Research Article Global Chassis Control System Using ...downloads.hindawi.com/journals/mpe/2015/263424.pdf · Research Article Global Chassis Control System Using Suspension, Steering,

Research ArticleGlobal Chassis Control System Using SuspensionSteering and Braking Subsystems

Carlos A Vivas-Lopez1 Juan C Tudon-Martinez2

Diana Hernandez-Alcantara1 and Ruben Morales-Menendez1

1Tecnologico de Monterrey School of Engineering and Sciences Avenida E Garza Sada No 2501 64849 Monterrey NL Mexico2Universidad de Monterrey Avenida Ignacio Morones Prieto No 4500 66238 San Pedro Garza Garcıa NL Mexico

Correspondence should be addressed to Carlos A Vivas-Lopez a00794204itesmmx

Received 4 August 2015 Accepted 21 October 2015

Academic Editor Xinggang Yan

Copyright copy 2015 Carlos A Vivas-Lopez et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

AnovelGlobal Chassis Control (GCC) systembased on amultilayer architecturewith three levels top decision layermiddle controllayer and bottom system layer is presented The main contribution of this work is the development of a data-based classificationand coordination algorithm into a single control problem Based on a clustering technique the decision layer classifies thecurrent driving condition Afterwards heuristic rules are used to coordinate the performance of the considered vehicle subsystems(suspension steering and braking) using local controllers hosted in the control layer The control allocation system uses fuzzylogic controllers The performance of the proposed GCC system was evaluated under different standard tests Simulation resultsillustrate the effectiveness of the proposed system compared to an uncontrolled vehicle and a vehicle with a noncoordinated controlThe proposed system decreases by 14 the braking distance in the hard braking test with respect to the uncontrolled vehicle theroll and yaw movements are reduced by 10 and 12 respectively in the Double Line Change test and the oscillations caused byload transfer are reduced by 7 in a cornering situation

1 Introduction

A road vehicle has a conjunction of interconnected subsys-tems such as brakes steering suspension engine and tireswhich is difficult to be controlled [1]These subsystems inter-act among them modifying their individual behavior andconsequently the overall performance of the vehicle theseinteractions could cause negative effects For example theway the suspension system is tuned can dramatically affectthe performance of the steering system a soft suspensionaffects the tire grip decreasing the ability of the vehicle tosteer if the suspension is too stiff tires will hop causing loss ofcontrol Additionally all vehicle subsystems have a nonlinearbehavior making their coordination a complex task

Normally each vehicle subsystem has an independentcontrol system to accomplish a specific objective For exam-ple the brake system has the Antilock Braking System (ABS)to prevent tires from locking during hard braking avoidingskidding and loss of control [2] Also it has the Electronic

Stability Control (ESC) which creates a turning momentusing the brakes to prevent loss of control Both controlsystems have conflicting principles the ABS releases thebrake pressure whereas the ESC generates an additional oneTable 1 summarizes the used acronyms in this document

Studies in global trends aim towards achieving intelligentvehicles in upcoming years [3]These vehicles are required tomeet present and future state regulations related to efficiencyautonomy ecology safety and comfort [4] Particularly theglobal automotive industry is paying special attention tosafety systems that guarantee the integrity of occupantspedestrians andor other drivers when an accident occursEven the newest safety features (Collision Mitigation or LineKeeping Systems) are oriented to prevent possible dangeroussituations themain topic of research refers to the systems thatreact against a dangerous situation [5]

These opportunities demand more of the actual VehicleControl Systems (VCS) The standard solutions was to inde-pendently treat any new objective by adding a new VCS

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 263424 18 pageshttpdxdoiorg1011552015263424

2 Mathematical Problems in Engineering

Table 1 Acronyms definition

Acronyms DescriptionABS Antilock Braking SystemAS Active SteeringAFS Active Front SteeringCDC Continuous Damping ControllerDC Decentralized ControllersDL Decision LogicDLC Double Line ChangeDoF Degree of FreedomDBC Data-Based ControllerEMB Electromechanical BrakingESC Electronic Stability ControlECU Electronic Control UnitFH Fish HookFCS Force control systemFL Fuzzy logicFIS Fuzzy Inference SystemGCC Global Chassis ControlIVDC Integrated Vehicle Dynamics Control119896-NN 119896-Nearest NeighborLPV Linear parameter varyingMBC Model-Based ControllerMF Membership FunctionPC Principal ComponentPCA Principal Component AnalysisRMS Root Mean SquareROC Receiver operating characteristicSA SemiactiveSAS Semiactive suspensionSAP Suspension Adjustment PlaneSCS Steering control systemSISO Single-Input Single-OutputSMC Sliding Mode ControlTRC Traction ControlUC UncontrolledVCS Vehicle Control SystemVDC Vehicle Dynamics Control4WIB Four-Wheel Independent Braking4WS Four-Wheel Steering

This parallel architecture can lead to some drawbacks forexample a VCS is normally designed to seek a specific goalbut when it interacts with other VCS the result could degradethe global performance overruling the original objectives ofthe individual controllers due to inherent coupling effectsSince those controllers have to work simultaneously theyhave their own information system and Electronic ControlUnit (ECU) demanding more costs and space that is vehicleinfrastructure and complexity increase [6]

The concept of GCC also called Integrated VehicleDynamics Control (IVDC) proposes the coordinated integra-tion of those different VCS to pursuit a common goal [7]

This integration offers (1) the ability to simultaneously controlvarious subsystems (2) the ability to coordinate the actionsof individual subsystems regarding a general goal [8] and (3)the ability to share information from sensors and actuators(also functions) [9]

This concept has been investigated in the literatureThe approaches can be differentiated regarding the numberof Degrees of Freedom (DoF) in which they act (verticallongitudinal or lateral dynamics) Some cases have beenstudied as functional integrations (specific objective or singleDoF) In [10] an integration of the braking and Semiactive(SA) suspension system is proposed to decrease brakingdistance in an emergency maneuver but in this case thereis no coordination An integration of active suspension andbraking is proposed in [11] to prevent a rollover situationusing a Linear Parameter-Varying (LPV) controller driven bya scheduling parameter related to load transfer the controlleris highly model dependent

Most of the research of this topic lays in the case ofmultipurpose integration (ie multiple DoF) An integrationof steering and braking to enhance horizontal dynamicsusing robust control is proposed in [12] however the coor-dination algorithm and controller synthesis are not clearIn [13] the authors proposed a controller based on inverse-model dynamics to generate the desired control commandsfor braking and steering subsystems the method is highlydependent in an accurate model of the system and sensitiveto modeled dynamics In [14] an integration of steering andbraking systems is proposed The goal is to maintain anoptimum tire forces using Sliding Mode Control (SMC) Ituses an optimization procedure to compute the optimumforce distribution among the tires In [15] a control strategyto improve the horizontal dynamics involving the brakingand steering subsystems is proposed it uses an optimizationprocedure to allocate the desired yaw moment but the costfunctions have to be modified depending on the situationIn [16] a loss prevention control system is introduced usingthe braking and steering subsystems this strategy relies onphysical infrastructure in the road to calculate the referencesignals which nowadays is not available in most roads

Only few works have been published on full dynamicsintegration (able to act in the vertical longitudinal and lateraldynamics) In [17] an integration of an active suspension a4-Wheel Steering (4WS) and a drivingbraking force controlusing Traction Control (TRC) and ABS is proposed but thecoordination algorithm is not clear and the use of activesuspension and 4WS is expensive In [1] a strategy usingthe differential braking for horizontal dynamics and theactive suspension for vertical is proposed this method hasto calculate the control command of each sampling time byoptimization this demands a lot of computational resourcesThe authors in [18] divide the problem they treated verticaland horizontal dynamics separately For vertical dynamics itdetermines the desired force for each damper based on theLPV framework but its performance is fixed by design Forhorizontal dynamics it uses a gain scheduling parameter todecide when to apply braking control or a combination ofsteering with braking control It defines some driving con-ditions (ie stable or unstable) but they are limitedThe work

Mathematical Problems in Engineering 3

of [19] proposed a control architecture capable of identifyingthe actual driving situation based on the estimated situationthe control mode of each subsystem is changed Even whenthis method is capable of reacting against different situationsit does not consider the switching implications in the controlsystem which could lead to unexpected behaviors In [20] acontrol systembased on LPV is proposed in this case all threedirections are simultaneously controlled using two varyingparameters one for suspension-steering and another forbraking however the controller operates under predefinedconditions without depending on the driving situation

Although there are interesting results they do not includethe full dynamics integration others are strongly model-dependent or they are robust to some uncertainty whichcould generate conservatism issues Furthermore some ofthem are not easy to implement in on-board Vehicle Dynam-ics Controllers

The main contribution of this proposal lays in a newGCC system based on a discrimination of the operationconditions of the vehicle The strategy architecture is asupervisory decentralized control to improve flexibility andmodularity [21] The goal is to identify the current drivingsituation based on vehicle measurements using clusteringmethods [22] then the control modes of each subsystem arecoordinated to ensure the best global performanceThe coor-dination includes three subsystems SAS AFS and 4-WheelIndependent Braking (4WIB) a full dynamics integrationTheeffectiveness of the new strategy was validated in CarSim

The paper is organized as follows Section 2 describesthe problem Section 3 presents the GCC architecture andmodules in detail Section 4 discusses the results based ona case study Section 5 concludes the research and proposesfuture work Tables 2 and 3 summarize all the used variablesin this work

2 Problem Description

Passenger vehicles are equipped with a wide diversity of on-board VCS and those focused on the management of thedynamical behavior of the vehicle are calledVehicle DynamicsControllers (VDC) for example Continuous Damping Con-troller (CDC) and Electronic Stability Control (ESC) Usuallyeach VDC operates in a set of DoF defined by the vehiclereference system Figure 1 the most important variables foreach vehicle motion are as follows

