Direct yaw moment control system based on driver b

V ol.46,Supplement,2008,

911–921

Direct yaw moment control system based on driver behaviour

recognition

Pongsathorn Raksincharoensak*,Takuya Mizushima and Masao Nagai

Department of Mechanical Systems Engineering,Tokyo University of Agriculture and Technology,

Koganei-shi,Tokyo,Japan

(Received 31July 2007;final version received 6March 2008)

This paper proposes a direct yaw moment control (DYC)algorithm based on the recognition of driver steering intention.To reflect the driver steering behaviour on DYC algorithm,two types of desired yaw rates are proposed.One is for the regulation of lateral deviation as lane-keeping function and the other is for the regulation of side-slip angle as vehicle stability control.In the control algorithm,two types of desired yaw rates are switched by a weighting coefficient according to the driver steering behaviour,which is recognised with the application of the Hidden Markov Model.Finally,the effectiveness of recognition algorithm is verified and the effectiveness of the proposed DYC system on driver–vehicle system is proved by using experimental vehicle.

Keywords:active safety;vehicle dynamics;direct yaw moment control;driver-assistance system;driver behaviour

AMS Subject Classification :70E50;70Q05;93D15

Nomenclature C f front tyre equivalent cornering stiffness C r rear tyre equivalent cornering stiffness d vehicle tread I yaw moment of inertia k γd desired yaw rate gain l wheelbase l f

distance between centre of gravity and front wheel axle l r

distance between centre of gravity and rear wheel axle l s

distance from CG to camera preview point m

vehicle mass M

yaw moment control input n

overall steering gear ratio r w effective radius of tyre

*Corresponding author.Email:pong@cc.tuat.ac.jp

ISSN 0042-3114print /ISSN 1744-5159online ©2008Taylor &Francis DOI:10.1080/00423110802037156http://www.informaworld.com

D o w n l o a d e d B y : [G o r d o n , J o h n ][U n i v e r s i t y o f C a l i f o r n i a B e r k e l e y ] A t : 15:16 24 S e p t e m b e r 2008

912P .Raksincharoensak et al.

s Laplacian operator t time T mr l command driving torque of left tyre T mr r command driving torque of right tyre T st driving torque for straight running V vehicle velocity y sr preview lateral deviation observed by the CCD camera βbody side slip angle γ∗c desired yaw rate γ∗d desired yaw rate from driver behaviour δsw steering wheel angle μδl membership function of steering wheel angle μ˙δm membership function of steering wheel angular velocity τγd time constant of yaw rate response 1.Introduction This research aims to develop a vehicle dynamics control algorithm that adapts its functionality to driving tasks.Concerning vehicle lateral control,there are driving tasks such as lane keeping,lane changing,cornering,etc.To enhance vehicle active safety,it is important to secure drive safety by enhancing its driving stability as well as reducing driver’s driving workload.As our previous researches,a sophisticated driving system configuration of electric vehicle with driv-ing motors integrated in each wheel independently has potential in controlling vehicle lateral dynamics together with longitudinal dynamics.With this structural merit,vehicle dynamics control system for enhancing vehicle active safety can be effectively synthesised.As the first step of authors’works,the individual wheel torque distribution control algorithm of electric vehicle by utilising its drive-by-wire system in order to achieve direct yaw moment (abbrevi-ated as DYC)for enhancing vehicle handling and stability has been studied from theoretical analysis and experimental validation [1].This type of control system is typically useful in the case of emergency manoeuvre.The other functionality to enhance vehicle active safety is the lane-keeping assistance function as examined in the past report [2].The automatic lane-keeping control by utilising drive-by-wire system of electric vehicle was described.The effectiveness of the proposed system was verified by using computer simulation and experiments.Based on previous studies,this paper describes an integration of both functionalities to enhance active safety depending on the lateral control task of driver.In general,the driver-assistance system added to driver–vehicle system should not cause a sense of discomfort

in

Figure 1.Description of the proposed adaptive DYC system.

D o w n l o a d e d B y : [G o r d o n , J o h n ][U n i v e r s i t y o f C a l i f o r n i a B e r k e l e y ] A t : 15:16 24 S e p t e m b e r 2008

Vehicle System Dynamics 913

driving to the driver.If driver is concentrating on the lane-keeping task,direct yaw moment control (DYC)system provides yaw moment to reduce steering workload.On the other hand,if driver intends to make a severe lane changing manoeuvre,e.g.due to obstacle appearance,it is preferable to provide yaw moment to stabilise vehicle motion by regulating body side slip angle.In order to make a seamless control strategy between dual control modes –the lane-keeping control mode and the vehicle stability control mode –the vehicle yaw rate model fol-lowing control is employed to design the DYC algorithm for drive-by-wire system.The descrip-tion of the control system presented in this paper can be shown as a block diagram in Figure 1.

