Estimation of the Maximum Lateral Tire-Road Friction Coefficient Using the 6-DoF Sensor

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1 015 15th International Conerence on Control, Atomation and Systems (ICCAS 015) Oct , 015 in BEXCO, Bsan, Korea Estimation o the Maimm Lateral Tire-Road Friction Coeicient Using the 6-DoF Sensor Kyong Seok Han 1, Enjae Lee and Seibm Choi 3* 1, School o Mechanical Aerospace & Systems Engineering, Division o Mechanical Engineering, KAIST, Daejeon,Korea (Tel: ; hks8804@kaist.ac.kr, asphaltgy@kaist.ac.kr) 3 School o Mechanical Aerospace & Systems Engineering, Division o Mechanical Engineering, KAIST, Daejeon,Korea (Tel: ; sbchoi@kaist.ac.kr) Abstract: Estimated peak tire-road riction coeicient can be implemented on varios vehicle active saety control systems. Bt, it is not easy to get the actal data rom the road case o cost, eqipment installation, maintenance and technical isses. The demands or real-time estimation o peak riction coeicient have been increased de to the above mentioned technical shortcomings. This paper provides the lateral tire-road riction coeicient estimation method sing a simpliied Dgo tire model nder the pre side slip condition. The rearranged Dgo model respect to lateral riction coeicient consists o lateral tire orce, normal tire orce, wheel side slip angle and cornering stiness. Thereore, aorementioned parameters are also identiied based on vehicle model or it is assmed to be constant vales in the proposed algorithm. The perormance o developed algorithm is veriied by Carsim and Matlab/Simlink. The simlation reslts encorage possible development o the proposed method in this paper. Keywords: tire-road riction coeicient, Dgo tire model, pre side slip. 1. INTRODUCTION The tire-road riction coeicient estimation is promising research area in atomotive indstry de to the increasing demands or vehicle saety system. There have been varios estimation approaches rom pblished stdies. Those developed identiication methods can be divided into two scheme according to vehicle motion. First scheme only considers vehicle longitdinal motion [1, ] so their application area is restricted to longitdinal saety control system like Antilock Braking System (ABS). The remainder incldes lateral dynamics in their estimation strategies [3, 4] bt it contains intentional driver s brake or steering inpt or strategic prposes. In the real world, however, sch a periodic driver inpts cannot be observed easily. Instead, sdden change o steering inpt is oten occrred or varios reasons. This paper mainly deals with those driving sitations: ramp steering, step steering (no braking). The longitdinal tire orce or individal wheels can be assmed to be negligible in the above mentioned driving conditions. Becase longitdinal tire orce and tire slip are inter-related bt there is no slip when vehicle drives on the constant speed. By this way, we can concentrate on lateral tire-road riction coeicient assming a tiny longitdinal riction coeicient. There has been similar estimation approach previosly in [5]. Domiati et al also neglected longitdinal orce in their tire model bt ltimate goal o this paper is estimation o lateral tire orce, not road riction coeicient. Thereore, this paper assmed that riction coeicient on the proving grond is known vale in their eperimental veriication. Jorge Villagra et al [6] took a similar estimation strategy sing a Dgo tire model [7]. However, algorithm veriication was done in the vehicle longitdinal motion nder the pre slip condition. In this paper, simpliied Dgo tire model is sed nder the pre side slip condition. The maimm tire-road riction coeicient depends on vehicle lateral orce and normal orce in aorementioned sitation. Thereore accrate lateral/normal tire orce estimation is also reqired. The 6-DoF inertial measrements are sed to estimate lateral/normal tire orce. The real-time lateral tire-road riction can be calclated ater tire orce estimation. Finally, the maimm tire-road riction coeicient, ltimate goal o this paper, is