Adaptive Scheme for Real-Time Estimation of the Tire-Road Friction Coefficient and Vehicle Velocity

Transcription

1 Adaptive Scheme or Real-Time Estimation o the Tire-Road Friction Coeicient and Vehicle Velocity Kyoungseok Han, Eunjae Lee, Mooryong Choi and Seibum B. Choi Abstract It is well known that both the tire-road riction coeicient and the absolute vehicle velocity are crucial actors or vehicle saety control systems. Thereore, numerous eorts have been made to resolve these problems, but none have presented satisactory results in all cases. In this paper, cost-eective observers are designed based on an adaptive scheme and a recursive least squares algorithm without the addition o extra sensors on a production vehicle or modiication o the vehicle control system. This paper has three major contributions. First, the ront biased braking characteristics o production vehicles such that the ront wheel brake torques are saturated irst are exploited when estimating the tire-road riction coeicient. Second, the vehicle absolute speed is identiied during the riction coeicient estimation process. Third, unlike the conventional method, this paper proposes using already available excitation signals in production vehicles. In order to veriy the perormance o the proposed observers, experiments based on real production vehicles are conducted, and the results reveal that the proposed algorithm can enhance the perormance o any vehicle dynamics control systems. Index Terms adaptive law; braking characteristics; tire-road riction coeicient; vehicle absolute speed; tire stiness; excitation signal. M I. INTRODUCTION OST drivers rarely experience dangerous situations such as wheels locking up or un-steerable conditions during general driving. For this reason, the importance o vehicle saety control systems has become increased only ater This work was supported by a National Research Foundation o Korea (NRF) grant unded by the Korean government (MSIP) (No ) unded by the Ministry o Science, ICT and Future Planning (MISP), Korea, under the Inormation Technology Research Center (ITRC) support program (IITP-2016-H ) supervised by the Institute or Inormation & Communications Technology Promotion (IITP), and the BK21 + program. Kyounseok Han is with KAIST, Daejoen, Korea (tel: ; ax: ; mail:hks8804@kaist.ac.kr) Eunjae Lee is with Hankook Tire, Daejoen, Korea (tel: ; ax: ; mail:asphaltguy@hankooktire.com) Mooryong Choi is with Hyundai Motors Group, Uiwang-si, Gyeonggi-do Korea (tel: ; mail: mucho@hyundai.com) Seibum Choi is with KAIST, Daejoen, Korea (tel: ; ax: ; sbchoi@kaist.ac.kr) Corresponding Author avoiding such situations with an aid o active chassis control systems. Consequently, the mandatory installation o saety control systems or newly released vehicles is becoming more common in automotive companies and institutes. According to a technical report on chassis control [1], rule-based control algorithms are predominantly used to manage the numerous practical concerns. Because unpredictable situations occur requently in the real world, and these cannot be described using prevailing theory, the use o a rule-based algorithm that considers as much data as possible is inevitable to provide appropriate saety margins or production vehicles. However, these algorithms typically impose very severe computational burdens on the vehicle s electronic control units (ECU) because the control systems should be designed to consider all possible driving conditions. For this reason, numerous attempts have been made to resolve this problem. For example, the state eedback control or the active control system [2-5] can simpliy the algorithm complexity where tire-road riction coeicient is well known as the most important state enabling the prediction o a vehicle s behavior. However, the tire-road riction coeicient varies signiicantly or dierent road suraces and cannot be easily obtained in real-time or numerous reasons. Some notable conventional saety control systems include antilock brake system (ABS) [6, 7] and electronic stability control (ESC) [2]. Both systems have areas o commonality, i.e. they need to adjust the individual tire orce in order to achieve the desired vehicle motion. I the maximum tire-road riction coeicient is accurately estimated in real-time using the data given in a production vehicle, novel saety control laws can be designed that resolve the above problems. Such a necessity or the accurate state estimation has increased the importance o studies on peak riction coeicient estimation and numerous published studies have proposed various approaches. Within these approaches, one widely chosen or estimating the riction coeicient is the tire stiness-based method originally proposed in [8] with more recent developments being presented in [9-12]. Another approach is the dynamic-based method [13], which oten requires additional sensor inormation such as global positioning system (GPS) inormation or speciic motor signals associated with steering [14-16] and driving [17]. In these methods, lateral dynamics are usually considered in order to excite the estimators, but the longitudinal dynamics are