2.Experimental vehicle ‘NOVEL-I’The micro-scale electric vehicle named Nagai Onward Vehicle Laboratory (NOVEL)-I is used for verifying the effectiveness of DYC algorithm.The vehicle,with its weight of 400kg (including driver)and maximum speed of 50km /h,is equipped with two in-wheel-motors at rear axle.The drive system of electric vehicle is implemented so that it can distribute the driving torque in transverse direction.The vehicle-mounted CCD camera is used to recognise the lane marker and measure the preview lateral deviation,together with PC for image processing.To control each in-wheel-motor independently with drive-by-wire,the vehicle is equipped with digital signal processing (DSP)-embedded PC including measurement data from various sensors such as driver pedal operation,steering wheel angle,yaw rate,lateral acceleration,vehicle speed,etc.The vehicle sensor and actuator system are shown in Figure 2.

3.Control system design This chapter describes an algorithm of DYC which has two functionalities in vehicle dynamics control.First,the lane-keeping control objective is to regulate the lateral deviation of vehicle with respect to the given desired lane for keeping the vehicle in the centre of the lane.Most studies deal with such type of control problem by using full-state feedback control algorithm [3–5].However,DYC is practically a strategy,which uses tyre longitudinal forces to control yaw motion,so it is not suitable to use DYC for controlling lateral motion directly.

Therefore,

Figure 2.Systems on micro-scale electric vehicle NOVEL-I.

D o w n l o a d e d B y : [G o r d o n , J o h n ][U n i v e r s i t y o f C a l i f o r n i a B e r k e l e y ] A t : 15:16 24 S e p t e m b e r 2008

914P .Raksincharoensak et al.

to fulfil the task of lane-keeping assistance system,this paper proposes an alternative strategy of vehicle control by converting the lateral deviation,measured by the charge coupled device (CCD)camera,into the desired yaw rate.Moreover,to permit the driver steering intervention,this paper also considers the yaw rate which should be generated according to steering operation.Two types of desired yaw rate are integrated as a hybrid yaw rate model.Then,the required DYC input is theoretically calculated to trace the desired yaw rate.Finally,the driving torque of each in-wheel-motor is calculated to induce the command DYC input value.Based on this methodology,the control system design procedure of DYC system is divided into three parts:(1)the desired yaw rate model,(2)the yaw moment controller,and (3)the torque distribution system.3.1.Desired yaw rate model As described in the previous paper [2],the desired yaw rate for lane keeping can be calculated by the following algorithm,which is originally derived from the second-order predictive value of the lateral displacement of the vehicle.γ∗c (t)=−2V l s y sr (t)(1)where,γ∗c indicates the desired yaw rate for lane keeping,V the vehicle velocity,l s the distance from CG to camera preview point,y sr the preview lateral deviation observed by the CCD camera,and t the time.Moreover,this paper considers the yaw rate which should be generated in the driver steering operation in order to make the controlled vehicle move according to the driver’s steering behaviour.In this case,the desired yaw rate is determined as the general first-order delay system with respect to the steering wheel angle.γ∗d (s)=k γd τγd s +1δsw (s)(2)where,γ∗d indicates the desired yaw rate from driver behaviour,k γd the desired yaw rate gain,τγd the time constant of yaw rate response,δsw the steering wheel angle,and s the Laplacian operator.The desired yaw rate gain and time constant are set in order to regulate the side slip angle in steady state as follows:k γ=2C f V n

2(l f C f −l r C r )+mV 2 ,τγ=I V 2(l 2f C f +l 2r C r )where,n denotes the overall steering gear ratio.Finally,the desired yaw rate is determined as the integration of two types of desired yaw rate indicated in Equations (1)and (2).Here,the weighting coefficient w is multiplied to the desired yaw rate from the vision system γ∗c ,and the coefficient 1−w is multiplied to the desired yaw rate from the driver steering behaviour γ∗d .

γ∗(t)=w(t)·γ∗c (t)+[1−w(t)]·γ∗d (t)(3)

According to Equation (3),the yaw rate weighting coefficient is switched from 1to 0or vice versa depending on the recognised driver steering behaviour,which is assumed to be a discrete value to express the driver operation mode switching.The determination of weighting coefficient will be described in the next section.

