vehiclestabilitycontrolstrategybasedonrecognitionofdriver...

Research ArticleVehicle Stability Control Strategy Based on Recognition of DriverTurning Intention for Dual-Motor Drive Electric Vehicle

Shu Wang Xuan Zhao and Qiang Yu

School of Automobile Changrsquoan University Xirsquoan 710064 China

Correspondence should be addressed to Shu Wang shuwangchdeducn and Xuan Zhao zhaoxuanchdeducn

Received 9 July 2019 Revised 24 November 2019 Accepted 17 December 2019 Published 13 January 2020

Academic Editor Luis J Yebra

Copyright copy 2020 Shu Wang et al is 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 isproperly cited

Vehicle stability control should accurately interpret the driving intention and ensure that the actual state of the vehicle is asconsistent as possible with the desired state is paper proposes a vehicle stability control strategy which is based on recognitionof the driverrsquos turning intention for a dual-motor drive electric vehicle A hybrid model consisting of Gaussian mixture hiddenMarkov (GHMM) and Generalized Growing and Pruning RBF (GGAP-RBF) neural network is constructed to recognize thedriver turning intention in real timee turning urgency coefficient which is computed on the basis of the recognition results isused to establish a modified reference model for vehicle stability control en the upper controller of the vehicle stability controlsystem is constructed using the linear model predictive control theory e minimum of the quadratic sum of the working loadrate of the vehicle tire is taken as the optimization objective e tire-road adhesion condition performance of the motor andbraking system and state of the motor are taken as constraints In addition a lower controller is established for the vehicle stabilitycontrol system with the task of optimizing the allocation of additional yaw moment Finally vehicle tests were carried out byconducting double-lane change and single-lane change experiments on a platform for dual-motor drive electric vehicles by usingthe virtual controller of the AampD5435 hardware e results show that the stability control system functions appropriately usingthis control strategy and effectively improves the stability of the vehicle

1 Introduction

Vehicle stability control which relies on the antilock brakingsystem (ABS) and traction control system (TCS) of a vehicleplays a significant role in preventing single-vehicle accidentscaused by vehicle instability [1] e mechanical structuredynamic characteristics response characteristics and ac-tuator complexity of a dual-motor drive electric vehiclediffer significantly from those of a single-drive vehicleerefore dual-motor drive electric vehicles also require anefficient and stable stability control system

Depending on the system structure two types of vehiclestability system controllers are used centralized and hier-archical Compared with the centralized controller the hi-erarchical controller system has superior extendibility andfault tolerance and allows more convenient system main-tenance and debugging [2 3] Furthermore the much higher

level of integration of the vehicle electrification chassismakes it possible to realize coordination control with othersystems such as the X-wire control system and active safetysystems eg electric control braking (ECB) electric brakeforce distribution (EBD) and active front steering (AFS)

Based on the current state of the vehicle and the driverrsquosintention the upper layer of the hierarchical vehicle stabilitycontroller makes decision regarding the additional yawmoment to restore the stable state of the vehicle Zhang andWang proposed a vehicle stability control system usinggeneralized proportion integration (PI) control [4] Wanget al developed a stability control strategy based on anintegral separation PID controller to eliminate integral ac-cumulation of the control system [5] Zhao et al designed avehicle stability control system based on a T-S fuzzy model[6 7] Some scholars also adopted robust control to improvethe influence of uncertain factors such as system loss tire

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 3143620 18 pageshttpsdoiorg10115520203143620

load fluctuation and side wind [8ndash12] However the PIDalgorithm guarantees neither optimal control of the systemnor its control stability e rules of fuzzy control areestablished on the basis of a large number of experimentsand expert experience and need to be adjusted according tothe driving environment which is both high time andeconomic consuming e most notable disadvantage ofslide mode control is chattering which occurs when thesystem approaches the slide mode surface and which canonly be reduced but not eliminated Model predictivecontrol (MPC) can directly consider actuator constraintsand system state constraints during controller design Inaddition MPC can effectively control a multiobjectiveconstrained system in complex engineering systems andhas strong portability [13] Jalali et al proposed a vehiclestability controller using MPC [14ndash17] And the desiredyaw rate and sideslip angle were obtained through thedriver steering wheel angle

e lower layer of a vehicle stability controller selectsthe appropriate actuator and reallocates the additional yawmoment based on certain rules At present the mostcommonly used method relies on two allocation strategiesrule-based and optimization theory-based [18] e in-creasing actuators and growing complexity of the electroniccontrol systems of vehicles have resulted in the allocationrules becoming more complex hence the allocation ac-curacy cannot be guaranteed to the same extent as beforeerefore the optimization theory-based allocation strat-egy is more suitable

e allocation strategy based on optimization theoryusually takes the slip rate of the tire the minimum of thesum of the working load of the tire and the minimum ofthe sum of the longitudinal force of the tire as the opti-mization objectives At the same time the optimizationstrategy considering the actuator failure and energyeconomy are gradually put forward Yin proposed theadditional yaw moment and traction force distributionstrategy for the purpose of minimizing the tire load [19]Zhai et al proposed an average torque distribution strategytire-dynamic-load-based torque distribution strategy andminimum-objective-function-based optimal torque dis-tribution strategy to control the motor driving torque orregenerative braking torque for vehicle stability enhance-ment [20] Park et al proposed a torque distributionstrategy that considers the driving economics driverrsquosacceleration demand and tire slip and used fuzzy logic toselect a suitable distribution strategy [21] Kim and Kimchose the regenerative braking and an electrohydraulicbrake as the actuators in the vehicle stability controllerAiming to minimize EHB energy consumption the brakingforce distribution ratio of the front and rear axles wereoptimized [22]

According to the above studies the hierarchical vehiclestability controller obtains the desired driving state by usingthe driver steering wheel angle However in-depth researchshowed that the use of only the steering wheel angle isinadequate to express the driver intention and obtain thedesired driving state vehicle stability controller

e driver turning intention is initiated based on ex-perience depending on the condition of the road envi-ronment and vehicle state en the driver manipulates thevehicle actuator such that the vehicle responds consistentlywith their intentionerefore the driverrsquos turning intentionreflects their subjective demand for the vehicle state Whendrivers take sharp turning operation such as go throughcontinuous S-turn hairpin bend and the other roads with asmaller radius curvature as well as emergency obstacleavoidance or sudden overtaking the driver would be con-sidered to intend rapidly maneuvering the vehicle undercurrent road conditions which also means the driver hascertain expectations in terms of the vehicle yaw rate andsideslip However for some drivers because of constraintssuch as their driving experience the driving environmenttheoretical knowledge and other factors this expectationignores correct judgment of the lateral motion stability of thevehicle During the process of vehicle stability control if it isa significant difference between the actual and expected stateof the vehicle the driver would proceed with the turningoperation and the vehicle stability would deteriorate andeven cause the driver to distrust the system

erefore accurate interpretation and prediction of thedriving intention during the process of vehicle stabilitycontrol and ensuring the actual vehicle state is maintained asclosely as possible to the expected vehicle state would greatlyimprove the stability and driving safety of the vehicle Driverintention can be obtained using fuzzy reasoning supportvector machine (SVM) artificial neural network (ANN) andhidden Markov model (HMM) [23ndash27] Fuzzy reasoningSVM and ANN are used to recognize the intentions ofdriver at a certain moment However neural network andfuzzy logic are difficult to deal with temporal-ordered in-formation us they are mainly used for static recognitionproblems HMM as a kind of dynamic information pro-cessing method based on time-series cumulative probabilityconsiders only the state sequence with the maximum log-likelihood and ignores the possibility of small probabilityevents erefore it is difficult to recognize easily confusedintentions using HMM

All the above analysis motivated us to develop a methodto detect the driverrsquos turning intention establish a steeringurgency coefficient for sharp turning and propose a vehiclestability control reference model considering the driverrsquosturning intention Based on the abovementioned results weproposed a stability control strategy for a dual-motor driveelectric vehicle As a result of this research the desiredcontrol target of stability control is no longer only based onthe steering wheel angle and the vehicle state in accordancewith the driving intention is under control to a certainextent is paper is organized as follows e method toidentify the driverrsquos turning intention is presented in Section 1A modified reference model for vehicle stability consideringthe driverrsquos turning intention is presented in Section 2Construction of the vehicle stability control strategy basedon the modified reference model is discussed in Section 3Section 4 compares the vehicle stability control strategybased on the modified reference model constructed in this

2 Mathematical Problems in Engineering

work with the traditional strategy Finally Section 5 presentsthe conclusions of this study

2 Driverrsquos Turning Intention RecognitionHybrid Model of GHMM and GGAP-RBFNeural Network

e turning operation is a complex event that continues fora certain period of time e observation sequence of theturning process is a set of temporal data e Gaussianhidden Markov model (GHMM) displays a strong mod-eling ability for dynamic time sequences However themodel does not take into account overlaps between dif-ferent classes and this is a severe limitation In contrastgeneralized growing and pruning RBF (GGAP-RBF) anengineering model can simulate the thinking mechanismof the human brain has strong classification and decision-making abilities and can describe uncertain informationus it compensates for the inadequacies of HMM Inaddition the model allows insignificant neurons to beremoved in each iterative training cycle to effectivelycontrol the growth of the neural network and simplify thestructure of a network with large data capacity Howeverthe ability of GGAP-RBF to describe dynamic sequentialprocesses is not especially strong [28ndash30] is led us toconstruct a hybrid model in the form of a GHMMGGAP-RBF neural network Given the advantages of sequentialmodel building and its nonlinear mapping ability thehybrid model can obtain newly identified informationthereby considerably increasing the accuracy of the clas-sification of classes with slight differences [27] At the sametime to improve the real-time performance this work usesthe initial stage of the turning operation to identify thedriverrsquos turning intention

e structure of the driver turning intention recognitionsystem based on the GHMMGGAP-RBF hybrid model isshown in Figure 1 e hybrid model includes a lower layer(the GHMM model) and an upper layer (the GGAP-RBFmodel) e lower layer of the model includes the sharpturning GHMM and the normal turning GHMM e ve-hicle speed the steering wheel angle the steering wheel anglevelocity and the steering wheel torque are the inputs of thelower layer e log-likelihood of the sharp turning GHMMand the normal turning GHMM are the outputs of the lowerlayer Based on the data of the turning initial stage thenormal turning and sharp turning GHMMs are designedand trained using the BaumndashWelch algorithm to calculatethe most likely sequence of states In addition a forwardalgorithm is used to calculate the log-likelihood of theGHMMs

In the upper layer the log-likelihood of the GHMM thevehicle yaw rate and the lateral acceleration form a vectorδ1T(1) δ1T(2) δ1T(N)1113966 1113967 e nonlinear combination ofthis vector is regarded as the input of the GGAP-RBF neuralnetwork and the nonlinear mapping ability of neural net-work-based methods is used to recognize the driver actualturning intention

21 Establishment of the GHMM e feature parameters ofthe GHMMGGAP-RBF hybrid model have a considerableeffect on the accuracy of the recognition of the driverrsquosturning intentione reliefF algorithm is used to collect theappropriate parameters is study employs the steeringwheel angle steering wheel angle velocity and steeringwheel torque as feature parameters to recognize the driverrsquossteering intention Based on the initial stage of the turningoperation sharp turning and normal turning GHMMs areestablished separately e observation sequence of theGHMM can be described as a multidimensional vector [31]

Ot a(t) b(t) c(t) (1)

where a(t) is the steering wheel angle b(t) is the steeringwheel torque and c(t) is the steering wheel angular velocity

e BaumndashWelch algorithm is used to optimize the threeparameters of the GHMM which are described asλ (π A B) where π is the initial state distribution A is thestate transition probability matrix and B is a probabilitydensity function

e probability density function of the model is

bi(O) 1113944M

j1ωijN O μij σij1113872 1113873 (2)

where N(O μij σij) is the j-dimensional Gauss probabilitydensity of state i O is the observation sequence μij is themean of the Gauss function and σij is the covariance of theGauss function

Assuming that εt(i j) is the probability of the jthGaussian mixture function in the state observation sequencei at time t the probability that the Markov chain is in state j

at time t + 1 is as follows

Data preprocessing and feature parameter extraction

Steering wheelangle

Steering wheeltorque

Steering wheelangular velocity Vehicle speed

Normal turningintention HMM

Sharp turningintention HMM

Log-likelihood

of theGHMMs

arrayTransmatMuMixPrior

GHMMtraining

Lowerlayer

GGAP-RBF

Normalization

Sharp turning

Normal turning

Training

Vehicle lateral acceleration Vehicle yaw rate

Upperlayer

Figure 1 Structure of the GHMMGGAP-RBF hybrid model

Mathematical Problems in Engineering 3

εt(i j) p st i st+1 j O | λ( 1113857

p(O | λ)

αt(i)βt(i)

1113936 αt(i)βt(i)times

ωijP O μij σ1113960 1113961

1113936K1 ωijP O μij σ1113960 1113961

(3)

where μij is the mean matrix of the Gaussian mixturefunction σ is the mixed covariance matrix and ωij is theweight of output probabilities of different Gaussian mixturefunctions Based on the Gaussian mixture model the pa-rameter re-estimation is as follows

