2

Late

ral a

ccel

erat

ion

(mmiddotsminus

2)

1 2 3 4 5 6 7 8 9 100Time (s)

Real Ay

Figure 6 Output of vehicle model and real lateral acceleration

According to the preview optimal curvature model 119881(119904)could be described as the dynamic response of 119886

119910to 120575sw

119881 (119904) =

119886119910

120575sw(119904) = 119866

119886119910

1 + 1198791199101119904 + 11987911991021199042

1 + 1198791119904 + 11987921199042 (8)

In the ideal situation 119881(119904) could be directly described as119866119886119910 Considering that the vehiclersquos dynamic response could

not be ignored when it is taking a sharp turning 1198791199101 1198791199102 1198791

and 1198792are constants to be identified and 119879

119886in (7) is defined

as (1198791minus 1198791199101)

The aim of parameters identification is to describe themathematic relation between the input and output of thesystem Since themechanismof the vehicle dynamic responseis not necessarily required in this research ARX modelwhich does not demand the explicit physical relationship ofthe system and works well when dealing with the higher-order system is adopted here to identify the parameters ofthe vehiclemodelThe expression of the ARXmodel is shownbelow

119860 (119911)119860119910(119911) = 119861 (119911) 119906 (119911) + 119890 (119911) (9)

where

119860 (119911) = 1 + 1198861119911minus1

+ 1198862119911minus2

+ sdot sdot sdot + 119886119899119911minus119899

119861 (119911) = 1 + 1198871119911minus1

+ 1198872119911minus2


(10)

Here 119899119898 = 2 119890(119911) is white noise 119906(119911) is 120575sw and 119860119910(119911) is119886119910Using the MATLAB toolbox to compute the real lateral

acceleration and the output of the identification model areshown in Figure 6 which demonstrates that the vehiclemodelbuilt here has a high accuracy and the identification rate is972

322 Offline Driver Model Parameters Identification for Dif-ferent Kinds of Drivers On the basis of the identificationof the vehicle model 119881(119904) driver behavior characteristicparameters 119879

119901 119905119889 and 119879

ℎ are to be identified Genetic algo-

rithm which simulates the mechanism of natural selection

Table 1 Constraints of driver behavior characteristic parameters

119879119901

119905119889

119879ℎ

[058 2072] [017 053] [008 036]

and biological evolutionism has been widely used in patternrecognition computing science automatic control and soforthHere genetic algorithm is adopted to identify the drivermodel parameters offline

Firstly the three model parameters of drivers should beconstrained to appropriate scope to guarantee the accuracyof identification results as well as accelerate the identificationprocedure As is demonstrated in the literature [22] theparameters are supposed to meet the requirements

119879119895isin (119880119895min 119880119895max) (11)

where 119879119895is 119879119901 119905119889 and 119879

ℎ 119880119895min and 119880119895max are the minimum

and maximum of 119879119901 119905119889 and 119879

ℎ respectively 119895 = 1 2 3

The parameters are constrained to a certain scope shownin Table 1

To ensure the precision of identification of driver behav-ior characteristic and that the dynamic responses of the drivermodel accord well with the experimental data the targetfunction is defined as the weighted value of the error squaresum of steering wheel angel lateral acceleration and lateraldisplacement

119869 = 1199081lowast 1198691+ 1199082lowast 1198692+ 1199083lowast 1198693 (12)

where 1198691 1198692 and 119869

3are the deviation indices of the steering

wheel angel the lateral acceleration and the lateral displace-ment respectively Their expressions are shown as

1198691=1

1199050

int

1199050

0

(120575sw minus 120575sw)2

119889119905

1198692=1

1199050

int

1199050

0

(119886119910minus 119886119910)2

119889119905

1198693=1

1199050

int

1199050

0

(119910 minus 119910)2

119889119905

(13)

where 120575sw 119886119910 and 119910 are the theoretical data based ondriver model and vehicle model 119908

1 1199082 and 119908

3are weight

coefficients and 1199050is the sampling time

Since there are three variables the fitness functionis determined according to the simple adaptive functionmethod Besides the binary encoding method proportionselection strategy single point switching strategy and simplemutation strategy are adopted [23]

Asmentioned in Section 2 the drivers can be divided intothree categories the skilled ones normal ones and noviceones With genetic algorithm the driverrsquos characteristicscould be identified quantitatively and the results of theidentification of parameters are listed in Table 2

When the offline identification is finished the resultsare adopted as the training output of the online BP neuralnetwork model used in online characteristics identification


Table 2 Identification results of driver behavior characteristicparameters

Driver Average Standard deviation Target varianceNovice drivers119879119901

07100 0096447016119890 minus 003119905

11988901489 00834

119879ℎ

03740 00637Skilled drivers119879119901

16954 0096155144119890 minus 003119905

11988903763 00720

119879ℎ

03632 00560Normal drivers119879119901

11534 0101575145119890 minus 003119905

11988902388 01132

119879ℎ

02577 00873

Input layer Hidden layer Output layer

f(X)

Tp120575sw

ay

y

Vx

y1

y2

y8

td

Th

Figure 7 Structure of the BP neural network model

323 Online Driver Behavior Characteristic Parameters Iden-tification Due to the genetic algorithmrsquos relative time-consuming low efficiency and absence of meeting the real-time requirement of the control system in this research BPneural network algorithm is designed for online identifica-tion of driver behavior characteristic parameters BP neuralnetwork is established as in Figure 7

The BP neural network model has 3 layers the numberof nodes of the input layer hidden layer and output layer119899 119897 and 119898 is 5 8 and 3 respectively The five nodes 119909

1sim1199095

in input layer are 120575sw 119891 119910 119886119910 and 119881119909 respectively 120575sw isdriverrsquos steering wheel angle 119891 is the lateral displacementof the target path 119910 is the real lateral displacement of thevehicle 119886

119910is the lateral acceleration of the vehicle and 119881

119909

is the longitudinal velocity of the vehicle The three nodes1199111sim1199113in output layer are 119879

119901 119905119889 and 119879

ℎ which are the driversquos

behavior characteristics to be identifiedThe output of the hidden layer is

119867119895= 119892(

119899

sum

119894=1

120596119894119895119909119894minus ℎ119895) 119895 = 1 2 119897 (14)

The output of the output layer is

119874119896=

119897

sum

119895=1

120596119895119896119867119895minus 119900119896 119896 = 1 2 119898 (15)

where 120596119894119895and 120596

119895119896are weighting coefficients of input layer to

hidden layer and hidden layer to output layer respectivelyThe thresholds of the hidden layer and output layer are ℎ and119900 respectively The 119892(119909) is the excitation function

119892 (119909) =1

1 + 119890minus119909 (16)

The deviation calculation function is used to calculate thedeviation of the desired output and the calculated output ofthe model

119890119896=1

2(119884119896minus 119874119896)2

119896 = 1 2 119898 (17)

where 119884119896is the desired output

In order to minimize the variance of the output back-propagation modification weight matrix is used as the learn-ing rule of the model

120596new119894119895= 120596119894119895+ 120578119867119895(1 minus 119867

119895) 119909 (119894)

119898

sum

119896=1

120596119895119896119890119896

119894 = 1 2 119899 119895 = 1 2 119897

120596new119895119896= 120596119895119896+ 120578119867119895119890119896 119895 = 1 2 119897 119896 = 1 2 119898

ℎnew119895= ℎ119895+ 120578119867119895(1 minus 119867

119895)

119898

sum

119896=1

120596119895119896119890119896 119895 = 1 2 119897

119900new119896= 119900119896+ 119890119896 119896 = 1 2 119898

(18)

where 120596new119894119895

and 120596new119895119896

are weighting coefficients after updateand ℎnew119895

and 119900new119896

are thresholds after update 120578 is the learningrate

The offline identification results obtained from geneticalgorithm are used to train the BP neural network modelAnd when the training performance is as shown in Figure 8the training is stopped The datasheet trained from neuralnetwork model could be directly used as driver behaviorcharacteristic parameters identificationmodelTherefore thedriver model whose characteristics fit the current driverrsquosbehavior is achieved

Thus when a driver is driving a car hisher behaviorcharacteristic parameters could be identified rapidly on thebasis of which the control system could be designed to fit thedriverrsquos characteristics

4 Design of Integrated Chassis Control System

The architecture of the proposed ICC system for AFSand DYC integration with driver behavior identification isshown in Figure 9 The control system is mainly consistedof driver identification module preview optimal curvaturedriver model 2-Degree-of-Freedom (DOF) vehicle reference


TrainValidation

TestBest

5 10 15 20 25 30 350Epochs

10minus3

10minus2

10minus1

100

101

Mea

n sq

uare

d er

ror (

mse

)

Figure 8 Performance of neural network model

Vehicle

Real driver

Targetpath

Driver model

Dat

a acq

uisit

ion

syste

m

2-DOFreference

model

MPC controller

ICCcontroller

Control system

Driver identification

modulePrediction

moduleTp

120575sw

120575sw

120575sw

120575fc

ay

y

Vx

Vx

Vx

td Th

120573d 120596rd

f

yf

Δ120575f ΔMz

120573 120596r

Figure 9 ICC system configurations with driver behavior identifi-cation

model andmodel prediction control (MPC) based controllermodule Different kinds of driversrsquo characteristics aremarkedby the three parameters119879

119901 119905119889 and119879

ℎas is shown in Section 3

the parameters 119879119901 119905119889 and 119879

ℎare identified online according

to the driverrsquos operation and the state of the vehicleWhen thecontroller is on the three parameters are used to build thedriver model 120575

119891119888is defined as predicted front wheel angle

based on driver model 120575119891119888

of the certain driver could bepredicted at next sample time according to the identificationresult along with vehicle motion state Based on the predicted120575119891119888 2-DOF referencemodel could output the desired yaw rate

and side slip angle which are the target of theMPC controllerTheMPC controller optimizes online the active control frontwheel steering angle Δ120575

119891and yaw moment Δ119872

119911

41 Linear 2-DOF Reference Model The 2-DOF referencevehicle model which considers both accuracy and simplicityis used for target outputs calculation as shown in Figure 10

Vx

120573f

120573rV Vy

Mz

120596r

120573120575f

FyrFyflrlf

Figure 10 2-DOF reference model

The side-slip angle 120573 and yaw rate 120596119903are described in the

modelThe vehicle state space equation is

= A0119909 + B0119906

119910 = C0119909

(19)

where

119909 = [120573 120596119903]T

119906 = [120575119891119872119885]T

A0= [

1198861111988612

1198862111988622

] =

[[[[[

[

minus

119888119891+ 119888119903

119898 sdot 119881119909

minus1 +

119888119903119897119903minus 119888119891119897119891

119898 sdot 119881119909

2

119888119903119897119903minus 119888119891119897119891

119868119911

minus

1198881199031198972

119903+ 1198881198911198972

119891

119868119911sdot 119881119909

]]]]]

]

B0= [

1198871111988712

1198872111988722

] =

[[[[

[

119888119891

119898 sdot 119881119909

0

119888119891119897119891

119868119911

1

119868119911

]]]]

]

C0= [

1198881111988812

1198882111988822

] = [

1 0

0 1]

(20)

where 119888119891 119888119903are front and rear axle cornering stiffness 119898 is

mass 119897119891 119897119903describe the distances from the vehicle CG to

the front and rear axle respectively 119868119911is yaw inertia of the

vehicle and 120575119891and119872

119911are the front wheel steering angle and

yaw moment of the vehicleTo guarantee the lateral stability of the vehicle the yaw

rate should be restricted within a stable fieldThe desired yawrate could be obtained from the steady-state gain of the yawrate of the reference model