(i) Vertical dynamics refers to the movements that affectmainly the comfort of the passengers (vibrationreductions) the important variables are pitch (turnaround 119910-axis 120601) roll (turn around 119909-axis 120579) andvertical acceleration () in the Chassis and wheels

(ii) Lateral dynamics refers mainly to the stability andhandling (safety) of the vehicle the important vari-ables are lateral displacement (119910) side slip angle (120573)and yaw (turn around 119911-axis 120595)

(iii) Longitudinal dynamics refers to vehicle stability(safety) and its performance (power train) the impor-tant variables are longitudinal velocity (119881

119909) wheel

rotational velocity (120596) and tire slip ratio (120582)

Table 2 Modeling variables description

Variable Description Units

1198861 1198862

Hysteresis coefficients related todisplacement and velocity sm 1m

119888119901 Viscous damping coefficient Nsm

119891brake 119891steerCut-off frequency of the actuatordynamics Hz

119891119888

Force coefficient due tomanipulation NV

119865119863 Damper force N

119865SA Semiactive damper force N119896119901 Stiffness coefficient Nm

119897 Vehicle wheel base m119898119904119898us Sprungunsprung mass kg

119879+

119887 120575+ Actuator output MPa deg

119879lowast

119887 120575lowast Actuator controller output MPa deg

119881119909 V119909119894119895

Vehicletire longitudinal vel ms

119909 119910 119911 Longitudinallateralverticaldisplacement m

Longitudinallateralverticalvelocity ms

Longitudinallateralverticalacceleration ms2

119911def def Damper deflection and velocity m ms

119911119903 119911119904 119911us

Roadsprung massunsprungmass vertical position m

120573 Vehicle side slip angle deg120575 Steering wheel angle deg120575driver Driverrsquos steering command deg120582 Tire slip ratio mdash120592 Damper manipulation V120601 120579 120595 Pitchrollyaw angle deg Pitchrollyaw rate degs119889

Desired yaw rate degs120596 Rotational speed of the tires rads

A VDC can have one ormore of these three control goalsstability handling or vibration mitigation

(1) Stability when a vehicle has crossed its handlinglimits and tires lost their grip it is said that the vehiclehas become unstable and cannot be controlled by theaction of the driver only here the main objective isto recover the driverrsquos control to guarantee passengerssafety

(2) Handling it refers to how well a vehicle can achievecornering at high speeds this condition is related tothe safety characteristic of the vehicle

(3) Vibration mitigation it refers to the comfort that thepassengers will experience during riding this consistsin the limitation of the unpleasant vibrations andmovements caused by road irregularities also road-holding is considered that is vibration reduction inthe unsprung mass at high vehicle velocities


Table 3 Algorithms variables description

Variable Description119886119898

Actuation vector

119886119906

Gain of the allocationcoordination

119886119906susp

119886119906braking

119886119906steer

Suspensionbrakingsteeringcoordination gain

119888min 119888maxSoftesthardest dampingcoefficient

119862119894

Driving class

Con119894119896

Contribution index of the 119894thvariable in a 119896 driving situation

CS119896

Minimal set of importantvariables for a driving situation

119889(119909 119910119895) Euclidian distance

119863119862

Driving situation119890(120573) 119890() Slip angleyaw rate error119866ABS ABS braking gainIS Initial set of vehicle variables119896119894

Number of nearest neighbors119897119896

First 119897 principal components119898 Number of measurements

MS Minimal set of importantvariables for all driving situations

119872119911

Corrective yaw moment

119899 119899lowast Originalreduced number ofvariables

119903 Number of driving conditions

119904119904

Driving situation criticalcondition

119904119894

Driving situation importance119905crit Situation changing waiting time119905con Variable contribution threshold119879driver Driver braking torque

119879ESC119903 119879ESC119897Rightleft corrective brakingpressure

119879119866

Pressure gain119905119899119910

Noise variance threshold

119906119888 119906lowast119888

Allocatedcoordinated controlleroutput

119880|rh 119880|conf

Full suspensionroad-holdingcomfortsuspension command

119906susp119894119895 119880lowast

suspSingle cornerfull suspensioncontrol command

119909 Data point

119883119894passive

119883119894controlled

Passivecontrolled 119894thperformance variable

119894119896

Residual data point of the 119894thmeasure in a 119896 driving situation

120573119889 119889

Desired vehicle slip angleyawrate

120575AFS Corrective steering angle

120575lowast

steering wheel 120575lowast

wheelsSteering wheelwheelsdirectional angle

Table 3 Continued

Variable Description120582crit Critical tire slip ratio

120590119909119894119896

Variance of the 119894th variable in a 119896

driving situationR119896 Covariance matrix

X119896 Data matrix of 119899 variables

P119896 P119896

Principalresiduals componentsmatrix

T119896 T119896 Principalresidual scores matrix

X119896 X119896

Principalresidual transformedvariables

119894 Variable number119896 Driving situation119895 Number of neighborhoods

ω λθ

ψ

X

Y

Z

υβ

120601

Figure 1 Vehicle reference system and important dynamical vari-ables

To develop a full dynamics integration in the vehicle itis necessary to controlcoordinate the different subsystemssimultaneously [17] Usually the selected subsystems are (1)Active Front Steering (2) Independent Braking and (3)SAS Another requirement is the use of different controllersacting in those subsystems depending on the current drivingsituation [23] but this feature leads to switching thosecontrollers which could cause unstability [24]

In road vehicles the inherent coupling effects amongtheir subsystems impact the overall performance of thevehicle The coupled effects plus the issues that come withthe interactions of different independent control systemsincrease the complexity of controlling the vehicle dynamics

The above conditions can be handled with integratedcontrol strategies where subsystems and control actions areefficiently coordinated Such strategies avoid contradictionsin the control goals of the subsystems to obtain a better globalperformance from them at each situation [25] Model-basedcontrol approaches represent a complex and unpracticalsolution considering the vehicle as a highly nonlinear systemOn the other hand Data-Based Controllers could representa reliable option in practice assuming that the vehicle


DBC

MBCPassive

02 04 06 08 1 12 14 160Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)

(a) Vertical acceleration (119904)

DBCMBC

Passive

02 04 06 08 1 12 14 160Time (s)

minus08

minus04

0

04

08

Pitc

h an

gle (

deg

)

(b) Pitch angle (120601)

Figure 2 Comparison of MBC and DBC approaches

dynamics is monitored by some sensors Figure 2 comparesthe two approaches under the road profile with bump testThistest is used to evaluate the road isolation characteristics ofthe control systems Here 3 cases are compared (1) Passivea vehicle with nominal shock absorbers (2) a Model-BasedController (MBC) a full suspension 119867

infincontroller designed

to minimize the vertical acceleration (119904) and the pitch

(120601) movements of the sprung mass and (3) a Data-BasedController (DBC) a controller that considers the classical Sky-Hook and Ground-Hook algorithms

From Figure 2 it can be seen that the two approacheshave a very similar performance Quantitatively the MBCimproved the vertical acceleration in 145 and the pitchmovements in 974with respect to the Passive case whereasthe DBC achieved an improvement of 91 and 178respectively Both approaches result in similar performancesbut the DBC is simpler and faster to implement comparedto the MBC which has large dimension matrices inside thecontroller

Based on the results of the literature review VDC systemsthat achieve full dynamics integration are still a researchtopic

3 Global Chassis Control

Thearchitecture of theGCC system is divided into threemainlayers Figure 3

(1) Decision layer it identifies the current driving situa-tion and its stability it decides how to coordinate thesubsystems actions and their operating mode

(2) Control layer it receives the control goal from thedecision layer and determines the proper orientationfor each of the local controllers

(3) Physical layer it comprehends the actuators andsensors from the vehicle it receives the control outputfrom the control layer and sends the process variablesfrom the sensors

This multilayer and hierarchical architecture has someadvantages (1) it divides the computational load into severalECUs (2) it allows information sharing (3) it improvessystem flexibility (reconfigurability) and (4) it introduces

Dec

ision

laye

rC

ontro

lla

yer

Phys

ical

laye

r

Info

rmat

ion

bus

FCS ABS SCS

Local controllers

Control allocation

Classification algorithm

Decision logic

Subsystems

Sens

ors

Control command(outer loop)

Control objective

Driving situation

Control command(inner loop)

Figure 3 GCC architecture hierarchical approach

a modular scheme capability [26] The information bus con-tains sensors measurements and actuators functions Sincethe methods to observe or estimate the considered variablesare not within the scope of this work they are assumed to beavailable Figure 4 shows a full scheme of the proposed GCCsystem

31 Decision Layer This layer has two main tasks (1) classifythe current driving situation and (2) coordinate the controlstrategy for the classified situation

311 Classification Algorithm The first step of the algorithmis to decide from an Initial Set (IS) of variables which is theMinimal Set (MS) to classify the current driving situationThe elements of IS must be variables that describe the global


Decision

logic

SAP

Sensorsactuators signals

Local controllersk-means

algorithm

SA suspension

Active frontsteering

Braking system

Physical layer

Sens

ors

Brake control

Angle control

Voltage control

ESC

AFS

Control layer

Decision layer

Suspcontrol

Control allocation

Actuators

aususp

austeer

aubraking

Tdriver

120575lowaststeering wheel =2874

118120575lowasttires

Tlowastb = GABS middot max(Tdriver T

lowastESC)

120575driver

cmin

cmax120592 =

10

90

rceilrfloorrceilrfloorrceilrfloor rceilrfloor997888rarr

Figure 4 Control scheme of the GCC system

behavior of the vehicle as well as variables that are commonlyused in VCS

MS sube IS |MS| le |IS| (1)