ωijprime

1113936Tt1εt(i j)

1113936Tt11113936

Kt1εt(i j)

μijprime

1113936Tt1εt(i j)Ot

1113936Tt1εt(i j)

σijprime

1113936Tt1εt(i j) Ot minus μij1113872 1113873 Ot minus μij1113872 1113873prime

1113936Tt1εt(i j)

(4)

After optimization of the parameters of the GHMM thematching between the collected data and GHMM is cal-culated using the forward-backward algorithm

22 Establishment of the GGAP-RBF Neural Network Inorder to ensure that small probability events can alsohappen function (5) is no longer used to recognize theturning intention Instead turning intention is described asa function of the log-likelihood of the two GHMMs giventest data (loglik1 and loglik2) the vehicle yaw rate ωr andthe lateral acceleration ay expressed as follows

inention max(loglik1 loglik2) (5)

inention F loglik1 loglik2ωr ay1113872 1113873 (6)

e input parameter of the input layer is loglik1lowastloglik2lowast ωlowastr and alowasty as shown in equation (7) e output ofthe layer is the driver turning intention as shown inequation (8)

xi loglik1lowast loglik2lowastωlowastr alowasty1113960 1113961 (7)

f xi( 1113857 loglik xi( 1113857 ω0 + 1113944K

k1ωk middot e

minus wkminus xi 2σ2

k( 1113857

(8)

where loglik1lowast loglik2lowast ωlowastr and alowasty represent the deviationstandardization of loglik1loglik2ωr and ay ωk is the centerof the RBF of the kth neuron and σk is the standard de-viation of the Gaussian function which indicates the widthof the Gaussian function

After the ith training iteration RAN is used to optimizethe growth of neurons e parameters of a neuron uponaddition of a new neuron are given as follows [32ndash35]

ωn ei yi minus f(iminus 1)(x)

wn xi

σn κ xi minus wir

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(9)

where ωn is the weight connecting the new neuron to theoutput neuron wn is the center of the new neuron σn is thewidth of the new neuron ei yi minus f(iminus 1)(x) is the error ofthe a priori estimate κ is an overlap factor that determinesthe overlap of the responses of the hidden neurons in theinput space and wir is the value of the center of the hiddenneuron nearest to xi

e worth of the new neuron is estimated using theconditions in inequality (10) If the conditions are met thenew training data are valuable to the network and thenetwork performance is improved effectively by the newneuron As the result the new neuron is added and thetraining data are accepted If not the training data and thenew neuron are rejected

xi minus wir

gt εi

ei yi minus f xi( 1113857gt emin

⎧⎨

⎩ (10)

where εi and emin are the threshold of the distance and theerror respectively wir is the value of the center of the hiddenneuron nearest to xi and ei is the error of the priori estimate

en insignificant neuron should be judged and re-moved using a pruning algorithm e mean squared errorof prediction output after the kth neuron is removed fromthe network in the ith training iteration as follows

Eq(k) ε(k 1) ε(k 1) ε(k n)q

1n

1113944

n

i1εq

(k i)⎛⎝ ⎞⎠

1q

ωk

q

1n

1113944

n

i1R

q

k xi( 1113857⎛⎝ ⎞⎠

1q

(11)

where Rk(xi) is the Gaussian RBF n is the training time q

is the norm and k is the kth hidden neurone inputs of the RBF loglik1lowast loglik2lowast ωlowastr and alowasty

follow the normal sampling distribution N(μ σ2) respec-tively e sample range of the ith training data (xi yi) is Xwhich is divided into J equal small parts Δj As Δj tends toinfinity the sum over the sample range becomes approxi-mately equal to the integral value

Esig(k) limJ⟶infin

Eq(k)

ωk

q

1113945

L

l11113946

bl

al

eminus wkminus xil

2σk2( 1113857

pl(x)dx1113888 1113889

1q

(12)

where Esig(k) is the significance of the kth neuron to thenetwork whichmeans the contribution of that neuron to theentire network and P1(x) is the probability distributionfunction If Esig(k) is less than the learning accuracy emin theneuron is considered to be insignificant and is removed


Otherwise the neuron is significant and should be retainedBecause insignificant neurons can be removed from theGGAP-RBF neural network the size of the network can belimited to a reasonable range

23 Establishment of GHMMGGAP-RBF Model e es-tablishment of GHMMGGAP-RBF model needs offlinetraining by using test data for which is obtained in realvehicle experiment

Driving experience gender and personality can affectdriverrsquos decision-making In order to eliminate the influenceof drivers on the test results three drivers with differentdriving experiences are selected According to the analysis ofSpecification for Design of Municipal Roads (CJJ37-2012)Specification for Design of Interactions on Urban Road(CJJ152-2010) and Vehicle Handling Stability Test Method(GBT6323-2 2014) the radius of turning the test road is setas 10m 25m 40m and 60m e radius of turning the testroad is set as 10m 25m 40m and 60m And the tests speedis set as 20 kmh 30 kmh and 40 kmh For distinguishingbetween the straight driving and turning straight drivingtests are also conducted at 20 kmh 30 kmh and 40 kmhe distribution of test data is shown in Table 1

e vehicle parameters are shown in Table 2 Because ofthe noise in the sensor data collected by the data acquisitioninstrument the data must be preprocessed T-testing isused to remove abnormal data e mixed Gaussianclustering method is then used to extract data pertaining tothe initial stage of the turning operation as part of the entireturning process ese preprocessed data can be dividedinto two parts 75 of the test data is used for model offlinetraining and the other is used for model online verificationAfter the offline training the initial state matrix the statetransition matrix the weight of each Gaussian function inthe GHMM the mean and covariance of each Gaussianfunction and the parameters of the GGAP-RBF could begotten

3 Reference Model of Vehicle Stability ControlSystem considering the Driverrsquos Intention

is paper proposes a reference model for vehicle stabilitycontrol e model which takes the driverrsquos turning in-tention into consideration is shown in Figure 2 First theGHMMGGAP-RBF hybrid model is used to recognize thedriverrsquos turning intention on the basis of data relating to thesteering wheel operation angle angular velocity andsteering wheel torque When at the initial stage of theturning operation the driverrsquos intention is identified assharp turning the vehicle is made to respond quickly to thedesired yaw rate for the current steering wheel angle (iethe yaw rate can follow the driverrsquos steering wheel oper-ation successfully) by correcting the reference yaw rate withthe aid of the established steering urgency coefficientWhen the steering operation enters the turning keepingstage and the turning reversal stage vehicle stability isensured by no longer modifying the reference yaw rate e

reference model is not modified when normal turning isintended

31 ReferenceModel Based on 2-DOFLinear Vehicle DynamicModel e most commonly used vehicle stability controlreference model is the 2-DOF linear vehicle dynamic modelwhich only considers the lateral motion and yaw motion ofthe vehicle [36] e state equations are as follows

m _v minus uωr1113872 1113873 k1 + k2( 1113857β

+1u

ak1 minus bk2( 1113857ωr minus k1δf (13)

IZ _ωr ak1 minus bk2( 1113857β +1u

a2k1 + b

2k21113872 1113873ωr minus ak1δf

(14)

us the ideal yaw rate and sideslip angle are as follows

ωrdes u

R

uδfa + b + mu2 bk2 minus ak1( 1113857( 11138572k1k2(a + b)( 1113857

βdes b minus a 2(a + b)k2( 1113857( 1113857mu2

a + b + mu2 bk2 minus ak1( 1113857( 11138572k1k2(a + b)( 1113857δf

(15)

When the vehicle is driving on a road with a low ad-hesion coefficient eg when the road surface is wet orcovered by snow or sand the adhesion force allowed by theadhesion conditions between the road surface and tiresdecreases and cannot produce the high yaw rate required bythe vehicle erefore when the 2-DOF linear vehicle dy-namicmodel is adopted as the ideal model it must be limitedby the conditions under which the tires adhere to the road

e upper boundary of the ideal yaw rate is

Table 1 e distribution of test data

20 kmh 30 kmh 40 kmhSharp turning 80 80 60Normal turning 88 88 68Straight driving 30 21 21

Table 2 Vehicle parameters

Parameter ValueVehicle mass 4439 kgAxle load distribution 45 55Wheelbase 1200mmAxle base 1550mmHeight of mass center 2819mmDistance from the center of mass to the front axis 8542mmDistance from the center of mass to the rear axis 6958mmRated power (kW) 32Peak power (kW) 80Rated torque (Nm) 80Peak torque (Nm) 160


ωrupper_bound 085μg

u (16)

erefore the reference value of the vehicle yaw rate forsteady-state steering is

ωrref ωrdes ωrdes

11138681113868111386811138681113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868

ωrupper_boundsgn ωrdes( 1113857 ωrdes1113868111386811138681113868

1113868111386811138681113868gt ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(17)

Similarly the upper bound of the ideal sideslip anglemust be specified such that it is not too large e upperboundary of the sideslip angle is

βupper_bound tanminus 1(002 μg) (18)

erefore the reference value of the sideslip angle forsteady-state steering is

βref βdes βdes

11138681113868111386811138681113868111386811138681113868le βupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868

βupper_bound sgn βdes( 1113857 βdes1113868111386811138681113868

1113868111386811138681113868gt βupper_bound11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(19)

is enables the basic control target of the stabilitycontrol system namely the reference yaw rate ωrref andsideslip angle βref to be obtained

32 Reference Model Considering Driverrsquos Intention Asmentioned in Section 1 for the same angle angular velocityand torque of steering wheel can be used as characteristicparameters to recognize the driverrsquos turning intentionerefore the steering wheel angular velocity and torque aretaken as parameters to establish the steering urgency co-efficient for sharp turning intention

When the vehicle is undergoing steady-state turning therelationship between the steering torque and the gradient oflateral acceleration satisfies [37]

dML

d v2ρ( 1113857

mnvlH

iLVLl1g

1iLVL

Fzvnv (20)

erefore according to the actual lateral accelerationthe ideal steering wheel torque for steady-state turning canbe calculated as

MLdes 11139461g

1iLVL

Fzvnvdv2

ρ1113888 1113889 (21)

According to equation (21) and the model of the steeringsystem the actual yaw rate and speed can be used to calculatethe ideal steering wheel angular velocity by differentiating

δwdes L 1 + Ku2( 1113857

uωr

K m

L2a

k2minus

b

k11113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

δswdes f δwdes( 1113857

(22)

e deviation between the actual torque and angularvelocity and the ideal torque and angular velocity of thesteering wheel is used to reflect the urgency of the driverrsquossharp turning intention Finally the steering urgency co-efficient for sharp turning intention is calculated by thefollowing equation

τ 12

δsw minus δswdes( 1113857

2+ ML minus MLdes( 1113857

21113969

(23)

where δsw δswdes ML and MLdes is the normalized actualsteering wheel torque actual angular velocity ideal steeringwheel torque and ideal angular velocity using the followingequation to avoid the impact caused by the different di-mensions of each parameter

x x minus min

max minus min (24)

When |ωrdes|le |ωr|le |ωrupper_bound| the reference yawrate is determined by the dynamic characteristics of thevehicle and the limitation generated by the adhesion con-dition of the road is not reached If the driver intention issharp turning at the same time the reference yaw rate wouldbe modified as follows

2-DOF vehiclelinear dynamics

model

Restrictions oftire-road condition

Ideal yaw rate

Bound of the yaw rate

Driverintention

identificationmodel

Steering wheel angle

Steering wheel angularvelocity

Steering wheel torque

Driver intention

Sharpturning

coefficient

Referenceyaw rate


Revisedreferenceyaw rate


0 10 20 30 40 500

02

04

06

08

1

Speed (ms)

δ = 10 δ = 9 δ = 8

μ = 1

μ = 01

δ = 7δ = 6

δ = 5

δ = 4

δ = 3

δ = 2δ = 1

Figure 2 Modified model of reference yaw rate


ωrref ωrdes + Δωr (25)

where Δωr τ(ωr minus ωrdes) is the correction of the referenceyaw rate considering the driver turning intention and isrelated to the urgency of the driver turning intention

When |ωrdes|le |ωrupper_bound|le |ωr| the reference yawrate is determined by the dynamic characteristics of thevehicle and the limitation generated by the adhesion con-dition of the road is also reached If equation (25) is stilladopted for modification the reference yaw rate may exceedthe limitation us under this condition the reference yawrate would be modified as follows

Δωr τ ωrupper_bound minus ωrdes1113872 1113873 (26)

When |ωrupper_bound|le |ωrdes| the reference yaw rate isdetermined by the adhesion condition of the road In orderto ensure the driving safety the reference yaw rate is nolonger modified

us for the sharp turning intention the reference yawrate is

ωlowastrref

ωrdes + τ ωr minus ωrdes( 1113857 when ωrdes1113868111386811138681113868

1113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868

ωrdes + τ ωrupper_bound minus ωrdes1113872 1113873 when ωrdes1113868111386811138681113868

1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868

ωrref when ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868le ωrdes1113868111386811138681113868