D o w n l o a d e d B y : [G o r d o n , J o h n ][U n i v e r s i t y o f C a l i f o r n i a B e r k e l e y ] A t : 15:16 24 S e p t e m b e r 2008

Vehicle System Dynamics 915

3.2.Yaw moment controller

The yaw moment controller is designed in order to trace the desired yaw rate expressed in Equation (3).From the linear two-wheel model in planar motion with linear tyre model,the yaw moment control (DYC)input can be calculated as the following expression:

M(t)=K 1 γ∗(t)−K 2δsw (t)

(4)

where,each coefficient in Equation (4)is as follows:

K 1=2l 2C f C r (1+KV 2)(C f r )V

K 2=V nl(1+KV 2)

where,l indicates the wheelbase,C f (C r )the front (rear)cornering stiffness (per one tyre),and K the stability factor.

3.3.Driving torque distribution system To realise the DYC input as described in Equation (4)on an actual electric vehicle,the differ-ential transverse driving forces must be generated.If the longitudinal slip of tyre is negligible,the command driving torque of left (right)tyre,T mr l (T mr r )can be derived as follows:Left tyre:T mr l (t)=T st (t)−r w d M(t)(5)Right tyre:T mr r (t)=T st (t)+r w d M(t)(6)where,T st indicates the necessary torque for straight running,r w the effective radius of tyre,and d the vehicle tread.

4.Driving behaviour recognition To switch the value of the desired yaw rate in Equation (3),the value of weighting coefficient w must be determined in real time.In Equation (3),if w =1,DYC controls the vehicle in a manner of lane-keeping control function assisting human driving task.On the other

hand,if w =0,DYC ignores the information from the vision system and respects the driver steering operation by controlling the vehicle in a manner of handling control function.The weighting coefficient w is varied in real time according to the driver steering behaviour.Practically,it is difficult to identify what the driver is thinking and wants to do.This paper proposes a method to recognise the behaviour of the driver by using the information of steering wheel angle behaviour.The vehicle control system detects the driver steering operation,then recognises the driver’s present steering task,and renews the value of w in order to assist the driver appropriately.In order to recognise the driver operation task in real-time applications,recently there are a number of challenges by using probability-based methodologies [6–12].In this paper,Hidden Markov Model (HMM),which utilises the theory of probability based on the Markov process,is applied to recognise the driver behaviour [13].The state flow diagram of HMM is shown in Figure 3.

D o w n l o a d e d B y : [G o r d o n , J o h n ][U n i v e r s i t y o f C a l i f o r n i a B e r k e l e y ] A t : 15:16 24 S e p t e m b e r 2008

916P .Raksincharoensak et

al.Figure 3.State flow diagram for HMM.

The algorithm for driver steering behaviour recognition,as shown in Figure 4,will be described.First,the data pre-processing by using membership function shown in Figure 5is conducted to symbolise the data of steering wheel angle and steering wheel velocity.The digitised symbols y d (number 1to 9)are determined according to the following equation:C n (t)=μδl (t)·μ˙δm (t)(7)where,n =3(l −1)+m ;l,m =1,2,3.y d (t)=arg n max [C n (t)](8)Based on the obtained digitised symbol,the steering behaviour recognition is conducted.First,in Figure 3,there are three states of driving behaviour,S 1:lane keeping,S 2:stand-by,

and Figure 4.Description of steering behaviour

recognition.

Figure 5.Membership functions for symbolising steering behaviour.D o w n l o a d e d B y : [G o r d o n , J o h n ][U n i v e r s i t y o f C a l i f o r n i a B e r k e l e y ] A t : 15:16 24 S e p t e m b e r 2008

S 3:lane changing.Each state has its probability of occurrence according to the sequence of digitised symbols y d ,also called visible state,and the transitional probabilities a ij and the probability of the emission b ij of a visible state.

First,the probability of each state is expressed as the following matrix.

P t |t = P 1t |t P 2t |t P 3t |t T (9)

where,the summation of probabilities of all states must be 1,and the superscript refers to the index number of state.The probability of each state can be calculated from the following expressions:P t |t −1[3×1]=A T [3×3]P t −1|t −1[3×1](10)P t |t [3×1]=B d (y d (t))[3×3]P t |t −1[3×1]d (y d (t))[3×3]P t |t −1[3×1](11)A [3×3]={a ij }i,j =1,2,3(12)B [3×9]={b in }i =1,2,3n =1,2,3,...,9(13)B d (y d (t))[3×3]=diag {b in }n =y d (t)(14)where,the probability matrices A and B are determined from learning procedure of HMM by using Baum–Welch’s algorithm.This paper used the experimental data of single lane changing manoeuvre to determine the parameters of HMM.From the probability matrix obtained from Equation (11),the maximum probability in matrix means the maximum likelihood of the state at a specific time,so the mathematical expression for steering behaviour recognition can be written as the following if–then rules.if arg i max P t |t =1then w(t)=1(15)if arg i max P t |t =2then w(t)=w(t −1)(16)if arg i max P t |t =3then w(t)=0

(17)Figure 6.Recognition result by HMM during lane keeping and lane changing.