2 excluded rom the algorithms. In [18-21], both longitudinal and lateral dynamics are considered in order to deal with the combined slip condition. Although signiicant developments have been made in tire-road riction coeicient estimation in recent decades, the proposed algorithms are yet to be used in production vehicles or numerous reasons. One o the challenges is that several o the proposed methods require extensive maneuvering o the vehicle such as severe accelerating, decelerating, and steering. That is, speciic vehicle motions are required to excite the estimation algorithm beore the goal is achieved. In order to resolve this problem, this paper proposes an early detection algorithm o the riction coeicient using only the signal when the vehicle is decelerating mildly. Furthermore, as in the previous studies, the tire model is used to represent the riction coeicient as a state. For example, the most well-known tire model or vehicle dynamics, i.e. the Fiala brush tire model [22], can express the tire orce using the normal orce, tire slip, cornering stiness, and tire-road riction coeicient. A challenge in this model is that additional estimations should be conducted in order to obtain the ultimate state like riction coeicient or tire orce. That is, the normal orce, individual tire slip, and cornering stiness should be identiied accurately in order to represent the tire orce. I the aorementioned additional estimations have inerior results, they can also deteriorate the estimation perormance o the inal state. This issue is the reason why the previous methods assume that these states are measurable or have known values. In order to increase the easibility o the proposed algorithm being implemented in production vehicles, these practical concerns are considered and a solution to this problem is proposed in this paper. In addition, the individual tire slip is the most diicult to obtain since the absolute vehicle velocity is required to represent the tire slip, but it cannot be obtained easily while braking. In act, the vehicle velocity at a constant speed or while accelerating has almost the same value as the un-driven wheel speed, which is a readily available signal in production vehicles. Thereore, the vehicle velocity can be replaced with the un-driven wheel speed in those conditions. However, it is not the case during the braking. For this reason, an accurate vehicle velocity estimation method while braking is also proposed in this paper, based on the tire-road riction coeicient estimation results. This paper uses some assumptions rom previous works, particularly in [8, 9]. In those works, the peak tire-road riction coeicient is assumed to be represented by the tire stiness, and they concentrated on estimating the tire stiness in real-time. In this paper, the proposed algorithm also identiies the tire stiness using an adaptive scheme, but the braking characteristics o the production vehicle are used to improve the estimation perormance. The main dierences that clearly distinguish this paper rom the previous methods is summarized as ollows. First, the estimation steps are reduced using the vehicle s braking characteristics. According to the literature review presented in next section, all previous dynamic-based estimation approaches require an additional estimation step to identiy the tire slip because the algorithms in the previous works exploit the conventional tire model, e.g. Fiala brush tire model [22], Dugo model [23], Lugre riction model [24] or magic ormula [25]. Unlike the previous works, this paper eliminates the tire slip identiication step rom the overall structure, thereby reducing the likelihood o perormance degradation associated with the tire slip estimation. In order to prevent oversteering, most production brake systems are designed to be ront biased such that the ront wheel brake torques are saturated irst. Thereore, ront wheel slips tend to be larger than the rear ones during the braking. Using these characteristics, it is possible to take an advanced approach to removing the tire slip estimation step. In addition, a novel vehicle velocity observer is constructed using only the wheel speeds and longitudinal acceleration. The inverse tire model is used in this process to estimate the tire slip, which contains the vehicle velocity, and the recursive least square method is adopted to obtain the tire slip. This scheme diers rom the existing methods, where the longitudinal dynamics model including many uncertainties, such as mass, road slope, and other related orces, is used to obtain the vehicle speed [26]. The most widely adopted method to obtain the vehicle velocity is the use o an additional sensor such as GPS or an estimation scheme [11]. However, accurate estimation o the vehicle velocity is diicult or many reasons. Lastly, the proposed algorithm is veriied in a real