1113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(27)

When the turning operation reaches the second stage-mdashkeeping stage and the third stagemdashreturning stage thereference yaw rate is no longer modified for the sake of thedriving safetye conversion from themodifiedmodel to thereference model causes the reference yaw rate to changesuddenly and this is most likely to influence the stability ofthe vehicle In order to make the reference yaw rate smootherthe S-shaped acceleration and deceleration curve is chosen asthe transition function which is shown in Figure 3 [38]

When the inequality

ωlowastrref minus ωrref gt ε (28)

is satisfied the modified reference yaw rate is

ωlowastrref(t)

ωlowastrref t0( 1113857 +12

Jt2 t0 le tle t1

ωlowastrref t0( 1113857 minus Jt21 + 2Jt1t minus12

Jt2 t1 lt tle t2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(29)

e flow of the calculation to obtain the reference yawrate is shown in Figure 4

4 Vehicle Stability Control Strategy

e proposed stability controller for dual-motor driveelectric vehicle adopts a hierarchical structure which in-cludes the upper layer controllermdashwith a decision layer forthe additional yaw momentmdashand the lower layer con-trollermdashwith a distribution layer for the additional yawmoment e structure of this system is shown in Figure 5

e upper layer controller includes the vehicle stateestimator model the driver turning intention recognitionmodel the modified stability control reference model andthe additional yaw moment decision model is controllerchooses the angle angular velocity and torque of thesteering wheel as inputs to recognize the driverrsquos turningintentione reference yaw rate and reference sideslip angleunder steady-state steering are determined by using the 2-DOF linear vehicle dynamics model and by simultaneouslyconsidering the adhesion conditions According to theturning intention the reference model is modified as thefinal stability control target en based on the differencebetween the actual and the reference yaw rate and sideslipangle using the additional yaw moment decision model theadditional yaw moment that needs to be applied to restorethe vehicle to the stable state is determined and used as inputfor the lower controller

e lower layer controllermdashthe additional yaw momentdistribution layermdashincludes the longitudinal force distri-bution model and the actuator model e generation ofadditional yaw moment requires the longitudinal force ofthe tire to be controlled and this should take into consid-eration the vehicle drive form performance of themotor andhydraulic brake system and the road conditions e op-timization algorithm allocates additional yaw moment to getadditional torque of the motor and hydraulic braking systemwhich will eventually improve the stability of the vehicle

41 Design of Upper Controller for Vehicle Stability ControlMPC is used to make decision of additional yaw momentsAnd linear 3-DoF vehicle dynamics model including

t (s)

t1t0 t2

ωrref

ωlowast

rref

Figure 3 Switching transition function of reference yaw rate


longitudinal motion lateral motion and yaw motion isselected as the predictive model which is shown in Figure 6Taking the yaw rate and the sideslip angle as the state

variables the vehicle state can be obtained as shown inequation (30)ndash(32) [39 40] For both accuracy and effi-ciency the tire cornering stiffness estimator based on

Driver turningintention

N

Normal turning Sharp turning

Turning start stage

Y

N

Y

N

Y

ωlowast

rref = ωrref

ωlowast

rref = ωrdes + τ(ωr ndash ωrdes)

ωlowast

rref = ωrref + τ(ωrupper_bound ndash ωrdes)

ωlowast

rref = ωrref

ωlowast

rref = ωrrefωrupper_bound

ωrupper_bound

gt ωrdes

ωr le

Figure 4 Flowchart of reference yaw rate

Turningintention

identificationmodel

Steering wheel angle Fsw

Steering wheel angle velocity ωsw

Steering wheel torque Tsw

Turningintention

Referencemodel

Driverinput

Lateral tire force Fyf Fyr

Yaw rate ωr

Longitudinal speed uLateral speed v

Front wheel angle δLongitudinal wheel speed uij

Wheel speed ωij

Lateral acceleration ay

Decision onadditional yaw

moments

M

Distribution ofadditional yaw

momentsDrive motor

Hydraulic brake

Fxfl

Fxfr

Fxrl

Fxrr

Vehicle

Tbij

Txij

Upperlayer

controller

Vehicledynamic

model

Lowerlayer

controller

Sideslip angle β

βlowast

rref ωlowast

rref

Figure 5 Structure of stability control system for dual-motor drive electric vehicle


recursive least square method with forgetting factor (FFRLS)is used to estimate the tire stiffness which will be used forcalculating the tire lateral force in real time en the es-timated tire cornering stiffness is applied to the linear dy-namic model is improves the effectiveness of the controlsystem in the nonlinear region of the tire [41]

_V cos β

mcos δflFxrl minus sin δflFyfl + cos δfrFxfr1113872

minus sin δfrFyfr + Fxrl + Fxrr1113873 +sin β

msin δflFxrl1113872

+ cos δflFyfl + sin δfrFxfr + cos δfrFyfr + Fyrr + Fyrl1113873

(30)

ωr 1Iz

cos δfrFxrl minus cos δflFxfl1113872 1113873Bf

2+ Fxrr minus Fxrl( 1113857

Br

21113890

+ a sin δfrFxrl + b sin δflFxfl

+Bf

2sin δfl + a cos δfl1113888 1113889Fyfl

+ minusBf

2sin δfr + a cos δfr1113888 1113889Fyfr + aFyrl + bFyrr1113891

(31)

_β cos βmV

sin δflFxrl + cos δflFyfl + sin δfrFxfr1113872

+ cos δfrFyfr + Fyrl + Fyrr1113873 minussin βmV

cos δflFxrl1113872

minus sin δflFyfl + cos δfrFxfr minus sin δfrFyfr + Fxrr + Fxrl1113873

middot Fyfl minus ωr

(32)

e state equation can be expressed in standard form asfollows

_X AcX + BucU + BdcD

Yc CcX

⎧⎨

⎩ (33)

where X [ωr β V] Yc [ωr β] Cc [1 0 0 0 1 0] U isthe additional yaw moment and D δf

Equation (33) is discretized and converted into incre-mental form to obtain

ΔX(k + 1) AΔX(k) + BuΔU(k) + BdΔD(k)

Y(k) CΔX(k) + Y(k minus 1)1113896 (34)

whereΔX(k) X(k) minus X(k minus 1)ΔU(k) U(k)minus U(k minus 1)

ΔD(k) D(k) minus D(k minus 1) A eAcT Bu 1113946T

0e

AcτBucdτ

C [1 0 0 1] and T is the control periode objective of vehicle stability control is to enable the

actual vehicle yaw rate and sideslip angle to follow thereference value through the action of additional yaw mo-ment erefore at time k the MPC optimization problembased on the linear model can be described as

min J Y(k) Uk( 1113857 Y(k) minus Yref(k)

2Q

+ΔU(k)2R

1113944

Np

i

Y(k + i | k) minus Yref(k + i | k)

2Q

+ 1113944

Ncminus 1

i

ΔU(k + i | k)2R

(35)

e constraints of control variables the increment ofvariables and output of the model are as follows

Umin leU(k)leUmax

ΔUmin leΔU(k)leΔUmax

Ymin leY(k)leYmax

⎧⎪⎪⎨

⎪⎪⎩(36)

In this model the predictive horizon Np 5 the controlhorizon Nc 3 and the reference of the predictive model isYref [ωlowastrref β

lowastref ]

e desired control performance can be adjusted byusing the weight matrix Q and R where Q reflects the ac-curacy requirements of the system and R reflects the size ofthe action required by the controller

In this research

Q 10 0

0 151113890 1113891

R

500 0 0

0 500 0

0 0 8000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)

O

Fyfl

Fyrr

Fyrl

Fyfr

y

xvu

b a

L

Br Bf

Fxrl

Fxrr Fxfr

Fxf l

αrl

αrr

αf l

αfr

ωr

β

δfl

δfr

Figure 6 3-DOF linear vehicle dynamics model


As shown in equation (38)ΔU(k) is the increment of thesequence of control inputs which is obtained by using theoptimization objective and constraints during the samplingtime of k and Y(k) is the control output sequence which isobtained from the prediction model

Y(k)

Y(k + 1 | k)

Y(k + 2 | k)

Y(k + 3 | k)

Y(k + 4 | k)

Y(k + 5 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ΔU(k)

ΔM(k | k)

ΔM(k + 1 | k)

ΔM(k + 2 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(38)

Y(k + 1 | k) CAx(k) + CBΔU(k)

Y(k + 2 | k) CA2x(k) + CABΔU(k) + CBΔU(k + 1)

⋮

Y(k + 5 | k) 11139445

i1CA

ix(k) + 1113944

5

i1CA

iminus 1BΔU(k)

+ middot middot middot + 11139443

i1CA

iminus 1BΔU(k + 4) + 1113944

3

i1CA

iminus 1BΔd(k) + Y(k)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(39)

Finally only the first element of the optimized solution isapplied to the system us the additional yaw moment isexpressed by the following equation

M(k) M(k minus 1) + ΔM(k minus 1 | k) (40)

42 Design of the Lower Controller for Vehicle StabilityControl e lower layer controller distributes the longi-tudinal forces of each wheel according to the output ofadditional yaw moment decision layer e distribution isrestricted by the adhesion condition between the tire and theroad Excessive additional longitudinal force which causeslongitudinal slip and further deteriorates the vehicle sta-bility should be avoided is force is restricted by theperformance of the motor and braking system Excessiveadditional torque causes the motor and mechanical brakingsystem to overload e torque is also restricted by theworking state of the motor therefore a state of systemfailure in which the motor cannot provide braking forceshould be avoided Under the above constraints the dis-tributed longitudinal force needs to meet the demand ofadditional yaw moment

421 Optimization Objective e longitudinal and lateralforces the tire can provide are limited by the vertical loadAs the longitudinal force of each tire should be distributedaccording to the vertical load wheels with higher adhesionwould be expected to play a greater role erefore theoptimization objective is to minimize the sum of the square

of operating working load rate of each tire Because of thelimitation imposed by practical conditions the lateral forceof wheels cannot be directly controlled In this study thelongitudinal force of tires is controlled to generate additionalyaw moment us the optimization objective is expressedby the following equation

min J Cfl

Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732

+ Crl

Fxrl + ΔFxrl( 11138572

μrlFzrl( 11138572 + Crr

Fxrr + ΔFxrr( 11138572

μrrFzrr( 11138572

(41)

422 Optimization Constraints

(1) Equality Constraints e strategy for distributing ad-ditional yaw moment should not only minimize the sum ofthe operating working load rate but also ensure that thelongitudinal force meets the requirements of braking andacceleration operations of the driver and that the additionalyawmomentmeets the requirements of the upper controller

maxq Fxfl + ΔFxfl1113872 1113873cos δwfl + Fxfr + ΔFxfr1113872 1113873cos δwfr

+ Fxrl + ΔFxrl + Fxrr + ΔFxrr

ΔM ΔFxfl cos δwfl

2minusΔFxfr cos δwfr

2+ΔFxrl

2minusΔFxrr

2

(42)

(2) Inequality Constraint

(1) Adhesion condition constraint when additional yawmoment is distributed it is necessary to ensure thatthe longitudinal and lateral forces of the tire arewithin the tire adhesion ellipse to avoid longitudinaland lateral vehicle slip

F2

xij + F2yij

1113969le μijFzij (43)

(2) Motor and brake system performance constraintsthe additional longitudinal force is also limited by theperformance of the actuators e additional lon-gitudinal force of the two rear driving wheels islimited by the performance of the driving motoretwo nondriving front wheels can only providebraking force thus the additional longitudinal forceof the four wheels is limited by the performance ofthe mechanical braking system

e braking torque generated by motor is limited by thecharacteristics of the motor which cannot exceed themaximum torque limit determined by the power generatedat the current speed e large dynamic fluctuation of thebraking torque of the motor and the inverse proportion


between themaximum braking torque and speed prevent themotor from generating an adequate amount of reverseelectromotive force such that the braking force generated bythe motor is ineffective Due to the large dynamic fluctuationof motor braking torque and the inverse proportion betweenthe maximum braking torque and speed the reverse elec-tromotive force generated by the motor is too little when themotor is at low speed e motor cannot generate effectivebraking force erefore 500 rmin is set as the speedthreshold When the speed is lower than threshold thesystem no longer uses motor braking erefore the motorbraking torque is required meet the limitation provided inthe following equation [42]

Tdmax

0 0lt nle 500

Te 500lt nle nN

9550Peηn

nN lt nle nmax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(44)

At the same time control signal failure power converterfailure insulation failure and other types of failures of themotor may occur due to the design defects the serviceenvironment and service life of the motor us the driving

motor is no longer suitable to provide longitudinal force sothe motor failure coefficient τij is introduced

τij 0 motor is failed

1 motor is working properly1113896 (45)

erefore considering the above factors comprehen-sively additional longitudinal force of wheels would have tomeet the constraints

