Embedded Estimation of the Tire/Road Forces and Validation in a Laboratory Vehicle

20080490 AVEC '08 - 090 Embedded estimation of the tire/road forces and validation in a laboratory vehicle Moustapha DOUMIATI*(Corresponding author), Guillaume BAFFET*, Daniel LECHNER**, Alessandro VICTORINO*, Ali CHARARA*, * HEUDIASYC, UMR 6599 CNRS-UTC ** INRETS-MA Laboratory Centre de recherches de Royallieu, 60200 Compiègne, France Phone: 33 (0)3 44 23 44 23 Fax: 33 (0)3 44 23 44 77 E-mail: mdoumiat@hds.utc.fr, guillaume.baffet@emn.fr, acorreav@hds.utc.fr, acharara@hds.utc.fr Chemin de la Croix Blanche 13300 Salon de Provence, France Phone: 33 (0)4 90 56 86 14 Fax: 33 (0)4 90 56 25 51 E-mail: daniel.lechner@inrets.fr This paper proposes a new estimation process for tire-road forces and sideslip angle. This method uses measurements from currently available standard sensors (suspension sensors, yaw rate, longitudinal/lateral accelerations, steering angle and angular wheel velocities). This estimation process is separated into three principal blocks: the role of the first block is to estimate vertical tire forces, the second block contains an observer whose principal role is to calculate tire-road forces without a descriptive force model, while in the third block an observer estimates the sideslip angle and the cornering stiffness with an adaptive tire-force model. These different observers are based on Kalman Filter. The estimation process was applied and compared to real experimental data, notably sideslip angle and wheel force measurements acquired using the INRETS-MA Laboratory car. Experimental results show the accuracy and potential of this approach which enables practical realization of a low cost solution for tire-road contact forces and sideslip angle calculation. Topics / Vehicle Dynamics and Vehicle Control, Active Safety and Passive Safety developed approach has proved robustness in critical driving situations. Another specificity of this study is that the estimation process is separated into three cascaded blocks (see figure 1). In the first block, proposed observers take into account roll dynamics and coupling longitudinal and lateral acceleration, for the wheel vertical forces estimation. In the second block, an observer based on four-wheel vehicle model, in which forces are modeled without tire-road parameters was developed in order to estimate wheel lateral forces. One advantage of this formulation is that the estimations will not be influenced by tire-road parameters. Consequently estimations will be robust with respect to the road friction changes. In the third block, this study proposes an observer developed from a sideslip angle model and a linear adaptive tire-force model for sideslip angle and wheel cornering stiffness estimation. The linear adaptive force model is proposed with an eye to correct errors resulting from road friction changes. This model adds into the linear force model a readjustment variable correcting the cornering stiffness. The different proposed observers are based on Kalman filter [9]. By using cascaded observers, the observability problems entailed by an inappropriate 1. INTRODUCTION Knowledge of tire forces is essential for safety enhancement, in particular for active safety systems. That is why, the last few years have seen emergence of on-board control systems in cars, in order to improve security and help to prevent dangerous situations. Controllers such as Anti-lock Braking Systems (ABS), and ESP (Electronic Stability Programs) could be improved if the dynamic potential of the car was better known. Nowadays the tire forces and the sideslip angle are only measurable with high cost sensors, which could probably never be integrated in a standard car for both economical and technical reasons. As a consequence the "virtual sensing" approach (observer) proposed here may be of particular interest. In this context, we developed an estimation process of tire forces and vehicle sideslip angle. The estimation of tire forces and sideslip angle is an important topic in studying vehicle stability and dynamics. Consequently, this subject has been widely discussed in the