Some vehicle variables are correlated for example pitchis correlated to deflections of the suspension Besides not allvariables have the same importance in all driving situationsfor example in a riding situation the vertical acceleration willgain more importance but during cornering yaw momentcould be the most important To determine the most rep-resentative vehicle variables during a driving situation aPrincipal Component Analysis (PCA) is carried out

Measurements of the variables in the IS set under differentdriving situations are used in this step where 119903 is thenumber of driving situations to be considered X

119896 with 119896 =

1 2 119903 is the data matrix of 119899 variables and |IS| = 119899and119898measurements with zero mean and unit variance aftera scaling process To neglect the noise effect in the scalingprocess variables with small variance are not considered120590119909119894119896

lt 119905119899119910 where 119905

119899119910gt 0 is a defined threshold

Based on [27] P119896

isin R119899times119897119896 is obtained it contains thefirst 119897119896eigenvectors from the covariance matrix R

119896and P

119896isin

R119899times(119899minus119897119896) which contains the last 119897119896minus 119899 eigenvectors The first

119897119896eigenvectors associated with the PC have to explain at least

90 of the total variance of the original data for each driving

situation Then the scores matrices T119896

isin R119898times119897119896 and T119896

isin

R119898times(119899minus119897119896) are obtained

T119896= X119896P119896

T119896= X119896P119896

(2)

By decomposing X119896= X119896+ X119896with

X119896= T119896P119879119896

X119896= T119896P119879k

(3)

the modeled data is obtained with principal and residualcomponents respectively

According to [28] using the residual components X119896

the contribution of each variable 119894 can be obtained in each119896 driving situation as

Con119894119896

=sum119898

119895=12

119894119896(119895)

sum119899

119894=1sum119898

119895=12

119894119896(119895)

forall119894 = 1 2 119899 (4)

Once the contributions are obtained if Con119894119896

gt 119905conthen Con

119894119896997891rarr CS

119896 where CS

119896is the set of the variables


and

lfloorlceil

rfloorrceilDC119894

[si] lt DC119895[si]

DC119894[ss] = DC119895

[ss] = 0

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t gt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t lt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1or

DC119894DCj

DC119894[si] lt DC119895

[si]

middot middot middot middot middot middot

Figure 5 Graph for the DL module

that contributes in each 119896 driving situation and 119905con gt 0 isa defined threshold Finally the MS set is formed by

MS =

119903

⋃

119896=1

CS119896

forall119896 = 1 2 119903 (5)

with the resultant number variables equal to |MS| = 119899lowast

After defining theMS set that contains themost represen-tative variables for all studied driving situations a clusteringtechnique is exploited as classifier Because of its easy com-putation fast clustering response and good performance the119896-Nearest Neighbor (119896-NN) algorithm was used

The 119896-NN approach is one of the simplest machinelearning algorithms which it is based on the minimumdistance criterion A data set of reference patterns in amultidimensional feature space is required to establish thelearning of this classifier where the Euclidian distance isthe most common metric In this case MS set contains thereference patterns of the studied driving situations

Given a new data vector 1199091 1199092 119909

119899of 119899 variables the

119896-NN algorithm assigns each new observation into a class ofdriving situation 119862

119894according to

119909 isin 119862119894when min

119862

1

119896119894

119896119894

sum

119895=1

119889 (119909 119910119895) (6)

where 119896119894is the number of nearest neighbors used in the

classification associated with the driving situation 119894 and119889(119909 119910

119895) is the Euclidian distance between a new observation

119909 and the nearest neighbors of reference defined by 119910 A largevalue of 119896 reduces the effect of noise in the classificationcross-validation can be used to define this parameter For thevehicle the sensor measurements contained in theMS set areused to construct the features space The online result givenby this clustering technique is sent to theDecision Logic (DL)module to classify the situation

312 Decision LogicModule Based on a set of heuristic rulesthe DL module is in charge to decide (1) whether a drivingsituation is critical or normal (2) if the control actions shouldchange and (3) when to change from one situation to anotherbased on the importance of the previous situation

First the structure for a driving situation 119863119862 must be

defined For this purpose the DL module depends on thenumber of subsystems to use and the amount of drivingsituations 119903 to consider The definition of a119863

119862is as follows

(i) Each driving situation is defined with a vector in R3

in the form119863119862= [119904119904 119904119894 119886119898]

(ii) 119904119904isin 0 1 refers to normal (119904

119904= 0) or critical (119904

119904= 1)

situation(iii) 119904119894isin 1 119902 indicates the critical level of the driving

situation 119904119894rarr 1 is a stable situation with negligible

danger while 119904119894

rarr 119902 corresponds to the mostdangerous condition

(iv) 119886119898

isin R119906 is the actuation vector for the 119906 subsystemsthat must be accomplished according to the detecteddriving situation that is 119886

119898= 1198861 119886

119906 Consid-

ering an on-off control law for each subsystem thecontrol output is dichotomic 119886

119894isin [0 1]

Then a set of rules that manage the transition betweendriving situations is defined Figure 5 shows the graph dia-gram with the transition rules the DL rules are carried asfollows

(1) A 119863119862with bigger 119904

119894overrules a 119863

119862with a smaller 119904

119894

index and 119886119898is updated

(2) At any safe driving situation independently of the 119904119894

index the current119863119862updates the actuation vector 119886

119898

(3) In an unsafe driving situation the current 119863119862keeps

the actuation vector in safe mode until the 119904119894index

decreases through the time (119905 gt 119905crit) to ensurecompletely the vehicle safety and avoid any falsealarms

Finally the DL layer sends the mode of operation of thesubsystems controllers in the control layer

32 Control Layer This layer comprehends the controlactions (allocation manipulation) to be taken through thephysical layer The desired control allocation is determinedbased on the information received from the previous layerand then the desired control manipulations are computed


321 Control Allocation Based on the driving situation thedesired control action for each subsystem is defined in thissublayer The control mode acts as a gain in the form of

119906lowast

119888= 119886119906sdot 119906119888 (7)

where 119906lowast

119888is the controller output which depends directly on

the gain of the coordinated allocation 119886119906 that is 119886

119906= 1means

that the GCC demands the actuation on the subsystemand vice versa (ie when 119886

119906= 0) Thus 119906

119888is the local

controller output of the subsystem obtained from any controllaw but before the full dynamics integration The allocationcontrollers for each subsystems are defined as follows

(i) SAS The SA dampers must always receive a manipulationthe decision is whether to select a manipulation oriented tocomfort (119880|comf ) or to road-holding (119880|rh) for each corner ofthe vehicle

119880lowast

susp = (1 minus 119886119906susp

) sdot 119880|comf + 119886119906susp

sdot 119880|rh (8)

where 119880lowast

susp = 119906susp119865119871

119906susp119865119877

119906susp119877119871

119906susp119877119877

Note thataccording to the driving situation the GCC can orient thesuspension to comfort or to road-holding using theweightingparameter 119886

119906susp At each corner the SAS controller output can

be oriented to comfort (119906119894119895|comf ) or to road-holding (119906

119894119895|rh)

inspired in the classical Sky-Hook and Ground-Hook controlstrategies

119906119894119895

10038161003816100381610038161003816rh =

119888min if minus 119906119904

sdot def le 0

119888max if minus 119906119904

sdot def gt 0

119906119894119895

10038161003816100381610038161003816comf =

119888min if 119904sdot def le 0

119888max if 119904sdot def gt 0

(9)

where 119888min = 0 and 119888max = 1 represent the softest and hardestdamping coefficient respectively

(ii) Braking System The braking action is computed by thefuzzy logic (FL) controller [29] It uses two inputs (1) side slipangle error (119890(120573) = 120573 minus 120573

119889isin [minus10 10]) and (2) yaw rate error

(119890() = minus 119889

isin [minus10 10]) and one output (1) correctiveyaw moment (119872

119911isin [minus1 1]) The control goal is to reduce

the errors to zero for this purpose the reference signals aredefined as 120573

119889= 0 since the goal is to have 120573 as close to zero

as possible and

119889=

119881119909

119897120575driver (10)

where 119881119909is the longitudinal velocity of the vehicle 119897 is the

wheel base and 120575driver is the drivers steering angle commandFor the two input variables five fuzzy sets with triangular

Membership Functions (MFs) were used for each variable119890(120573) 119890() = NBNSZPSPB whereas for the outputvariable seven fuzzy sets also with triangular MFs were used119872119911 = NBNMNSZPSPMPB Table 4 describes the

meanings of the used linguistic terms and Table 5 shows

Table 4 Linguistic terms

NB Negative bigNMH Negative medium highNM Negative mediumNMS Negative medium smallNS Negative smallZ ZeroPS Positive smallPMS Positive medium smallPM Positive mediumPMH Positive medium highPB Positive big

Table 5 FL inference rules for the braking system

119890(120573)119890()

NB NS Z PS PBNB PB PB NS NB NBNS PB PM NS NM NBZ PM PS Z NS NMPS PB PM PS NM NBPB PB PS PS NS NB

the rules for the proposed FL controller This FL controlleruses aMamdani Fuzzy Inference System (FIS)

To allocate the desired output for the braking localcontrollers119872

119911is transformed in terms of ESCs as

119872119911gt 0 997888rarr Brake rear left wheel

119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911

119872119911= 0 997888rarr No added braking

119879ESC119903 = 0 119879ESC119897 = 0

119872119911lt 0 997888rarr Brake rear right wheel

119879ESC119903 = minus119879119866sdot 119872119911 119879ESC119897 = 0

(11)

where 119879119866

is a parameter that relates the corrective yawmoment (119872

119911) and the brake pressure to be applied by the

braking systemAdditionally the coordinated allocation affects the action

of the braking FL controller including or ignoring it usingthe value of 119886

119906brakingas a gain

119879lowast

ESC = 119886119906braking

sdot 119879ESC (12)

(iii) AFS System For this subsystem the allocation decides tointroduce or not the AFS control action as