Tbflmax

rminus Fxfl leΔFxfl le minus Fxfl

Tbfrmax

rminus Fxfr leΔFxfr le minus Fxfr

Tbrlmax

r+

Tdmaxiτrl

r minus Fxrl

leΔFxrl leTdmaxiτrl

r minus Fxrl

Tbrrmax

r+

Tdmaxiτrr

r minus Fxrr

leΔFxrr leTdmaxiτrr

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(46)

erefore the optimal distribution of additional yawingmoment can be expressed as follows

min J ΔFxflΔFxfrΔFxrlΔFxrr1113872 1113873 Cfl

Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732 + Crl




μrrFzrr( 11138572

st Fxfl + ΔFxfl1113872 1113873cos δwfl + Fxfr + ΔFxfr1113872 1113873cos δwfr + Fxrl + ΔFxrl + Fxrr + ΔFxrr maxq

ΔFxfl cos δwfl


2+ΔFxrl

2minusΔFxrr

2 ΔM

F2

xij + F2yij

1113969le μijFzij (ij fl fr rl rr)

Tbflmax


Tbfrmax


Tbrlmax

rminus Fxrl leΔFxrl le

Tdmaxi

r minus Fxrl

Tbrrmax

rminus Fxrr leΔFxrr le

Tdmaxi

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

5 Test Verification

Considering the practical difficulties associated with con-troller development ie a long development cycle and high

cost we built a test platform for a dual-motor drive electricvehicle based on the AampD5435 semiphysical simulationsystem and rapid prototyping technology e tests werecarried out under both double-lane and single-lane change


conditions respectively to verify the feasibility and accuracyof the proposed stability control strategy

51 Dual-Motor Drive EV Test Platform Based on theAampD5435 Semiphysical Simulation System In this study adual-motor drive electric vehicle test platform was builtbased on the AampD5435 hardware in the loop simulationsystem and a dual-motor drive electric test vehicle estability control system proposed in this paper was testedand verified by using this platform in which the AampD5435replaces the vehicle control unit e input signals of thecontroller include angle angular velocity and torque of thesteering wheel accelerator pedal opening brake pedalopening vehicle speed wheel speed motor torque andmotor power e output signals include the following themotor drive torque and the brake torque of both the motorand the hydraulic braking system e input signal

mentioned above can be obtained by using the followingsensors e angle angular velocity and torque of thesteering wheel can be collected using the steering wheel

Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build

Configuredisplaycontrols

and result

Configure themapping of controls and

variables

Model executionor

Real-time model and ADXinterface transmission

Signal Variable

Signal collection

Steeringwheel

angle andtorquesensor

Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN

AampD5435 virtual controller

Test vehicle

Drive control system

Motor controller

Left motor Right motor

Figure 7 e dual-motor drive electric vehicle test platform

Figure 8 Changrsquoan University vehicle comprehensive perfor-mance proving ground


torque and angle sensor manufactured by SensorWay whichis mounted on the steering column A hall noncontact speedsensor is used to record the speed of the four wheels APassat B5 accelerator pedal sensor which has two channelsis used to measure the accelerator pedal opening Likewisethe brake pedal opening is measured by the brake pedalsensor e longitudinal acceleration lateral accelerationand yaw rate of the vehicle are acquired by a three-axisgyroscopeemotor speed torque and power are obtainedfrom the CAN signal of the motor controller e vehicleparameters are shown in Table 2 e dual-motor driveelectric vehicle test platform is shown in Figure 7

52 Test Verification Road Tests e stability controlstrategy of dual-motor drive EV proposed in this paper wasverified by carrying out vehicle road tests involving bothdouble-lane and single-lane change respectively At thesame time in order to demonstrate the effect of the proposedcontrol strategy the slide mode control (SMC) with thevehicle reference model considering the driverrsquos intention ischosen as the comparative controller

e vehicle road test was conducted on the stabilityperformance test square of the Changrsquoan University vehiclecomprehensive performance proving ground as shown inFigure 8

521 Double-Lane Change Condition e test was con-ducted under ISO 3888-1 which specifies the standarddouble-lane change condition [43]e target driving path isshown in Figure 9 e adhesion coefficient of the test roadwas 06

First the driver was required to keep the vehicle parallelwith the road and keep the steering wheel facing forwardSubsequently the driver controlled the vehicle to rapidlyproceed ahead such that the vehicle speed before enteringthe target path reached 70 kmh during which time thesteering wheel was not to be operated e driver could thendrive freely by negotiating the cone track

e identification result of driver turning intention isshown in Figure 10 e yaw rate sideslip angle lateralacceleration and vehicle trajectory are shown inFigures 11ndash14 e comparison with the control experimentis presented in Table 3

Figure 11 shows that the maximum yaw rate withoutcontrol is minus 35517degs whereas the reference yaw rate isminus 1866degs indicative of poor vehicle stability At 73 s thecurrent initial stage of sharp turning intention is identifiedwhereupon the reference yaw rate is modified and the

stability control system activated After 845 s the modelidentified that the current intention is normal turning thusthe reference yaw rate was no longer modified As a result ofthe control provided by the vehicle stability system themaximum yaw rate decreased by 4722 to 18744degs themaximum sideslip angle decreased by 5526 to minus 4391degand the maximum lateral acceleration decreased by 191 to4638ms2 Although dangerous conditions such as sideslipand spin without control did not arise the actual sideslipangle and yaw rate are much higher than the reference estability system clearly reduces the sideslip angle and yawrate to effectively improve the vehicle stability us thevehicle stability control system enables the vehicle to work

15m 30m 25m 25m 15m 15m

d1 d2

Figure 9 Schematic diagram for double-lane change test(d1 11L + 025 d2 13L + 025 L is the vehicle width)

0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts

Steering wheel torque (Nm)Steering wheelangle (deg)Steering wheelangular velocity (degs)

Recognition resultof sharp turning modelRecognition resultof normal turning modelTurning intention

Figure 10 Driver turning intention recognition result

0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)

Without controlWith controlWith SMC

Reference without intentionReference with intention

Figure 11 Yaw rate with control and without control


much more smoothly e actual driving trajectory is shownin Figure 14 Meanwhile it can be seen from Table 3 thatboth the controller proposed in this paper and SMC with thevehicle reference model considering the driverrsquos intentioncan track the control target well and the control effect ofsome areas is better than that of the contrast controller

522 Single-Lane Change Condition e test was con-ducted by performing a single-lane change e targetdriving path is shown in Figure 15 e adhesion coefficientof the test road was 04 First the driver was required to keepthe vehicle parallel with the road and keep the steering wheelfacing forward Subsequently the driver controlled the

vehicle to rapidly proceed ahead such that the vehicle speedbefore entering the target path reached 40 kmh duringwhich time the steering wheel was not to be operated edriver was then allowed to drive freely by following the conetrack

e identification result of driver turning intention isshown in Figure 16 e yaw rate sideslip angle lateralacceleration and vehicle trajectory are shown inFigures 17ndash20 e comparison with the control effect ispresented in Table 4

Figures 17 and 18 show that the vehicle slips and spinsafter 75 s without stability control e maximum yawvelocity reached minus 62779degs and the maximum sideslipangle reached 70740deg which are much more than thereference model us the vehicle stability control systemwas activated Furthermore the model identified that thecurrent intention was normal turning hence the referenceyaw rate was no longer modified e vehicle stabilitysystem reduced the maximum yaw rate by 651 and themaximum sideslip angle by 927 e stability systemtherefore improved the vehicle stability effectively evehicle stability control system enables the vehicle to runmuch more smoothly in comparison preventing danger-ous conditions such as sideslip and spin e actual driving

0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)

Without controlWith control

With SMCReference without intention

Figure 12 Sideslip angle with control and without control

0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )


Figure 13 Lateral acceleration with control and without control

20 40 60 80 100 120 140 160

0

2

4

6

8

10

12

Longitudinal displacement (m)

Late

ral d

ispla

cem

ent (

m)

Without controlControl with intentionControl without intention

Control with SMCCone

Figure 14 Vehicle track with control

Table 3 Control effect comparison

Yaw rate Sideslip angle Lateral accelerationWithout control minus 35517degs 9947deg 5733ms2

With control minus 18744degs 4391deg 4638ms2

With SMC minus 18953degs 4568deg 4895ms2

Reference minus 18660degs 4036deg mdashDecrease 4722 5585 1910


trajectory is shown in Figure 20 Meanwhile it can be seenfrom Table 4 that both the controller proposed in this paperand SMC with the vehicle reference model considering the

l1l2

l3

d1

h

b

d2

Figure 15 Schematic diagram for single-lane change test(h 35m b 12L + 025m L is the vehicle width d1 50ml2 100m l3 15u)

0 1 2 3 4 5 6 7 8 9ndash800ndash700ndash600ndash500ndash400ndash300ndash200ndash100

0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone



driverrsquos intention can track the control target well and thecontrol effect of some areas is better than that of thecontrast controller

6 Conclusion

is paper proposes a vehicle stability control strategyconsidering the driverrsquos turning intention for dual-motordrive electric vehicle

(1) e upper controller of the hierarchical vehiclestability control system was constructed with themodified reference model as the control target ismodel is modified by using turning urgency coeffi-cient which is calculated on the basis of the recog-nition results of the GHMMGGAP-RBF hybridturning intention model e lower layer controllertakes the minimized sum of the square of operatingworking load rate of each tire as optimization ob-jective and takes motor and road adhesion condi-tions as constraints to optimize the allocationadditional yaw torque e results show that theproposed vehicle stability control strategy can worksatisfactorily and effectively improve the vehiclestability

(2) Further studies could apart from the turning in-tention also consider the driverrsquos acceleration in-tention braking intention and complex intention toimprove the stability control strategy X-by-wiresystem and advanced assisted driving system iscould be expected to improve the safety and comfortof vehicle operation

Nomenclature

GHMM Gaussian hidden Markov modelGGAP-RBF

Generalized growing and pruning radial basisfunction

ABS Antilock braking systemTCS Traction control systemECB Electric control brakingEBD Electric brake force distributionAFS Active front steeringm Vehicle massωr Yaw ratea b Distance from the center of mass to front and

rear axleIszz Moment of inertia of the vehicle around the z-

axisμ Road adhesion coefficientay Lateral acceleration

axq Required longitudinal accelerationωrdes Ideal yaw rateωrref Reference yaw rateβdes Ideal sideslip angleβref Reference sideslip anglek1 k2 Cornering stiffness of the front and rear axleu v Vehicle longitudinal and lateral speedsδf Front wheel anglei Transmission ratio of power trainδwdes Ideal front wheel angleδswdes Ideal steering wheel angleρ Turning radiusiL Steering system angle ratioVL Steering power-assisted factorFzv Static axle loadnv Sum of pneumatic trail and king pinK Stability factorM Additional yaw momentΔFxij Variation in longitudinal tire forceCij Cornering stiffness of tireFxij Longitudinal tire forceFyij Lateral tire forceFzij Tire loadTdmax Motor peak torque at different speedsTe Motor peak torqueTbijmax Maximum braking force of each wheelPe Maximum motor powernN Motor nom speednmax Maximum motor speedη Motor efficiency

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was funded by National Key RampD Program ofChina (no 2018YFB1600700) China Postdoctoral ScienceFoundation (nos 2018T111006 and 2017M613034) andShaanxi Province Industrial Innovation Chain Project (no2018ZDCXL-GY-05-03-01)

References

[1] National Highway Traffic Safety Administration EstimatingLives Saved by Electronic Stability Control 2011ndash2015 Na-tional Highway Traffic Safety Administration WashingtonDC USA 2017

[2] W Jiang Z Yu and L Zhang ldquoA review on integrated chassiscontrolrdquo Automotive Engineering vol 29 no 5 pp 420ndash4252007

[3] W Chen Q Wang and H Xiao Automobile System Dy-namics and Integrated Control Beijing Science Press BeijingChina 2014



With control 21913degs 5157deg 2705ms2

With SMC 21926degs 4566deg 3124ms2

Reference 2176degs 5208deg mdashDecrease 651 927 5304


[4] H Zhang and J Wang ldquoVehicle lateral dynamics controlthrough AFSDYC and robust gain-scheduling approachrdquoIEEE Transactions on Vehicular Technology vol 65 no 1pp 489ndash494 2016

[5] C Wang C Song and J Li ldquoImprovement of active yawmoment control based on electric-wheel vehicle ESC testplatformrdquo in Proceedings of the Fifth International Conferenceon Instrumentation and Measurement Computer Commu-nication and Control pp 55ndash58 IEEE New York NY USAMay 2016

[6] J Zhao J Huang B Zhu et al ldquoNonlinear control of vehiclechassis planar stability based on T-S fuzzy modelrdquo in Pro-ceedings of the SAE 2016 World Congress and ExhibitionWarrendale PA USA April 2016

[7] J Xiao and T Zhao ldquoOverview and prospect of T-S fuzzycontrolrdquo Journal of Southwest Jiaotong University vol 51no 3 pp 462ndash474 2016

[8] W Zhao X Qin and C Wang ldquoYaw and lateral stabilitycontrol for four-wheel steer-by-wire systemrdquo IEEEASMETransactions on Mechatronics vol 23 no 6 pp 2628ndash26372018