120596119903119889=

119881119909sdot 120575119891

(119897119891+ 119897119903) sdot [1 + (119881

119909Vch)2

]

(21)

where

V2ch =119888119891sdot 119888119903sdot (119897119891+ 119897119903)2

119898(119888119903119897119903minus 119888119891119897119891)

(22)

Also the desired yaw rate should be restricted accordingto the road friction coefficient 120583

10038161003816100381610038161205961199031198891003816100381610038161003816 le 120583 sdot

119892

119881119909

(23)


To maintain lateral stability it is important to sustaindriverrsquos control authority which can be achieved when thevehicle sideslip angle is small According to some literatures[24] the desired sideslip angle can be chosen as

120573119889= 0 (24)

42 Design of Integrated Chassis Controller Based on MPCAs a novel methodology with prediction of future states tominimize the deviation between the ideal and actual output ofthe system the model predictive control (MPC) shows goodstability and robust performance [20 25ndash27] So it drawsattentions by the design of integrated chassis control systemwith consideration of driver behaviors

In this paper the actual and expected side slip angle andyaw rate are selected as the inputs of the MPC controller andthe outputs are expected active yaw moment and front steer-ing angle In the controller the predictive model based onthe 2-DOF reference model is built to predict the controlledoutput firstlyThen the quadratic programming is developedfor the optimal solution

First the state space function (21) is discretized as

119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896)

119910 (119896) = 119862119909 (119896)

(25)

And the increment equation could be written as

Δ119909 (119896 + 1) = 119860Δ119909 (119896) + 119861Δ119906 (119896)

119910 (119896) = 119862Δ119909 (119896) + 119910 (119896 minus 1)

(26)

where

Δ119909 (119896) = 119909 (119896) minus 119909 (119896 minus 1)

Δ119906 (119896) = 119906 (119896) minus 119906 (119896 minus 1)

(27)

119860 = 119868 + 1198791199041198600 119861 = 119879

1199041198610 and 119862 = 119862

0 where 119879

119904is the discrete

sampling timeThen the predictive controlled output is

119884 (119896 + 1 | 119896) = 119878Δ119909 (119896) + 119864119910 (119896) + 119865Δ119880 (119896) (28)

where

119884 (119896 + 1 | 119896) =

[[[[[[

[

119910 (119896 + 1 | 119896)

119910 (119896 + 2 | 119896)

119910 (119896 + 119901 | 119896)

]]]]]]

]

Δ119880 (119896) =

[[[[[[

[

Δ119906 (119896)

Δ119906 (119896 + 1)

Δ119906 (119896 + 119888 minus 1)

]]]]]]

]

119878 =

[[[[[[[[[[

[

119862119860

1198621198602

+ 119862119860

119901

sum

119894=1

119862119860119894

]]]]]]]]]]

]

119865 =

[[[[[[[[[[[[[[[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

2

sum

119894=1

119862119860119894minus1

119861 119862119861 0 sdot sdot sdot 0

sdot sdot sdot

119862

sum

119894=1

119862119860119894minus1

119861

119862minus1

sum

119894=1

119862119860119894minus1

119861 sdot sdot sdot 119862119861

sdot sdot sdot

119875

sum

119894=1

119862119860119894minus1

119861

119875minus1

sum

119894=1

119862119860119894minus1

119861 sdot sdot sdot

119875minus119862+1

sum

119894=1

119862119860119894minus1

119861

]]]]]]]]]]]]]]]]]]]]

]

119864 =

[[[[[[

[

119868

119868

119868

]]]]]]

]

(29)

where 119901 and 119888 are the predictive and control horizonsrespectively and 119888 le 119901

The cost function could be described as

119869 (119910 (119896) Δ119880 (119896)) =10038171003817100381710038171003817120582119910(119884 (119896 + 1 | 119896) minus 119884

119889(119896 + 1))

10038171003817100381710038171003817

2

+1003817100381710038171003817120582119906Δ119880 (119896)

1003817100381710038171003817

2

(30)

where 120582119910is the weight coefficient of the output deviation 120582

119906

is theweight coefficient of control input increment and119884119889(119896+

1) is the desired output in the prediction horizon namely

119884119889(119896 + 1) = [120573

119889120596119903119889]T (31)

At each time step the following optimization problem issolved

minΔ119880(119896)

119869 (119910 (119896) Δ119880 (119896)) (32)

With the constraints of the inputs the variation of inputs andthe outputs respectively is

119906min (119896 + 119895) le 119906 (119896 + 119895) le 119906max (119896 + 119895)

119895 = 0 1 119888 minus 1

(33)

minusΔ119906min (119896 + 119895) le Δ119906 (119896 + 119895) le Δ119906max (119896 + 119895)

119895 = 0 1 119888 minus 1

(34)

119910min (119896 + 119895) le 119910 (119896 + 119895) le 119910max (119896 + 119895)

119895 = 0 1 119901 minus 1

(35)


Table 3 Vehicle parameters for simulation

Parameters Symbol ValuesMass (kg) 119898 2210Front axle cornering stiffness (Nrad) 119888

11989162800

Rear axle cornering stiffness (Nrad) 119888119903

68000Distance from vehicle CG to the front axle (m) 119897

119891107

Distance from vehicle CG to the rear axle (m) 119897119903

223Vehicle moment of inertia about the z-axis (kgm2) 119868

11991143316

where inequalities (34) limit the control inputs and (35)constrain the changes of the control input while (36) areconstraints on system output variables

Obviously it is a typical constraint optimization problemand can be transformed into a quadratic programming (QP)problem

minΔ119880(119896)

1

2Δ119880 (119896)

119879

119882119867Δ119880 (119896) + 119882

119879

119866Δ119880 (119896)

st 119860constΔ119880 (119896) ge 119887const

(36)

where

119882119867= 2 (119878

119879

120582119879

119910120582119910119878 + 120582119879

119906120582119906)

119882119866= minus2119878

119879

120582119879

119910120582119910119864119901(119896 + 1 | 119896)

119864119901(119896 + 1 | 119896) = 119884

119889(119896 + 1) minus 119878Δ119909 (119896) minus 119864119910 (119896)

(37)

where 119860const and 119887const are the constrained matricesThen the first sample of the results is used to compute

the optimal steering angle and direct yaw moment by thefollowing feedback control law

Δ119906 (119896) = [

1 0 0 sdot sdot sdot 0

0 1 0 sdot sdot sdot 0]

2times2119862

Δ119880 (119896)

119906 (119896) = 119906 (119896 minus 1) + Δ119906 (119896)

(38)

5 Analysis and Simulation

In order to verify the integrated vehicle chassis controlstrategy based on driver behavior identification the cosimu-lation of MATLABSimulink and CarSim is adopted and theprimary parameters of vehicle are shown in Table 3

The simulation is carried out under a typical doublelane change working condition The driver model in CarSimis used and its characteristic is identified by the algorithmonline To verify the robust performance of the controlstrategy when the speed varies the simulation is started at thelongitudinal speed of 60Kmh and 80Kmh respectively

According to the online identification results the threesteering parameters of driver model in CarSim are shown inTable 4

The three parameters are adopted in the preview optimalcurvature driver model built in MATLABSimulink The testresults of the control strategy are shown in Figures 11-12 inwhich (a) is the trajectories (b) and (c) are yaw rate and lateral


119879119901

119905119889

119879ℎ

13886 04176 01589

acceleration respectively and (d) and (e) are the controlledsteering angle and direct yaw moment respectively It isseen that both vehicles can track the target path acceptablymoreover the path-following performance of the vehicle isclearly further improved by the usage of driver behavioridentification (DBI) and MPC compared to the vehicle withonly MPC In the meanwhile both the yaw rate and thelateral acceleration of the vehicle withDBI andMPC track thedesired valuemore closely than vehiclewith onlyMPCwhichindicates that the handling and stability are further improvedby the introduction of DBI into MPC Furthermore bothactuators execute reduced output magnitude It is impliedthat their energy consumption are optimized compared tothe vehicle equipped with only MPC controller besides asnormally implemented by active braking control a reduceddirect yaw moment control will also lessen the losses ofvehicle speed and engine power

Therefore on double lane change the integrated chassiscontrol system based onMPC can effectively ensure the vehi-cle driving stabilityWhen combinedwithDBI the integratedcontroller further regulates the lateral displacement yaw rateand lateral acceleration to a desired region with reducedoutput of actuators

6 Conclusion

This paper presents an integrated control strategy with driverbehavior identification

Firstly the driver behavior data acquisition system isdesigned and established based on dSPACE real-time sim-ulation platform and the driver inputs of different kindsof drivers were collected under the double lane change testcondition As is shown in collected data among the driversrsquooperating signals the steering wheel angles show the mostsignificant difference among different kinds of drivers

Based on this preview optimal curvature model is intro-duced to analyze the driver steering behavior The geneticalgorithm for offline usage and a neural network algorithmfor online usage are designed to recognize different patternsof drivers specifically to identify the three steering parame-ters of driver model

Then an integrated control strategy for active steeringangle and direct yaw moment is proposed The identifieddriver model is used to predict the steering angle next sampletime according to the target path and vehicle state A linear 2-DOF reference model is adopted to calculate the desired stateof the vehicle and model predictive control (MPC) is used tocalculate the active control quantity to be exerted on vehicle

Finally simulations are carried out with the cosimulationof MATLABSimulink and CarSim The results indicate thatthe proposedmethod could identify the driver behavior char-acteristic parameters and enable the control system to adjust


Target pathOnly MPCDBI and MPC

minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)

TargetOnly MPCDBI and MPC

minus15

minus10

minus5

0

5

10

15

5 10 150Time (s)

Yaw

rate

(deg

sminus1)

(b)

0 5 10 15Time (s)

UncontrolledOnly MPCDBI and MPC

minus4

minus2

0

2

4

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)

Figure 11 Test results at speed of 60Kmh



minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

Yaw

rate

(deg

sminus1)

5 10 150Time (s)

(b)


5 10 150Time (s)

minus5

0

5

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)



its parameters according to the driver behavior identificationresults Meanwhile the integrated control considering thedriverrsquos characteristics further enhanced the vehiclersquos han-dling and stability performance compared to individualMPCcontrol

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is partially supported by the National Natural Sci-ence Foundation of China (51105169 51205156 and 51475206)and Jilin Province Science andTechnologyDevelopment PlanProjects (20140204010GX)

References

[1] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) HarbinChina September 2008

[2] Y Kou H Peng and D Jung ldquoDevelopment and evaluation ofan integrated chassis control systemrdquo JSAE Review of Automo-tive Engineering vol 29 no 3 2008

[3] A Elmarakbi C Rengaraj A Wheately and M Elkady ldquoNewintegrated chassis control systems for vehicle handling perfor-mance enhancementrdquo International Journal of Dynamics andControl vol 1 no 4 pp 360ndash384 2013

[4] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo SAE Paper2011-01-0958 2011

[5] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[6] A Trachtler ldquoIntegrated vehicle dynamics control using activebrake steering and suspension systemsrdquo International Journalof Vehicle Design vol 36 no 1 pp 1ndash12 2004

[7] J C Fell and M Freedman The Relative Frequency of UnsafeDriving Acts in Serious TrafficCrashes National Highway TrafficSafety Administration Ishington DC USA 2001

[8] T Toledo ldquoDriving behaviour models and challengesrdquo Trans-port Reviews vol 27 no 1 pp 65ndash84 2007