predicted based on real-time lateral riction coeicient. The estimated lateral riction coeicient can be sed in vehicle lateral saety control system like Electronic Stability Control (ESC). This paper is organied as ollows. The simpliied tire model is eplained to develop the proposed identiier in Section. All sorts o parameters which are needed in this paper are estimated in Section 3. Simlation Reslts are shown in Section 4 sing a Carsim and Matlab/Simlink. This paper is conclded in Section 5.. TIRE MODEL AND PARAMETER ADAPTATION CONCEPT There are several tire model to relect highly nonlinear phenomenon when vehicle generates tire orce according to related parameters sch as slip angle and slip ratio. A typical model rom Pacejka, Magic Formla [8], gives a lly accrate reslts based on nmeros eperiments. However, this model has a lot o nknown parameter to be determined and its parameters are diiclt to identiy on real-time level. The Dgo

2 tire-model is chosen in this paper becase o its ncomplicated strctre compared to Magic ormla. A complete epression or Dgo model is as ollows. σ F = Cσ ( λ) (1) 1+ σ Fy = Cα tan( α) ( λ) () where: ( λλ ), λ< 1 ( λ) = 1, λ > 1 μmaf( 1+ σ) λ = C σ + C tan( α) ( σ ) ( α ) where C σ is the longitdinal stiness, C α the cornering stiness, σ the longitdinal slip ratio and α the wheel side slip angle. The above tire model is developed based on integrated longitdinal and lateral tire model. However, in this paper, longitdinal tire orce is assmed to be negligible. The simpliied Dgo tire model can be derived as ollows nder the pre side slip condition. Fy = Cα tan( α) ( λ) (3) where: ( λλ ), λ< 1 ( λ) = 1, λ > 1 μma, yf λ = tan( α) C α The lateral tire orce has a linear property on low wheel side slip angle region and it is satrated at the behind o speciic side slip as shown in Fig. 1. Nonlinear region on Fig. 1 has to be investigated becase peak vale is placed on these region, not linear region. Considering these aspects, (3) can be rearranged respective to lateral tire-road riction coeicient as ollows. ma, yf ma, yf F = y C μ μ α tan( α) ( ) Cα tan( α) Cα tan( α) (4) The maimm tire-road riction coeicient then can be written as below. Cα tan( α) ± Cα tan( α) ( Cα tan( α) Fy ) μma, y = (5) F Fig. 1 Lateral tire orce verss wheel side slip angle (5) has always positive soltion becase Cα tan( α) Fy is always semi-positive. In the aorementioned derived eqation (5), lateral tire-road riction coeicient is dependent vale with regard to lateral tire orce, normal tire orce, cornering stiness and wheel side slip angle. Thereore, those parameter estimation has to be preceded. 3. PARAMETER ESTIMATION 3.1 Normal tire orce estimation The proposed individal normal tire orce estimation method incldes additional dynamic sspension eect and it incorporates all the vehicle s motion abot 6-DoF. The estimated normal orces are made o static weight, longitdinal load transer, lateral load transer and sspension dynamic eect. The whole mass o vehicle is divided into or part as shown in Fig. and all the component in (6) ecept static weight have dierent sign according to their mass position. ( ms + m ) cgh F,ij = ( ms,ij + m,ij ) g± ( l + lr) staticweight (6) sspensiondynamiceect longitdinalload transer ( + ) lw ms m ycgh ± ms cg ± l θ ± φ ± m ± l w where wheel (i,j), i {F.R}, j {L,R}, lateralload transer F is the vertical tire orce at the individal,ij m s and m are sprng mass and n-sprng mass o qarter car model, h the height o the mass center, g the gravity acceleration constant, θ and φ are pitch and roll acceleration at the center o gravity, cg the normal acceleration, y the lateral acceleration, cg the longitdinal cg acceleration at the center o gravity and l and l r are distances rom mass center to ront and rear wheels, l the track width. w Fig. Qarter car model. All the normal tire orce or qarter car model can be estimated with the above method ( F,,, FFL R F RL). In this method, road distrbance sch as bmp and pothole can be considered sing sspension dynamics.