[9] P Hang X Chen S Fang and F Luo ldquoRobust control forfour-wheel-independent-steering electric vehicle with steer-by-wire systemrdquo International Journal of Automotive Tech-nology vol 18 no 5 pp 785ndash797 2017

[10] W Zhao and H Zhang ldquoCoupling control strategy of forceand displacement for electric differential power steeringsystem of electric vehicle with motorized wheelsrdquo IEEETransactions on Vehicular Technology vol 67 no 9pp 8118ndash8128 2018

[11] W Zhao M Fan C Wang Z Jin and Y Li ldquoHinfinextensionstability control of automotive active front steering systemrdquoMechanical Systems and Signal Processing vol 115 no 115pp 621ndash636 2019

[12] Z Wang Y Wang L Zhang et al ldquoVehicle stability en-hancement through hierarchical control for a four wheelindependently actuated electric vehiclerdquo Energies vol 10no 7 2017

[13] H Chen Model Predictive Control Beijing Science PressBeijing China 2013

[14] M Jalali A Khajepour S-k Chen and B Litkouhi ldquoInte-grated stability and traction control for electric vehicles usingmodel predictive controlrdquo Control Engineering Practicevol 54 pp 256ndash266 2016

[15] O Barbarisi G Palmieri S Scala et al ldquoLTV-MPC for yawrate control and side slip control with dynamically con-strained differential brakingrdquo European Journal of Controlvol 15 no 3-4 pp 468ndash479 2009

[16] F Paolo H E Tseng B Francesco et al ldquoMPC-based yaw andlateral stabilisation via active front steering and brakingrdquoVehicle System Dynamics vol 46 no sup1 pp 611ndash628 2008

[17] S Wang X Zhao Q Yu et al ldquoResearch on strategy of thestability control system of dual-motor drive electric vehiclerdquoin Proceedings of the IEEE International Symposium on Cir-cuits and Systems (ISCAS) Sapporo Japan May 2019

[18] Z Yu P Yang and X Lu ldquoApplication of control allocationin distributed drive electric vehiclerdquo Journal of MechanicalEngineering vol 50 no 18 pp 99ndash107 2014

[19] D Yin D Shan and B C Chen ldquoA torque distributionapproach to electronic stability control for in-wheel motorelectric vehiclesrdquo in Proceedings of the International Con-ference on Applied System Innovation pp 1ndash4 IEEE OsakaJapan May 2016

[20] L Zhai T Sun and J Wang ldquoElectronic stability controlbased on motor driving and braking torque distribution for afour in-wheel motor drive electric vehiclerdquo IEEE Transactionson Vehicular Technology vol 65 no 6 pp 4726ndash4739 2016

[21] J Park H Jeong I Jang and S-H Hwang ldquoTorque distri-bution algorithm for an independently driven electric vehicleusing a fuzzy control methodrdquo Energies vol 8 no 8pp 8537ndash8561 2015

[22] D Kim and H Kim ldquoVehicle stability control with regen-erative braking and electronic brake force distribution for afour-wheel drive hybrid electric vehiclerdquo Proceedings of theInstitution of Mechanical Engineers Part D Journal of Au-tomobile Engineering vol 220 no 6 pp 683ndash693 2006

[23] Q Wang L Sun X Tang et al ldquoA study on braking intentionidentification for HEVrdquo Automotive Engineering vol 9pp 769ndash831 2013

[24] G Ma Z Liu X Pei et al ldquoIdentification of cut-in maneuverof side lane vehicles based on fuzzy support vector machinesrdquoAutomotive Engineering vol 36 no 3 pp 316ndash320 2014

[25] W Zhao Development and Test of Intention Recognition andBraking Force Distribution Control Strategies for Tractor-Semitrailer JiLin University Changchun China 2013

[26] L Xiong G W Teng Z P Yu W X Zhang and Y FengldquoNovel stability control strategy for distributed drive electricvehicle based on driver operation intentionrdquo InternationalJournal of Automotive Technology vol 17 no 4 pp 651ndash6632016

[27] S Wang Q Yu and X Zhao ldquoStudy on driverrsquos turningintention recognition hybrid model of GHMM and GGAP-RBF neural networkrdquo Advances in Mechanical Engineeringvol 10 no 3 pp 1ndash16 2018

[28] H Berndt J Emmert K Ditemater et al ldquoContinuous driverintention recognition with hidden markov modelsrdquo in Pro-ceedings of the 11th International IEEE Conference on Intel-ligent Transportation Systems Beijing China October 2008

[29] X Zheng Qe Study of Cough Signal Recognition Based onHMM-ANN Hybrid Model Chongqing University Chongq-ing China 2011

[30] L He B Ma and C Zong ldquoEmergency steering control basedon driver steering intention recognition for steer-by-wirevehiclerdquo Journal of Hunan University (Natural Sciences)vol 1 pp 81ndash86 2014

[31] R Pongsathorn M Takuya and N Masao ldquoDirect yawmoment control system based on driver behavior recogni-tionrdquo Vehicle System Dynamics vol 46 pp 911ndash921 2008

[32] G-B Huang P Saratchandran and N Sundararajan ldquoAnefficient sequential learning algorithm for growing andpruning RBF (GAP-RBF) networksrdquo IEEE Transactions onSystems Man and Cybernetics Part B (Cybernetics) vol 34no 6 pp 2284ndash2292 2004

[33] Y Lu Yingwei N Sundararajan and P SaratchandranldquoPerformance evaluation of a sequential minimal radial basisfunction (RBF) neural network learning algorithmrdquo IEEETransactions on Neural Networks vol 9 no 2 pp 308ndash3181998

[34] G B Huang P Saratchandran and N Sundararajan ldquoAgeneralized growing and pruning RBF (GGAP-RBF) neuralnetwork for function approximationrdquo IEEE Transactions onNeural Networks vol 16 no 16 pp 57ndash67 2005

[35] V Kadirkamanathan and M Niranjan ldquoA function estima-tion approach to sequential learning with neural networksrdquoNeural Computation vol 5 no 6 pp 954ndash975 1993

[36] Z Yu Automobile Qeory China Machine Press BeijingChina 5th edition 2010


[37] Y Chen and Q Yu Automotive Dynamics Tsinghua Uni-versity Press Beijing China 4th edition 2009

[38] F Huang Qe Acceleration and Deceleration Algorithm andSimulation of Position and Pressure Control ConversionProcess of Electro-Hydraulic Servo System Wuhan Universityof Science and Technology Wuhan China 2011

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

[40] L Liu Nonlinear Analysis and Control Strategy Evaluation onthe Stability of Vehicle 3-DOF PlanarMotion JiLin UniversityChangchun China 2010

[41] S Wang Research on Vehicle Stability Control System forDual-Motor Drive Electric Vehicle Changrsquoan UniversityXirsquoan China 2018

[42] Q Jin and Z Zhong ldquoAnalysis of electric braking charac-teristics and control strategy of electric vehiclerdquo Shang HaiAutomobile no 2 pp 32ndash34 2003

[43] ISO 3888-22011 Passenger Cars-Test Track for a Severe Lane-Change ManoeuvrendashPart 2 Obstacle Avoidance InternationalOrganization for Standardization Geneva Switzerland 2011


Hindawiwwwhindawicom Volume 2018

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Submit your manuscripts atwwwhindawicom

load fluctuation and side wind [8ndash12] However the PIDalgorithm guarantees neither optimal control of the systemnor its control stability e rules of fuzzy control areestablished on the basis of a large number of experimentsand expert experience and need to be adjusted according tothe driving environment which is both high time andeconomic consuming e most notable disadvantage ofslide mode control is chattering which occurs when thesystem approaches the slide mode surface and which canonly be reduced but not eliminated Model predictivecontrol (MPC) can directly consider actuator constraintsand system state constraints during controller design Inaddition MPC can effectively control a multiobjectiveconstrained system in complex engineering systems andhas strong portability [13] Jalali et al proposed a vehiclestability controller using MPC [14ndash17] And the desiredyaw rate and sideslip angle were obtained through thedriver steering wheel angle

e lower layer of a vehicle stability controller selectsthe appropriate actuator and reallocates the additional yawmoment based on certain rules At present the mostcommonly used method relies on two allocation strategiesrule-based and optimization theory-based [18] e in-creasing actuators and growing complexity of the electroniccontrol systems of vehicles have resulted in the allocationrules becoming more complex hence the allocation ac-curacy cannot be guaranteed to the same extent as beforeerefore the optimization theory-based allocation strat-egy is more suitable

e allocation strategy based on optimization theoryusually takes the slip rate of the tire the minimum of thesum of the working load of the tire and the minimum ofthe sum of the longitudinal force of the tire as the opti-mization objectives At the same time the optimizationstrategy considering the actuator failure and energyeconomy are gradually put forward Yin proposed theadditional yaw moment and traction force distributionstrategy for the purpose of minimizing the tire load [19]Zhai et al proposed an average torque distribution strategytire-dynamic-load-based torque distribution strategy andminimum-objective-function-based optimal torque dis-tribution strategy to control the motor driving torque orregenerative braking torque for vehicle stability enhance-ment [20] Park et al proposed a torque distributionstrategy that considers the driving economics driverrsquosacceleration demand and tire slip and used fuzzy logic toselect a suitable distribution strategy [21] Kim and Kimchose the regenerative braking and an electrohydraulicbrake as the actuators in the vehicle stability controllerAiming to minimize EHB energy consumption the brakingforce distribution ratio of the front and rear axles wereoptimized [22]

According to the above studies the hierarchical vehiclestability controller obtains the desired driving state by usingthe driver steering wheel angle However in-depth researchshowed that the use of only the steering wheel angle isinadequate to express the driver intention and obtain thedesired driving state vehicle stability controller

e driver turning intention is initiated based on ex-perience depending on the condition of the road envi-ronment and vehicle state en the driver manipulates thevehicle actuator such that the vehicle responds consistentlywith their intentionerefore the driverrsquos turning intentionreflects their subjective demand for the vehicle state Whendrivers take sharp turning operation such as go throughcontinuous S-turn hairpin bend and the other roads with asmaller radius curvature as well as emergency obstacleavoidance or sudden overtaking the driver would be con-sidered to intend rapidly maneuvering the vehicle undercurrent road conditions which also means the driver hascertain expectations in terms of the vehicle yaw rate andsideslip However for some drivers because of constraintssuch as their driving experience the driving environmenttheoretical knowledge and other factors this expectationignores correct judgment of the lateral motion stability of thevehicle During the process of vehicle stability control if it isa significant difference between the actual and expected stateof the vehicle the driver would proceed with the turningoperation and the vehicle stability would deteriorate andeven cause the driver to distrust the system

erefore accurate interpretation and prediction of thedriving intention during the process of vehicle stabilitycontrol and ensuring the actual vehicle state is maintained asclosely as possible to the expected vehicle state would greatlyimprove the stability and driving safety of the vehicle Driverintention can be obtained using fuzzy reasoning supportvector machine (SVM) artificial neural network (ANN) andhidden Markov model (HMM) [23ndash27] Fuzzy reasoningSVM and ANN are used to recognize the intentions ofdriver at a certain moment However neural network andfuzzy logic are difficult to deal with temporal-ordered in-formation us they are mainly used for static recognitionproblems HMM as a kind of dynamic information pro-cessing method based on time-series cumulative probabilityconsiders only the state sequence with the maximum log-likelihood and ignores the possibility of small probabilityevents erefore it is difficult to recognize easily confusedintentions using HMM

All the above analysis motivated us to develop a methodto detect the driverrsquos turning intention establish a steeringurgency coefficient for sharp turning and propose a vehiclestability control reference model considering the driverrsquosturning intention Based on the abovementioned results weproposed a stability control strategy for a dual-motor driveelectric vehicle As a result of this research the desiredcontrol target of stability control is no longer only based onthe steering wheel angle and the vehicle state in accordancewith the driving intention is under control to a certainextent is paper is organized as follows e method toidentify the driverrsquos turning intention is presented in Section 1A modified reference model for vehicle stability consideringthe driverrsquos turning intention is presented in Section 2Construction of the vehicle stability control strategy basedon the modified reference model is discussed in Section 3Section 4 compares the vehicle stability control strategybased on the modified reference model constructed in this








Ot a(t) b(t) c(t) (1)




bi(O) 1113944M

j1ωijN O μij σij1113872 1113873 (2)





Steering wheelangle





Log-likelihood

of theGHMMs


GHMMtraining

Lowerlayer

GGAP-RBF

Normalization

Sharp turning

Normal turning

Training


Upperlayer



εt(i j) p st i st+1 j O | λ( 1113857

p(O | λ)

αt(i)βt(i)


ωijP O μij σ1113960 1113961

1113936K1 ωijP O μij σ1113960 1113961

(3)


ωijprime

1113936Tt1εt(i j)

1113936Tt11113936

Kt1εt(i j)

μijprime


1113936Tt1εt(i j)

σijprime


1113936Tt1εt(i j)

(4)







f xi( 1113857 loglik xi( 1113857 ω0 + 1113944K

k1ωk middot e


k( 1113857

(8)




wn xi

σn κ xi minus wir

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(9)



xi minus wir

gt εi


⎧⎨

⎩ (10)