120575lowast

= 120575driver + 119886119906steer

sdot 120575AFS (13)

where 120575lowast is the desired steering wheel angle 120575driver is

the driverrsquos command and 120575AFS is the compensation anglecalculated by the AFS system From (13) it can be seen


Table 6 FL inference rules for the steering system

120573 120575driver119890()

NB NS Z PS PB

Low

NB NS NS Z PB PBNS NMS NMS Z PMH PMHZ NM NM Z PM PMPS NMH NMH Z PMS PMSPB NH NH Z PS PS

High

NB NH NH Z PS PSNS NMH NMH Z PMS PMSZ NM NM NS PMS PMSPS NMS NMS NS NS NSPB NS NS NS NS NS

that the driverrsquos command is always considered but thecompensation angle is considered if 119886

119906steer= 1 or not if 119886

119906steer=

0As for the braking system the steering action is computed

using a FL controller [30]Three input variableswere selected(1) side slip angle (120573 isin [minus10 10]) (2) yaw rate error(119890() = minus

119889isin [minus10 10]) and (3) steering angle input

(120575driver isin [minus10 10]) and one output (1) steering correctionangle (120575AFS isin [minus5 5]) The FL controller is oriented to createa steering wheel angle correction that minimizes the yaw rateerror the desired yaw rate is calculated using (10)

For input 120573 two fuzzy sets with sigmoid MFs were used120573 = LowHigh For the other two input variables fivefuzzy sets with triangular MFs were used 119890() 120575driver =

NBNSZPSPB whereas for the output variable elevenfuzzy sets also with triangular standard MFs were used120575AFS = NBNMHNMNMSNSZPSPMSPMPMHPB Table 6 shows the rules for the proposed FL controllerwhose linguistic definitions are given in Table 4

322 Local Controllers This sublayer contains the localcontrollers for each subsystem These controllers are Single-Input Single-Output (SISO) and only interact with theirparticular subsystem These controllers receive the desiredset-point 119906

lowast

119888from the control allocation sublayer and are

in charge of executing it Also these controllers have to beselected regarding the subsystem to control The subsystemcontrollers for this strategy are the following

(i) SAS because the control command coming from theallocation step is binary the force control system isdefined as follows

[119888min

119888max] = [

0

1] 997891997888rarr 120592 = [

1090

] (14)

where 120592 is the manipulation delivered to the SAdamper (ie electric current voltage and duty cycle)

(ii) Steering the command in terms of tire angles totransform it to a single gain controller is

120575lowast

steering wheel =2874

118120575lowast

tires (15)

(iii) Braking the local controller is an ABS it modifies thedesired command as

119879lowast

119887= 119866ABS sdotmax (119879driver 119879

lowast

ESC) (16)

where 119879driver is the driver braking command 119879ESCis the braking command from the allocation systemand 119866ABS is the gain of the ABS that releases thetire when it is locked This control law selects themaximum between the command coming from theallocation system and the command from the driverThe 119866ABS gain is obtained by the function

119866ABS119894119895 =

0 if 120582119894119895

ge 120582crit

1 if 120582119894119895

lt 120582crit(17)

with

120582119894119895

=

119881119909minus V119909119894119895

119881119909

(18)

where 120582119894119895

is the slip ratio for each wheel Theoperation of this ABS controller is guided by 120582 if 120582grows beyond the admissible range (120582crit = 01) thebraking system releases the tire until it recovers gripand the slip ratio decreases to the admissible rangewhere the braking torque is again applied to the tire

33 Physical Layer The physical layer is integrated by thesensors and actuators of the SAS AFS system and 4WIBsystem

331 Suspension System Thesuspension system is composedof a linear spring and a SA shock absorberThe key element isthe set of SA shock absorber one at each corner which needsto be modeled as a function of a manipulation signal (120592) Thedamper force (119865

119863) is modeled as a function of the damper

deflection (119911def ) deflection velocity (def ) and manipulationsignal [31]

119865119863

= 119888119901(def) + 119896

119901(119911def) + 119865SA (19)

where 119865SA = 120592 sdot 119891119888sdot tanh(119886

1sdot def + 119886

2sdot 119911def ) is the SA force

due to 120592 119888119901is a viscous damping coefficient 119896

119901is a stiffness

coefficient and 1198861and 119886

2are hysteresis coefficients due to

velocity and displacement respectively The SA dampingforce at each damper is continuous from [minus10000 6000]N

332 Steering System A steer-by-wire Active Steering (AS)system is used to provide an additional steering angle forcorrective purposes the actuator model is given by [32]

+

= 2120587119891steer (120575lowast

minus 120575+

) (20)

where 119891steer = 10Hz is the cut-off frequency of the actuatordynamics 120575

lowast is the steering controller output and 120575+ is

the actuator output the bounded limits of actuation are[minus5∘ +5∘]


50 100 150 2000Station (m)

minus10

0

10

z r(m

m)

(a) Road profile with bump (b) Brake distance test (hard braking)

(c) DLC test (rapid steering) (d) FH test (cornering)

(e) Split 120583-surface braking (loss of vehicle control)

Figure 6 Implemented tests in CarSim

333 Braking System The corrective front and rear brakingtorques are provided by brake-by-wire ElectromechanicalBraking (EMB) actuators the model of these EMB actuatorsis given by [32]

+

119887= 2120587119891brake (119879

lowast

119887minus 119879+

119887) (21)

where 119891brake = 10Hz is the cut-off frequency of the actuatordynamics 119879lowast

119887is the braking controller output and 119879

+

119887is the

actuator output The bounded limits of actuation for eachbraking actuator are [0 15]MPa

4 GCC System Evaluation

The results of this proposal are presented based on a casestudy

41 Case Study CarSim was used to generate an accuratevehicle model whose VDC were hosted in MatlabSimulinkA 119863-class sedan was the selected vehicle Seven drivingsituations were considered (119903 = 7) Figure 6 illustrates some

of the implemented tests to represent the driving situationsthese tests are as follows

(a) Road profile with bump test this test is intendedto evaluate the road isolation characteristics of thecontrol strategy it consists in a rough road with asharp bump of 35mm height and 400mm length

(b) Brake distance test it consists in a hard braking actionby the driver to measure the distance that takes thevehicle when it goes from 100 kmh to a full stop

(c) Double Line Change (DLC) maneuver it consists ina change of driving line to simulate an obstacleavoidance maneuver or an overtaking action at highspeed (120 kmh) a rapid steering maneuver is takenby the driver to change from the original line andthen another rapid steering action to turn back to theoriginal line

(d) Fish Hook (FH) maneuver this maneuver consists ina wide but constant steering action first a movementof 270∘ of the steering wheel is taken to one sideat a constant turning rate then a turn of 540∘ to


Table 7 IS set

ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate

the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit

(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver

42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation

421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle

Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected

To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of

5

10

15

20

Varia

bles

Variables correlations matrix

5 10 15 2000

Variables

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation

90 of thevariance

4 components

0

50

100

Cum

ulat

ive v

aria

nce (

)

5 10 15 211Number of components

0

2

4

6

8Ei

genv

alue

Figure 8 PCA result for the rapid steering situation

120595

0

5

10

15

20

25

Con

trib

utio

n to

dat

a var

ianc

e (

)

5 10 15 200Variables

120575

x

120601

Figure 9 Contribution plot of the variables in the IS set

the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4

It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted


Table 8 PCA results

ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19

04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)

CorneringLoss of controlRapid steeringRiding

CorneringRapid steeringRidingCentroids

Figure 10 Clustering distribution for 2 dimensions

line) are considered the most representative variables in thisdriving situation they integrate the MS set

Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =

5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs

A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)

To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863

119862= 1)

afterwards it has a rapid steering maneuver (119863119862

= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863

119862= 5

FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because

Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)

Figure 11 Validation test for the 119896-NN classifier

the two conditions (119863119862

= 5 and 119863119862

= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions

Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)

From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement

To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area


DC = 6

DC = 5

DC = 1

02 04 06 08 10False positive rate

0

02

04

06

08

1

True

pos

itive

rate

Figure 12 ROC for the 119896-NN classifier

aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]

10 2 3minus2 minus1minus3

Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)

RidingHard brakingAccelerationbrakingLoss of control

Road irregularityCorneringRapid steering

Figure 13 Suspension Adjustment Plane (SAP)

was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)

In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking

Table 9119863119862vectors for different driving conditions

Driving situation 119863119862

119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking

Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1

whereas the horizontal central zone refers to primarily rollmovements like cornering

422 Decision Logic Table 9 presents the proposed valuesfor vector119863

119862at each driving situation

43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals

To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using

of Improvement

=RMS (119883

119894Passive) minus RMS (119883

119894Controlled)

RMS (119883119894Passive

)

(22)

431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the

vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case

432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and


GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)


Figure 14 Road profile with bump test

0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)


Figure 15 Brake distance test

(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated

433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases

After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having

GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)

Figure 16 Vehicle trajectory for a DLC test

a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case

434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more


GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)

(a) Roll angle (120579)

GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)

(b) Yaw angle (120595)

Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)

Figure 18 Vehicle trajectory for FH test

GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)

(b) Lateral acceleration ()

Figure 19 FH test

handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases

The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of

load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC

435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path


GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)

Figure 20 Vehicle trajectory for Split 120583-surface braking test

GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)

(a) Steering wheel angle (120575)

GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()

Figure 21 Split 120583-surface braking test

The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by

the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC

Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC

5 Conclusions

A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and


heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures

The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations

Conflict of Interests

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

Acknowledgments

The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects

References

[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005

[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995

[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012

[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013

[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015

[6] 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) pp 1ndash6Harbin China September 2008