3 3. Lateral tire orce estimation The lateral tire orce or bicycle model can be written in terms o ront and rear lateral orce as (7), (8). Those relationship can be derived rom Newton s second law o motion and procedre o derivation is well docmented in [9]. ml ray + I r Fy = (7) l + lr ml ay I r Fyr = (8) l + lr Where F and y, F are the lateral tire orces o the y,r ront and rear wheels, a y the lateral acceleration, r the yaw acceleration and I the yaw inertia. In this conventional way, the sm o each side hand lateral tire orce can be calclated bt the individal lateral tire orce or each side hand also is needed to be determined. The estimated lateral orce can be distribted into both side according to their estimated normal tire orce. However, it has a deect to apply directly in atomotive indstry de to their inaccracy. In the tre, distribtion o those lmped lateral orce is main residal task to implement the sggested algorithm in this paper. 3.3 Wheel side slip angle estimation In [3], wheel side slip angle can be estimated rom ollowing eqations in the ront drive vehicle. Vy + lr l r V β + V αfl δfl Vy + lr δ F l β + r (9) α δ V 1 δ F 1 V = tan = tan α RL δ RL Vy lrr 0 l r β r αrr δrr V 0 V Vy lrr l r β r V V where δ is the steering angle o wheel, β the vehicle side slip angle and r the yaw rate. β cannot be directly measred in the prodction car so it is reqired to be identiied as ollowing method. Generally, bicycle dynamic model can be presented in terms o yaw rate and side slip angle [10] (Fig. 3). = A + B y= C (10) where : β =, = δ r ( C + Cr) ( Crlr Cl ) 1 a11 a1 mv mv A = a 1 a = ( Cl r r Cl) ( Cl + Cl r r ) I Iv C b1 mv B=, C [ 0 1] b = = Cl I where C, Cr are the cornering stiness or rear/ront wheel. Fig. 3 Bicycle model or vehicle lateral dynamics. In this paper, we assmed that inertia component and cornering stiness are constant known vale. The vehicle absolte velocity is almost same with wheel speed becase o pre side slip condition. The yaw rate can be measred real-time in the prodction car. Finally, the Lenberger observer can be constrcted as ollows. = A+ B + L( y C) (11) In act, estimation o vehicle side slip is also major isse in vehicle research area. All the relevant vales, however, in (11) ecept or β are assmed to be known or measrable, and then the strctre o dynamic eqation has a sitable ormat to apply Lenberger observer. 4. SIMULATION RESULTS The perormance o the proposed algorithm was veriied by simlation sing Carsim and MATLAB/Simlink. The target vehicle is an A-class model which is stored in Carsim and vehicle trns at 10sec with mild wheel steering angle inpt (ramp inpt : 0 to 30 degree dring 5 seconds). Fig. 4 shows that normal orce estimation reslts or ront wheel. The estimated vales well track the measred vales rom Carsim. The signiicant lateral load transer occrs at the 10 sec. (a) Normal orce or ront let

4 however, rther stdy shold be condcted to improve possibility o implementation. (b) Normal orce or ront right Fig. 4 Normal orce estimation reslts. The estimation reslts rom (7), (8) can be identiied in Fig. 5. The sm o each side hand lateral orces is well estimated rom bicycle model. However, distribted lateral tire orces according to their estimated normal orce have minor error as shown in Fig. 6. As mentioned beore, those estimation strategy shold modiied in the tre or better perormance regarding to each side hand lateral tire orce. (a) Front let lateral tire orce (ll model) (b) Front right lateral tire orce (ll model) Fig. 6 Distribted lateral tire orce or each side hand. (a) Front lateral orce estimation (bicycle model) (b) Rear lateral orce estimation (bicycle model) Fig. 5 Lateral tire orce estimation sing bicycle model. I severe wheel steering inpt is eerted to vehicle, the estimation reslts o distribted lateral tire orce might be more degraded. On the other hand, the lmped lateral orce identiication rom bicycle model is almost same vale with actal orces in any sitation. In this simlation stdy, we assmed that mild steering inpt is eerted on vehicle so the estimated reslts can be sed to be applied to Dgo model. As mentioned beore, The maimm tire-road riction estimation reslt rom (5) is plotted in Fig. 7. Ater obtaining tire orce inormation, lateral riction coeicient is identiied nder the pre side slip condition. The vehicle side slip angle starts to increase when the steering inpt is eerted arond 10sec. The maimm riction coeicient can be determined rom Dgo tire model and it can be identiied more qickly than measred vale rom ratio o normal orce and lateral ( μ y = Fy / F ) orce. The measred vale cannot reach the maimm lateral tire-road riction coeicient de to insicient wheel side slip angle. The peak riction coeicient can be observed at the speciic wheel side slip angle as shown in Fig. 1. The steering inpt is not lly to reach peak vale in this simlation environment. On the other hand, estimated vale can identiy real vale becase o tire-model strctre. The qick tire-road riction identiication than conventional method (measred vale) is demonstrated in this simlation stdy, whose ltimate goal o this paper. In act, tire-road riction coeicient estimation reslt has a meaningl vale beore tire-orce satration. The real-time riction coeicient can be identiied easily throgh conventional method bt the peak vale identiication in the low wheel side slip angle region is more important in the view o vehicle lateral control. Those task was realied in this paper sing Dgo tire model.