1n

1113944

n

i1εq

(k i)⎛⎝ ⎞⎠

1q

ωk

q

1n

1113944

n

i1R

q

k xi( 1113857⎛⎝ ⎞⎠

1q

(11)





Eq(k)

ωk

q

1113945

L

l11113946

bl

al

eminus wkminus xil

2σk2( 1113857

pl(x)dx1113888 1113889

1q

(12)











m _v minus uωr1113872 1113873 k1 + k2( 1113857β

+1u



a2k1 + b

2k21113872 1113873ωr minus ak1δf

(14)


ωrdes u

R




(15)









u (16)



11138681113868111386811138681113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868gt ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(17)




βref βdes βdes

11138681113868111386811138681113868111386811138681113868le βupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868gt βupper_bound11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(19)




dML

d v2ρ( 1113857

mnvlH

iLVLl1g

1iLVL

Fzvnv (20)


MLdes 11139461g

1iLVL

Fzvnvdv2

ρ1113888 1113889 (21)


δwdes L 1 + Ku2( 1113857

uωr

K m

L2a

k2minus

b

k11113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩


(22)


τ 12



21113969

(23)


x x minus min

max minus min (24)



model


Ideal yaw rate


Driverintention

identificationmodel




Driver intention

Sharpturning

coefficient

Referenceyaw rate




0 10 20 30 40 500

02

04

06

08

1

Speed (ms)

δ = 10 δ = 9 δ = 8

μ = 1

μ = 01

δ = 7δ = 6

δ = 5

δ = 4

δ = 3

δ = 2δ = 1









ωlowastrref


1113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868


11138681113868111386811138681113868

11138681113868111386811138681113868le ωrdes1113868111386811138681113868

1113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(27)


When the inequality



ωlowastrref(t)


Jt2 t0 le tle t1


Jt2 t1 lt tle t2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(29)







t (s)

t1t0 t2

ωrref

ωlowast

rref






N


Turning start stage

Y

N

Y

N

Y

ωlowast

rref = ωrref

ωlowast


ωlowast


ωlowast

rref = ωrref

ωlowast


ωrupper_bound

gt ωrdes

ωr le


Turningintention

identificationmodel




Turningintention

Referencemodel

Driverinput


Yaw rate ωr



Wheel speed ωij



moments

M


momentsDrive motor

Hydraulic brake

Fxfl

Fxfr

Fxrl

Fxrr

Vehicle

Tbij

Txij

Upperlayer

controller

Vehicledynamic

model

Lowerlayer

controller

Sideslip angle β

βlowast

rref ωlowast

rref




_V cos β





(30)

ωr 1Iz



Br

21113890


+Bf


+ minusBf


(31)

_β cos βmV



cos δflFxrl1113872



(32)



Yc CcX

⎧⎨

⎩ (33)




Y(k) CΔX(k) + Y(k minus 1)1113896 (34)



0e

AcτBucdτ




2Q

+ΔU(k)2R

1113944

Np

i


2Q

+ 1113944

Ncminus 1

i

ΔU(k + i | k)2R

(35)


Umin leU(k)leUmax


Ymin leY(k)leYmax

⎧⎪⎪⎨

⎪⎪⎩(36)


lowastref ]


In this research

Q 10 0

0 151113890 1113891

R

500 0 0

0 500 0

0 0 8000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)

O

Fyfl

Fyrr

Fyrl

Fyfr

y

xvu

b a

L

Br Bf

Fxrl

Fxrr Fxfr

Fxf l

αrl

αrr

αf l

αfr

ωr

β

δfl

δfr




Y(k)

Y(k + 1 | k)

Y(k + 2 | k)

Y(k + 3 | k)

Y(k + 4 | k)

Y(k + 5 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ΔU(k)

ΔM(k | k)

ΔM(k + 1 | k)

ΔM(k + 2 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(38)



⋮

Y(k + 5 | k) 11139445

i1CA

ix(k) + 1113944

5

i1CA

iminus 1BΔU(k)


i1CA

iminus 1BΔU(k + 4) + 1113944

3

i1CA


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(39)






min J Cfl

Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732

+ Crl




μrrFzrr( 11138572

(41)







2+ΔFxrl

2minusΔFxrr

2

(42)



F2

xij + F2yij






Tdmax

0 0lt nle 500

Te 500lt nle nN

9550Peηn

nN lt nle nmax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(44)






Tbflmax


Tbfrmax


Tbrlmax

r+

Tdmaxiτrl

r minus Fxrl


r minus Fxrl

Tbrrmax

r+

Tdmaxiτrr

r minus Fxrr


r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(46)



Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732 + Crl




μrrFzrr( 11138572


ΔFxfl cos δwfl


2+ΔFxrl

2minusΔFxrr

2 ΔM

F2

xij + F2yij


Tbflmax


Tbfrmax


Tbrlmax


Tdmaxi

r minus Fxrl

Tbrrmax


Tdmaxi

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

5 Test Verification







Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build


and result


variables

Model executionor


Signal Variable

Signal collection

Steeringwheel


Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN


Test vehicle


Motor controller













15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018














Ot a(t) b(t) c(t) (1)




bi(O) 1113944M

j1ωijN O μij σij1113872 1113873 (2)





Steering wheelangle





Log-likelihood

of theGHMMs


GHMMtraining

Lowerlayer

GGAP-RBF

Normalization

Sharp turning

Normal turning

Training


Upperlayer



εt(i j) p st i st+1 j O | λ( 1113857

p(O | λ)

αt(i)βt(i)


ωijP O μij σ1113960 1113961

1113936K1 ωijP O μij σ1113960 1113961

(3)


ωijprime

1113936Tt1εt(i j)

1113936Tt11113936

Kt1εt(i j)

μijprime


1113936Tt1εt(i j)

σijprime


1113936Tt1εt(i j)

(4)







f xi( 1113857 loglik xi( 1113857 ω0 + 1113944K

k1ωk middot e


k( 1113857

(8)




wn xi

σn κ xi minus wir

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(9)



xi minus wir

gt εi


⎧⎨

⎩ (10)




1n

1113944

n

i1εq

(k i)⎛⎝ ⎞⎠

1q

ωk

q

1n

1113944

n

i1R

q

k xi( 1113857⎛⎝ ⎞⎠

1q

(11)





Eq(k)

ωk

q

1113945

L

l11113946

bl

al

eminus wkminus xil

2σk2( 1113857

pl(x)dx1113888 1113889

1q

(12)











m _v minus uωr1113872 1113873 k1 + k2( 1113857β

+1u



a2k1 + b

2k21113872 1113873ωr minus ak1δf

(14)


ωrdes u

R




(15)









u (16)



11138681113868111386811138681113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868gt ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(17)




βref βdes βdes

11138681113868111386811138681113868111386811138681113868le βupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868gt βupper_bound11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(19)




dML

d v2ρ( 1113857

mnvlH

iLVLl1g

1iLVL

Fzvnv (20)


MLdes 11139461g

1iLVL

Fzvnvdv2

ρ1113888 1113889 (21)


δwdes L 1 + Ku2( 1113857

uωr

K m

L2a

k2minus

b

k11113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩


(22)


τ 12



21113969

(23)


x x minus min

max minus min (24)



model


Ideal yaw rate


Driverintention

identificationmodel




Driver intention

Sharpturning

coefficient

Referenceyaw rate




0 10 20 30 40 500

02

04

06

08

1

Speed (ms)

δ = 10 δ = 9 δ = 8

μ = 1

μ = 01

δ = 7δ = 6

δ = 5

δ = 4

δ = 3

δ = 2δ = 1









ωlowastrref


1113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868


11138681113868111386811138681113868

11138681113868111386811138681113868le ωrdes1113868111386811138681113868

1113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(27)


When the inequality



ωlowastrref(t)


Jt2 t0 le tle t1


Jt2 t1 lt tle t2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(29)







t (s)

t1t0 t2

ωrref

ωlowast

rref






N


Turning start stage

Y

N

Y

N

Y

ωlowast

rref = ωrref

ωlowast


ωlowast


ωlowast

rref = ωrref

ωlowast


ωrupper_bound

gt ωrdes

ωr le


Turningintention

identificationmodel




Turningintention

Referencemodel

Driverinput


Yaw rate ωr



Wheel speed ωij



moments

M


momentsDrive motor

Hydraulic brake

Fxfl

Fxfr

Fxrl

Fxrr

Vehicle

Tbij

Txij

Upperlayer

controller

Vehicledynamic

model

Lowerlayer

controller

Sideslip angle β

βlowast

rref ωlowast

rref




_V cos β





(30)

ωr 1Iz



Br

21113890


+Bf


+ minusBf


(31)

_β cos βmV



cos δflFxrl1113872



(32)



Yc CcX

⎧⎨

⎩ (33)




Y(k) CΔX(k) + Y(k minus 1)1113896 (34)



0e

AcτBucdτ




2Q

+ΔU(k)2R

1113944

Np

i


2Q

+ 1113944

Ncminus 1

i

ΔU(k + i | k)2R

(35)


Umin leU(k)leUmax


Ymin leY(k)leYmax

⎧⎪⎪⎨

⎪⎪⎩(36)


lowastref ]


In this research

Q 10 0

0 151113890 1113891

R

500 0 0

0 500 0

0 0 8000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)

O

Fyfl

Fyrr

Fyrl

Fyfr

y

xvu

b a

L

Br Bf

Fxrl

Fxrr Fxfr

Fxf l

αrl

αrr

αf l

αfr

ωr

β

δfl

δfr




Y(k)

Y(k + 1 | k)

Y(k + 2 | k)

Y(k + 3 | k)

Y(k + 4 | k)

Y(k + 5 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ΔU(k)

ΔM(k | k)

ΔM(k + 1 | k)

ΔM(k + 2 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(38)



⋮

Y(k + 5 | k) 11139445

i1CA

ix(k) + 1113944

5

i1CA

iminus 1BΔU(k)


i1CA

iminus 1BΔU(k + 4) + 1113944

3

i1CA


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(39)






min J Cfl

Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732

+ Crl




μrrFzrr( 11138572

(41)







2+ΔFxrl

2minusΔFxrr

2

(42)



F2

xij + F2yij






Tdmax

0 0lt nle 500

Te 500lt nle nN

9550Peηn

nN lt nle nmax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(44)






Tbflmax


Tbfrmax


Tbrlmax

r+

Tdmaxiτrl

r minus Fxrl


r minus Fxrl

Tbrrmax

r+

Tdmaxiτrr

r minus Fxrr


r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(46)



Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732 + Crl




μrrFzrr( 11138572


ΔFxfl cos δwfl


2+ΔFxrl

2minusΔFxrr

2 ΔM

F2

xij + F2yij


Tbflmax


Tbfrmax


Tbrlmax


Tdmaxi

r minus Fxrl

Tbrrmax


Tdmaxi

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

5 Test Verification







Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build


and result


variables

Model executionor


Signal Variable

Signal collection

Steeringwheel


Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN


Test vehicle


Motor controller













15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018








εt(i j) p st i st+1 j O | λ( 1113857

p(O | λ)

αt(i)βt(i)


ωijP O μij σ1113960 1113961

1113936K1 ωijP O μij σ1113960 1113961

(3)


ωijprime

1113936Tt1εt(i j)

1113936Tt11113936

Kt1εt(i j)

μijprime


1113936Tt1εt(i j)

σijprime


1113936Tt1εt(i j)

(4)







f xi( 1113857 loglik xi( 1113857 ω0 + 1113944K

k1ωk middot e


k( 1113857

(8)




wn xi

σn κ xi minus wir

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(9)



xi minus wir

gt εi


⎧⎨

⎩ (10)




1n

1113944

n

i1εq

(k i)⎛⎝ ⎞⎠

1q

ωk

q

1n

1113944

n

i1R

q

k xi( 1113857⎛⎝ ⎞⎠

1q

(11)





Eq(k)

ωk

q

1113945

L

l11113946

bl

al

eminus wkminus xil

2σk2( 1113857

pl(x)dx1113888 1113889

1q

(12)











m _v minus uωr1113872 1113873 k1 + k2( 1113857β

+1u



a2k1 + b

2k21113872 1113873ωr minus ak1δf

(14)


ωrdes u

R




(15)









u (16)



11138681113868111386811138681113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868gt ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(17)




βref βdes βdes

11138681113868111386811138681113868111386811138681113868le βupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868gt βupper_bound11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(19)




dML

d v2ρ( 1113857

mnvlH

iLVLl1g

1iLVL

Fzvnv (20)


MLdes 11139461g

1iLVL

Fzvnvdv2

ρ1113888 1113889 (21)


δwdes L 1 + Ku2( 1113857

uωr

K m

L2a

k2minus

b

k11113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩


(22)


τ 12



21113969

(23)


x x minus min

max minus min (24)



model


Ideal yaw rate


Driverintention

identificationmodel




Driver intention

Sharpturning

coefficient

Referenceyaw rate




0 10 20 30 40 500

02

04

06

08

1

Speed (ms)