production vehicle in order to manage practical concerns. The experimental results reveal that early identiication o the tire-road riction limit is possible with ewer estimation steps than the conventional works. The remainder o this paper is organized as ollows. In Section 2, the existing approaches are reviewed briely in order to dierentiate this study rom previous works. The detailed description o the proposed algorithm is presented in Section 3. Experiments with a production vehicle on various road surace conditions demonstrate the perormance o the proposed observers in Section 4. Finally, conclusions are presented in Section 5. II. LITERATURE REVIEW Several authors have assumed that tire stiness, which is proportional to its slip ratio in the low slip region, has dierentiable values according to the road surace conditions. Thereore, they have insisted that a well-estimated tire stiness can be used to calculate the tire-road riction coeicient. These approaches have been adopted in [8-12] and this paper is also motivated rom the tire stiness-based approaches. Diering to the works in [8-12], this paper establishes a new observation strategy using the vehicle s braking characteristics. In this section, an important aspect o the published results [8-12] is briely reviewed and the limitations o its perormance are discussed. The tire stiness-based approaches use the ollowing common ramework as depicted in ig. 1, where the ultimate goal is to obtain the tire stiness in real-time. The critical issue o the previous architecture is that additional tire orce and tire slip estimations should be perormed in order to

3 Figure 1. Tire stiness-based tire-road riction coeicient estimation ramework achieve the goal. I satisactory additional estimation results are not guaranteed, the tire stiness estimation result is also signiicantly aected by the estimation results. It is generally believed that the tire orce can be predicted relatively easily when the vehicle is traveling in a straight line. However, none o the tire slip estimations are accurate during braking, although there have been many eorts to estimate it. For this reason, the algorithm to estimate the tire orces proposed in this paper is very similar to the previous algorithms, but a novel tire slip estimation algorithm is introduced with the objective o being implemented on a production vehicle without the addition o extra sensors. The relationship between the normalized tire orce and the tire slip is ormulated using equation (1): Fˆ x nor Cx, (1) Fˆ where μ nor is the normalized tire orce, F x and F z are the estimated longitudinal tire orce and normal orce, respectively, C x is the tire stiness, and λ is the tire slip. The ultimate goal o the tire stiness-based approach is to estimate C x (estimated parameter) in real-time based on λ (input regression, an estimated or measured value) and μ nor (measured output, an estimated value). The recursive least squares method [27] has been widely adopted to identiy tire stiness in real-time. Details o the background principles are described comprehensively in [9, 11]. The tire slip during braking can be written as ollows: V rw, (2) V V rwr r, (3) V where λ and λ r are the ront and rear tire slip, respectively, V is the absolute vehicle speed, r the eective radius o wheel and w and w r are the ront and rear wheel speed, respectively. The only unknown value in equations (2) and, (3) is the absolute vehicle speed because production vehicles equipped with ABS provide accurate wheel speed inormation in real-time, i the vehicle travels aster than 10km/h. Also, the eective radius o the wheel is assumed to be known. The absolute vehicle speed can be calculated out o GPS signal [28, 29]. However, inluenced by the noise o wheel speed and GPS measurements, the calculated slip ratio oscillates signiicantly z as described in the next sub-section. In addition, the eective radius o wheel, which is assumed to be constant, can luctuate signiicantly by many actors such as tire pressure and type o road surace. Consequently, inaccuracy in the eective radius o wheel also aects the estimation perormance. Furthermore, GPS-based measurements is not quite dependable in some environments such as urban and orested regions. As a resolution or this issue, an estimation scheme or vehicle speed has been proposed in [11, 26, 30, 31] using longitudinal dynamics as ollows: mvˆ F F F ( R R ) mg sin, (4) x aero x xr x xr aerodynamicorce longitudinal tireorce rolling resistance roadinclination Note that many uncertainties that are included in equation (4) inluence the longitudinal dynamics. For example, vehicle mass, which changes according to the number o passengers or amount o luggage, should be estimated as in [32]. Moreover, the road inclination inormation is not available without an additional estimation scheme as in [33]. The details o the vehicle speed observer well described in [11]. In summary, longitudinal dynamic-based vehicle speed estimation approaches require