literature [1, 2, 3, 4, 5, 6]. One original feature of the present study is that the estimation process furnishes tire force estimations without requiring the wheel torque measurement. This induces some simplifications in the modeling of the system. Although these simplifications, the 533 AVEC '08 freedom for the suspension that connects the sprung and unsprung mass, and its sprung mass is assumed to rotate about the roll center. During cornering, the roll angle depends on the roll stiffness of the axle and on the position of the roll center. In reality, the roll center of the vehicle does not remain constant, but in this study a stationary roll center is assumed in order to simplify the model. The roll axis is defined as the line which passes through the roll centers of the front and rear axles. According to the torque balance in the roll axis, the roll dynamics of the vehicle body can be described by the following differential equation (for small roll angle): use of the complete modeling equations are avoided enabling the estimation process to be carried out in a simple and practical way. The rest of the paper is organized as follows. The second section describes the first block for the estimation of vertical forces, then the third and fourth sections present the second and the third block for the estimation of lateral/longitudinal forces and sideslip angle. The fifth section deals with vehicle weight identification method. Section 6 provides experimental results: the different observers are evaluated with respect to sideslip angle and tire-road force measurements. Finally, concluding remarks are given in section 7. .. . I xx θ + C R θ + K Rθ = ms a y hcr + ms hcr gθ (1) where Ixx is the moment of inertia of the sprung mass with respect to the roll axis, CR and KR denote respectively the total damping and spring coefficients of the roll motion of the vehicle system, ay is the lateral acceleration and hcr the height of the sprung mass about the roll axis. Summing the moments about the front and rear roll centers, the simplified steady-sate equation for the Fig. 1 Estimation process Fig. 2 Roll dynamics lateral load transfer applied to the left-hand side of the vehicle is given by the dynamic relationship [8]: 2. FIRST BLOCK: VERTICAL FORCES OBSERVER ∆Fzl = ( Fz11 + Fz 21 - Fz12 - Fz 22 ) This section deals with the first block which main role is to estimate wheel vertical force. This block is composed of two parts: in the first part a linear observer is proposed in order to estimate lateral load transfer, the obtained result is considered as an essential measure for the second part where a nonlinear observer is considered to estimate vertical forces. kf k = ( m + m21-m12 -m22 ) g - 2( + r )θ 11 e1 e2 ay l lf r - 2 ms ( e + e ) l h f 1 hr 2 (2) where Fzij is the vertical force (i=1,2 (front, rear) and j=1,2 (left, right)), mij is the vehicle quarter mass, h is the height of the center of gravity, hf and hr are the heights of the front and rear roll centers, ef and er the vehicle's front and rear track, kf and kr the front and rear roll stiffnesses, lf and lr the distances from the cog to the front and rear axles respectively and l is the wheelbase (l= lf+lr) (see figure 3). 2.1 Part I: Lateral transfer load Model The lateral load transfer model we have developed is based on the vehicle's roll dynamics. We use a roll plane model including the roll angle θ , as shown in figure 2. This model has a roll degree of 534 AVEC '08 vary during a journey. The force due to the longitudinal acceleration at the cog causes a pitch torque which increases the rear axle load and reduces the front axle load (in braking case, the opposite is to be considered ). In addition, during cornering the lateral acceleration causes a roll torque which increases the load on the outside and decreases it on the inside of the vehicle (see figure 3). The load distribution can be expressed by the vertical forces that act on each of the four wheels. These equations are [7]: The lateral acceleration ay used in equation (2) is generated at the cog. The accelerometer, however, is unable to distinguish between the acceleration caused