[9] Y Koh K Yi and K Kim ldquoA tire slip-angle based speed controldriver model for analysis of vehicle-driver systems at limithandlingrdquo SAE Technical Paper 2015-01-1566 2015

[10] C Miyajima Y Nishiwaki K Ozawa et al ldquoDriver modelingbased on driving behavior and its evaluation in driver identifi-cationrdquo Proceedings of the IEEE vol 95 no 2 pp 427ndash437 2007

[11] P Bolia T Weiskircher and S Muller ldquoDriver steering modelfor closed-loop steering function analysisrdquo Vehicle SystemDynamics vol 52 no 1 pp 16ndash30 2014

[12] Y Lin P TangW J Zhang andQ Yu ldquoArtificial neural networkmodelling of driver handling behaviour in a driver-vehicle-environment systemrdquo International Journal of Vehicle Designvol 37 no 1 pp 24ndash45 2005

[13] A Sathyanarayana P Boyraz and J H L Hansen ldquoInformationfusion for robust rsquocontext and driver awarersquo active vehicle safetysystemsrdquo Information Fusion vol 12 no 4 pp 293ndash303 2011

[14] C C Macadam ldquoUnderstanding and modeling the humandriverrdquo Vehicle System Dynamics vol 40 no 1ndash3 pp 101ndash1342003

[15] W Hoult and D J Cole ldquoA neuromuscular model featuringco-activation for use in driver simulationrdquo Vehicle SystemDynamics vol 46 no 1 pp 175ndash189 2008

[16] YW Chai Y Abe Y Kano andM Abe ldquoA study on adaptationof SBW parameters to individual driverrsquos steer characteristicsfor improved driver-vehicle system performancerdquo Vehicle Sys-tem Dynamics vol 44 supplement 1 pp 874ndash882 2006

[17] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 supplement 1 pp 911ndash9212008

[18] A Sathyanarayana P Boyraz Z Purohit R Lubag and J HL Hansen ldquoDriver adaptive and context aware active safetysystems using CAN-bus signalsrdquo in Proceedings of the IEEEIntelligent Vehicles Symposium (IV rsquo10) pp 1236ndash1241 IEEEJune 2010

[19] C Fu P T Freeman and J R Wagner ldquoDriver models forvirtual testing of automotive run-off-road and recovery controlsystems and education strategiesrdquo SAE Paper 2015-01-02562015

[20] S D Keen and D J Cole ldquoBias-free identification of a linearmodel-predictive steering controller from measured driversteering behaviorrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 42 no 2 pp 434ndash443 2012

[21] A Y Ungoren and H Peng ldquoAn adaptive lateral preview drivermodelrdquo Vehicle System Dynamics vol 43 no 4 pp 245ndash2592005

[22] K Guo F Ma and F Kong ldquoDriver model identification ofdriver-vehicle-road closed-loop systemrdquo Automotive Engineer-ing vol 24 no 1 2002

[23] L Davis Ed Handbook of Genetic Algorithms vol 115 VanNostrand Reinhold New York NY USA 1991

[24] X Shen and F Yu ldquoInvestigation on integrated vehicle chassiscontrol based on vertical and lateral tyre behaviour correlativ-ityrdquo Vehicle System Dynamics vol 44 no 1 pp 506ndash519 2006

[25] D Q Mayne J B Rawlings C V Rao and P O ScokaertldquoConstrained model predictive control stability and optimal-ityrdquo Automatica vol 36 no 6 pp 789ndash814 2000

[26] T Qu H Chen Y Ji H Guo and D Cao ldquoModeling driversteering control based on stochastic model predictive controlrdquoin Proceedings of the IEEE International Conference on SystemsMan and Cybernetics (SMC rsquo13) pp 3704ndash3709 October 2013

[27] HOkuda X Guo Y Tazaki T Suzuki and B Levedahl ldquoModelpredictive driver assistance control for cooperative cruise basedon hybrid system driver modelrdquo in Proceedings of the AmericanControl Conference (ACC rsquo14) pp 4630ndash4636 June 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


interaction at limit handling [9] Miyajima et al modeleddriverrsquos behavior such as turning the steering wheel orhitting the pedal with Gaussian mixture model (GMM)to identify different kinds of drivers Compared with themethod using raw pedal operation signals spectral analysismethod proposed shows a far better accuracy [10] Bolia et alproposed a two-level preview driver steering control modelThe outer loop focuses on path following while the inner onetries to capture driverrsquos physical behavior [11] Lin et al usedseveral sophisticated artificial neural network architecturesto develop driver models in a Driver-Vehicle-Environment(DVE) system [12] Sathyanarayana et al proposed a ldquocontextand driver awarerdquo (CDA) active vehicle system combiningGMM universal background model and likelihood max-imization based on information fusion to identify driverstatus and predict driverrsquos distracted behavior [13] Profoundand enlightening works above endeavored to explain whatkind of a role driver is playing in a driver-vehicle closed-loop system With further research early efforts have beenmade to design the active control system on the basis ofdriverrsquos characteristics Macadam studied the physiologicallimits and physical characteristics of drivers in detail and thenestablished the lateral and longitudinal manipulating modelof drivers [14] Hoult and Cole built a neuromuscular linearmodel which considers the coactivation of neuromuscularsystem muscle body and vehicle [15] Chai et al describeda method to adjust the parameters of steer-by-wire (SBW)system according to the driverrsquos steer characteristics whichcould be estimated from experimental data based on thegeneral driverrsquos model [16] Raksincharoensak et al Japaneseresearchers designed the direct yaw moment control systembased on the identification of driverrsquos intention and theperformance of the vehicle is significantly improved [17] Inthe literature [18] a driver behavior signal capturing systemwas introduced based onwhich the riding comfort and safetyof the vehicle are enhanced Fu et al integrated a drivermodelwith a run-off-road recovery controller considering driverrsquostarget planning pursuit behavior compensate behavior andphysical limitations [19] Keen and Cole proposed a steeringcontroller based on linear model predictive control A formalsystem identification procedure is applied to avoid bias fromthe closed-loop operation of the driver-vehicle system [20]Although the driver behavior identification methods havemade remarkable progress in practical applications thedriver behavior observation equipment mentioned above isseldom used due to its disadvantages in prize and portability

The active chassis control systems and the driver havemutual influence for vehicle control with strong couplingsDue to the complexity polytrope and uncertainty of driverbehavior it is extremely essential to fully understand thecharacteristics of drivers and control systems build thecollaborative optimization mechanism and optimize theperformance of the Driver-Vehicle-Environment system

To design the personalized vehicle control system one ofthe most important prerequisites is identifying the driverrsquosindividualities On the basis of the literature [14] ProfessorGuo proposed a ldquoPreview-Followingrdquo system theory whichdefines the decision procedure of drivers as preview andcompensation According to this theory Preview Optimal

Driver

Torquewheel

ADC

CAN

ADC

Brakepedal

Accelerationpedal

CarSimvirtualscene

dSPACE real-timesimulation

system

Figure 1 Structure of the driver behavior data acquisition system

Curvature Model is established As it demonstrates clearly arelationship between the vehicle stability and driverrsquos charac-teristics this theory has been widely used in the research ofvehicle stability control and adaptive cruise control due to itshigh precision and independence of special equipment [21]Simulation and test results show that this theory preciselydepicts driverrsquos steering procedure The key to applying thistheory is the identification of driverrsquos steering characteristics

In this paper an integrated chassis control strategy basedon the identification of driver characteristics is proposedFirst a real-time driver operation signal acquisition systembased on dSPACE is built Using this system 10 skilled10 normal and 10 novice driversrsquo manipulation signals onthe same path are collected Then genetic algorithm isapplied to analyzing the steering characteristics of differentkinds of drivers based on the Preview Optimal CurvatureModel An online driver behavior identification method isestablished using BP neural network An integrated chas-sis control (ICC) system with active front steering (AFS)and direct yaw moment control (DYC) is designed usingmodel predictive control (MPC) and considering the driverbehavior characteristics Finally simulations are carried outto validate the proposed method through the cosimulationof MATLABSimulink and CarSim Test results show thatthe proposed method enables the control system to adjustits parameters according to the driver behavior identificationresults and the vehicle stability is effectively enhanced

2 Driver Behavior Data Acquisition

21 Driver Behavior Data Acquisition System In order toprecisely analyze the driver behavior the driver behaviordata acquisition system is designed and established basedon dSPACE real-time simulation platform as shown inFigure 1 The dSPACE real-time simulation system couldrealize the seamless connection to MatlabSimulink throughthe automatic code generation and downloading Real-timeInterface (RTI) And with the test software ControlDeskthe dSPACE can accomplish the visual management andautomatic control of the tests

In this system dSPACE DS1006 is used as real-time sim-ulation processor which collects the opening of accelerator



1m

12m 135m 11m 125m 12m

3m











119910 = 119910 (119905)

119910 = 119910 (119905)

(1)


119879 =119889

119881119909

(2)



119891 (119905 + 119879) = 119910 (119905) + 119879 sdot 119910 (119905) +1198792

2119910 (119905) (3)

Considering

119910 =1198812

119909

119877=120575sw1198941198711198812

119909 (4)


120575sw =2119894119871

1198892(119891 (119905 + 119879) minus 119910 (119905) minus 119879 sdot 119910 (119905)) (5)


120575sw119891(119904)

=21198620(1 + 119879

119888119904) 119890minus1199051198891199041199042

1198792119901(1 + 119879

ℎ119904) 1199042 + 2119862

0(1 + 119879

119888119904) (1 + 119879

119901119904) 119890minus119905119889119904 (119886

119910120575sw)

(6)




119888is the




020406080

100

Ope

ning

of a

ccel

erat

or

peda

l (

)

2 4 6 8 10 12 14 16 18 200Time (s)



020406080

100

Ope

ning

of b

rake

pe

dal (

)

2 4 6 8 10 12 14 16 18 200Time (s)



minus200

minus100

0

100

200

Stee

ring

whe

el an

gle (

rad)

2 4 6 8 10 12 14 16 18 200Time (s)



020406080

100120

Spee

d (k

m hminus1)

2 4 6 8 10 12 14 16 18 200Time (s)

(d) Vehicle speed


f(t)

y(t)

t


t + T

T middot y(t)



119879119888= 119905119889+ 119879ℎ+ 119879119886minus

119886119879119901

3

1198620=1

119866119886119910

(7)


order 119866119886119910




f(X)

1y

minus

minus

+V(s)

yTp

eTps2C0(1 + Tcs)e

minustds

T2p(1 + Ths)

1

s

1

s

120575sw ay



119901 119905119889 and 119879

ℎcould





Output of ARX model

minus25

minus2

minus15

minus1

minus05

005

115

2

Late

ral a

ccel

erat

ion

(mmiddotsminus

2)

1 2 3 4 5 6 7 8 9 100Time (s)

Real Ay



119910to 120575sw

119881 (119904) =

119886119910

120575sw(119904) = 119866

119886119910

1 + 1198791199101119904 + 11987911991021199042

1 + 1198791119904 + 11987921199042 (8)





as (1198791minus 1198791199101)


119860 (119911)119860119910(119911) = 119861 (119911) 119906 (119911) + 119890 (119911) (9)

where

119860 (119911) = 1 + 1198861119911minus1

+ 1198862119911minus2


119861 (119911) = 1 + 1198871119911minus1

+ 1198872119911minus2


(10)




119901 119905119889 and 119879




119879119901

119905119889

119879ℎ

[058 2072] [017 053] [008 036]



