A novel cost effective method for vehicle tire-road friction coefficient estimation

Transcription

1 Univerity of Wollongong Reearch Online Faculty of Engineering and Information Science - Paper: Part A Faculty of Engineering and Information Science 23 A novel cot effective method for vehicle tire-road friction coefficient etimation Boyuan Li Univerity of Wollongong, bl995@uowmail.edu.au Haiping Du Univerity of Wollongong, hdu@uow.edu.au Weihua Li Univerity of Wollongong, weihuali@uow.edu.au Publication Detail B. Li, H. Du & W. Li, "A novel cot effective method for vehicle tire-road friction coefficient etimation," in 23 IEEE/ASME International Conference on Advanced Intelligent Mechatronic (AIM, 23, pp Reearch Online i the open acce intitutional repoitory for the Univerity of Wollongong. For further information contact the UOW Library: reearch-pub@uow.edu.au

2 A novel cot effective method for vehicle tire-road friction coefficient etimation Abtract he tire-road friction coefficient i critical to vehicle longitudinal, lateral and roll dynamic and control becaue tire i the only contact part between the vehicle body and the road. However, direct meaurement of tire-road friction coefficient i impoible in practice. hi paper preent a novel cot effective method for vehicle tire-road friction coefficient etimation. hi method only need the meaurement of the wheel angular velocity, the traction/brae torque and the longitudinal acceleration, which are all available from the commonly intalled enor in ordinary paenger vehicle, and can be ued to etimate the individual tireroad friction coefficient. here are three tep in the propoed method. Firtly, the longitudinal lip ratio i etimated by uing a nonlinear filter with the meaured wheel angular velocity. hen the tire longitudinal force i etimated by uing a Kalman filter with the meaured traction/brae torque and longitudinal acceleration. At lat, the friction coefficient i etimated by uing the recurive leat quare (RLS method and the reult obtained from the firt two tep. Numerical imulation are provided to validate the effectivene of the propoed method. It i hown by the imulation reult that the propoed method i effective in etimating the tire-road friction coefficient. Keyword coefficient, friction, vehicle, method, road, etimation, effective, cot, tire, novel Dicipline Engineering Science and echnology Studie Publication Detail B. Li, H. Du & W. Li, "A novel cot effective method for vehicle tire-road friction coefficient etimation," in 23 IEEE/ASME International Conference on Advanced Intelligent Mechatronic (AIM, 23, pp hi conference paper i available at Reearch Online:

3 A Novel Cot Effective Method for Vehicle ire-road Friction Coefficient Etimation B. Li, H. Du, and W. Li Abtract he tire-road friction coefficient i critical to vehicle longitudinal, lateral and roll dynamic and control becaue tire i the only contact part between the vehicle body and the road. However, direct meaurement of tire-road friction coefficient i impoible in practice. hi paper preent a novel cot effective method for vehicle tire-road friction coefficient etimation. hi method only need the meaurement of the wheel angular velocity, the traction/brae torque and the longitudinal acceleration, which are all available from the commonly intalled enor in ordinary paenger vehicle, and can be ued to etimate the individual tire-road friction coefficient. here are three tep in the propoed method. Firtly, the longitudinal lip ratio i etimated by uing a nonlinear filter with the meaured wheel angular velocity. hen the tire longitudinal force i etimated by uing a Kalman filter with the meaured traction/brae torque and longitudinal acceleration. At lat, the friction coefficient i etimated by uing the recurive leat quare (RLS method and the reult obtained from the firt two tep. Numerical imulation are provided to validate the effectivene of the propoed method. It i hown by the imulation reult that the propoed method i effective in etimating the tire-road friction coefficient. Key word tire-road friction, friction coefficient etimation, velocity etimation, tire force etimation I. INRODUCION Becaue the tire i the only contact part between the vehicle body and the road, the tire-road friction coefficient i critical to vehicle longitudinal, lateral and roll dynamic and control. For example, for the electronic tability control (ESC ytem, the yaw rate will be controlled to prevent idding. If the friction coefficient can be etimated, the yaw rate feedbac with the nowledge of friction coefficient can be ent bac to the controller to control the yaw rate adaptively []-[3]. For the four-wheel-driving (4WD vehicle, the etimation of individual tire friction coefficient can help to detect which wheel need the maximum drive torque [4]. In the adaptive cruie control and colliionavoidance ytem, the etimated friction coefficient can help to adjut the braing ditance in real time [5]. And for road maintenance in winter, the etimation of friction coefficient B. Li i with the School of Electrical, Computer and elecommunication Engineering, Univerity of Wollongong, Wollongong, NSW 2522, Autralia ( bl995@ uowmail.edu.au. H. Du i with the School of Electrical, Computer and elecommunication Engineering, Univerity of Wollongong, Wollongong, NSW 2522, Autralia ( hdu@uow.edu.au. W. Li i with the School of Mechanical, Material and Mechatronic Engineering, Univerity of Wollongong, Wollongong, NSW 2522, Autralia ( Weihuali@uow.edu.au. can be ued to adjut the de-icing material on the icy road [6]. Many reearche have been done on the etimation of tire-road friction coefficient in recent year. Some of them only focu on the vehicle longitudinal motion with vehicle traction or braing operation, and ome of them alo conider the vehicle lateral motion. hree main method have been propoed o far. hey are lip lop method, extended Kalman filter (EKF method, and individual wheel friction etimation method. he lip lope method i a longitudinal friction coefficient etimation method and a lot of paper have tudied on thi method. Gutafon [7] developed a lip lope friction etimation ytem in the traction condition. Müller and Uchani [8] propoed the lip lope friction etimation in the brae ituation. Wang, Alexander and Rajamani [9] developed the lip lope etimation method for the front wheel, rear wheel and four wheel traction/brae ytem under linear and nonlinear tire region. he EKF method i baed on both the longitudinal and lateral dynamic. hi etimation method include two part: the tate etimation part, which i done by the EKF, and the friction identification part. Ray [] developed the EKF method baed on a 8 degree of freedom (DOF vehicle dynamic model. Dahlallah et al. [] propoed an EKF etimation method baed on a impler vehicle dynamic model, which only conider vehicle longitudinal dynamic, lateral dynamic and yaw dynamic. he individual wheel friction etimation method [2] i alo a vehicle longitudinal dynamic baed method. here are three tep in thi etimation method: ( etimate the longitudinal tire force; (2 etimate the tire longitudinal lip ratio; and (3 calculate the friction coefficient by uing the recurive leat quare (RLS method. milar to the lip lope method, the friction coefficient i calculated by the RLS method when the longitudinal lip ratio and longitudinal tire force are etimated. he lip lope method need the global poitioning ytem (GPS to meaure the vehicle abolute velocity and the anti-loc braing ytem (ABS to meaure the wheel angular velocity. he longitudinal tire force can be etimated by the accelerometer, which i not accurate enough. he individual tire force etimation method doe not need GPS to meaure the abolute vehicle velocity and can etimate the friction coefficient of each tire. However, the etimation reult are not accurate and the etimation gain need to be