[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the

International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988

[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011

[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005

[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004

[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007

[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989

[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006

[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006

[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012

[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013

[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992

[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008

[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867

infincontrol coordination strategy

involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012

[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003

[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol


32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015

[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007

[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012

[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008

[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011

[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010

[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006

[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014

[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006

[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013

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


Table 1 Acronyms definition

Acronyms DescriptionABS Antilock Braking SystemAS Active SteeringAFS Active Front SteeringCDC Continuous Damping ControllerDC Decentralized ControllersDL Decision LogicDLC Double Line ChangeDoF Degree of FreedomDBC Data-Based ControllerEMB Electromechanical BrakingESC Electronic Stability ControlECU Electronic Control UnitFH Fish HookFCS Force control systemFL Fuzzy logicFIS Fuzzy Inference SystemGCC Global Chassis ControlIVDC Integrated Vehicle Dynamics Control119896-NN 119896-Nearest NeighborLPV Linear parameter varyingMBC Model-Based ControllerMF Membership FunctionPC Principal ComponentPCA Principal Component AnalysisRMS Root Mean SquareROC Receiver operating characteristicSA SemiactiveSAS Semiactive suspensionSAP Suspension Adjustment PlaneSCS Steering control systemSISO Single-Input Single-OutputSMC Sliding Mode ControlTRC Traction ControlUC UncontrolledVCS Vehicle Control SystemVDC Vehicle Dynamics Control4WIB Four-Wheel Independent Braking4WS Four-Wheel Steering

This parallel architecture can lead to some drawbacks forexample a VCS is normally designed to seek a specific goalbut when it interacts with other VCS the result could degradethe global performance overruling the original objectives ofthe individual controllers due to inherent coupling effectsSince those controllers have to work simultaneously theyhave their own information system and Electronic ControlUnit (ECU) demanding more costs and space that is vehicleinfrastructure and complexity increase [6]

The concept of GCC also called Integrated VehicleDynamics Control (IVDC) proposes the coordinated integra-tion of those different VCS to pursuit a common goal [7]

This integration offers (1) the ability to simultaneously controlvarious subsystems (2) the ability to coordinate the actionsof individual subsystems regarding a general goal [8] and (3)the ability to share information from sensors and actuators(also functions) [9]

This concept has been investigated in the literatureThe approaches can be differentiated regarding the numberof Degrees of Freedom (DoF) in which they act (verticallongitudinal or lateral dynamics) Some cases have beenstudied as functional integrations (specific objective or singleDoF) In [10] an integration of the braking and Semiactive(SA) suspension system is proposed to decrease brakingdistance in an emergency maneuver but in this case thereis no coordination An integration of active suspension andbraking is proposed in [11] to prevent a rollover situationusing a Linear Parameter-Varying (LPV) controller driven bya scheduling parameter related to load transfer the controlleris highly model dependent

Most of the research of this topic lays in the case ofmultipurpose integration (ie multiple DoF) An integrationof steering and braking to enhance horizontal dynamicsusing robust control is proposed in [12] however the coor-dination algorithm and controller synthesis are not clearIn [13] the authors proposed a controller based on inverse-model dynamics to generate the desired control commandsfor braking and steering subsystems the method is highlydependent in an accurate model of the system and sensitiveto modeled dynamics In [14] an integration of steering andbraking systems is proposed The goal is to maintain anoptimum tire forces using Sliding Mode Control (SMC) Ituses an optimization procedure to compute the optimumforce distribution among the tires In [15] a control strategyto improve the horizontal dynamics involving the brakingand steering subsystems is proposed it uses an optimizationprocedure to allocate the desired yaw moment but the costfunctions have to be modified depending on the situationIn [16] a loss prevention control system is introduced usingthe braking and steering subsystems this strategy relies onphysical infrastructure in the road to calculate the referencesignals which nowadays is not available in most roads

Only few works have been published on full dynamicsintegration (able to act in the vertical longitudinal and lateraldynamics) In [17] an integration of an active suspension a4-Wheel Steering (4WS) and a drivingbraking force controlusing Traction Control (TRC) and ABS is proposed but thecoordination algorithm is not clear and the use of activesuspension and 4WS is expensive In [1] a strategy usingthe differential braking for horizontal dynamics and theactive suspension for vertical is proposed this method hasto calculate the control command of each sampling time byoptimization this demands a lot of computational resourcesThe authors in [18] divide the problem they treated verticaland horizontal dynamics separately For vertical dynamics itdetermines the desired force for each damper based on theLPV framework but its performance is fixed by design Forhorizontal dynamics it uses a gain scheduling parameter todecide when to apply braking control or a combination ofsteering with braking control It defines some driving con-ditions (ie stable or unstable) but they are limitedThe work











119909) wheel




1198861 1198862




119891119888





119879+


119879lowast


119881119909 V119909119894119895






119911119903 119911119904 119911us











Actuation vector

119886119906


119886119906susp

119886119906braking

119886119906steer



119862119894

Driving class

Con119894119896


CS119896



119863119862





119872119911




119904119904


119904119894



119879119866

Pressure gain119905119899119910


119906119888 119906lowast119888


119880|rh 119880|conf


119906susp119894119895 119880lowast


119909 Data point

119883119894passive



119894119896


120573119889 119889



120575lowast



Table 3 Continued


120590119909119894119896




P119896 P119896



X119896 X119896



ω λθ

ψ

X

Y

Z

υβ

120601






DBC

MBCPassive

02 04 06 08 1 12 14 160Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


DBCMBC

Passive

02 04 06 08 1 12 14 160Time (s)

minus08

minus04

0

04

08

Pitc

h an

gle (

deg

)















Dec

ision

laye

rC

ontro

lla

yer

Phys

ical

laye

r

Info

rmat

ion

bus

FCS ABS SCS

Local controllers

Control allocation


Decision logic

Subsystems

Sens

ors


Control objective

Driving situation







Decision

logic

SAP



algorithm

SA suspension


Braking system

Physical layer

Sens

ors

Brake control

Angle control

Voltage control

ESC

AFS

Control layer

Decision layer

Suspcontrol

Control allocation

Actuators

aususp

austeer

aubraking

Tdriver




lowastESC)

120575driver

cmin

cmax120592 =

10

90







119896 with 119896 =


lt 119905119899119910 where 119905


Based on [27] P119896


119896and P

119896isin





isin R119898times119897119896 and T119896

isin


T119896= X119896P119896

T119896= X119896P119896

(2)


X119896= T119896P119879119896

X119896= T119896P119879k

(3)




Con119894119896

=sum119898

119895=12

119894119896(119895)

sum119899

119894=1sum119898

119895=12

119894119896(119895)

forall119894 = 1 2 119899 (4)



119894119896997891rarr CS

119896 where CS



and

lfloorlceil

rfloorrceilDC119894


DC119894[ss] = DC119895

[ss] = 0

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t gt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t lt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1or

DC119894DCj

DC119894[si] lt DC119895

[si]




MS =

119903

⋃

119896=1

CS119896

forall119896 = 1 2 119903 (5)







119894according to

119909 isin 119862119894when min

119862

1

119896119894

119896119894

sum

119895=1

119889 (119909 119910119895) (6)








119862is as follows


in the form119863119862= [119904119904 119904119894 119886119898]


119904= 0) or critical (119904

119904= 1)





(iv) 119886119898


119898= 1198861 119886

119906 Consid-


119894isin [0 1]


(1) A 119863119862with bigger 119904



119894




119898








119906lowast

119888= 119886119906sdot 119906119888 (7)

where 119906lowast



119906= 1means


119906= 0) Thus 119906

119888is the local



119880lowast


) sdot 119880|comf + 119886119906susp

sdot 119880|rh (8)

where 119880lowast

susp = 119906susp119865119871

119906susp119865119877

119906susp119877119871

119906susp119877119877




119894119895|rh)


119906119894119895

10038161003816100381610038161003816rh =

119888min if minus 119906119904

sdot def le 0

119888max if minus 119906119904

sdot def gt 0

119906119894119895

10038161003816100381610038161003816comf =



(9)




(119890() = minus 119889





as possible and

119889=

119881119909

119897120575driver (10)








119890(120573)119890()






119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911


119879ESC119903 = 0 119879ESC119897 = 0



(11)

where 119879119866






119879lowast


sdot 119879ESC (12)


120575lowast

= 120575driver + 119886119906steer

sdot 120575AFS (13)





120573 120575driver119890()

NB NS Z PS PB

Low


High



119906steer= 1 or not if 119886

119906steer=








lowast




[119888min

119888max] = [

0

1] 997891997888rarr 120592 = [

1090

] (14)



120575lowast


118120575lowast

tires (15)


119879lowast


lowast

ESC) (16)


119866ABS119894119895 =

0 if 120582119894119895

ge 120582crit

1 if 120582119894119895

lt 120582crit(17)

with

120582119894119895

=

119881119909minus V119909119894119895

119881119909

(18)

where 120582119894119895






119865119863

= 119888119901(def) + 119896

119901(119911def) + 119865SA (19)


1sdot def + 119886








+

= 2120587119891steer (120575lowast

minus 120575+

) (20)





50 100 150 2000Station (m)

minus10

0

10

z r(m

m)






+

119887= 2120587119891brake (119879

lowast

119887minus 119879+

119887) (21)



+

119887is the











Table 7 IS set








5

10

15

20

Varia

bles


5 10 15 2000

Variables

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


90 of thevariance

4 components

0

50

100

Cum

ulat

ive v

aria

nce (

)


0

2

4

6

8Ei

genv

alue


120595

0

5

10

15

20

25

Con

trib

utio

n to

dat

a var

ianc

e (

)


120575

x

120601





Table 8 PCA results


04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)









119862= 1)



119862= 5


Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)