5 ACKNOWLEDGEMENT This research was spported by the MSIP(Ministry o Science, ICT and Ftre Planning), Korea, nder the C-ITRC (Convergence Inormation Technology Research Center) (IITP-015-H ) spervised by the IITP(Institte or Inormation & commnications Technology Promotion) and This work was spported by the National Research Fondation o Korea(NRF) grant nded by the Korea government( ) Fig. 7 Tire-road riction coeicient estimation on medim m ( μ =0.5) In order to veriy the robstness o the proposed algorithm, simlation stdies are contined on the low m road srace (0.3) as shown in Fig. 8. All the simlation environment is identical to Fig. 7 ecept or riction coeicient. The reslt shows similar tendency with the reslt on the medim m (0.5). The estimated vale can reach the real maimm riction coeicient, bt measred vale cannot identiy the m. ma Fig. 8 Tire-road riction coeicient estimation on medim m ( μ =0.3) ma 5. CONCLUSION This paper presents maimm tire-road riction coeicient estimation method sing 6DoF sensor measrements. The main advantage o the proposed algorithm is that maimm riction coeicient can be identiied qickly than conventional method. The lateral tire orce distribtion stdy shold be done in the tre or algorithm robstness. In the simlation stdies, the homogenos road srace is only considered de to an imperect knowledge o split lateral tire orce. The distribtion o the lmped lateral tire orce wasn t attained in this paper. The algorithm veriication was not condcted in the split m. The estimated vale, however, match well in the homogenos road srace. REFERENCES [1] R. Rajamani, "Friction estimation on highway vehicles sing longitdinal measrements," 004. [] K. Yi, K. Hedrick, and S.-C. Lee, "Estimation o tire-road riction sing observer based identiiers," Vehicle System Dynamics, vol. 31, pp , [3] M. Choi, J. J. Oh, and S. B. Choi, "Linearied Recrsive Least Sqares Methods or Real-Time Identiication o Tire Road Friction Coeicient," Vehiclar Technology, IEEE Transactions on, vol. 6, pp , 013. [4] J.-O. Hahn, R. Rajamani, and L. Aleander, "GPS-based real-time identiication o tire-road riction coeicient," Control Systems Technology, IEEE Transactions on, vol. 10, pp , 00. [5] M. Domiati, A. C. Victorino, A. Charara, and D. Lechner, "Onboard real-time estimation o vehicle lateral tire road orces and sideslip angle," Mechatronics, IEEE/ASME Transactions on, vol. 16, pp , 011. [6] J. Villagra, B. d Andréa-Novel, M. Fliess, and H. Monier, "A diagnosis-based approach or tire road orces and maimm riction estimation," Control engineering practice, vol. 19, pp , 011. [7] H. Dgo, P. Fancher, and L. Segel, "An analysis o tire traction properties and their inlence on vehicle dynamic perormance," SAE Technical Paper1970. [8] H. Pacejka, Tire and vehicle dynamics: Elsevier, 005. [9] R. Rajamani, Vehicle dynamics and control: Springer Science & Bsiness Media, 011. [10] J. Oh, S. Choi, and D. Kim, "Distrbance observer design based on linearied vehicle model or neqal tractive/braking orce identiication," in Control, Atomation and Systems (ICCAS), 01 1th International Conerence on, 01, pp