D o w n l o a d e d B y : [G o r d o n , J o h n ][U n i v e r s i t y o f C a l i f o r n i a B e r k e l e y ] A t : 15:16 24 S e p t e m b e r 2008

Figure 6shows an example of recognition result of lateral control task during single lane changing manoeuvre by using the micro-scale electric vehicle NOVEL-I at vehicle speed of 30km /h with lane change width of 2.0m and length of 10.0m.

5.Experimental results

This section describes experimental investigations on the effectiveness of the proposed adaptive DYC algorithm,mentioned in Sections 3and 4.Here,the course is set as the

single Figure 7.Single lane change course for experimental

validation.

Figure 8.Vehicle behaviour in the case of lane-keeping DYC control (without yaw rate switching).D o w n l o a d e d B y : [G o r d o n , J o h n ][U n i v e r s i t y o f C a l i f o r n i a B e r k e l e y ] A t : 15:16 24 S e p t e m b e r 2008

lane change at width of 2.0m during longitudinal distance of 10.0m as shown in Figure 7.The vehicle speed is 35km /h.Figures 8and 9show the experimental results by a driver in the case without switching the desired yaw rate and the case of the proposed control algorithm,respectively.From the value of weighting coefficient w ,it was confirmed that DYC switched its desired yaw rate from the camera information to the driver steering manoeuvre at the beginning of lane changing.In the case of lane keeping (w =1),the desired yaw rate is proportional to the lateral deviation information from the camera,while in the case of lane changing (w =0),the desired yaw rate is proportional to the driver steering wheel angle.The body side slip angle (here,the estimated value with linear model based observer)was suppressed during lane changing so the vehicle stability was effectively secured by DYC.In this case,the actual yaw rate traced the desired value well which means that the yaw moment controller was effective.In addition,as shown in Figure 10,when comparing the steering wheel angular velocity,it was found that switching yaw rate control with the proposed control effectively reduced the steering wheel angular velocity at the beginning of the lane changing,since there was no yaw moment control input that opposed with the driver steering behaviour.In the case of lane-keeping control,yaw moment tried to bring the vehicle back to the centre of the lane which deteriorated the

ease

Figure 9.Vehicle behaviour in the case of the proposed DYC control (with steering behaviour recognition).D o w n l o a d e d B y : [G o r d o n , J o h n ][U n i v e r s i t y o f C a l i f o r n i a B e r k e l e y ] A t : 15:16 24 S e p t e m b e r 2008

Figure 10.Effect of yaw rate switching on steering wheel

velocity.Figure 11.Effect of yaw rate switching on side slip angle.of driver steering intervention like lane changing manoeuvre.Finally,the Lissajous diagram between steering wheel angle and side slip angle is shown in Figure 11.The Lissajous diagram is drawn to evaluate the stability of vehicle during lane change manoeuvre by the effect of DYC system for side slip angle regulation.When compared with the case of lane-keeping control system without yaw rate switching,it was found that the steering wheel angle and the side slip angle were significantly reduced by the proposed adaptive DYC.This fact shows that the vehicle handling and stability can be effectively enhanced during lane changing manoeuvre by switching DYC mode into the stability control mode.

6.Conclusions

This paper examined the effectiveness of the new control algorithm of DYC by switching the desired yaw rate according to the driver’s driving task in real time,e.g.lane keeping and lane changing,in order to realise the cooperative driving characteristics between the driver and DYC system.This paper employs the hybrid yaw rate control system approach in order to combine the information from camera and driver steering information together.From the experimental studies using actual driving tests by the micro-scale electric vehicle,it was found that the system has capability in reducing steering physical workload and enhancing vehicle stability.The experimental studies proved that comfortable driving and safe driving can be achieved by using the proposed vehicle control system.

D o w n l o a d e d B y : [G o r d o n , J o h n ][U n i v e r s i t y o f C a l i f o r n i a B e r k e l e y ] A t : 15:16 24 S e p t e m b e r 2008

This research was conducted as a part of the Core Research for Evolutional Science and Technology(CREST)research programs entitled‘Mobility Sensing for Safety and Security’,funded by Japan Science and TechnologyAgency(JST). The authors would like to deeply thank this body for theirfinancial support in executing this research. References

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