by the vehicle's motion on the one hand, and the gravitational acceleration on the other. In fact the acceleration aym, measured by the lateral accelerometer, is a combination of the gravitational force and the vehicle acceleration as represented in the following equation (for small roll angle): a ym = a y + gθ (3) Measuring the roll angle requires additional sensors, which makes it a difficult and costly operation. In this study we consider that the roll angle can be calculated using relative suspension sensors. During cornering on a smooth road, the suspension is compressed on the outside and extended on the inside of the vehicle. If we neglect pitch dynamic effects on roll motion, the roll angle can be calculated by applying the following equation based on the geometry of the roll motion [5]: θ = ( ∆11 - ∆12 + ∆ 21 - ∆ 22 ) − mv a ym h 2e f Fz11,12 = Fz 21,22 = . . X = [ ∆ F zl , ∆ F zr , a y , a y θ , θ ] (4) Fig. 3 load distribution Using relations (8) and the estimated results from the first part, a nonlinear observer O1N is constructed in order to estimate wheel vertical forces. The state vector is composed of: . . X = [ Fz 11 , Fz 12 , Fz 21 , Fz 22 , a x , a x , a y , a y ] (5) X 0 = [( m11 + m21 − m12 − m22 ) g , − ( m11 + m21 − m12 − m22 ) g , 0, 0, 0, 0] X 0 = [ m11 g , m12 g , m21 g , m22 g , 0, 0, 0, 0] (6) . Y = [ a ym , (∆Fzl + ∆Fzr ), θ , θ , ∆Fzl ] Y = [ ∆Fzl , ( Fz11 + Fz12 ), a x , a y , ∑ Fzij ] = [Y1 , Y2 , Y3 , Y4 , Y5 ] (7) • = [Y1 , Y2 , Y3 , Y4 , Y5 ] • • (10) The measurement model is: The measurement vector Y and the measurement model are: • (9) and it is initialized as follows: and it is initialized as follows: • (8) kt where △ij is the suspension deflection, kt is the roll stiffness resulting from tire stiffness and mv is the vehicle weight. By combining the relations (1), (2), (3) and (4), a linear observer O1L is developed to estimate the one-side lateral load transfer. The state vector is composed of: • mv lr h lr h h ay ( g − a x ) ± mv ( g − a x ) l l l ef g 2 l lf mv l f h h h ay ( g + a x ) ± mv ( g + a x ) l l l er g 2 l • Y1: lateral acceleration measured by accelerometer; Y2: the sum of right and left transfer loads is assumed to be null at each instant; Y3: roll angle calculated from equation (4); Y4: roll rate measured by gyrometer; Y5: left transfer load calculated from equation (2) • • • (11) Y1 is provided by the second block; Y2 is calculated directly from (8); Y3 is measured using accelerometer; Y4 is provided by the second block; Y5 is assumed to be equal to mvg at each instant. 3. SECOND BLOCK: LATERAL FORCE OBSERVER This section describes the second block that contains observer O2N constructed from a fourwheel vehicle model (see figure 4), where ψ is the yaw angle, β the center of gravity sideslip angle, Vg is the center of gravity velocity. Fx,y,i,j are the longitudinal and lateral tire-road forces, δ1,2 are the 2.2 Part II: Wheel ground vertical contact force Model Due to the longitudinal and lateral accelerations of the vehicle, the load distribution can significantly 535 AVEC '08 and Fy22 to be differentiated in the sum (Fy21+Fy22): as a consequence only the sum (Fy2=Fy21+Fy22) is observable. Moreover, when driving in a straight line, yaw rate is small, δ1 and δ2 are approximately null, and hence there is no significant knowledge in equations (12, 13, 14) differentiating Fy11 and Fy12 in the sum (Fy11+Fy12), so only the sum (Fy1=Fy11+Fy12) is observable. These observations lead us to develop the O2N system with a state vector composed of sums of forces: front left and right steering angles respectively, and E is the vehicle track (E=(ef+er)/2). In order to develop an observable system (notably in the case of null steering angles), rear longitudinal forces are neglected relative to the front longitudinal forces. The simplified equation for yaw acceleration (four-wheel vehicle model) can be formulated as the following dynamic relationship (O2N model): .. 