4 adjuted. he EKF method in the literature need to meaure the tire force, which i quite hard to meaure and i not cot effective. In thi paper, a more reliable and cot effective friction etimation method will be developed. hi etimator can etimate the friction coefficient individually and i cot effective in term of the required meaurement. he paper i organied a follow. Section 2 preent the baic modeling of the vehicle. Section 3 decribe the novel cot effective friction etimation method. Section 4 provide the actual imulation reult to validate the effectivene of the propoed method. Concluion will be given in Section 5. where µ i the friction coefficient. F z, Fi, Fti are the vertical load, the ide tire force and the tractive tire force, where i=f, r denote front and rear, repectively. C i i the longitudinal cornering tiffne and C i the lateral α cornering tiffne. S i i the longitudinal lip ratio and αi i the lateral lip angle. u i i the vehicle velocity component in wheel plane and ε r i the contant value. he integrated vehicle dynamic model and tire model will be ued to imulate the actual vehicle motion and validate the propoed method. II. VEHICLE MODELING A. Vehicle Dynamic Model In thi tudy, the vehicle dynamic model conider the longitudinal dynamic, the lateral dynamic, the yaw dynamic, and the wheel rotation dynamic. he motion of equation are decribed a m v x v m y r = I f r ( F coδ f + Fyf inδ f + F + vyr ( Fyf coδ f F inδ f + Fyr v ( L f ( Fyf coδ ff inδ f Lr Fyr ( F R + I I where,,,, x y f r ( F R + f r ( v v r are longitudinal velocity, lateral velocity, yaw rate, front wheel angular velocity and rear wheel angular velocity, repectively. F, F, Fyf, F yr are the front and rear longitudinal and lateral force. δ,, repreent the front teer angle f f r and the applied front and rear traction/brae torque, repectively. B. he ire Model he Dugoff tire model i ued in thi reearch, which i preented by the following equation: µ F 2 2 zi ε rui + tan α i ( λ = Ci + Cα tan αi λ( 2 λ if λ < f ( λ = if λ > (2 Cα tanαi Fi = f ( λ CS i i Fti = f ( λ S i III. HE NOVEL COS EFFECIVE IRE-ROAD FRICION COEFFICIEN ESIMAION MEHOD A novel cot effective tire-road friction coefficient etimation method i propoed here. hi method only need to meaure the wheel angular velocity (meaured by the ABS ytem, the traction/brae torque and the longitudinal acceleration. In the pat year, the meaurement of traction torque relie on the engine torque meaurement and the meaurement of brae torque depend on brae preure enor, which i too expenive to be implemented [9]. However, recently the information of engine torque and brae torque can be obtained from CAN bu of the vehicle [2]. he longitudinal acceleration can be meaured by the longitudinal accelerometer. he vehicle abolute velocity can be etimated by the nonlinear filter without uing the expenive GPS. here are mainly three tep in thi friction etimator: ( the etimation of the longitudinal lip ratio, which need to meaure the wheel angular velocity; (2 the etimation of the tire longitudinal force, which need to meaure the traction/brae torque and longitudinal acceleration; and (3 the etimation of friction coefficient according to the reult of the firt two tep. Figure how the bloc diagram of the whole procedure. he wheel angular velocity he traction/ brae torque he vehicle longitudinal acceleration Vehicle abolute velocity (Nonlinear filter Equation (4 ire longitudinal lip Equation (3 he Extended Kalman Filter Equation (7 ire longitudinal force RLS etimation method Equation ( Slip lope + Friction coefficient Figure. he bloc diagram of the whole friction etimation procedure

5 A. he Etimation of the Vehicle Longitudinal Slip Ratio he vehicle longitudinal lip ratio can be calculated by the following equation: R Vx = (3 max( V, R where i the wheel angular velocity, which can be eaily meaured. R i the effective turn radiu. he vehicle abolute velocity can be etimated by the following nonlinear filter [3]. he mathematical equation of thi nonlinear filter i: y ( = Rg Sat( y( x( (4 y( t = = y where y( i the etimated vehicle abolute velocity. x( i the vehicle wheel angular velocity multiplied by wheel radiu. ' R g ' denote the change of vehicle velocity (acceleration, which ha the following relationhip with traction/brae torque: R g = f, r ( he aturation function Sat(x i defined a:, x> d (6 Sat( x =, x <d x / d, ele where d i a mall number lie.. hi velocity etimation method ue the input traction/brae torque to etimate the velocity, which doe not need to integrate the meaurement value of the acceleration. he meaurement value of acceleration ha noie and the integration of the value will induce even larger noie, which i not accurate for the etimation of the velocity. he accuracy of the etimated vehicle abolute velocity i important to the etimation reult of vehicle longitudinal lip. herefore, the imple controller i ued to adjut the etimation reult of the velocity according to the meaured acceleration, which i hown in Figure R g Nonlinear filter (equation 4 K + x Integration Etimated acceleration Error Etimated velocity B. he Etimation of the Vehicle Longitudinal Force In thi method, the vehicle tire force will be etimated intead of uing expenive enor to meaure. he vehicle acceleration and the wheel angular velocity can be utilied a the meaurement information to update the error gain and improve the etimation reult. herefore, thi etimation method i cot effective and reliable. In addition, thi etimator can etimate the front and rear tire force individually. he etimator i written in the dicrete time a: ax ( + = ( F ( + F ( m ( + = ( F ( R + ( af I ar ( + = I F ( + = CS f ( F ( + = CSr ( ( F ( R + ( where a f, ar repreent the derivative of the wheel angular velocity of front and rear wheel. Equation (7 i further written in the following form a: x+ = f ( x, u, w z = h( x, v (8 + where x i the tate vector, u i the input vector and z i the meaurement value. w i the proceing noie and v i the meaurement noie. x ( ( ( ( ( = ax af ar F F u ( ( ( ( = [ ] f r f z = ax ( After chooing the initial value for r f r x and P (7, the Extended Kalman Filter (EKF recurive algorithm can be achieved (ee Figure 3 [4]. he left column i the time update proce and the tate vector can be updated by equation (7 in dicrete time. he right column i the meaurement update proce, which mean that the tate vector alo need to be updated according to the error between the meaured value and etimation value. - Meaured acceleration Figure 2. he control bloc diagram of the abolute velocity etimator