additional estimation steps, which can aect the inal estimation result. In consideration o the practical issues, a more simpliied estimation approach or vehicle speed is required. A. Braking Characteristics III. ALGORITHM DESCRIPTIONS The wheel dynamics can be described by the ollowing equation: J R F T T R F, (5) e x d b e rr where J ω is wheel rotational inertia, ω ω is the wheel angular velocity, R e is the wheel eective radius, F x is the tire longitudinal orce, F rr is the rolling resistance, and T d and T b are drive torque and brake torque, respectively. The brake torque can be written with the ollowing design parameters or the ront and rear wheels: T k P A r P, (6) b, mc pad mc T k P A r P, (7) b, r r mc pad r r mc where T b, and T b,r are brake torques o ront and rear wheel respectively, k and k r are the brake gains, P mc is the master cylinder pressure, μ pad is the pad riction coeicient, A and A r

4 are brake piston eective areas, and r and r r are the brake disc eective radii. In general, the brake gain at the ront wheel is conigured to be much larger than the rear one or saety reasons. The tire orce has highly nonlinear characteristics including the riction ellipse eect and tire orce saturation [22]. I the longitudinal slip goes beyond the stable area, the vehicle cannot be steered due to the coupled eect between the longitudinal orce and lateral orce. Especially, the tire orce saturation at the rear wheel usually causes oversteering, which is the most critical condition to be prevented, due to the loss o lateral orce. Considering these concerns, it should be remembered that the rear wheels are managed to stay in the stable region as much as possible even when the ront wheels move into an unstable region. In order to veriy the aorementioned braking characteristics, the simulation using CarSim, which is a widely adopted vehicle dynamics solver, was conducted as depicted in ig. 2(a). The target vehicle decelerated on a high mu road surace and the individual longitudinal tire orce versus slip ratio plot could be obtained. The plot illustrated the slip dierence that existed between the rear wheels and ront wheels. The rear tire slip remained in the stable region when the ront tire slip reached an unstable region, where ABS was activated. In order to extend these aspects to a real vehicle, experiments were also conducted. Fig 2(b) depicts the slip ratio or a medium sized car tested on a dry asphalt surace with dierent levels o deceleration. The slip dierence between rear wheels and ront wheels was quite distinguished when a greater level o brake orce was commanded by the driver. It should be note that the goal o this study is detecting the peak riction coeicient o a road surace beore the riction orce is saturated and ABS is activated. Thus, consistency o the objective can be maintained. That is, the vehicle speed and tire-road riction coeicient observations or the unstable region are excluded rom the scope o this study that is depicted in right bottom plot in ig. 2(b). B. Proposed Algorithm Architecture In this sub-section, overall architecture o the proposed algorithm is introduced, and the improvement o its unctionality is briely discussed. Figure 2. Braking characteristics. (a) Individual longitudinal tire orce versus slip ratio in CarSim. (b) Individual slip ratios with dierent decelerations in real vehicle. Most tire-road riction coeicient estimation algorithms are designed based on the tire stiness estimation, which is depicted on ig. 1. The most recent study on tire stiness-based tire-road riction coeicient estimation [11] exhibited satisactory perormance. However, the method requires an additional GPS sensor or vehicle velocity observer in order to estimate the tire stiness, and its limitation was discussed in Section 2. Fig. 3 describes the overall architecture o the proposed algorithm. The primary dierence compared with ig. 1 is that the tire stiness can be estimated using only the estimated tire orces and measured wheel speeds. Figure 3. Overall architecture o the proposed algorithm.

5 Moreover, the tire slip is obtained using the inverse tire model. The tire orce estimation scheme itsel is not signiicantly dierent rom previous works. In this way, the estimation scheme can be made to be ree rom the eect o the error associated with the vehicle speed estimation. Detailed descriptions o the algorithm are provided in the ollowing sub-sections. C. Tire Force Estimation Several estimation schemes or the individual tire orces have been introduced in previous studies [34, 35]. In this paper, a tire orce observer that does not require a signiicant computational burden is developed using both vehicle longitudinal dynamics and wheel dynamics. It is generally assumed that an individual wheel speed can be measured at all times. Thereore, the longitudinal orce can be estimated based on the wheel dynamics in equation (5) or individual wheels. F J T T d b x, (8) Re The rolling resistance, which is relatively small compared with