119879119895isin (119880119895min 119880119895max) (11)

where 119879119895is 119879119901 119905119889 and 119879







where 1198691 1198692 and 119869



1198691=1

1199050

int

1199050

0

(120575sw minus 120575sw)2

119889119905

1198692=1

1199050

int

1199050

0

(119886119910minus 119886119910)2

119889119905

1198693=1

1199050

int

1199050

0

(119910 minus 119910)2

119889119905

(13)


1 1199082 and 119908

3are weight








07100 0096447016119890 minus 003119905

11988901489 00834

119879ℎ

03740 00637Skilled drivers119879119901

16954 0096155144119890 minus 003119905

11988903763 00720

119879ℎ

03632 00560Normal drivers119879119901

11534 0101575145119890 minus 003119905

11988902388 01132

119879ℎ

02577 00873


f(X)

Tp120575sw

ay

y

Vx

y1

y2

y8

td

Th




1sim1199095



119909


119901 119905119889 and 119879



119867119895= 119892(

119899

sum

119894=1

120596119894119895119909119894minus ℎ119895) 119895 = 1 2 119897 (14)


119874119896=

119897

sum

119895=1

120596119895119896119867119895minus 119900119896 119896 = 1 2 119898 (15)

where 120596119894119895and 120596



119892 (119909) =1

1 + 119890minus119909 (16)


119890119896=1

2(119884119896minus 119874119896)2

119896 = 1 2 119898 (17)



120596new119894119895= 120596119894119895+ 120578119867119895(1 minus 119867

119895) 119909 (119894)

119898

sum

119896=1

120596119895119896119890119896

119894 = 1 2 119899 119895 = 1 2 119897

120596new119895119896= 120596119895119896+ 120578119867119895119890119896 119895 = 1 2 119897 119896 = 1 2 119898

ℎnew119895= ℎ119895+ 120578119867119895(1 minus 119867

119895)

119898

sum

119896=1

120596119895119896119890119896 119895 = 1 2 119897

119900new119896= 119900119896+ 119890119896 119896 = 1 2 119898

(18)

where 120596new119894119895

and 120596new119895119896


and 119900new119896







TrainValidation

TestBest

5 10 15 20 25 30 350Epochs

10minus3

10minus2

10minus1

100

101

Mea

n sq

uare

d er

ror (

mse

)


Vehicle

Real driver

Targetpath

Driver model

Dat

a acq

uisit

ion

syste

m

2-DOFreference

model

MPC controller

ICCcontroller

Control system


modulePrediction

moduleTp

120575sw

120575sw

120575sw

120575fc

ay

y

Vx

Vx

Vx

td Th

120573d 120596rd

f

yf

Δ120575f ΔMz

120573 120596r



119901 119905119889 and119879










119911


Vx

120573f

120573rV Vy

Mz

120596r

120573120575f

FyrFyflrlf




= A0119909 + B0119906

119910 = C0119909

(19)

where

119909 = [120573 120596119903]T

119906 = [120575119891119872119885]T

A0= [

1198861111988612

1198862111988622

] =

[[[[[

[

minus

119888119891+ 119888119903

119898 sdot 119881119909

minus1 +

119888119903119897119903minus 119888119891119897119891

119898 sdot 119881119909

2

119888119903119897119903minus 119888119891119897119891

119868119911

minus

1198881199031198972

119903+ 1198881198911198972

119891

119868119911sdot 119881119909

]]]]]

]

B0= [

1198871111988712

1198872111988722

] =

[[[[

[

119888119891

119898 sdot 119881119909

0

119888119891119897119891

119868119911

1

119868119911

]]]]

]

C0= [

1198881111988812

1198882111988822

] = [

1 0

0 1]

(20)




vehicle and 120575119891and119872




120596119903119889=

119881119909sdot 120575119891

(119897119891+ 119897119903) sdot [1 + (119881

119909Vch)2

]

(21)

where

V2ch =119888119891sdot 119888119903sdot (119897119891+ 119897119903)2

119898(119888119903119897119903minus 119888119891119897119891)

(22)


10038161003816100381610038161205961199031198891003816100381610038161003816 le 120583 sdot

119892

119881119909

(23)



120573119889= 0 (24)




119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896)

119910 (119896) = 119862119909 (119896)

(25)


Δ119909 (119896 + 1) = 119860Δ119909 (119896) + 119861Δ119906 (119896)

119910 (119896) = 119862Δ119909 (119896) + 119910 (119896 minus 1)

(26)

where

Δ119909 (119896) = 119909 (119896) minus 119909 (119896 minus 1)

Δ119906 (119896) = 119906 (119896) minus 119906 (119896 minus 1)

(27)

119860 = 119868 + 1198791199041198600 119861 = 119879

1199041198610 and 119862 = 119862

0 where 119879



119884 (119896 + 1 | 119896) = 119878Δ119909 (119896) + 119864119910 (119896) + 119865Δ119880 (119896) (28)

where

119884 (119896 + 1 | 119896) =

[[[[[[

[

119910 (119896 + 1 | 119896)

119910 (119896 + 2 | 119896)

119910 (119896 + 119901 | 119896)

]]]]]]

]

Δ119880 (119896) =

[[[[[[

[

Δ119906 (119896)

Δ119906 (119896 + 1)

Δ119906 (119896 + 119888 minus 1)

]]]]]]

]

119878 =

[[[[[[[[[[

[

119862119860

1198621198602

+ 119862119860

119901

sum

119894=1

119862119860119894

]]]]]]]]]]

]

119865 =

[[[[[[[[[[[[[[[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

2

sum

119894=1

119862119860119894minus1

119861 119862119861 0 sdot sdot sdot 0

sdot sdot sdot

119862

sum

119894=1

119862119860119894minus1

119861

119862minus1

sum

119894=1

119862119860119894minus1

119861 sdot sdot sdot 119862119861

sdot sdot sdot

119875

sum

119894=1

119862119860119894minus1

119861

119875minus1

sum

119894=1

119862119860119894minus1


119875minus119862+1

sum

119894=1

119862119860119894minus1

119861

]]]]]]]]]]]]]]]]]]]]

]

119864 =

[[[[[[

[

119868

119868

119868

]]]]]]

]

(29)



119869 (119910 (119896) Δ119880 (119896)) =10038171003817100381710038171003817120582119910(119884 (119896 + 1 | 119896) minus 119884

119889(119896 + 1))

10038171003817100381710038171003817

2

+1003817100381710038171003817120582119906Δ119880 (119896)

1003817100381710038171003817

2

(30)


119906



119884119889(119896 + 1) = [120573

119889120596119903119889]T (31)


minΔ119880(119896)

119869 (119910 (119896) Δ119880 (119896)) (32)


119906min (119896 + 119895) le 119906 (119896 + 119895) le 119906max (119896 + 119895)

119895 = 0 1 119888 minus 1

(33)


119895 = 0 1 119888 minus 1

(34)

119910min (119896 + 119895) le 119910 (119896 + 119895) le 119910max (119896 + 119895)

119895 = 0 1 119901 minus 1

(35)




11989162800



119891107



11991143316



minΔ119880(119896)

1

2Δ119880 (119896)

119879

119882119867Δ119880 (119896) + 119882

119879

119866Δ119880 (119896)


(36)

where

119882119867= 2 (119878

119879

120582119879

119910120582119910119878 + 120582119879

119906120582119906)

119882119866= minus2119878

119879

120582119879

119910120582119910119864119901(119896 + 1 | 119896)

119864119901(119896 + 1 | 119896) = 119884

119889(119896 + 1) minus 119878Δ119909 (119896) minus 119864119910 (119896)

(37)



Δ119906 (119896) = [



2times2119862

Δ119880 (119896)

119906 (119896) = 119906 (119896 minus 1) + Δ119906 (119896)

(38)







119879119901

119905119889

119879ℎ

13886 04176 01589



6 Conclusion








minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

5 10 150Time (s)

Yaw

rate

(deg

sminus1)

(b)

0 5 10 15Time (s)


minus4

minus2

0

2

4

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)




minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

Yaw

rate

(deg

sminus1)

5 10 150Time (s)

(b)


5 10 150Time (s)

minus5

0

5

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)






Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1m

12m 135m 11m 125m 12m

3m











119910 = 119910 (119905)

119910 = 119910 (119905)

(1)


119879 =119889

119881119909

(2)



119891 (119905 + 119879) = 119910 (119905) + 119879 sdot 119910 (119905) +1198792

2119910 (119905) (3)

Considering

119910 =1198812

119909

119877=120575sw1198941198711198812

119909 (4)


120575sw =2119894119871

1198892(119891 (119905 + 119879) minus 119910 (119905) minus 119879 sdot 119910 (119905)) (5)


120575sw119891(119904)

=21198620(1 + 119879

119888119904) 119890minus1199051198891199041199042

1198792119901(1 + 119879

ℎ119904) 1199042 + 2119862

0(1 + 119879

119888119904) (1 + 119879

119901119904) 119890minus119905119889119904 (119886

119910120575sw)

(6)




119888is the




020406080

100

Ope

ning

of a

ccel

erat

or

peda

l (

)

2 4 6 8 10 12 14 16 18 200Time (s)



020406080

100

Ope

ning

of b

rake

pe

dal (

)

2 4 6 8 10 12 14 16 18 200Time (s)



minus200

minus100

0

100

200

Stee

ring

whe

el an

gle (

rad)

2 4 6 8 10 12 14 16 18 200Time (s)



020406080

100120

Spee

d (k

m hminus1)

2 4 6 8 10 12 14 16 18 200Time (s)

(d) Vehicle speed


f(t)

y(t)

t


t + T

T middot y(t)



119879119888= 119905119889+ 119879ℎ+ 119879119886minus

119886119879119901

3

1198620=1

119866119886119910

(7)


order 119866119886119910




f(X)

1y

minus

minus

+V(s)

yTp

eTps2C0(1 + Tcs)e

minustds

T2p(1 + Ths)

1

s

1

s

120575sw ay



119901 119905119889 and 119879

ℎcould





Output of ARX model

minus25

minus2

minus15

minus1

minus05

005

115

2

Late

ral a

ccel

erat

ion

(mmiddotsminus

2)

1 2 3 4 5 6 7 8 9 100Time (s)

Real Ay



119910to 120575sw

119881 (119904) =

119886119910

120575sw(119904) = 119866

119886119910

1 + 1198791199101119904 + 11987911991021199042

1 + 1198791119904 + 11987921199042 (8)





as (1198791minus 1198791199101)


119860 (119911)119860119910(119911) = 119861 (119911) 119906 (119911) + 119890 (119911) (9)

where

119860 (119911) = 1 + 1198861119911minus1

+ 1198862119911minus2


119861 (119911) = 1 + 1198871119911minus1

+ 1198872119911minus2


(10)




119901 119905119889 and 119879




119879119901

119905119889

119879ℎ

[058 2072] [017 053] [008 036]



119879119895isin (119880119895min 119880119895max) (11)

where 119879119895is 119879119901 119905119889 and 119879







where 1198691 1198692 and 119869



1198691=1

1199050

int

1199050

0

(120575sw minus 120575sw)2

119889119905

1198692=1

1199050

int

1199050

0

(119886119910minus 119886119910)2

119889119905

1198693=1

1199050

int

1199050

0

(119910 minus 119910)2

119889119905

(13)


1 1199082 and 119908

3are weight








07100 0096447016119890 minus 003119905

11988901489 00834

119879ℎ

03740 00637Skilled drivers119879119901

16954 0096155144119890 minus 003119905

11988903763 00720

119879ℎ

03632 00560Normal drivers119879119901

11534 0101575145119890 minus 003119905

11988902388 01132

119879ℎ

02577 00873


f(X)