δ = 10 δ = 9 δ = 8

μ = 1

μ = 01

δ = 7δ = 6

δ = 5

δ = 4

δ = 3

δ = 2δ = 1









ωlowastrref


1113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868


11138681113868111386811138681113868

11138681113868111386811138681113868le ωrdes1113868111386811138681113868

1113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(27)


When the inequality



ωlowastrref(t)


Jt2 t0 le tle t1


Jt2 t1 lt tle t2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(29)







t (s)

t1t0 t2

ωrref

ωlowast

rref






N


Turning start stage

Y

N

Y

N

Y

ωlowast

rref = ωrref

ωlowast


ωlowast


ωlowast

rref = ωrref

ωlowast


ωrupper_bound

gt ωrdes

ωr le


Turningintention

identificationmodel




Turningintention

Referencemodel

Driverinput


Yaw rate ωr



Wheel speed ωij



moments

M


momentsDrive motor

Hydraulic brake

Fxfl

Fxfr

Fxrl

Fxrr

Vehicle

Tbij

Txij

Upperlayer

controller

Vehicledynamic

model

Lowerlayer

controller

Sideslip angle β

βlowast

rref ωlowast

rref




_V cos β





(30)

ωr 1Iz



Br

21113890


+Bf


+ minusBf


(31)

_β cos βmV



cos δflFxrl1113872



(32)



Yc CcX

⎧⎨

⎩ (33)




Y(k) CΔX(k) + Y(k minus 1)1113896 (34)



0e

AcτBucdτ




2Q

+ΔU(k)2R

1113944

Np

i


2Q

+ 1113944

Ncminus 1

i

ΔU(k + i | k)2R

(35)


Umin leU(k)leUmax


Ymin leY(k)leYmax

⎧⎪⎪⎨

⎪⎪⎩(36)


lowastref ]


In this research

Q 10 0

0 151113890 1113891

R

500 0 0

0 500 0

0 0 8000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)

O

Fyfl

Fyrr

Fyrl

Fyfr

y

xvu

b a

L

Br Bf

Fxrl

Fxrr Fxfr

Fxf l

αrl

αrr

αf l

αfr

ωr

β

δfl

δfr




Y(k)

Y(k + 1 | k)

Y(k + 2 | k)

Y(k + 3 | k)

Y(k + 4 | k)

Y(k + 5 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ΔU(k)

ΔM(k | k)

ΔM(k + 1 | k)

ΔM(k + 2 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(38)



⋮

Y(k + 5 | k) 11139445

i1CA

ix(k) + 1113944

5

i1CA

iminus 1BΔU(k)


i1CA

iminus 1BΔU(k + 4) + 1113944

3

i1CA


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(39)






min J Cfl

Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732

+ Crl




μrrFzrr( 11138572

(41)







2+ΔFxrl

2minusΔFxrr

2

(42)



F2

xij + F2yij






Tdmax

0 0lt nle 500

Te 500lt nle nN

9550Peηn

nN lt nle nmax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(44)






Tbflmax


Tbfrmax


Tbrlmax

r+

Tdmaxiτrl

r minus Fxrl


r minus Fxrl

Tbrrmax

r+

Tdmaxiτrr

r minus Fxrr


r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(46)



Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732 + Crl




μrrFzrr( 11138572


ΔFxfl cos δwfl


2+ΔFxrl

2minusΔFxrr

2 ΔM

F2

xij + F2yij


Tbflmax


Tbfrmax


Tbrlmax


Tdmaxi

r minus Fxrl

Tbrrmax


Tdmaxi

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

5 Test Verification







Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build


and result


variables

Model executionor


Signal Variable

Signal collection

Steeringwheel


Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN


Test vehicle


Motor controller













15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018
















m _v minus uωr1113872 1113873 k1 + k2( 1113857β

+1u



a2k1 + b

2k21113872 1113873ωr minus ak1δf

(14)


ωrdes u

R




(15)









u (16)



11138681113868111386811138681113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868gt ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(17)




βref βdes βdes

11138681113868111386811138681113868111386811138681113868le βupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868gt βupper_bound11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(19)




dML

d v2ρ( 1113857

mnvlH

iLVLl1g

1iLVL

Fzvnv (20)


MLdes 11139461g

1iLVL

Fzvnvdv2

ρ1113888 1113889 (21)


δwdes L 1 + Ku2( 1113857

uωr

K m

L2a

k2minus

b

k11113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩


(22)


τ 12



21113969

(23)


x x minus min

max minus min (24)



model


Ideal yaw rate


Driverintention

identificationmodel




Driver intention

Sharpturning

coefficient

Referenceyaw rate




0 10 20 30 40 500

02

04

06

08

1

Speed (ms)

δ = 10 δ = 9 δ = 8

μ = 1

μ = 01

δ = 7δ = 6

δ = 5

δ = 4

δ = 3

δ = 2δ = 1









ωlowastrref


1113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868


11138681113868111386811138681113868

11138681113868111386811138681113868le ωrdes1113868111386811138681113868

1113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(27)


When the inequality



ωlowastrref(t)


Jt2 t0 le tle t1


Jt2 t1 lt tle t2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(29)







t (s)

t1t0 t2

ωrref

ωlowast

rref






N


Turning start stage

Y

N

Y

N

Y

ωlowast

rref = ωrref

ωlowast


ωlowast


ωlowast

rref = ωrref

ωlowast


ωrupper_bound

gt ωrdes

ωr le


Turningintention

identificationmodel




Turningintention

Referencemodel

Driverinput


Yaw rate ωr



Wheel speed ωij



moments

M


momentsDrive motor

Hydraulic brake

Fxfl

Fxfr

Fxrl

Fxrr

Vehicle

Tbij

Txij

Upperlayer

controller

Vehicledynamic

model

Lowerlayer

controller

Sideslip angle β

βlowast

rref ωlowast

rref




_V cos β





(30)

ωr 1Iz



Br

21113890


+Bf


+ minusBf


(31)

_β cos βmV



cos δflFxrl1113872



(32)



Yc CcX

⎧⎨

⎩ (33)




Y(k) CΔX(k) + Y(k minus 1)1113896 (34)



0e

AcτBucdτ




2Q

+ΔU(k)2R

1113944

Np

i


2Q

+ 1113944

Ncminus 1

i

ΔU(k + i | k)2R

(35)


Umin leU(k)leUmax


Ymin leY(k)leYmax

⎧⎪⎪⎨

⎪⎪⎩(36)


lowastref ]


In this research

Q 10 0

0 151113890 1113891

R

500 0 0

0 500 0

0 0 8000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)

O

Fyfl

Fyrr

Fyrl

Fyfr

y

xvu

b a

L

Br Bf

Fxrl

Fxrr Fxfr

Fxf l

αrl

αrr

αf l

αfr

ωr

β

δfl

δfr




Y(k)

Y(k + 1 | k)

Y(k + 2 | k)

Y(k + 3 | k)

Y(k + 4 | k)

Y(k + 5 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ΔU(k)

ΔM(k | k)

ΔM(k + 1 | k)

ΔM(k + 2 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(38)



⋮

Y(k + 5 | k) 11139445

i1CA

ix(k) + 1113944

5

i1CA

iminus 1BΔU(k)


i1CA

iminus 1BΔU(k + 4) + 1113944

3

i1CA


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(39)






min J Cfl

Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732

+ Crl




μrrFzrr( 11138572

(41)







2+ΔFxrl

2minusΔFxrr

2

(42)



F2

xij + F2yij






Tdmax

0 0lt nle 500

Te 500lt nle nN

9550Peηn

nN lt nle nmax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(44)






Tbflmax


Tbfrmax


Tbrlmax

r+

Tdmaxiτrl

r minus Fxrl


r minus Fxrl

Tbrrmax

r+

Tdmaxiτrr

r minus Fxrr


r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(46)



Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732 + Crl




μrrFzrr( 11138572


ΔFxfl cos δwfl


2+ΔFxrl

2minusΔFxrr

2 ΔM

F2

xij + F2yij


Tbflmax


Tbfrmax


Tbrlmax


Tdmaxi

r minus Fxrl

Tbrrmax


Tdmaxi

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

5 Test Verification







Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build


and result


variables

Model executionor


Signal Variable

Signal collection

Steeringwheel


Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN


Test vehicle


Motor controller













15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018









u (16)



11138681113868111386811138681113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868gt ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(17)




βref βdes βdes

11138681113868111386811138681113868111386811138681113868le βupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868gt βupper_bound11138681113868111386811138681113868

11138681113868111386811138681113868

⎧⎪⎨

⎪⎩

(19)




dML

d v2ρ( 1113857

mnvlH

iLVLl1g

1iLVL

Fzvnv (20)


MLdes 11139461g

1iLVL

Fzvnvdv2

ρ1113888 1113889 (21)


δwdes L 1 + Ku2( 1113857

uωr

K m

L2a

k2minus

b

k11113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩


(22)


τ 12



21113969

(23)


x x minus min

max minus min (24)



model


Ideal yaw rate


Driverintention

identificationmodel




Driver intention

Sharpturning

coefficient

Referenceyaw rate




0 10 20 30 40 500

02

04

06

08

1

Speed (ms)

δ = 10 δ = 9 δ = 8

μ = 1

μ = 01

δ = 7δ = 6

δ = 5

δ = 4

δ = 3

δ = 2δ = 1









ωlowastrref


1113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868


11138681113868111386811138681113868

11138681113868111386811138681113868le ωrdes1113868111386811138681113868

1113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(27)


When the inequality



ωlowastrref(t)


Jt2 t0 le tle t1


Jt2 t1 lt tle t2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(29)







t (s)

t1t0 t2

ωrref

ωlowast

rref






N


Turning start stage

Y

N

Y

N

Y

ωlowast

rref = ωrref

ωlowast


ωlowast


ωlowast

rref = ωrref

ωlowast


ωrupper_bound

gt ωrdes

ωr le


Turningintention

identificationmodel




Turningintention

Referencemodel

Driverinput


Yaw rate ωr



Wheel speed ωij



moments

M


momentsDrive motor

Hydraulic brake

Fxfl

Fxfr

Fxrl

Fxrr

Vehicle

Tbij

Txij

Upperlayer

controller

Vehicledynamic

model

Lowerlayer

controller

Sideslip angle β

βlowast

rref ωlowast

rref




_V cos β





(30)

ωr 1Iz



Br

21113890


+Bf


+ minusBf


(31)

_β cos βmV



cos δflFxrl1113872



(32)



Yc CcX

⎧⎨

⎩ (33)




Y(k) CΔX(k) + Y(k minus 1)1113896 (34)



0e

AcτBucdτ




2Q

+ΔU(k)2R

1113944

Np

i


2Q

+ 1113944

Ncminus 1

i

ΔU(k + i | k)2R

(35)


Umin leU(k)leUmax


Ymin leY(k)leYmax

⎧⎪⎪⎨

⎪⎪⎩(36)


lowastref ]


In this research

Q 10 0

0 151113890 1113891

R

500 0 0

0 500 0

0 0 8000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)

O

Fyfl

Fyrr

Fyrl

Fyfr

y

xvu

b a

L

Br Bf

Fxrl

Fxrr Fxfr

Fxf l

αrl

αrr

αf l

αfr

ωr

β

δfl

δfr




Y(k)

Y(k + 1 | k)

Y(k + 2 | k)

Y(k + 3 | k)

Y(k + 4 | k)

Y(k + 5 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ΔU(k)

ΔM(k | k)

ΔM(k + 1 | k)

ΔM(k + 2 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(38)



⋮

Y(k + 5 | k) 11139445

i1CA

ix(k) + 1113944

5

i1CA

iminus 1BΔU(k)


i1CA

iminus 1BΔU(k + 4) + 1113944

3

i1CA


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(39)






min J Cfl

Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732

+ Crl




μrrFzrr( 11138572

(41)







2+ΔFxrl

2minusΔFxrr

2

(42)



F2

xij + F2yij






Tdmax

0 0lt nle 500

Te 500lt nle nN

9550Peηn

nN lt nle nmax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(44)






Tbflmax


Tbfrmax


Tbrlmax

r+

Tdmaxiτrl

r minus Fxrl


r minus Fxrl

Tbrrmax

r+

Tdmaxiτrr

r minus Fxrr


r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(46)



Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732 + Crl




μrrFzrr( 11138572


ΔFxfl cos δwfl


2+ΔFxrl

2minusΔFxrr

2 ΔM

F2

xij + F2yij


Tbflmax


Tbfrmax


Tbrlmax


Tdmaxi

r minus Fxrl

Tbrrmax


Tdmaxi

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

5 Test Verification







Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build


and result


variables

Model executionor


Signal Variable

Signal collection

Steeringwheel


Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN


Test vehicle


Motor controller













15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018














ωlowastrref


1113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868


1113868111386811138681113868le ωrupper_bound

11138681113868111386811138681113868

11138681113868111386811138681113868le ωr1113868111386811138681113868

1113868111386811138681113868


11138681113868111386811138681113868

11138681113868111386811138681113868le ωrdes1113868111386811138681113868

1113868111386811138681113868

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(27)


When the inequality



ωlowastrref(t)