the other terms, is neglected. Furthermore, the drive torque is assumed to be zero because only the braking condition is considered in this paper. As seen rom ig. 3, the tire normal orces are also needed to ormulate the normalized orce in equation (1), where the deceleration can cause the weight shiting rom the rear to the ront while braking. Considering dynamic weight siting due to the vehicle deceleration, ront and rear wheel normal loads are calculated as ollows, F F z zr mglr mxh, (9) l l mgl l r mxh, (10) l where x is the longitudinal acceleration, g is the gravitational constant, l and l r are the distances rom the center o gravity to the ront and rear axles, h is the height o the center o gravity, and m is the vehicle weight. D. Tire-Road Friction Coeicient Estimation Note that the tire-road riction coeicient should be estimated early enough within the stable area o the mu-slip curve since the goal o the estimation is to obtain the surace condition beore ABS is engaged. In this way, ABS can be tuned ully utilizing the estimated value, and signiicant reduction o the stopping distance is expected. For this reason, the wheel slip at the saturated region o the mu-slip curve is not considered. It is generally accepted that the relationship between the normalized tire orce and tire slip in a stable area exhibits a linear shape regardless o the type o road surace as depicted in ig. 4. Thereore, a simple linear tire model is used in stable regions in this paper. r Figure 4. Mu-slip curve o the linear tire model. One distinction in this paper is that the slip dierence between the ront and rear wheel is used to identiy the tire stiness and such dierential braking pattern was conirmed by simulations and experiments in Section 3.A. Using equations (2) and (3), the vehicle speed can be expressed as ollows: rw rwr V, (11) 1 1 Next, equation (11) is divided into measurable and unknown parts, as ollows: 1 r wr 1 (during braking), (12) 1 w It must be noted that this paper uses η as an excitation signal or estimating the tire stiness while others use λ and λ r in [8-12]. The reason or changing the excitation signal is that the tire slip is inluenced by the wheel speed measurement noise greatly as well as the vehicle speed estimation which is not accurate enough during braking. However, the new excitation signal, η is calculated using only the directly measured individual wheel speeds. Manipulating equation (12) leads to the ollowing:, (13) ( 1)(1 ). r Using the deinition o a slope in a coordinate system, the tire stiness, C x can be expressed as ollows: C x r r r r r. (14) Substituting equation (13) into equation (14), 1 r Cx. (15) 11 Manipulating equation (15) using λ =μ /C x, then tire stiness can be express as ollows, r C x (16) 1 Since the measurements o η is not noise ree, the adaptive scheme [36] is used to estimate C x. To ormulate standard adaptation orm, (16) is divided into two parts: y ( 1) C, (17) r x

6 where η is the excitation signal, μ and μ r were obtained rom the tire orce estimations, and y is the output that can be measured or estimated. Considering the ollowing:, (18) y * u() t where θ =C x and u(t)= η-1. Based on this, the adaptation law can be established using the gradient method, as ollows: ˆ * u() t, (19) where γ is a positive adaptation gain and ε=y-y. For stability analysis, the Lyapunov unction is chosen as ollows: 2 V ( ) 2. (20) Dierentiating above equation (20) with respect to time leas to ( y) ˆ ( ˆ* ut ( )) V ( ). (21) I adaptive law such as (19) is selected, then the time derivative o the Lyapunov unction is always negative semi-deinite, as ollows: (( u( t)) u( t)) 2 2 V ( ) u ( t) 0. (22) Thereore, by applying Barbalat s lemma [37], it can be proved that the error, ε converges to zero. E. Tire Slip Observer Once the tire stiness inormation is obtained, the tire slip can be recursively estimated as described in ig. 3. Based on the inverse linear tire model in equation (23) motivated by equation (1), the recursive least squares (RLS) algorithm can be ormulated as described in (24) and (25). Cˆ, (23) ˆnor Here, μ nor is obtained using the tire orce estimation and C x is estimated using the adaptive scheme deined in equation (21). Thereore, the only unknown parameter is the tire slip in equation (23). Now, a standard RLS algorithm can be applied to the system described as equation (23) as ollows: where ˆ ˆ ˆ Fx () t ( ) ( 1) ( ) ˆ t t K t ( t 1) Cx ( t) Fˆ, (24) z () t P( t 1) C ( t) Kt () k P t t x 2 ( 1)C x( ) P ( t 1)C x ( t) P( t) P( t 1) 2 k k P( t 1)C x( t) x. (25) Here, K(t) is an updated gain vector and P(t) indicates an error covariance matrix, which should be minimized. k is a orgetting actor that is used to reduce the inluence o old data. Figure 5. Comparison o a general road surace and an undistinguishable road surace. It may be argued that the basic principle o tire stiness-based approaches becomes invalid or undistinguishable road suraces as depicted in ig. 5. The road suraces a and b exhibit