Tp120575sw

ay

y

Vx

y1

y2

y8

td

Th




1sim1199095



119909


119901 119905119889 and 119879



119867119895= 119892(

119899

sum

119894=1

120596119894119895119909119894minus ℎ119895) 119895 = 1 2 119897 (14)


119874119896=

119897

sum

119895=1

120596119895119896119867119895minus 119900119896 119896 = 1 2 119898 (15)

where 120596119894119895and 120596



119892 (119909) =1

1 + 119890minus119909 (16)


119890119896=1

2(119884119896minus 119874119896)2

119896 = 1 2 119898 (17)



120596new119894119895= 120596119894119895+ 120578119867119895(1 minus 119867

119895) 119909 (119894)

119898

sum

119896=1

120596119895119896119890119896

119894 = 1 2 119899 119895 = 1 2 119897

120596new119895119896= 120596119895119896+ 120578119867119895119890119896 119895 = 1 2 119897 119896 = 1 2 119898

ℎnew119895= ℎ119895+ 120578119867119895(1 minus 119867

119895)

119898

sum

119896=1

120596119895119896119890119896 119895 = 1 2 119897

119900new119896= 119900119896+ 119890119896 119896 = 1 2 119898

(18)

where 120596new119894119895

and 120596new119895119896


and 119900new119896







TrainValidation

TestBest

5 10 15 20 25 30 350Epochs

10minus3

10minus2

10minus1

100

101

Mea

n sq

uare

d er

ror (

mse

)


Vehicle

Real driver

Targetpath

Driver model

Dat

a acq

uisit

ion

syste

m

2-DOFreference

model

MPC controller

ICCcontroller

Control system


modulePrediction

moduleTp

120575sw

120575sw

120575sw

120575fc

ay

y

Vx

Vx

Vx

td Th

120573d 120596rd

f

yf

Δ120575f ΔMz

120573 120596r



119901 119905119889 and119879










119911


Vx

120573f

120573rV Vy

Mz

120596r

120573120575f

FyrFyflrlf




= A0119909 + B0119906

119910 = C0119909

(19)

where

119909 = [120573 120596119903]T

119906 = [120575119891119872119885]T

A0= [

1198861111988612

1198862111988622

] =

[[[[[

[

minus

119888119891+ 119888119903

119898 sdot 119881119909

minus1 +

119888119903119897119903minus 119888119891119897119891

119898 sdot 119881119909

2

119888119903119897119903minus 119888119891119897119891

119868119911

minus

1198881199031198972

119903+ 1198881198911198972

119891

119868119911sdot 119881119909

]]]]]

]

B0= [

1198871111988712

1198872111988722

] =

[[[[

[

119888119891

119898 sdot 119881119909

0

119888119891119897119891

119868119911

1

119868119911

]]]]

]

C0= [

1198881111988812

1198882111988822

] = [

1 0

0 1]

(20)




vehicle and 120575119891and119872




120596119903119889=

119881119909sdot 120575119891

(119897119891+ 119897119903) sdot [1 + (119881

119909Vch)2

]

(21)

where

V2ch =119888119891sdot 119888119903sdot (119897119891+ 119897119903)2

119898(119888119903119897119903minus 119888119891119897119891)

(22)


10038161003816100381610038161205961199031198891003816100381610038161003816 le 120583 sdot

119892

119881119909

(23)



120573119889= 0 (24)




119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896)

119910 (119896) = 119862119909 (119896)

(25)


Δ119909 (119896 + 1) = 119860Δ119909 (119896) + 119861Δ119906 (119896)

119910 (119896) = 119862Δ119909 (119896) + 119910 (119896 minus 1)

(26)

where

Δ119909 (119896) = 119909 (119896) minus 119909 (119896 minus 1)

Δ119906 (119896) = 119906 (119896) minus 119906 (119896 minus 1)

(27)

119860 = 119868 + 1198791199041198600 119861 = 119879

1199041198610 and 119862 = 119862

0 where 119879



119884 (119896 + 1 | 119896) = 119878Δ119909 (119896) + 119864119910 (119896) + 119865Δ119880 (119896) (28)

where

119884 (119896 + 1 | 119896) =

[[[[[[

[

119910 (119896 + 1 | 119896)

119910 (119896 + 2 | 119896)

119910 (119896 + 119901 | 119896)

]]]]]]

]

Δ119880 (119896) =

[[[[[[

[

Δ119906 (119896)

Δ119906 (119896 + 1)

Δ119906 (119896 + 119888 minus 1)

]]]]]]

]

119878 =

[[[[[[[[[[

[

119862119860

1198621198602

+ 119862119860

119901

sum

119894=1

119862119860119894

]]]]]]]]]]

]

119865 =

[[[[[[[[[[[[[[[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

2

sum

119894=1

119862119860119894minus1

119861 119862119861 0 sdot sdot sdot 0

sdot sdot sdot

119862

sum

119894=1

119862119860119894minus1

119861

119862minus1

sum

119894=1

119862119860119894minus1

119861 sdot sdot sdot 119862119861

sdot sdot sdot

119875

sum

119894=1

119862119860119894minus1

119861

119875minus1

sum

119894=1

119862119860119894minus1


119875minus119862+1

sum

119894=1

119862119860119894minus1

119861

]]]]]]]]]]]]]]]]]]]]

]

119864 =

[[[[[[

[

119868

119868

119868

]]]]]]

]

(29)



119869 (119910 (119896) Δ119880 (119896)) =10038171003817100381710038171003817120582119910(119884 (119896 + 1 | 119896) minus 119884

119889(119896 + 1))

10038171003817100381710038171003817

2

+1003817100381710038171003817120582119906Δ119880 (119896)

1003817100381710038171003817

2

(30)


119906



119884119889(119896 + 1) = [120573

119889120596119903119889]T (31)


minΔ119880(119896)

119869 (119910 (119896) Δ119880 (119896)) (32)


119906min (119896 + 119895) le 119906 (119896 + 119895) le 119906max (119896 + 119895)

119895 = 0 1 119888 minus 1

(33)


119895 = 0 1 119888 minus 1

(34)

119910min (119896 + 119895) le 119910 (119896 + 119895) le 119910max (119896 + 119895)

119895 = 0 1 119901 minus 1

(35)




11989162800



119891107



11991143316



minΔ119880(119896)

1

2Δ119880 (119896)

119879

119882119867Δ119880 (119896) + 119882

119879

119866Δ119880 (119896)


(36)

where

119882119867= 2 (119878

119879

120582119879

119910120582119910119878 + 120582119879

119906120582119906)

119882119866= minus2119878

119879

120582119879

119910120582119910119864119901(119896 + 1 | 119896)

119864119901(119896 + 1 | 119896) = 119884

119889(119896 + 1) minus 119878Δ119909 (119896) minus 119864119910 (119896)

(37)



Δ119906 (119896) = [



2times2119862

Δ119880 (119896)

119906 (119896) = 119906 (119896 minus 1) + Δ119906 (119896)

(38)







119879119901

119905119889

119879ℎ

13886 04176 01589



6 Conclusion








minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

5 10 150Time (s)

Yaw

rate

(deg

sminus1)

(b)

0 5 10 15Time (s)


minus4

minus2

0

2

4

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)




minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

Yaw

rate

(deg

sminus1)

5 10 150Time (s)

(b)


5 10 150Time (s)

minus5

0

5

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)






Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











020406080

100

Ope

ning

of a

ccel

erat

or

peda

l (

)

2 4 6 8 10 12 14 16 18 200Time (s)



020406080

100

Ope

ning

of b

rake

pe

dal (

)

2 4 6 8 10 12 14 16 18 200Time (s)



minus200

minus100

0

100

200

Stee

ring

whe

el an

gle (

rad)

2 4 6 8 10 12 14 16 18 200Time (s)



020406080

100120

Spee

d (k

m hminus1)

2 4 6 8 10 12 14 16 18 200Time (s)

(d) Vehicle speed


f(t)

y(t)

t


t + T

T middot y(t)



119879119888= 119905119889+ 119879ℎ+ 119879119886minus

119886119879119901

3

1198620=1

119866119886119910

(7)


order 119866119886119910




f(X)

1y

minus

minus

+V(s)

yTp

eTps2C0(1 + Tcs)e

minustds

T2p(1 + Ths)

1

s

1

s

120575sw ay



119901 119905119889 and 119879

ℎcould





Output of ARX model

minus25

minus2

minus15

minus1

minus05

005

115

2

Late

ral a

ccel

erat

ion

(mmiddotsminus

2)

1 2 3 4 5 6 7 8 9 100Time (s)

Real Ay



119910to 120575sw

119881 (119904) =

119886119910

120575sw(119904) = 119866

119886119910

1 + 1198791199101119904 + 11987911991021199042

1 + 1198791119904 + 11987921199042 (8)





as (1198791minus 1198791199101)


119860 (119911)119860119910(119911) = 119861 (119911) 119906 (119911) + 119890 (119911) (9)

where

119860 (119911) = 1 + 1198861119911minus1

+ 1198862119911minus2


119861 (119911) = 1 + 1198871119911minus1

+ 1198872119911minus2


(10)




119901 119905119889 and 119879




119879119901

119905119889

119879ℎ

[058 2072] [017 053] [008 036]



119879119895isin (119880119895min 119880119895max) (11)

where 119879119895is 119879119901 119905119889 and 119879







where 1198691 1198692 and 119869



1198691=1

1199050

int

1199050

0

(120575sw minus 120575sw)2

119889119905

1198692=1

1199050

int

1199050

0

(119886119910minus 119886119910)2

119889119905

1198693=1

1199050

int

1199050

0

(119910 minus 119910)2

119889119905

(13)


1 1199082 and 119908

3are weight








07100 0096447016119890 minus 003119905

11988901489 00834

119879ℎ

03740 00637Skilled drivers119879119901

16954 0096155144119890 minus 003119905

11988903763 00720

119879ℎ

03632 00560Normal drivers119879119901

11534 0101575145119890 minus 003119905

11988902388 01132

119879ℎ

02577 00873


f(X)

Tp120575sw

ay

y

Vx

y1

y2

y8

td

Th




1sim1199095



119909


119901 119905119889 and 119879



119867119895= 119892(

119899

sum

119894=1

120596119894119895119909119894minus ℎ119895) 119895 = 1 2 119897 (14)


119874119896=

119897

sum

119895=1

120596119895119896119867119895minus 119900119896 119896 = 1 2 119898 (15)

where 120596119894119895and 120596



119892 (119909) =1

1 + 119890minus119909 (16)


119890119896=1

2(119884119896minus 119874119896)2

119896 = 1 2 119898 (17)



120596new119894119895= 120596119894119895+ 120578119867119895(1 minus 119867

119895) 119909 (119894)

119898

sum

119896=1

120596119895119896119890119896

119894 = 1 2 119899 119895 = 1 2 119897

120596new119895119896= 120596119895119896+ 120578119867119895119890119896 119895 = 1 2 119897 119896 = 1 2 119898

ℎnew119895= ℎ119895+ 120578119867119895(1 minus 119867

119895)

119898

sum

119896=1

120596119895119896119890119896 119895 = 1 2 119897

119900new119896= 119900119896+ 119890119896 119896 = 1 2 119898

(18)

where 120596new119894119895

and 120596new119895119896


and 119900new119896







TrainValidation

TestBest

5 10 15 20 25 30 350Epochs

10minus3

10minus2

10minus1

100

101

Mea

n sq

uare

d er

ror (

mse

)