= 5 and 119863119862






DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















119909) wheel




1198861 1198862




119891119888





119879+


119879lowast


119881119909 V119909119894119895






119911119903 119911119904 119911us











Actuation vector

119886119906


119886119906susp

119886119906braking

119886119906steer



119862119894

Driving class

Con119894119896


CS119896



119863119862





119872119911




119904119904


119904119894



119879119866

Pressure gain119905119899119910


119906119888 119906lowast119888


119880|rh 119880|conf


119906susp119894119895 119880lowast


119909 Data point

119883119894passive



119894119896


120573119889 119889



120575lowast



Table 3 Continued


120590119909119894119896




P119896 P119896



X119896 X119896



ω λθ

ψ

X

Y

Z

υβ

120601






DBC

MBCPassive

02 04 06 08 1 12 14 160Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


DBCMBC

Passive

02 04 06 08 1 12 14 160Time (s)

minus08

minus04

0

04

08

Pitc

h an

gle (

deg

)















Dec

ision

laye

rC

ontro

lla

yer

Phys

ical

laye

r

Info

rmat

ion

bus

FCS ABS SCS

Local controllers

Control allocation


Decision logic

Subsystems

Sens

ors


Control objective

Driving situation







Decision

logic

SAP



algorithm

SA suspension


Braking system

Physical layer

Sens

ors

Brake control

Angle control

Voltage control

ESC

AFS

Control layer

Decision layer

Suspcontrol

Control allocation

Actuators

aususp

austeer

aubraking

Tdriver




lowastESC)

120575driver

cmin

cmax120592 =

10

90







119896 with 119896 =


lt 119905119899119910 where 119905


Based on [27] P119896


119896and P

119896isin





isin R119898times119897119896 and T119896

isin


T119896= X119896P119896

T119896= X119896P119896

(2)


X119896= T119896P119879119896

X119896= T119896P119879k

(3)




Con119894119896

=sum119898

119895=12

119894119896(119895)

sum119899

119894=1sum119898

119895=12

119894119896(119895)

forall119894 = 1 2 119899 (4)



119894119896997891rarr CS

119896 where CS



and

lfloorlceil

rfloorrceilDC119894


DC119894[ss] = DC119895

[ss] = 0

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t gt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t lt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1or

DC119894DCj

DC119894[si] lt DC119895

[si]




MS =

119903

⋃

119896=1

CS119896

forall119896 = 1 2 119903 (5)







119894according to

119909 isin 119862119894when min

119862

1

119896119894

119896119894

sum

119895=1

119889 (119909 119910119895) (6)








119862is as follows


in the form119863119862= [119904119904 119904119894 119886119898]


119904= 0) or critical (119904

119904= 1)





(iv) 119886119898


119898= 1198861 119886

119906 Consid-


119894isin [0 1]


(1) A 119863119862with bigger 119904



119894




119898








119906lowast

119888= 119886119906sdot 119906119888 (7)

where 119906lowast



119906= 1means


119906= 0) Thus 119906

119888is the local



119880lowast


) sdot 119880|comf + 119886119906susp

sdot 119880|rh (8)

where 119880lowast

susp = 119906susp119865119871

119906susp119865119877

119906susp119877119871

119906susp119877119877




119894119895|rh)


119906119894119895

10038161003816100381610038161003816rh =

119888min if minus 119906119904

sdot def le 0

119888max if minus 119906119904

sdot def gt 0

119906119894119895

10038161003816100381610038161003816comf =



(9)




(119890() = minus 119889





as possible and

119889=

119881119909

119897120575driver (10)








119890(120573)119890()






119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911


119879ESC119903 = 0 119879ESC119897 = 0



(11)

where 119879119866






119879lowast


sdot 119879ESC (12)


120575lowast

= 120575driver + 119886119906steer

sdot 120575AFS (13)





120573 120575driver119890()

NB NS Z PS PB

Low


High



119906steer= 1 or not if 119886

119906steer=








lowast




[119888min

119888max] = [

0

1] 997891997888rarr 120592 = [

1090

] (14)



120575lowast


118120575lowast

tires (15)


119879lowast


lowast

ESC) (16)


119866ABS119894119895 =

0 if 120582119894119895

ge 120582crit

1 if 120582119894119895

lt 120582crit(17)

with

120582119894119895

=

119881119909minus V119909119894119895

119881119909

(18)

where 120582119894119895






119865119863

= 119888119901(def) + 119896

119901(119911def) + 119865SA (19)


1sdot def + 119886








+

= 2120587119891steer (120575lowast

minus 120575+

) (20)





50 100 150 2000Station (m)

minus10

0

10

z r(m

m)






+

119887= 2120587119891brake (119879

lowast

119887minus 119879+

119887) (21)



+

119887is the











Table 7 IS set








5

10

15

20

Varia

bles


5 10 15 2000

Variables

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


90 of thevariance

4 components

0

50

100

Cum

ulat

ive v

aria

nce (

)


0

2

4

6

8Ei

genv

alue


120595

0

5

10

15

20

25

Con

trib

utio

n to

dat

a var

ianc

e (

)


120575

x

120601





Table 8 PCA results


04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)









119862= 1)



119862= 5


Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)



= 5 and 119863119862






DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Actuation vector

119886119906


119886119906susp

119886119906braking

119886119906steer



119862119894

Driving class

Con119894119896


CS119896



119863119862





119872119911




119904119904


119904119894



119879119866

Pressure gain119905119899119910


119906119888 119906lowast119888


119880|rh 119880|conf


119906susp119894119895 119880lowast


119909 Data point

119883119894passive



119894119896


120573119889 119889



120575lowast



Table 3 Continued


120590119909119894119896




P119896 P119896



X119896 X119896



ω λθ

ψ

X

Y

Z

υβ

120601






DBC

MBCPassive

02 04 06 08 1 12 14 160Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


DBCMBC

Passive

02 04 06 08 1 12 14 160Time (s)

minus08

minus04

0

04

08

Pitc

h an

gle (

deg

)















Dec

ision

laye

rC

ontro

lla

yer

Phys

ical

laye

r

Info

rmat

ion

bus

FCS ABS SCS

Local controllers

Control allocation


Decision logic

Subsystems

Sens

ors


Control objective

Driving situation







Decision

logic

SAP



algorithm

SA suspension


Braking system

Physical layer

Sens

ors

Brake control

Angle control

Voltage control

ESC

AFS

Control layer

Decision layer

Suspcontrol

Control allocation

Actuators

aususp

austeer

aubraking

Tdriver




lowastESC)

120575driver

cmin

cmax120592 =

10

90







119896 with 119896 =


lt 119905119899119910 where 119905


Based on [27] P119896


119896and P

119896isin





isin R119898times119897119896 and T119896

isin


T119896= X119896P119896

T119896= X119896P119896

(2)


X119896= T119896P119879119896

X119896= T119896P119879k

(3)




Con119894119896

=sum119898

119895=12

119894119896(119895)

sum119899

119894=1sum119898

119895=12

119894119896(119895)

forall119894 = 1 2 119899 (4)



119894119896997891rarr CS

119896 where CS



and

lfloorlceil

rfloorrceilDC119894


DC119894[ss] = DC119895

[ss] = 0

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t gt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t lt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1or

DC119894DCj

DC119894[si] lt DC119895

[si]




MS =

119903

⋃

119896=1

CS119896

forall119896 = 1 2 119903 (5)







119894according to

119909 isin 119862119894when min

119862

1

119896119894

119896119894

sum

119895=1

119889 (119909 119910119895) (6)








119862is as follows


in the form119863119862= [119904119904 119904119894 119886119898]


119904= 0) or critical (119904

119904= 1)





(iv) 119886119898


119898= 1198861 119886

119906 Consid-


119894isin [0 1]


(1) A 119863119862with bigger 119904



119894




119898








119906lowast

119888= 119886119906sdot 119906119888 (7)

where 119906lowast



119906= 1means


119906= 0) Thus 119906

119888is the local



119880lowast


) sdot 119880|comf + 119886119906susp

sdot 119880|rh (8)

where 119880lowast

susp = 119906susp119865119871

119906susp119865119877

119906susp119877119871

119906susp119877119877




119894119895|rh)


119906119894119895

10038161003816100381610038161003816rh =

119888min if minus 119906119904

sdot def le 0

119888max if minus 119906119904

sdot def gt 0

119906119894119895

10038161003816100381610038161003816comf =



(9)




(119890() = minus 119889





as possible and

119889=

119881119909

119897120575driver (10)








119890(120573)119890()






119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911


119879ESC119903 = 0 119879ESC119897 = 0



(11)

where 119879119866






119879lowast


sdot 119879ESC (12)


120575lowast

= 120575driver + 119886119906steer

sdot 120575AFS (13)





120573 120575driver119890()

NB NS Z PS PB

Low


High



119906steer= 1 or not if 119886

119906steer=








lowast




[119888min

119888max] = [

0

1] 997891997888rarr 120592 = [

1090

] (14)



120575lowast


118120575lowast

tires (15)


119879lowast


lowast

ESC) (16)


119866ABS119894119895 =

0 if 120582119894119895

ge 120582crit

1 if 120582119894119895

lt 120582crit(17)

with

120582119894119895

=

119881119909minus V119909119894119895

119881119909

(18)

where 120582119894119895






119865119863

= 119888119901(def) + 119896

119901(119911def) + 119865SA (19)


1sdot def + 119886








+

= 2120587119891steer (120575lowast

minus 120575+

) (20)





50 100 150 2000Station (m)

minus10

0

10

z r(m

m)






+

119887= 2120587119891brake (119879

lowast

119887minus 119879+

119887) (21)



+

119887is the











Table 7 IS set








5

10

15

20

Varia

bles


5 10 15 2000

Variables

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


90 of thevariance

4 components

0

50

100

Cum

ulat

ive v

aria

nce (

)


0

2

4

6

8Ei

genv

alue


120595

0

5

10

15

20

25

Con

trib

utio

n to

dat

a var

ianc

e (

)