a same linear shape beore they reach the tire orce saturation. However, they have signiicantly dierent peak riction coeicients. Thereore, this type o unresolved problem still remains as a challenge while dealing with various types o road surace. Nevertheless, many published works [8-12] adopted tire stiness-based approaches due to its intuitiveness. This paper also cannot present a clear solution to this problem. However, the tire slip estimation result is still valid with respect to any type o road surace because undistinguishable road suraces also maintain a linear shape in a stable region, as depicted in ig. 5. Thereore, it can be concluded that cost-eective estimations o the tire slip and tire-road riction coeicients can be realized. The advantage o the proposed algorithm is its ability to identiy the tire-road riction coeicient estimation with better perormance than the conventional tire stiness-based approaches. Furthermore, the tire slip can be estimated even i the vehicle is traveling on an undistinguishable surace such as b in ig. 5. A. Experimental Setup IV. EXPERIMENTAL STUDY Using a real production vehicle without any modiication o the control system, experiments were conducted in order to veriy the perormance o the developed algorithms. The data was collected at 200 Hz sampling requency via CanBus. For veriication, RT-3100 model, which is a high-accuracy vehicle dynamic testing tool, was used to measure the actual vehicle state. The only signals used or the proposed observers were longitudinal acceleration, which is the aordable signal in production vehicles, and wheel speeds. Test scenarios were conducted on various road surace conditions but road inclination was not considered. Note again that the objective o the proposed algorithm is to improve the

7 perormance o the tire stiness-based approach while reducing the number o necessary sensor signals at the same time. B. Experimental Results The ocus o this study is on the estimation o the tire stiness and tire slip in the low slip region. Hence, i the proposed observers can provide satisactory results with a small excitation signal, it is most desirable. Experiments with various decelerations were conducted in order to veriy the robustness o the developed algorithms. The irst test was perormed on dry asphalt with mild deceleration to veriy the responsiveness o the adaptive algorithms even or the very minimum excitation signal input. Fig. 6(a) and 6(b) describe vehicle speed trajectory and its deceleration. Fig. 6(c) illustrates the normalized tire orces or the ront and rear wheel calculated rom the estimated longitudinal orce and normal orce. As expected, the normalized orce at the ront wheel is signiicantly larger than the rear one and it can also be seen in ig. 6(), where the ront slip ratio measured using RT-3100 and wheel speed sensor was approximately 0.02 but the rear slip ratio was less than Fig. 6(d) presents the excitation signal used or the adaptations. In order to emphasize the virtue o using an adaptive scheme without a GPS signal or additional vehicle speed estimation, the proposed algorithm is compared with the results o a conventional tire stiness-based observer. The same levels o low pass iltering and rate limiting to smooth the estimated results were applied to maintain the airness. The conventional method uses the individual tire slip ratio as an excitation signal, but it is largely inluenced by the noise eect as depicted in ig. 6(). In contrast, the proposed excitation signal described in ig. 6(d) is more robust against the noise eect since it can exclude vehicle speed term in its calculation process. Accordingly, the estimated tire stiness converged to the true value, which is approximately 20, with much less oscillation as depicted in ig. 6(e). However, the conventional method based on the measured GPS signal oscillated due to its measurement noise. Especially, the conventional method responded excessively to the measurement noise when the wheel slip is existing only marginally. In contrast, the adaptive scheme-based observer did not react to such level o slip. Next, Fig. 6() describes the estimated tire slip ratio at ront and rear wheels. Because the tire slip includes an unknown vehicle speed term in equations (2) and (3), the results also mean the vehicle absolute speed estimation when braking is applied. During braking, estimation o absolute vehicle speed is very diicult since brake pressure is always applied to all wheels. However, ig. 6(e) and () indicate that the developed adaptive scheme and RLS algorithm can estimate tire stiness and wheel slip accurately. Figure 6. Experiment results on a dry asphalt obtained by using proposed adaptive scheme with mild intensity o the brake orce.

8 Figure 7. Experiment results on a dry asphalt obtained by using proposed adaptive scheme with medium intensity o the brake orce. Figure 8. Experiment results on a dry asphalt obtained by using proposed adaptive scheme with high intensity o the brake orce.