Jt2 t0 le tle t1


Jt2 t1 lt tle t2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(29)







t (s)

t1t0 t2

ωrref

ωlowast

rref






N


Turning start stage

Y

N

Y

N

Y

ωlowast

rref = ωrref

ωlowast


ωlowast


ωlowast

rref = ωrref

ωlowast


ωrupper_bound

gt ωrdes

ωr le


Turningintention

identificationmodel




Turningintention

Referencemodel

Driverinput


Yaw rate ωr



Wheel speed ωij



moments

M


momentsDrive motor

Hydraulic brake

Fxfl

Fxfr

Fxrl

Fxrr

Vehicle

Tbij

Txij

Upperlayer

controller

Vehicledynamic

model

Lowerlayer

controller

Sideslip angle β

βlowast

rref ωlowast

rref




_V cos β





(30)

ωr 1Iz



Br

21113890


+Bf


+ minusBf


(31)

_β cos βmV



cos δflFxrl1113872



(32)



Yc CcX

⎧⎨

⎩ (33)




Y(k) CΔX(k) + Y(k minus 1)1113896 (34)



0e

AcτBucdτ




2Q

+ΔU(k)2R

1113944

Np

i


2Q

+ 1113944

Ncminus 1

i

ΔU(k + i | k)2R

(35)


Umin leU(k)leUmax


Ymin leY(k)leYmax

⎧⎪⎪⎨

⎪⎪⎩(36)


lowastref ]


In this research

Q 10 0

0 151113890 1113891

R

500 0 0

0 500 0

0 0 8000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)

O

Fyfl

Fyrr

Fyrl

Fyfr

y

xvu

b a

L

Br Bf

Fxrl

Fxrr Fxfr

Fxf l

αrl

αrr

αf l

αfr

ωr

β

δfl

δfr




Y(k)

Y(k + 1 | k)

Y(k + 2 | k)

Y(k + 3 | k)

Y(k + 4 | k)

Y(k + 5 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ΔU(k)

ΔM(k | k)

ΔM(k + 1 | k)

ΔM(k + 2 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(38)



⋮

Y(k + 5 | k) 11139445

i1CA

ix(k) + 1113944

5

i1CA

iminus 1BΔU(k)


i1CA

iminus 1BΔU(k + 4) + 1113944

3

i1CA


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(39)






min J Cfl

Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732

+ Crl




μrrFzrr( 11138572

(41)







2+ΔFxrl

2minusΔFxrr

2

(42)



F2

xij + F2yij






Tdmax

0 0lt nle 500

Te 500lt nle nN

9550Peηn

nN lt nle nmax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(44)






Tbflmax


Tbfrmax


Tbrlmax

r+

Tdmaxiτrl

r minus Fxrl


r minus Fxrl

Tbrrmax

r+

Tdmaxiτrr

r minus Fxrr


r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(46)



Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732 + Crl




μrrFzrr( 11138572


ΔFxfl cos δwfl


2+ΔFxrl

2minusΔFxrr

2 ΔM

F2

xij + F2yij


Tbflmax


Tbfrmax


Tbrlmax


Tdmaxi

r minus Fxrl

Tbrrmax


Tdmaxi

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

5 Test Verification







Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build


and result


variables

Model executionor


Signal Variable

Signal collection

Steeringwheel


Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN


Test vehicle


Motor controller













15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018











N


Turning start stage

Y

N

Y

N

Y

ωlowast

rref = ωrref

ωlowast


ωlowast


ωlowast

rref = ωrref

ωlowast


ωrupper_bound

gt ωrdes

ωr le


Turningintention

identificationmodel




Turningintention

Referencemodel

Driverinput


Yaw rate ωr



Wheel speed ωij



moments

M


momentsDrive motor

Hydraulic brake

Fxfl

Fxfr

Fxrl

Fxrr

Vehicle

Tbij

Txij

Upperlayer

controller

Vehicledynamic

model

Lowerlayer

controller

Sideslip angle β

βlowast

rref ωlowast

rref




_V cos β





(30)

ωr 1Iz



Br

21113890


+Bf


+ minusBf


(31)

_β cos βmV



cos δflFxrl1113872



(32)



Yc CcX

⎧⎨

⎩ (33)




Y(k) CΔX(k) + Y(k minus 1)1113896 (34)



0e

AcτBucdτ




2Q

+ΔU(k)2R

1113944

Np

i


2Q

+ 1113944

Ncminus 1

i

ΔU(k + i | k)2R

(35)


Umin leU(k)leUmax


Ymin leY(k)leYmax

⎧⎪⎪⎨

⎪⎪⎩(36)


lowastref ]


In this research

Q 10 0

0 151113890 1113891

R

500 0 0

0 500 0

0 0 8000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)

O

Fyfl

Fyrr

Fyrl

Fyfr

y

xvu

b a

L

Br Bf

Fxrl

Fxrr Fxfr

Fxf l

αrl

αrr

αf l

αfr

ωr

β

δfl

δfr




Y(k)

Y(k + 1 | k)

Y(k + 2 | k)

Y(k + 3 | k)

Y(k + 4 | k)

Y(k + 5 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ΔU(k)

ΔM(k | k)

ΔM(k + 1 | k)

ΔM(k + 2 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(38)



⋮

Y(k + 5 | k) 11139445

i1CA

ix(k) + 1113944

5

i1CA

iminus 1BΔU(k)


i1CA

iminus 1BΔU(k + 4) + 1113944

3

i1CA


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(39)






min J Cfl

Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732

+ Crl




μrrFzrr( 11138572

(41)







2+ΔFxrl

2minusΔFxrr

2

(42)



F2

xij + F2yij






Tdmax

0 0lt nle 500

Te 500lt nle nN

9550Peηn

nN lt nle nmax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(44)






Tbflmax


Tbfrmax


Tbrlmax

r+

Tdmaxiτrl

r minus Fxrl


r minus Fxrl

Tbrrmax

r+

Tdmaxiτrr

r minus Fxrr


r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(46)



Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732 + Crl




μrrFzrr( 11138572


ΔFxfl cos δwfl


2+ΔFxrl

2minusΔFxrr

2 ΔM

F2

xij + F2yij


Tbflmax


Tbfrmax


Tbrlmax


Tdmaxi

r minus Fxrl

Tbrrmax


Tdmaxi

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

5 Test Verification







Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build


and result


variables

Model executionor


Signal Variable

Signal collection

Steeringwheel


Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN


Test vehicle


Motor controller













15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018









_V cos β





(30)

ωr 1Iz



Br

21113890


+Bf


+ minusBf


(31)

_β cos βmV



cos δflFxrl1113872



(32)



Yc CcX

⎧⎨

⎩ (33)




Y(k) CΔX(k) + Y(k minus 1)1113896 (34)



0e

AcτBucdτ




2Q

+ΔU(k)2R

1113944

Np

i


2Q

+ 1113944

Ncminus 1

i

ΔU(k + i | k)2R

(35)


Umin leU(k)leUmax


Ymin leY(k)leYmax

⎧⎪⎪⎨

⎪⎪⎩(36)


lowastref ]


In this research

Q 10 0

0 151113890 1113891

R

500 0 0

0 500 0

0 0 8000

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(37)

O

Fyfl

Fyrr

Fyrl

Fyfr

y

xvu

b a

L

Br Bf

Fxrl

Fxrr Fxfr

Fxf l

αrl

αrr

αf l

αfr

ωr

β

δfl

δfr




Y(k)

Y(k + 1 | k)

Y(k + 2 | k)

Y(k + 3 | k)

Y(k + 4 | k)

Y(k + 5 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ΔU(k)

ΔM(k | k)

ΔM(k + 1 | k)

ΔM(k + 2 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(38)



⋮

Y(k + 5 | k) 11139445

i1CA

ix(k) + 1113944

5

i1CA

iminus 1BΔU(k)


i1CA

iminus 1BΔU(k + 4) + 1113944

3

i1CA


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(39)






min J Cfl

Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732

+ Crl




μrrFzrr( 11138572

(41)







2+ΔFxrl

2minusΔFxrr

2

(42)



F2

xij + F2yij






Tdmax

0 0lt nle 500

Te 500lt nle nN

9550Peηn

nN lt nle nmax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(44)






Tbflmax


Tbfrmax


Tbrlmax

r+

Tdmaxiτrl

r minus Fxrl


r minus Fxrl

Tbrrmax

r+

Tdmaxiτrr

r minus Fxrr


r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(46)



Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732 + Crl




μrrFzrr( 11138572


ΔFxfl cos δwfl


2+ΔFxrl

2minusΔFxrr

2 ΔM

F2

xij + F2yij


Tbflmax


Tbfrmax


Tbrlmax


Tdmaxi

r minus Fxrl

Tbrrmax


Tdmaxi

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

5 Test Verification







Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build


and result


variables

Model executionor


Signal Variable

Signal collection

Steeringwheel


Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN


Test vehicle


Motor controller













15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018









Y(k)

Y(k + 1 | k)

Y(k + 2 | k)

Y(k + 3 | k)

Y(k + 4 | k)

Y(k + 5 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ΔU(k)

ΔM(k | k)

ΔM(k + 1 | k)

ΔM(k + 2 | k)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(38)



⋮

Y(k + 5 | k) 11139445

i1CA

ix(k) + 1113944

5

i1CA

iminus 1BΔU(k)


i1CA

iminus 1BΔU(k + 4) + 1113944

3

i1CA


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(39)






min J Cfl

Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732

+ Crl




μrrFzrr( 11138572

(41)







2+ΔFxrl

2minusΔFxrr

2

(42)



F2

xij + F2yij






Tdmax

0 0lt nle 500

Te 500lt nle nN

9550Peηn

nN lt nle nmax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(44)






Tbflmax


Tbfrmax


Tbrlmax

r+

Tdmaxiτrl

r minus Fxrl


r minus Fxrl

Tbrrmax

r+

Tdmaxiτrr

r minus Fxrr


r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(46)



Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732 + Crl




μrrFzrr( 11138572


ΔFxfl cos δwfl


2+ΔFxrl

2minusΔFxrr

2 ΔM

F2

xij + F2yij


Tbflmax


Tbfrmax


Tbrlmax


Tdmaxi

r minus Fxrl

Tbrrmax


Tdmaxi

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

5 Test Verification







Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build


and result


variables

Model executionor


Signal Variable

Signal collection

Steeringwheel


Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN


Test vehicle


Motor controller













15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018









Tdmax

0 0lt nle 500

Te 500lt nle nN

9550Peηn

nN lt nle nmax

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(44)






Tbflmax


Tbfrmax


Tbrlmax

r+

Tdmaxiτrl

r minus Fxrl


r minus Fxrl

Tbrrmax

r+

Tdmaxiτrr

r minus Fxrr


r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(46)



Fxfl + ΔFxfl1113872 11138732

μflFzfl1113872 11138732 + Cfr

Fxfr + ΔFxfr1113872 11138732

μfrFzfr1113872 11138732 + Crl




μrrFzrr( 11138572


ΔFxfl cos δwfl


2+ΔFxrl

2minusΔFxrr

2 ΔM

F2

xij + F2yij


Tbflmax


Tbfrmax


Tbrlmax


Tdmaxi

r minus Fxrl

Tbrrmax


Tdmaxi

r minus Fxrr

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(47)

5 Test Verification







Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build


and result


variables

Model executionor


Signal Variable

Signal collection

Steeringwheel


Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN


Test vehicle


Motor controller













15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018











Matlab

Model building

Modelcompilation

Simulink

Real-timeworkshop

Software setup

Modeldefinition

Signaldefinition

Variabledefinition

GUI build


and result


variables

Model executionor


Signal Variable

Signal collection

Steeringwheel


Pedalsensor

Gyroscope

Speedsensor

CAN

IO

CAN

CAN

CAN CAN

CAN


Test vehicle


Motor controller













15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018
















15m 30m 25m 25m 15m 15m

d1 d2


0 2 4 6 8 10 12 14 16ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

t (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lts




0 5 10 15ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)










0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018













0 5 10 15ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

t (s)

Side

slip

angl

e (deg)




0 2 4 6 8 10 12 14 16ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



20 40 60 80 100 120 140 160

0

2

4

6

8

10

12


Late

ral d

ispla

cem

ent (

m)











l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018









l1l2

l3

d1

h

b

d2



0100200300

Time (s)

Colle

ctio

n da

ta an

d re

cogn

ition

resu

lt




0 2 4 6 8ndash50

ndash40

ndash30

ndash20

ndash10

0

10

20

30

40

t (s)

Yaw

rate

(degs

)


With SMCReference


0 2 4 6 8

0

10

20

30

40

50

60

70

t (s)

Side

slip

ange

l (deg)


With SMCReference


0 2 4 6 8ndash6

ndash4

ndash2

0

2

4

6

t (s)

Late

ral a

ccel

erat

ion

(ms

2 )



0 20 40 60 80 100 120 140ndash5

0

5

10


Late

ral d

ispla

cem

ent (

m)


With SMCCone




6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018









6 Conclusion




Nomenclature







Data Availability




Acknowledgments


References



























































Journal of












Journal of







Volume 2018






Volume 2018

























































Journal of












Journal of







Volume 2018






Volume 2018








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