Vehicle

Real driver

Targetpath

Driver model

Dat

a acq

uisit

ion

syste

m

2-DOFreference

model

MPC controller

ICCcontroller

Control system


modulePrediction

moduleTp

120575sw

120575sw

120575sw

120575fc

ay

y

Vx

Vx

Vx

td Th

120573d 120596rd

f

yf

Δ120575f ΔMz

120573 120596r



119901 119905119889 and119879










119911


Vx

120573f

120573rV Vy

Mz

120596r

120573120575f

FyrFyflrlf




= A0119909 + B0119906

119910 = C0119909

(19)

where

119909 = [120573 120596119903]T

119906 = [120575119891119872119885]T

A0= [

1198861111988612

1198862111988622

] =

[[[[[

[

minus

119888119891+ 119888119903

119898 sdot 119881119909

minus1 +

119888119903119897119903minus 119888119891119897119891

119898 sdot 119881119909

2

119888119903119897119903minus 119888119891119897119891

119868119911

minus

1198881199031198972

119903+ 1198881198911198972

119891

119868119911sdot 119881119909

]]]]]

]

B0= [

1198871111988712

1198872111988722

] =

[[[[

[

119888119891

119898 sdot 119881119909

0

119888119891119897119891

119868119911

1

119868119911

]]]]

]

C0= [

1198881111988812

1198882111988822

] = [

1 0

0 1]

(20)




vehicle and 120575119891and119872




120596119903119889=

119881119909sdot 120575119891

(119897119891+ 119897119903) sdot [1 + (119881

119909Vch)2

]

(21)

where

V2ch =119888119891sdot 119888119903sdot (119897119891+ 119897119903)2

119898(119888119903119897119903minus 119888119891119897119891)

(22)


10038161003816100381610038161205961199031198891003816100381610038161003816 le 120583 sdot

119892

119881119909

(23)



120573119889= 0 (24)




119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896)

119910 (119896) = 119862119909 (119896)

(25)


Δ119909 (119896 + 1) = 119860Δ119909 (119896) + 119861Δ119906 (119896)

119910 (119896) = 119862Δ119909 (119896) + 119910 (119896 minus 1)

(26)

where

Δ119909 (119896) = 119909 (119896) minus 119909 (119896 minus 1)

Δ119906 (119896) = 119906 (119896) minus 119906 (119896 minus 1)

(27)

119860 = 119868 + 1198791199041198600 119861 = 119879

1199041198610 and 119862 = 119862

0 where 119879



119884 (119896 + 1 | 119896) = 119878Δ119909 (119896) + 119864119910 (119896) + 119865Δ119880 (119896) (28)

where

119884 (119896 + 1 | 119896) =

[[[[[[

[

119910 (119896 + 1 | 119896)

119910 (119896 + 2 | 119896)

119910 (119896 + 119901 | 119896)

]]]]]]

]

Δ119880 (119896) =

[[[[[[

[

Δ119906 (119896)

Δ119906 (119896 + 1)

Δ119906 (119896 + 119888 minus 1)

]]]]]]

]

119878 =

[[[[[[[[[[

[

119862119860

1198621198602

+ 119862119860

119901

sum

119894=1

119862119860119894

]]]]]]]]]]

]

119865 =

[[[[[[[[[[[[[[[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

2

sum

119894=1

119862119860119894minus1

119861 119862119861 0 sdot sdot sdot 0

sdot sdot sdot

119862

sum

119894=1

119862119860119894minus1

119861

119862minus1

sum

119894=1

119862119860119894minus1

119861 sdot sdot sdot 119862119861

sdot sdot sdot

119875

sum

119894=1

119862119860119894minus1

119861

119875minus1

sum

119894=1

119862119860119894minus1


119875minus119862+1

sum

119894=1

119862119860119894minus1

119861

]]]]]]]]]]]]]]]]]]]]

]

119864 =

[[[[[[

[

119868

119868

119868

]]]]]]

]

(29)



119869 (119910 (119896) Δ119880 (119896)) =10038171003817100381710038171003817120582119910(119884 (119896 + 1 | 119896) minus 119884

119889(119896 + 1))

10038171003817100381710038171003817

2

+1003817100381710038171003817120582119906Δ119880 (119896)

1003817100381710038171003817

2

(30)


119906



119884119889(119896 + 1) = [120573

119889120596119903119889]T (31)


minΔ119880(119896)

119869 (119910 (119896) Δ119880 (119896)) (32)


119906min (119896 + 119895) le 119906 (119896 + 119895) le 119906max (119896 + 119895)

119895 = 0 1 119888 minus 1

(33)


119895 = 0 1 119888 minus 1

(34)

119910min (119896 + 119895) le 119910 (119896 + 119895) le 119910max (119896 + 119895)

119895 = 0 1 119901 minus 1

(35)




11989162800



119891107



11991143316



minΔ119880(119896)

1

2Δ119880 (119896)

119879

119882119867Δ119880 (119896) + 119882

119879

119866Δ119880 (119896)


(36)

where

119882119867= 2 (119878

119879

120582119879

119910120582119910119878 + 120582119879

119906120582119906)

119882119866= minus2119878

119879

120582119879

119910120582119910119864119901(119896 + 1 | 119896)

119864119901(119896 + 1 | 119896) = 119884

119889(119896 + 1) minus 119878Δ119909 (119896) minus 119864119910 (119896)

(37)



Δ119906 (119896) = [



2times2119862

Δ119880 (119896)

119906 (119896) = 119906 (119896 minus 1) + Δ119906 (119896)

(38)







119879119901

119905119889

119879ℎ

13886 04176 01589



6 Conclusion








minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

5 10 150Time (s)

Yaw

rate

(deg

sminus1)

(b)

0 5 10 15Time (s)


minus4

minus2

0

2

4

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)




minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

Yaw

rate

(deg

sminus1)

5 10 150Time (s)

(b)


5 10 150Time (s)

minus5

0

5

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)






Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Output of ARX model

minus25

minus2

minus15

minus1

minus05

005

115

2

Late

ral a

ccel

erat

ion

(mmiddotsminus

2)

1 2 3 4 5 6 7 8 9 100Time (s)

Real Ay



119910to 120575sw

119881 (119904) =

119886119910

120575sw(119904) = 119866

119886119910

1 + 1198791199101119904 + 11987911991021199042

1 + 1198791119904 + 11987921199042 (8)





as (1198791minus 1198791199101)


119860 (119911)119860119910(119911) = 119861 (119911) 119906 (119911) + 119890 (119911) (9)

where

119860 (119911) = 1 + 1198861119911minus1

+ 1198862119911minus2


119861 (119911) = 1 + 1198871119911minus1

+ 1198872119911minus2


(10)




119901 119905119889 and 119879




119879119901

119905119889

119879ℎ

[058 2072] [017 053] [008 036]



119879119895isin (119880119895min 119880119895max) (11)

where 119879119895is 119879119901 119905119889 and 119879







where 1198691 1198692 and 119869



1198691=1

1199050

int

1199050

0

(120575sw minus 120575sw)2

119889119905

1198692=1

1199050

int

1199050

0

(119886119910minus 119886119910)2

119889119905

1198693=1

1199050

int

1199050

0

(119910 minus 119910)2

119889119905

(13)


1 1199082 and 119908

3are weight








07100 0096447016119890 minus 003119905

11988901489 00834

119879ℎ

03740 00637Skilled drivers119879119901

16954 0096155144119890 minus 003119905

11988903763 00720

119879ℎ

03632 00560Normal drivers119879119901

11534 0101575145119890 minus 003119905

11988902388 01132

119879ℎ

02577 00873


f(X)

Tp120575sw

ay

y

Vx

y1

y2

y8

td

Th




1sim1199095



119909


119901 119905119889 and 119879



119867119895= 119892(

119899

sum

119894=1

120596119894119895119909119894minus ℎ119895) 119895 = 1 2 119897 (14)


119874119896=

119897

sum

119895=1

120596119895119896119867119895minus 119900119896 119896 = 1 2 119898 (15)

where 120596119894119895and 120596



119892 (119909) =1

1 + 119890minus119909 (16)


119890119896=1

2(119884119896minus 119874119896)2

119896 = 1 2 119898 (17)



120596new119894119895= 120596119894119895+ 120578119867119895(1 minus 119867

119895) 119909 (119894)

119898

sum

119896=1

120596119895119896119890119896

119894 = 1 2 119899 119895 = 1 2 119897

120596new119895119896= 120596119895119896+ 120578119867119895119890119896 119895 = 1 2 119897 119896 = 1 2 119898

ℎnew119895= ℎ119895+ 120578119867119895(1 minus 119867

119895)

119898

sum

119896=1

120596119895119896119890119896 119895 = 1 2 119897

119900new119896= 119900119896+ 119890119896 119896 = 1 2 119898

(18)

where 120596new119894119895

and 120596new119895119896


and 119900new119896







TrainValidation

TestBest

5 10 15 20 25 30 350Epochs

10minus3

10minus2

10minus1

100

101

Mea

n sq

uare

d er

ror (

mse

)


Vehicle

Real driver

Targetpath

Driver model

Dat

a acq

uisit

ion

syste

m

2-DOFreference

model

MPC controller

ICCcontroller

Control system


modulePrediction

moduleTp

120575sw

120575sw

120575sw

120575fc

ay

y

Vx

Vx

Vx

td Th

120573d 120596rd

f

yf

Δ120575f ΔMz

120573 120596r



119901 119905119889 and119879










119911


Vx

120573f

120573rV Vy

Mz

120596r

120573120575f

FyrFyflrlf




= A0119909 + B0119906

119910 = C0119909

(19)

where

119909 = [120573 120596119903]T

119906 = [120575119891119872119885]T

A0= [

1198861111988612

1198862111988622

] =

[[[[[

[

minus

119888119891+ 119888119903

119898 sdot 119881119909

minus1 +

119888119903119897119903minus 119888119891119897119891

119898 sdot 119881119909

2

119888119903119897119903minus 119888119891119897119891

119868119911

minus

1198881199031198972

119903+ 1198881198911198972

119891

119868119911sdot 119881119909

]]]]]

]

B0= [

1198871111988712

1198872111988722

] =

[[[[

[

119888119891

119898 sdot 119881119909

0

119888119891119897119891

119868119911

1

119868119911

]]]]

]

C0= [

1198881111988812

1198882111988822

] = [

1 0

0 1]

(20)




vehicle and 120575119891and119872




120596119903119889=

119881119909sdot 120575119891

(119897119891+ 119897119903) sdot [1 + (119881

119909Vch)2

]

(21)

where

V2ch =119888119891sdot 119888119903sdot (119897119891+ 119897119903)2

119898(119888119903119897119903minus 119888119891119897119891)

(22)


10038161003816100381610038161205961199031198891003816100381610038161003816 le 120583 sdot

119892

119881119909

(23)



120573119889= 0 (24)




119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896)

119910 (119896) = 119862119909 (119896)

(25)


Δ119909 (119896 + 1) = 119860Δ119909 (119896) + 119861Δ119906 (119896)

119910 (119896) = 119862Δ119909 (119896) + 119910 (119896 minus 1)

(26)

where

Δ119909 (119896) = 119909 (119896) minus 119909 (119896 minus 1)

Δ119906 (119896) = 119906 (119896) minus 119906 (119896 minus 1)

(27)

119860 = 119868 + 1198791199041198600 119861 = 119879

1199041198610 and 119862 = 119862

0 where 119879



119884 (119896 + 1 | 119896) = 119878Δ119909 (119896) + 119864119910 (119896) + 119865Δ119880 (119896) (28)

where

119884 (119896 + 1 | 119896) =

[[[[[[

[

119910 (119896 + 1 | 119896)