9 Figure 9. Experiment results on a basalt road surace obtained by using proposed adaptive scheme with mild intensity o the brake orce. Figure 10. Experiment results on a wet tile road surace obtained by using proposed adaptive scheme with mild intensity o the brake orce.

10 Accordingly, the absolute vehicle speed can be well constructed out o those signals. The estimation results presented in ig. 7 exhibit a similar pattern to that in ig. 6. In this case, medium intensity brake orce was applied and the proposed method simultaneously estimated the tire stiness and the tire slip. Since the tests were conducted on the same road surace using same tires, the estimated tire stiness in ig. 7(e) had the same value as that in ig. 6(e). The estimated value, i.e. approximately 20, represents the high μ road surace, which corresponds well to the proving ground road condition. The tire slip dierence between ront and rear wheel in ig. 7() is larger than that in ig. 6() due to the increased brake orce rom mild to medium intensity. However, the estimated value maintained its true value well enough as shown in ig. 7(e). Next, the experiment or the high intensity brake orce was perormed as depicted in ig. 8. It can be seen that the tire slip ratios at the ront let wheel and ront right wheel had a slightly dierent values as presented in ig. 8(). The reason or this phenomenon was not clearly identiied, but it was suspected that surace was not quite homogeneous and also the wheel slips have reached nonlinear regions in this case. However, it should be noted that the estimated tire slip or the ront wheel is the average value o the individual ront wheel slip as plotted in ig. 8(). In addition, it is apparent that the estimated tire stiness in ig. 8(e) was identical to that in ig. 6 (e) and 7(e) as expected since this test was also conducted on the same conditions. In ig. 9, the test vehicle was driven on a road surace covered with wet basalt that provided a riction with μ 0.4. The vehicle decelerated mildly as described in ig. 9(b), and its deceleration was nearly the same as ig. 6(b). It implied that the sum o tire orces in this test was similar to that o the irst test scenario in ig. 6. However, it was observed in ig. 9() that the tire slip ratios were much larger than those o ig. 6(), because a larger slip ratio was required to provide suicient amount o riction brake orce in low μ surace. As expected, the estimated tire stiness in ig. 9(e), i.e. approximately 11, was lower than that o dry asphalt. Moreover, the result is robust against noise eect when compared with the value rom conventional method. This was the basis o the proposed method and well supported by this test. Using an estimated tire stiness, luctuation o the estimated tire slips was much less than that o measured tire slips rom RT As seen rom ig. 9(e), the calculated tire slip ratios rom equations (2) and (3) were signiicantly aected by the measurements noise eect. Because wheel speed was measured based on a toothed metal ring with a predetermined number o teeth, accurate measure o wheel speed was quite diicult in low speed. Thereore, the proposed estimator is promising tool in this case. As described in ig. 10, the vehicle was maneuvered into a wet surace which provided a very low riction with μ 0.3. Fig. 10(e) depicted that the estimated tire stiness o wet tile surace was approximately 6. Based on this, the tire-road riction coeicient o this surace could be inerred. Similar to previous test, relatively large tire slip ratios were observed in ig. 10() to provide suicient amount o riction brake orce. The measured tire slip ratios luctuated signiicantly due to the noise eect. However, the estimated tire slip ratios did not luctuate that much since the proposed method was much ree rom the noise eect. V. CONCLUSIONS This paper proposed a novel estimation algorithm or both tire road riction coeicient and vehicle velocity based on an adaptive scheme, which aimed to provide meaningul inormation to a brake controller. The proposed algorithm distinguishes itsel rom the previous tire stiness-based approaches by using the dierential characteristics o production brake systems. Main contributions o this works are summarized as ollows. The proposed algorithm can estimate the tire stiness, which is related to the riction coeicient, without modiication o the control system or the addition o sensors. It proposes using a new excitation signal which is robust against measurement noise eects. It estimates vehicle absolute velocity rom the estimated tire stiness without extra sensors. Through various experiments using a production vehicle, the perormance o the designed observers was tested and it revealed that cost-eective tire-road riction coeicient and vehicle velocity observations are possible. The estimation perormance was compared with that o conventional tire stiness-based approaches, and it can be concluded that the proposed work can be a promising tool with ewer required signals. With the application o the proposed work in any vehicle dynamics control system, improved vehicle control perormance is anticipated. REFERENCES [1] A. T. Van Zanten, R. Erhardt, G. 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