120575

x

120601





Table 8 PCA results


04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)









119862= 1)



119862= 5


Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)



= 5 and 119863119862






DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










DBC

MBCPassive

02 04 06 08 1 12 14 160Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


DBCMBC

Passive

02 04 06 08 1 12 14 160Time (s)

minus08

minus04

0

04

08

Pitc

h an

gle (

deg

)















Dec

ision

laye

rC

ontro

lla

yer

Phys

ical

laye

r

Info

rmat

ion

bus

FCS ABS SCS

Local controllers

Control allocation


Decision logic

Subsystems

Sens

ors


Control objective

Driving situation







Decision

logic

SAP



algorithm

SA suspension


Braking system

Physical layer

Sens

ors

Brake control

Angle control

Voltage control

ESC

AFS

Control layer

Decision layer

Suspcontrol

Control allocation

Actuators

aususp

austeer

aubraking

Tdriver




lowastESC)

120575driver

cmin

cmax120592 =

10

90







119896 with 119896 =


lt 119905119899119910 where 119905


Based on [27] P119896


119896and P

119896isin





isin R119898times119897119896 and T119896

isin


T119896= X119896P119896

T119896= X119896P119896

(2)


X119896= T119896P119879119896

X119896= T119896P119879k

(3)




Con119894119896

=sum119898

119895=12

119894119896(119895)

sum119899

119894=1sum119898

119895=12

119894119896(119895)

forall119894 = 1 2 119899 (4)



119894119896997891rarr CS

119896 where CS



and

lfloorlceil

rfloorrceilDC119894


DC119894[ss] = DC119895

[ss] = 0

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t gt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t lt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1or

DC119894DCj

DC119894[si] lt DC119895

[si]




MS =

119903

⋃

119896=1

CS119896

forall119896 = 1 2 119903 (5)







119894according to

119909 isin 119862119894when min

119862

1

119896119894

119896119894

sum

119895=1

119889 (119909 119910119895) (6)








119862is as follows


in the form119863119862= [119904119904 119904119894 119886119898]


119904= 0) or critical (119904

119904= 1)





(iv) 119886119898


119898= 1198861 119886

119906 Consid-


119894isin [0 1]


(1) A 119863119862with bigger 119904



119894




119898








119906lowast

119888= 119886119906sdot 119906119888 (7)

where 119906lowast



119906= 1means


119906= 0) Thus 119906

119888is the local



119880lowast


) sdot 119880|comf + 119886119906susp

sdot 119880|rh (8)

where 119880lowast

susp = 119906susp119865119871

119906susp119865119877

119906susp119877119871

119906susp119877119877




119894119895|rh)


119906119894119895

10038161003816100381610038161003816rh =

119888min if minus 119906119904

sdot def le 0

119888max if minus 119906119904

sdot def gt 0

119906119894119895

10038161003816100381610038161003816comf =



(9)




(119890() = minus 119889





as possible and

119889=

119881119909

119897120575driver (10)








119890(120573)119890()






119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911


119879ESC119903 = 0 119879ESC119897 = 0



(11)

where 119879119866






119879lowast


sdot 119879ESC (12)


120575lowast

= 120575driver + 119886119906steer

sdot 120575AFS (13)





120573 120575driver119890()

NB NS Z PS PB

Low


High



119906steer= 1 or not if 119886

119906steer=








lowast




[119888min

119888max] = [

0

1] 997891997888rarr 120592 = [

1090

] (14)



120575lowast


118120575lowast

tires (15)


119879lowast


lowast

ESC) (16)


119866ABS119894119895 =

0 if 120582119894119895

ge 120582crit

1 if 120582119894119895

lt 120582crit(17)

with

120582119894119895

=

119881119909minus V119909119894119895

119881119909

(18)

where 120582119894119895






119865119863

= 119888119901(def) + 119896

119901(119911def) + 119865SA (19)


1sdot def + 119886








+

= 2120587119891steer (120575lowast

minus 120575+

) (20)





50 100 150 2000Station (m)

minus10

0

10

z r(m

m)






+

119887= 2120587119891brake (119879

lowast

119887minus 119879+

119887) (21)



+

119887is the











Table 7 IS set








5

10

15

20

Varia

bles


5 10 15 2000

Variables

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


90 of thevariance

4 components

0

50

100

Cum

ulat

ive v

aria

nce (

)


0

2

4

6

8Ei

genv

alue


120595

0

5

10

15

20

25

Con

trib

utio

n to

dat

a var

ianc

e (

)


120575

x

120601





Table 8 PCA results


04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)









119862= 1)



119862= 5


Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)



= 5 and 119863119862






DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Decision

logic

SAP



algorithm

SA suspension


Braking system

Physical layer

Sens

ors

Brake control

Angle control

Voltage control

ESC

AFS

Control layer

Decision layer

Suspcontrol

Control allocation

Actuators

aususp

austeer

aubraking

Tdriver




lowastESC)

120575driver

cmin

cmax120592 =

10

90







119896 with 119896 =


lt 119905119899119910 where 119905


Based on [27] P119896


119896and P

119896isin





isin R119898times119897119896 and T119896

isin


T119896= X119896P119896

T119896= X119896P119896

(2)


X119896= T119896P119879119896

X119896= T119896P119879k

(3)




Con119894119896

=sum119898

119895=12

119894119896(119895)

sum119899

119894=1sum119898

119895=12

119894119896(119895)

forall119894 = 1 2 119899 (4)



119894119896997891rarr CS

119896 where CS



and

lfloorlceil

rfloorrceilDC119894


DC119894[ss] = DC119895

[ss] = 0

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t gt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t lt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1or

DC119894DCj

DC119894[si] lt DC119895

[si]




MS =

119903

⋃

119896=1

CS119896

forall119896 = 1 2 119903 (5)







119894according to

119909 isin 119862119894when min

119862

1

119896119894

119896119894

sum

119895=1

119889 (119909 119910119895) (6)








119862is as follows


in the form119863119862= [119904119904 119904119894 119886119898]


119904= 0) or critical (119904

119904= 1)





(iv) 119886119898


119898= 1198861 119886

119906 Consid-


119894isin [0 1]


(1) A 119863119862with bigger 119904



119894




119898








119906lowast

119888= 119886119906sdot 119906119888 (7)

where 119906lowast



119906= 1means


119906= 0) Thus 119906

119888is the local



119880lowast


) sdot 119880|comf + 119886119906susp

sdot 119880|rh (8)

where 119880lowast

susp = 119906susp119865119871

119906susp119865119877

119906susp119877119871

119906susp119877119877




119894119895|rh)


119906119894119895

10038161003816100381610038161003816rh =

119888min if minus 119906119904

sdot def le 0

119888max if minus 119906119904

sdot def gt 0

119906119894119895

10038161003816100381610038161003816comf =



(9)




(119890() = minus 119889





as possible and

119889=

119881119909

119897120575driver (10)








119890(120573)119890()






119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911


119879ESC119903 = 0 119879ESC119897 = 0



(11)

where 119879119866






119879lowast


sdot 119879ESC (12)


120575lowast

= 120575driver + 119886119906steer

sdot 120575AFS (13)





120573 120575driver119890()

NB NS Z PS PB

Low


High



119906steer= 1 or not if 119886

119906steer=








lowast




[119888min

119888max] = [

0

1] 997891997888rarr 120592 = [

1090

] (14)



120575lowast


118120575lowast

tires (15)


119879lowast


lowast

ESC) (16)


119866ABS119894119895 =

0 if 120582119894119895

ge 120582crit

1 if 120582119894119895

lt 120582crit(17)

with

120582119894119895

=

119881119909minus V119909119894119895

119881119909

(18)

where 120582119894119895






119865119863

= 119888119901(def) + 119896

119901(119911def) + 119865SA (19)


1sdot def + 119886








+

= 2120587119891steer (120575lowast

minus 120575+

) (20)





50 100 150 2000Station (m)

minus10

0

10

z r(m

m)






+

119887= 2120587119891brake (119879

lowast

119887minus 119879+

119887) (21)



+

119887is the











Table 7 IS set








5

10

15

20

Varia

bles


5 10 15 2000

Variables

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


90 of thevariance

4 components

0

50

100

Cum

ulat

ive v

aria

nce (

)


0

2

4

6

8Ei

genv

alue


120595

0

5

10

15

20

25

Con

trib

utio

n to

dat

a var

ianc

e (

)


120575

x

120601





Table 8 PCA results


04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)









119862= 1)



119862= 5


Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)



= 5 and 119863119862






DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










and

lfloorlceil

rfloorrceilDC119894


DC119894[ss] = DC119895

[ss] = 0

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t gt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1

rceil

rfloor

[

lfloor

lceil[[[[[

[[[[and

and

t lt tcrit

DC119894[si] lt DC119895

[si]

DC119894[ss] le DC119895

[ss] = 1or

DC119894DCj

DC119894[si] lt DC119895

[si]




MS =

119903

⋃

119896=1

CS119896

forall119896 = 1 2 119903 (5)







119894according to

119909 isin 119862119894when min

119862

1

119896119894

119896119894

sum

119895=1

119889 (119909 119910119895) (6)








119862is as follows


in the form119863119862= [119904119904 119904119894 119886119898]


119904= 0) or critical (119904

119904= 1)





(iv) 119886119898


119898= 1198861 119886

119906 Consid-


119894isin [0 1]


(1) A 119863119862with bigger 119904



119894




119898








119906lowast

119888= 119886119906sdot 119906119888 (7)

where 119906lowast



119906= 1means


119906= 0) Thus 119906

119888is the local



119880lowast


) sdot 119880|comf + 119886119906susp

sdot 119880|rh (8)

where 119880lowast

susp = 119906susp119865119871

119906susp119865119877

119906susp119877119871

119906susp119877119877




119894119895|rh)