119910 (119896 + 2 | 119896)

119910 (119896 + 119901 | 119896)

]]]]]]

]

Δ119880 (119896) =

[[[[[[

[

Δ119906 (119896)

Δ119906 (119896 + 1)

Δ119906 (119896 + 119888 minus 1)

]]]]]]

]

119878 =

[[[[[[[[[[

[

119862119860

1198621198602

+ 119862119860

119901

sum

119894=1

119862119860119894

]]]]]]]]]]

]

119865 =

[[[[[[[[[[[[[[[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

2

sum

119894=1

119862119860119894minus1

119861 119862119861 0 sdot sdot sdot 0

sdot sdot sdot

119862

sum

119894=1

119862119860119894minus1

119861

119862minus1

sum

119894=1

119862119860119894minus1

119861 sdot sdot sdot 119862119861

sdot sdot sdot

119875

sum

119894=1

119862119860119894minus1

119861

119875minus1

sum

119894=1

119862119860119894minus1


119875minus119862+1

sum

119894=1

119862119860119894minus1

119861

]]]]]]]]]]]]]]]]]]]]

]

119864 =

[[[[[[

[

119868

119868

119868

]]]]]]

]

(29)



119869 (119910 (119896) Δ119880 (119896)) =10038171003817100381710038171003817120582119910(119884 (119896 + 1 | 119896) minus 119884

119889(119896 + 1))

10038171003817100381710038171003817

2

+1003817100381710038171003817120582119906Δ119880 (119896)

1003817100381710038171003817

2

(30)


119906



119884119889(119896 + 1) = [120573

119889120596119903119889]T (31)


minΔ119880(119896)

119869 (119910 (119896) Δ119880 (119896)) (32)


119906min (119896 + 119895) le 119906 (119896 + 119895) le 119906max (119896 + 119895)

119895 = 0 1 119888 minus 1

(33)


119895 = 0 1 119888 minus 1

(34)

119910min (119896 + 119895) le 119910 (119896 + 119895) le 119910max (119896 + 119895)

119895 = 0 1 119901 minus 1

(35)




11989162800



119891107



11991143316



minΔ119880(119896)

1

2Δ119880 (119896)

119879

119882119867Δ119880 (119896) + 119882

119879

119866Δ119880 (119896)


(36)

where

119882119867= 2 (119878

119879

120582119879

119910120582119910119878 + 120582119879

119906120582119906)

119882119866= minus2119878

119879

120582119879

119910120582119910119864119901(119896 + 1 | 119896)

119864119901(119896 + 1 | 119896) = 119884

119889(119896 + 1) minus 119878Δ119909 (119896) minus 119864119910 (119896)

(37)



Δ119906 (119896) = [



2times2119862

Δ119880 (119896)

119906 (119896) = 119906 (119896 minus 1) + Δ119906 (119896)

(38)







119879119901

119905119889

119879ℎ

13886 04176 01589



6 Conclusion








minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

5 10 150Time (s)

Yaw

rate

(deg

sminus1)

(b)

0 5 10 15Time (s)


minus4

minus2

0

2

4

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)




minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

Yaw

rate

(deg

sminus1)

5 10 150Time (s)

(b)


5 10 150Time (s)

minus5

0

5

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)






Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












07100 0096447016119890 minus 003119905

11988901489 00834

119879ℎ

03740 00637Skilled drivers119879119901

16954 0096155144119890 minus 003119905

11988903763 00720

119879ℎ

03632 00560Normal drivers119879119901

11534 0101575145119890 minus 003119905

11988902388 01132

119879ℎ

02577 00873


f(X)

Tp120575sw

ay

y

Vx

y1

y2

y8

td

Th




1sim1199095



119909


119901 119905119889 and 119879



119867119895= 119892(

119899

sum

119894=1

120596119894119895119909119894minus ℎ119895) 119895 = 1 2 119897 (14)


119874119896=

119897

sum

119895=1

120596119895119896119867119895minus 119900119896 119896 = 1 2 119898 (15)

where 120596119894119895and 120596



119892 (119909) =1

1 + 119890minus119909 (16)


119890119896=1

2(119884119896minus 119874119896)2

119896 = 1 2 119898 (17)



120596new119894119895= 120596119894119895+ 120578119867119895(1 minus 119867

119895) 119909 (119894)

119898

sum

119896=1

120596119895119896119890119896

119894 = 1 2 119899 119895 = 1 2 119897

120596new119895119896= 120596119895119896+ 120578119867119895119890119896 119895 = 1 2 119897 119896 = 1 2 119898

ℎnew119895= ℎ119895+ 120578119867119895(1 minus 119867

119895)

119898

sum

119896=1

120596119895119896119890119896 119895 = 1 2 119897

119900new119896= 119900119896+ 119890119896 119896 = 1 2 119898

(18)

where 120596new119894119895

and 120596new119895119896


and 119900new119896







TrainValidation

TestBest

5 10 15 20 25 30 350Epochs

10minus3

10minus2

10minus1

100

101

Mea

n sq

uare

d er

ror (

mse

)


Vehicle

Real driver

Targetpath

Driver model

Dat

a acq

uisit

ion

syste

m

2-DOFreference

model

MPC controller

ICCcontroller

Control system


modulePrediction

moduleTp

120575sw

120575sw

120575sw

120575fc

ay

y

Vx

Vx

Vx

td Th

120573d 120596rd

f

yf

Δ120575f ΔMz

120573 120596r



119901 119905119889 and119879










119911


Vx

120573f

120573rV Vy

Mz

120596r

120573120575f

FyrFyflrlf




= A0119909 + B0119906

119910 = C0119909

(19)

where

119909 = [120573 120596119903]T

119906 = [120575119891119872119885]T

A0= [

1198861111988612

1198862111988622

] =

[[[[[

[

minus

119888119891+ 119888119903

119898 sdot 119881119909

minus1 +

119888119903119897119903minus 119888119891119897119891

119898 sdot 119881119909

2

119888119903119897119903minus 119888119891119897119891

119868119911

minus

1198881199031198972

119903+ 1198881198911198972

119891

119868119911sdot 119881119909

]]]]]

]

B0= [

1198871111988712

1198872111988722

] =

[[[[

[

119888119891

119898 sdot 119881119909

0

119888119891119897119891

119868119911

1

119868119911

]]]]

]

C0= [

1198881111988812

1198882111988822

] = [

1 0

0 1]

(20)




vehicle and 120575119891and119872




120596119903119889=

119881119909sdot 120575119891

(119897119891+ 119897119903) sdot [1 + (119881

119909Vch)2

]

(21)

where

V2ch =119888119891sdot 119888119903sdot (119897119891+ 119897119903)2

119898(119888119903119897119903minus 119888119891119897119891)

(22)


10038161003816100381610038161205961199031198891003816100381610038161003816 le 120583 sdot

119892

119881119909

(23)



120573119889= 0 (24)




119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896)

119910 (119896) = 119862119909 (119896)

(25)


Δ119909 (119896 + 1) = 119860Δ119909 (119896) + 119861Δ119906 (119896)

119910 (119896) = 119862Δ119909 (119896) + 119910 (119896 minus 1)

(26)

where

Δ119909 (119896) = 119909 (119896) minus 119909 (119896 minus 1)

Δ119906 (119896) = 119906 (119896) minus 119906 (119896 minus 1)

(27)

119860 = 119868 + 1198791199041198600 119861 = 119879

1199041198610 and 119862 = 119862

0 where 119879



119884 (119896 + 1 | 119896) = 119878Δ119909 (119896) + 119864119910 (119896) + 119865Δ119880 (119896) (28)

where

119884 (119896 + 1 | 119896) =

[[[[[[

[

119910 (119896 + 1 | 119896)

119910 (119896 + 2 | 119896)

119910 (119896 + 119901 | 119896)

]]]]]]

]

Δ119880 (119896) =

[[[[[[

[

Δ119906 (119896)

Δ119906 (119896 + 1)

Δ119906 (119896 + 119888 minus 1)

]]]]]]

]

119878 =

[[[[[[[[[[

[

119862119860

1198621198602

+ 119862119860

119901

sum

119894=1

119862119860119894

]]]]]]]]]]

]

119865 =

[[[[[[[[[[[[[[[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

2

sum

119894=1

119862119860119894minus1

119861 119862119861 0 sdot sdot sdot 0

sdot sdot sdot

119862

sum

119894=1

119862119860119894minus1

119861

119862minus1

sum

119894=1

119862119860119894minus1

119861 sdot sdot sdot 119862119861

sdot sdot sdot

119875

sum

119894=1

119862119860119894minus1

119861

119875minus1

sum

119894=1

119862119860119894minus1


119875minus119862+1

sum

119894=1

119862119860119894minus1

119861

]]]]]]]]]]]]]]]]]]]]

]

119864 =

[[[[[[

[

119868

119868

119868

]]]]]]

]

(29)



119869 (119910 (119896) Δ119880 (119896)) =10038171003817100381710038171003817120582119910(119884 (119896 + 1 | 119896) minus 119884

119889(119896 + 1))

10038171003817100381710038171003817

2

+1003817100381710038171003817120582119906Δ119880 (119896)

1003817100381710038171003817

2

(30)


119906



119884119889(119896 + 1) = [120573

119889120596119903119889]T (31)


minΔ119880(119896)

119869 (119910 (119896) Δ119880 (119896)) (32)


119906min (119896 + 119895) le 119906 (119896 + 119895) le 119906max (119896 + 119895)

119895 = 0 1 119888 minus 1

(33)


119895 = 0 1 119888 minus 1

(34)

119910min (119896 + 119895) le 119910 (119896 + 119895) le 119910max (119896 + 119895)

119895 = 0 1 119901 minus 1

(35)




11989162800



119891107



11991143316



minΔ119880(119896)

1

2Δ119880 (119896)

119879

119882119867Δ119880 (119896) + 119882

119879

119866Δ119880 (119896)


(36)

where

119882119867= 2 (119878

119879

120582119879

119910120582119910119878 + 120582119879

119906120582119906)

119882119866= minus2119878

119879

120582119879

119910120582119910119864119901(119896 + 1 | 119896)

119864119901(119896 + 1 | 119896) = 119884

119889(119896 + 1) minus 119878Δ119909 (119896) minus 119864119910 (119896)

(37)



Δ119906 (119896) = [



2times2119862

Δ119880 (119896)

119906 (119896) = 119906 (119896 minus 1) + Δ119906 (119896)

(38)







119879119901

119905119889

119879ℎ

13886 04176 01589



6 Conclusion








minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

5 10 150Time (s)

Yaw

rate

(deg

sminus1)

(b)

0 5 10 15Time (s)


minus4

minus2

0

2

4

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)




minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

Yaw

rate

(deg

sminus1)

5 10 150Time (s)

(b)


5 10 150Time (s)

minus5

0

5

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)






Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










TrainValidation

TestBest

5 10 15 20 25 30 350Epochs

10minus3

10minus2

10minus1

100

101

Mea

n sq

uare

d er

ror (

mse

)