6 (State etimation x ˆ+ = f ( xˆ, u, (2State error covariance etimate P = A P A + W QW + Figure 3. he woring proce of Extended Kalman Filter A i the Jacobian matrix of partial derivative of f ( x, u, w with repect to x m m R I A = R I H i the Jacobian matrix of partial derivative of h x, v with repect to x ( H = m m C. Etimation of Friction Coefficient he lip lope i determined by the longitudinal tire force F x, vertical tire force F z and longitudinal lip ratio x. F x = xx Fz F x ime update = = F ( F + F zf + F = zr Initial input x and P (Compute the Kalman Gain K = + P H H P H V RV F zf + [ ] (2Update etimate with meaurement xˆ = xˆ + K z h( xˆ According to the etimated tire longitudinal force and lip ratio, the lip lope can be etimated by the RLS method. he RLS method can be decribed by the following equation according to equation (9: F [,] (3Update the error covariance P [ I K H ] P = Meaurement update zr (9 y( = ϕ ( θ ( + e( ( where θ ( i the etimated parameter, which i lip lope in thi reearch. y ( i the total longitudinal tire force and e( i the error. ϕ ( i the regreion vector, which i F + F. zf zr he RLS algorithm ha the procedure a following at each time tep [2]: Step : Get the meaurement value of the ytem output y( and determine the regreion vector ϕ (. Step 2: According to the difference between ytem actual output at thi time tep and the ytem output predicted in the previou time tep, determine the error e( : e( = y( ϕ ( θ ( t ( Step 3: he update gain vector K( can be calculated a: t ϕ( K( = (2 λ + ϕ ( t ϕ( And the covariance matrix P ( can be calculated by:. t ϕ( ϕ ( t = t λ λ + ϕ ( t ϕ( (3 Step 4: Update the etimated parameter θ ( t = θ ( t + K( e( (4 λ i called the forgetting factor, which i between (.9, When the lip lope i etimated, baed on the experimental data in the imulation, the tire-road friction coefficient can be etimated by the following equation: µ =. +.2 (5 IV. SIMULAION RESULS o validate the effectivene of the propoed method, two different et of imulation are conducted. In the firt et of imulation, the vehicle i accelerating. In the econd et of imulation, the vehicle i accelerating and then braing. he parameter value ued in the imulation are given in able. m ABLE I. SIMULAION PARAMEERS g L f m L r.454 m C 5 N/unit lip I z 627 gm 2 R w.35 m

7 I 2. gm 2 µ.9 ε r.5 /m C α 3 N/unit lip K (control gain in figure 2 A. he Firt Set of mulation In thi imulation, the traction torque i applied at the beginning a the following figure. he input traction torque i hown in Figure 2. he friction coefficient i et a.9 in the vehicle dynamic model. Input traction torque (N.m Vehicle velocity (m/ Figure 4. he vehicle input traction torque Figure 5. Compare the etimated vehicle abolute velocity with the actual value. Figure 5 compare the actual vehicle velocity with the etimated vehicle velocity, which prove that the nonlinear filter in equation (4 can uccefully etimate the vehicle abolute velocity. imilar to the hape of the engine torque in Figure 4. hi prove that the force etimation reult of the EKF i accurate. Figure 7 compare the actual friction coefficient and the etimated friction coefficient, which how that the etimation reult i acceptable becaue the etimated value i cloing to the actual value. From 6, the traction torque i applied on the vehicle and conequently the friction coefficient etimator can uccefully find the value after 6. Friction coefficient Figure 7. he etimated friction coefficient. B. he Second Set of mulation In thi imulation, the traction torque i applied at firt. hen the brae torque i applied at 2 a hown in Figure 8. he friction coefficient i et a.9 in the vehicle dynamic model. Input traction and brae torque (N.m Figure 8. he vehicle input traction and brae torque. 4 Front wheel longitudinal tire force (N Figure 6. he etimated front tire longitudinal force. Figure 6 how the tire force etimation reult of the applied EKF. he hape of the force curve in figure 6 i Vehicle velocity (m/ Figure 9. he vehicle velocity. Figure 9 compare the actual vehicle velocity with the etimated vehicle velocity, which prove that the nonlinear filter in equation (4 can alo uccefully etimate the vehicle abolute velocity in thi cae.