119906119894119895

10038161003816100381610038161003816rh =

119888min if minus 119906119904

sdot def le 0

119888max if minus 119906119904

sdot def gt 0

119906119894119895

10038161003816100381610038161003816comf =



(9)




(119890() = minus 119889





as possible and

119889=

119881119909

119897120575driver (10)








119890(120573)119890()






119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911


119879ESC119903 = 0 119879ESC119897 = 0



(11)

where 119879119866






119879lowast


sdot 119879ESC (12)


120575lowast

= 120575driver + 119886119906steer

sdot 120575AFS (13)





120573 120575driver119890()

NB NS Z PS PB

Low


High



119906steer= 1 or not if 119886

119906steer=








lowast




[119888min

119888max] = [

0

1] 997891997888rarr 120592 = [

1090

] (14)



120575lowast


118120575lowast

tires (15)


119879lowast


lowast

ESC) (16)


119866ABS119894119895 =

0 if 120582119894119895

ge 120582crit

1 if 120582119894119895

lt 120582crit(17)

with

120582119894119895

=

119881119909minus V119909119894119895

119881119909

(18)

where 120582119894119895






119865119863

= 119888119901(def) + 119896

119901(119911def) + 119865SA (19)


1sdot def + 119886








+

= 2120587119891steer (120575lowast

minus 120575+

) (20)





50 100 150 2000Station (m)

minus10

0

10

z r(m

m)






+

119887= 2120587119891brake (119879

lowast

119887minus 119879+

119887) (21)



+

119887is the











Table 7 IS set








5

10

15

20

Varia

bles


5 10 15 2000

Variables

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


90 of thevariance

4 components

0

50

100

Cum

ulat

ive v

aria

nce (

)


0

2

4

6

8Ei

genv

alue


120595

0

5

10

15

20

25

Con

trib

utio

n to

dat

a var

ianc

e (

)


120575

x

120601





Table 8 PCA results


04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)









119862= 1)



119862= 5


Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)



= 5 and 119863119862






DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119906lowast

119888= 119886119906sdot 119906119888 (7)

where 119906lowast



119906= 1means


119906= 0) Thus 119906

119888is the local



119880lowast


) sdot 119880|comf + 119886119906susp

sdot 119880|rh (8)

where 119880lowast

susp = 119906susp119865119871

119906susp119865119877

119906susp119877119871

119906susp119877119877




119894119895|rh)


119906119894119895

10038161003816100381610038161003816rh =

119888min if minus 119906119904

sdot def le 0

119888max if minus 119906119904

sdot def gt 0

119906119894119895

10038161003816100381610038161003816comf =



(9)




(119890() = minus 119889





as possible and

119889=

119881119909

119897120575driver (10)








119890(120573)119890()






119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911


119879ESC119903 = 0 119879ESC119897 = 0



(11)

where 119879119866






119879lowast


sdot 119879ESC (12)


120575lowast

= 120575driver + 119886119906steer

sdot 120575AFS (13)





120573 120575driver119890()

NB NS Z PS PB

Low


High



119906steer= 1 or not if 119886

119906steer=








lowast




[119888min

119888max] = [

0

1] 997891997888rarr 120592 = [

1090

] (14)



120575lowast


118120575lowast

tires (15)


119879lowast


lowast

ESC) (16)


119866ABS119894119895 =

0 if 120582119894119895

ge 120582crit

1 if 120582119894119895

lt 120582crit(17)

with

120582119894119895

=

119881119909minus V119909119894119895

119881119909

(18)

where 120582119894119895






119865119863

= 119888119901(def) + 119896

119901(119911def) + 119865SA (19)


1sdot def + 119886








+

= 2120587119891steer (120575lowast

minus 120575+

) (20)





50 100 150 2000Station (m)

minus10

0

10

z r(m

m)






+

119887= 2120587119891brake (119879

lowast

119887minus 119879+

119887) (21)



+

119887is the











Table 7 IS set








5

10

15

20

Varia

bles


5 10 15 2000

Variables

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


90 of thevariance

4 components

0

50

100

Cum

ulat

ive v

aria

nce (

)


0

2

4

6

8Ei

genv

alue


120595

0

5

10

15

20

25

Con

trib

utio

n to

dat

a var

ianc

e (

)


120575

x

120601





Table 8 PCA results


04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)









119862= 1)



119862= 5


Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)



= 5 and 119863119862






DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











120573 120575driver119890()

NB NS Z PS PB

Low


High



119906steer= 1 or not if 119886

119906steer=








lowast




[119888min

119888max] = [

0

1] 997891997888rarr 120592 = [

1090

] (14)



120575lowast


118120575lowast

tires (15)


119879lowast


lowast

ESC) (16)


119866ABS119894119895 =

0 if 120582119894119895

ge 120582crit

1 if 120582119894119895

lt 120582crit(17)

with

120582119894119895

=

119881119909minus V119909119894119895

119881119909

(18)

where 120582119894119895






119865119863

= 119888119901(def) + 119896

119901(119911def) + 119865SA (19)


1sdot def + 119886








+

= 2120587119891steer (120575lowast

minus 120575+

) (20)





50 100 150 2000Station (m)

minus10

0

10

z r(m

m)






+

119887= 2120587119891brake (119879

lowast

119887minus 119879+

119887) (21)



+

119887is the











Table 7 IS set








5

10

15

20

Varia

bles


5 10 15 2000

Variables

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


90 of thevariance

4 components

0

50

100

Cum

ulat

ive v

aria

nce (

)


0

2

4

6

8Ei

genv

alue


120595

0

5

10

15

20

25

Con

trib

utio

n to

dat

a var

ianc

e (

)


120575

x

120601





Table 8 PCA results


04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)









119862= 1)



119862= 5


Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)



= 5 and 119863119862






DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










50 100 150 2000Station (m)

minus10

0

10

z r(m

m)






+

119887= 2120587119891brake (119879

lowast

119887minus 119879+

119887) (21)



+

119887is the











Table 7 IS set








5

10

15

20

Varia

bles


5 10 15 2000

Variables

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


90 of thevariance

4 components

0

50

100

Cum

ulat

ive v

aria

nce (

)


0

2

4

6

8Ei

genv

alue


120595

0

5

10

15

20

25

Con

trib

utio

n to

dat

a var

ianc

e (

)


120575

x

120601





Table 8 PCA results


04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)









119862= 1)



119862= 5


Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)



= 5 and 119863119862






DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table 7 IS set








5

10

15

20

Varia

bles


5 10 15 2000

Variables

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1


90 of thevariance

4 components

0

50

100

Cum

ulat

ive v

aria

nce (

)


0

2

4

6

8Ei

genv

alue


120595

0

5

10

15

20

25

Con

trib

utio

n to

dat

a var

ianc

e (

)


120575

x

120601





Table 8 PCA results


04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)









119862= 1)



119862= 5


Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)



= 5 and 119863119862






DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table 8 PCA results


04 06 08 102Pitch (deg)

minus15

minus10

minus5

0

5

10

15

Roll

rate

(deg

s)









119862= 1)



119862= 5


Target

Output

DC = 6

DC = 5

DC = 1

5 10 15 20 250Time (s)



= 5 and 119863119862






DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










DC = 6

DC = 5

DC = 1


0

02

04

06

08

1

True

pos

itive

rate


aususp = [1 1 1 0]

aususp = [1 1 0 1]

aususp = [1 0 1 0]

aususp = [0 1 0 1]aususp = [0 0 1 1]

aususp = [1 1 0 0]


Roll (deg)

minus02

02

06

1

14

Pitc

h (d

eg)








119904119894

119904119904

119886119906susp

119886119906steer

119886119906braking







of Improvement

=RMS (119883


119894Controlled)


)

(22)





GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










GCC

UC

DC

05 1 150Time (s)

minus08

minus04

0

04

08Ve

rtic

al ac

cele

ratio

n (G

rsquos)


GCC

UC

DC

05 1 150Time (s)

minus04

0

04

08

12

Pitc

h an

gle (

deg

)



0

10

20

30

40

50

60

70

Brak

e dist

ance

(m)

1 2 3 4 5 6 70Time (s)

DC (63m)

UC (69m)

GCC (59m)

(a) Brake distance

GCCUC

DC

1 2 3 4 5 6 70Time (s)

0

04

08

12

16

Pitc

h (d

eg)






GCCUC

DC

50 100 150 200 2500x-coordinate (m)

minus2

minus1

0

1

2

3

4

y-c

oord

inat

e (m

)





GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










GCC

UC

DC

1 2 3 4 5 6 70Time (s)

minus2

minus1

0

1

2Ro

ll (d

eg)


GCC

UCDC

1 2 3 4 5 6 70Time (s)

minus10

minus6

minus2

2

6

Yaw

(deg

)


Figure 17 DLC test

GCC

UC

DC

minus5

0

5

10

15

20

25

y-c

oord

inat

e (m

)

20 40 60 80 1000x-coordinate (m)


GCC UC

DC1 2 3 4 50

Time (s)

minus4

minus2

0

2

4

Roll

(deg

)


GCC

UC

DC

1 2 3 4 50Time (s)

minus08

minus04

0

04

08

Late

ral a

cc (

g)


Figure 19 FH test






GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










GCC

UC

DC

10 20 30 40 50 600x-coordinate (m)

minus1

0

1

2

y-c

oord

inat

e (m

)


GCC

UC

DC

0

200

400

600

800

Stee

ring

whe

el an

gle (

deg

)

1 2 3 4 50Time (s)


GCC

UCDC

minus04

minus02

0

02

Late

ral a

ccel

erat

ion

(g)

1 2 3 4 50Time (s)


GCC

UC

DC

minus100

minus80

minus60

minus40

minus20

0

20

Yaw

rate

(deg

s)

1 2 3 4 50Time (s)

(c) Yaw rate ()





5 Conclusions







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
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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