Vehicle

Real driver

Targetpath

Driver model

Dat

a acq

uisit

ion

syste

m

2-DOFreference

model

MPC controller

ICCcontroller

Control system


modulePrediction

moduleTp

120575sw

120575sw

120575sw

120575fc

ay

y

Vx

Vx

Vx

td Th

120573d 120596rd

f

yf

Δ120575f ΔMz

120573 120596r



119901 119905119889 and119879










119911


Vx

120573f

120573rV Vy

Mz

120596r

120573120575f

FyrFyflrlf




= A0119909 + B0119906

119910 = C0119909

(19)

where

119909 = [120573 120596119903]T

119906 = [120575119891119872119885]T

A0= [

1198861111988612

1198862111988622

] =

[[[[[

[

minus

119888119891+ 119888119903

119898 sdot 119881119909

minus1 +

119888119903119897119903minus 119888119891119897119891

119898 sdot 119881119909

2

119888119903119897119903minus 119888119891119897119891

119868119911

minus

1198881199031198972

119903+ 1198881198911198972

119891

119868119911sdot 119881119909

]]]]]

]

B0= [

1198871111988712

1198872111988722

] =

[[[[

[

119888119891

119898 sdot 119881119909

0

119888119891119897119891

119868119911

1

119868119911

]]]]

]

C0= [

1198881111988812

1198882111988822

] = [

1 0

0 1]

(20)




vehicle and 120575119891and119872




120596119903119889=

119881119909sdot 120575119891

(119897119891+ 119897119903) sdot [1 + (119881

119909Vch)2

]

(21)

where

V2ch =119888119891sdot 119888119903sdot (119897119891+ 119897119903)2

119898(119888119903119897119903minus 119888119891119897119891)

(22)


10038161003816100381610038161205961199031198891003816100381610038161003816 le 120583 sdot

119892

119881119909

(23)



120573119889= 0 (24)




119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896)

119910 (119896) = 119862119909 (119896)

(25)


Δ119909 (119896 + 1) = 119860Δ119909 (119896) + 119861Δ119906 (119896)

119910 (119896) = 119862Δ119909 (119896) + 119910 (119896 minus 1)

(26)

where

Δ119909 (119896) = 119909 (119896) minus 119909 (119896 minus 1)

Δ119906 (119896) = 119906 (119896) minus 119906 (119896 minus 1)

(27)

119860 = 119868 + 1198791199041198600 119861 = 119879

1199041198610 and 119862 = 119862

0 where 119879



119884 (119896 + 1 | 119896) = 119878Δ119909 (119896) + 119864119910 (119896) + 119865Δ119880 (119896) (28)

where

119884 (119896 + 1 | 119896) =

[[[[[[

[

119910 (119896 + 1 | 119896)

119910 (119896 + 2 | 119896)

119910 (119896 + 119901 | 119896)

]]]]]]

]

Δ119880 (119896) =

[[[[[[

[

Δ119906 (119896)

Δ119906 (119896 + 1)

Δ119906 (119896 + 119888 minus 1)

]]]]]]

]

119878 =

[[[[[[[[[[

[

119862119860

1198621198602

+ 119862119860

119901

sum

119894=1

119862119860119894

]]]]]]]]]]

]

119865 =

[[[[[[[[[[[[[[[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

2

sum

119894=1

119862119860119894minus1

119861 119862119861 0 sdot sdot sdot 0

sdot sdot sdot

119862

sum

119894=1

119862119860119894minus1

119861

119862minus1

sum

119894=1

119862119860119894minus1

119861 sdot sdot sdot 119862119861

sdot sdot sdot

119875

sum

119894=1

119862119860119894minus1

119861

119875minus1

sum

119894=1

119862119860119894minus1


119875minus119862+1

sum

119894=1

119862119860119894minus1

119861

]]]]]]]]]]]]]]]]]]]]

]

119864 =

[[[[[[

[

119868

119868

119868

]]]]]]

]

(29)



119869 (119910 (119896) Δ119880 (119896)) =10038171003817100381710038171003817120582119910(119884 (119896 + 1 | 119896) minus 119884

119889(119896 + 1))

10038171003817100381710038171003817

2

+1003817100381710038171003817120582119906Δ119880 (119896)

1003817100381710038171003817

2

(30)


119906



119884119889(119896 + 1) = [120573

119889120596119903119889]T (31)


minΔ119880(119896)

119869 (119910 (119896) Δ119880 (119896)) (32)


119906min (119896 + 119895) le 119906 (119896 + 119895) le 119906max (119896 + 119895)

119895 = 0 1 119888 minus 1

(33)


119895 = 0 1 119888 minus 1

(34)

119910min (119896 + 119895) le 119910 (119896 + 119895) le 119910max (119896 + 119895)

119895 = 0 1 119901 minus 1

(35)




11989162800



119891107



11991143316



minΔ119880(119896)

1

2Δ119880 (119896)

119879

119882119867Δ119880 (119896) + 119882

119879

119866Δ119880 (119896)


(36)

where

119882119867= 2 (119878

119879

120582119879

119910120582119910119878 + 120582119879

119906120582119906)

119882119866= minus2119878

119879

120582119879

119910120582119910119864119901(119896 + 1 | 119896)

119864119901(119896 + 1 | 119896) = 119884

119889(119896 + 1) minus 119878Δ119909 (119896) minus 119864119910 (119896)

(37)



Δ119906 (119896) = [



2times2119862

Δ119880 (119896)

119906 (119896) = 119906 (119896 minus 1) + Δ119906 (119896)

(38)







119879119901

119905119889

119879ℎ

13886 04176 01589



6 Conclusion








minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

5 10 150Time (s)

Yaw

rate

(deg

sminus1)

(b)

0 5 10 15Time (s)


minus4

minus2

0

2

4

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)




minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

Yaw

rate

(deg

sminus1)

5 10 150Time (s)

(b)


5 10 150Time (s)

minus5

0

5

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)






Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











120573119889= 0 (24)




119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896)

119910 (119896) = 119862119909 (119896)

(25)


Δ119909 (119896 + 1) = 119860Δ119909 (119896) + 119861Δ119906 (119896)

119910 (119896) = 119862Δ119909 (119896) + 119910 (119896 minus 1)

(26)

where

Δ119909 (119896) = 119909 (119896) minus 119909 (119896 minus 1)

Δ119906 (119896) = 119906 (119896) minus 119906 (119896 minus 1)

(27)

119860 = 119868 + 1198791199041198600 119861 = 119879

1199041198610 and 119862 = 119862

0 where 119879



119884 (119896 + 1 | 119896) = 119878Δ119909 (119896) + 119864119910 (119896) + 119865Δ119880 (119896) (28)

where

119884 (119896 + 1 | 119896) =

[[[[[[

[

119910 (119896 + 1 | 119896)

119910 (119896 + 2 | 119896)

119910 (119896 + 119901 | 119896)

]]]]]]

]

Δ119880 (119896) =

[[[[[[

[

Δ119906 (119896)

Δ119906 (119896 + 1)

Δ119906 (119896 + 119888 minus 1)

]]]]]]

]

119878 =

[[[[[[[[[[

[

119862119860

1198621198602

+ 119862119860

119901

sum

119894=1

119862119860119894

]]]]]]]]]]

]

119865 =

[[[[[[[[[[[[[[[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

2

sum

119894=1

119862119860119894minus1

119861 119862119861 0 sdot sdot sdot 0

sdot sdot sdot

119862

sum

119894=1

119862119860119894minus1

119861

119862minus1

sum

119894=1

119862119860119894minus1

119861 sdot sdot sdot 119862119861

sdot sdot sdot

119875

sum

119894=1

119862119860119894minus1

119861

119875minus1

sum

119894=1

119862119860119894minus1


119875minus119862+1

sum

119894=1

119862119860119894minus1

119861

]]]]]]]]]]]]]]]]]]]]

]

119864 =

[[[[[[

[

119868

119868

119868

]]]]]]

]

(29)



119869 (119910 (119896) Δ119880 (119896)) =10038171003817100381710038171003817120582119910(119884 (119896 + 1 | 119896) minus 119884

119889(119896 + 1))

10038171003817100381710038171003817

2

+1003817100381710038171003817120582119906Δ119880 (119896)

1003817100381710038171003817

2

(30)


119906



119884119889(119896 + 1) = [120573

119889120596119903119889]T (31)


minΔ119880(119896)

119869 (119910 (119896) Δ119880 (119896)) (32)


119906min (119896 + 119895) le 119906 (119896 + 119895) le 119906max (119896 + 119895)

119895 = 0 1 119888 minus 1

(33)


119895 = 0 1 119888 minus 1

(34)

119910min (119896 + 119895) le 119910 (119896 + 119895) le 119910max (119896 + 119895)

119895 = 0 1 119901 minus 1

(35)




11989162800



119891107



11991143316



minΔ119880(119896)

1

2Δ119880 (119896)

119879

119882119867Δ119880 (119896) + 119882

119879

119866Δ119880 (119896)


(36)

where

119882119867= 2 (119878

119879

120582119879

119910120582119910119878 + 120582119879

119906120582119906)

119882119866= minus2119878

119879

120582119879

119910120582119910119864119901(119896 + 1 | 119896)

119864119901(119896 + 1 | 119896) = 119884

119889(119896 + 1) minus 119878Δ119909 (119896) minus 119864119910 (119896)

(37)



Δ119906 (119896) = [



2times2119862

Δ119880 (119896)

119906 (119896) = 119906 (119896 minus 1) + Δ119906 (119896)

(38)







119879119901

119905119889

119879ℎ

13886 04176 01589



6 Conclusion








minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

5 10 150Time (s)

Yaw

rate

(deg

sminus1)

(b)

0 5 10 15Time (s)


minus4

minus2

0

2

4

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)




minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

Yaw

rate

(deg

sminus1)

5 10 150Time (s)

(b)


5 10 150Time (s)

minus5

0

5

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)






Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












11989162800



119891107



11991143316



minΔ119880(119896)

1

2Δ119880 (119896)

119879

119882119867Δ119880 (119896) + 119882

119879

119866Δ119880 (119896)


(36)

where

119882119867= 2 (119878

119879

120582119879

119910120582119910119878 + 120582119879

119906120582119906)

119882119866= minus2119878

119879

120582119879

119910120582119910119864119901(119896 + 1 | 119896)

119864119901(119896 + 1 | 119896) = 119884

119889(119896 + 1) minus 119878Δ119909 (119896) minus 119864119910 (119896)

(37)



Δ119906 (119896) = [



2times2119862

Δ119880 (119896)

119906 (119896) = 119906 (119896 minus 1) + Δ119906 (119896)

(38)







119879119901

119905119889

119879ℎ

13886 04176 01589



6 Conclusion








minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

5 10 150Time (s)

Yaw

rate

(deg

sminus1)

(b)

0 5 10 15Time (s)


minus4

minus2

0

2

4

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)




minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

Yaw

rate

(deg

sminus1)

5 10 150Time (s)

(b)


5 10 150Time (s)

minus5

0

5

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)






Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

5 10 150Time (s)

Yaw

rate

(deg

sminus1)

(b)

0 5 10 15Time (s)


minus4

minus2

0

2

4

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)




minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

Yaw

rate

(deg

sminus1)

5 10 150Time (s)

(b)


5 10 150Time (s)

minus5

0

5

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)






Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











minus1

0

1

2

3

4

Disp

lace

men

t (m

)

5 10 150Time (s)

(a)


minus15

minus10

minus5

0

5

10

15

Yaw

rate

(deg

sminus1)

5 10 150Time (s)

(b)


5 10 150Time (s)

minus5

0

5

a y(m

sminus2)

(c)

Only MPCDBI and MPC

minus1

minus05

0

05

1St

eerin

g w

heel

angl

e (ra

d)

5 10 150Time (s)

(d)

Only MPCDBI and MPC

minus1500

minus1000

minus500

0

500

1000

1500

Yaw

mom

ent (

Nm

)

5 10 150Time (s)

(e)






Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article design of an integrated vehicle chassis ...carsim virtual scene dspace real-time...

Documents