8 Figure how the tire force etimation reult of the EKF. he hape of the force curve in figure i imilar to the hape of the engine torque in Figure 8. hi prove that the etimation reult of the EKF i accurate. Front wheel longitudinal tire force (N Figure. he etimated front tire longitudinal force. Friction coefficient Figure. he etimated friction coefficient. Figure compare the actual friction coefficient and the etimated friction coefficient, which how that the etimation reult i alo acceptable. However, from 2, the vehicle i changing from the traction into brae and the etimated friction coefficient i decreaing, but the etimation reult i till acceptable. Friction coefficient Figure 2. he etimated friction coefficient under random noie input. In Figure 2, the random noie between (-.5,.5 i applied on the meaurement ignal of longitudinal acceleration and the etimated friction coefficient i till acceptable, which verify the robutne of propoed etimator. V. CONCLUSION he lip lope method can only etimate the vehicle average friction coefficient. he individual tire force etimation method can etimate the friction coefficient of each tire but i not reliable. he EKF method in the literature need to meaure the tire force, which need expenive enor. In thi paper, a novel cot effective tire-road friction coefficient etimation method i propoed here. hi method only need to meaure the wheel angular velocity, the traction/brae torque and the longitudinal acceleration, which are all eay to be meaured uing available enor intalled in paenger vehicle. he vehicle abolute velocity can be etimated by the nonlinear filter without uing the expenive GPS. In addition, the individual tire-road friction coefficient can be etimated by thi method. mulation example are ued to validate the effective of the propoed method. In the future, the real experiment will be conducted to verify the propoed etimator. REFERENCES [] H. E. eng, D. Madau, B. Ahrafi,. Brown, and D. Recer, echnical challenge in the development of vehicle tability control ytem, in Proc. IEEE Int.Conf.Control Application, HI, Aug.999, pp w.-k. Chen, Linear Networ and Sytem (Boo tyle. Belmont, CA: Wadworth, 993, pp [2] A.. van Zanten, Boch ESP ytem: 5 year of experience, in Proc. SAE Automotive Dynamic and Stability Conf., roy. MI, May 2, Paper No [3] A. Nihio, K. ozu, H. Yamaguchi, K. Aano, and Y. Amano, Development of vehicle tability control ytem baed on vehicle idelip angle etimation, SAE Paper, No [4] L. Autin and D. Morrey, Recent advance in antiloc braing ytem and traction control ytem, Proc.Int.Mech.Eng.D, vol.24, no.6, pp , 2. [5] K. Yi and J. aeyoung, Oberver baed etimation of tire-road friction for colliion warning algorithm adaptation, JSME Int.J.Serie C. vol.4, no., pp.6-24, Mar.998. [6] G. Erdogan, L.Alexander, and R.Rajamani, Friction coefficient meaurement ytem for autonomou winter road maintenance, Vehicle Sytem Dynamic, vol.47, no.4, pp , 29. [7] F. Gutaffon, 997, Slip-Baed ire-road Friction Etimation, Automatica, vol.33, no.6, pp [8] S. Müller, M. Uchani, and H. Karl, Slip-Baed ire-road Friction Etimation During Braing, Proceeding of 2 ASME International Mechanical Engineering Congre and Expoition, New Yor, pp [9] J. Wang, L. Alexander, and R. Rajamani, Friction etimation on high-way vehicle uing longitudinal meaurement, ASME J. Dyn. Syt.,Mea. Control, vol.26, no.2, pp , 24. [] L. R. Ray, Nonlinear tire force etimation and road friction identification: mulation and experiment, Automatica, vol.33, pp , 997. [] J. Dahlallah, S. Glaer, S. Mammar, and Y. Sebadji, ire-road Force Etimation Uing Extended Kalman Filter and de lip Angle Evaluation, 28 American Control Conference, USA, 28. [2] R. Rajamani, G. Phanomchoeng, D. Piyabongarn, and J. Y. Lew, Algorithm for Real-ime Etimation of Individual Wheel ire-road Friction Coefficient, IEEE/ASME ranaction on Mechatronic, vol.7, no.6, 22. [3] F. Jiang, and Z. Gao, An Adaptive Nonlinear Filter Approach to the Vehicle Velocity Etimation for ABS, Proceeding of the 2 IEEE International Conference on Control Application, USA, 2. [4] G. Welch, and G. Bihop, An Introduction to the Kalman Filter, September 7, 997.