1 ψ = Iz  l [ F cos(δ ) + F cos(δ )  1 2  y12  f y11  + Fx11 sin(δ1 ) + Fx12 sin(δ 2 )]    − l [ Fy 21 + Fy 22 ] r  E  + 2 [ Fy11 sin(δ1 ) − Fy12 sin(δ 2 )  + F cos(δ ) − F cos(δ )]   x12  2 1 x11 . X = [ψ , Fy1, Fy 2 , Fx1 ] where Fx1 is the sum of front longitudinal forces (Fx1=Fx11+Fx12). Tire forces and force sums are associated according to the dispersion of vertical forces: (12) where Iz the yaw moment of inertia. The different force evolutions are modeled with a random walk model: . . F xij , F yij = [0,0], i = 1,2, j = 1,2 (15) (13) Fx11 = Fz12 Fz11 Fx1 Fx1, Fx12 = Fz11 + Fz12 Fz11 + Fz12 Fy11 = Fz12 Fz11 Fy1 Fy1, Fy12 = Fz11 + Fz12 Fz11 + Fz12 Fy 21 = Fz 22 Fz 21 Fy 2 Fy 2, Fy 22 = Fz 21 + Fz 22 Fz 21 + Fz 22 (16) where Fzij are the vertical forces estimated in the first block. The input vectors U of the O2N observer corresponds to: (17) U = [δ1, δ 2 , Fz11, Fz12 , Fz 21, Fz 22 ] 4. THIRD BLOCK: OBSERVER SIDESLIP ANGLE This section presents the third block that contains the observer O3N constructed from a sideslip angle model and a tire-force model. The sideslip angle model is based on the single-track model [6], with neglected rear longitudinal force: . Fig. 4 Four-wheel vehicle model β = Fx1 sin(δ − β ) + Fy1 cos(δ − β ) + Fy 2 cos( β ) (18) mvVg The measurement vector Y and the measurement model are: Front and rear sideslip angles are calculated as: . Y = [ψ , a y , ax ] = [Y1 , Y2 , Y3 ] β1 = δ − β − l f . Y1 = ψ 1 Y2 = [ Fy11 cos(δ1 ) + Fy12 cos(δ 2 ) mv + Fy 21 + Fy 22 + Fx11 sin(δ ) + Fx12 sin(δ )] 1 2 1 [− Fy11 sin(δ1 ) − Fy12 sin(δ 2 ) Y3 = mv + Fx11 cos(δ1 ) + Fx12 cos(δ 2 )] . −ψ (14) . . ψ ψ Vg , β 2 = − β + lr (19) Vg where δ is the mean of front steering angles. The dynamic of the tire-road contact is usually formulated by modeling the tire-force as a function of the slip between the tire and the road [1], [4]. Figure 5 illustrates different lateral tire-force models (linear, linear adaptive and Burckhardt) for various road surfaces [7]. In this study lateral wheel slips are assumed to be equal to the wheel sideslip angles. The O2N system (association between equations (12), random walk force equation (13), and the measurement equations (14) is not observable in the case where Fy21 and Fy22 are state vector components. For example, in these equations there is no relation allowing the rear lateral forces Fy21 536 AVEC '08 The estimation process operates in real-time in the INRETS-MA laboratory vehicle (see figure 6). This In current driving situations, lateral tire forces may be considered linear with respect to sideslip angle (linear model): Fyi ( βi ) = Ci βi , i = 1,2, (20) where Ci is the wheel cornering stiffness, a parameter closely related to tire-road friction. When road friction changes or when the nonlinear tire domain is reached, "real" wheel cornering Fig. 6 INRETS MA Laboratory Vehicle vehicle Peugeot 307 is equipped with a number of sensors including accelerometers, gyrometers, optical sensors measuring sideslip angles on the vehicle body or on the wheels, and four dynamometric wheels giving tire/road forces. This complete equipment allowed an experimental evaluation of the estimation process. A experimental test, performed on a real road in Côtes d'Armor (France), composed of a small bend to the right, followed by a sharper one to the left and another one to the right the double lane change manoeuvre, was chosen as the most demanding manoeuvre, where the dynamic contributions play an important role. Figure 7 presents the vehicle trajectory and the “g-g” accelerations diagram during the test. Accelerations diagrams show that large lateral accelerations up to 7 m/s² were obtained. Fig. 5 Lateral tire force models stiffness varies. In order a take the wheel cornering stiffness variations into account, we propose an adaptive tire-force model (known as the linear adaptive tire-force model, illustrated in figure 5). This model is based on the linear model at which a readjustment variable ∆Cai is added to correct wheel cornering stiffness errors [3]-[4]: Fyi ( βi ) = (Ci + ∆Cai ) βi , i = 1,2, (21) The variable ∆Cai is included in the state vector of the O3N observer and its evolution equation is formulated according to a random walk model. Input U', state X’ and measurement Y' are chosen as: . U' = [u1',u 2 ', u 3',u 4 '] = [δ , ψ ,Vg , Fx1 ], X' = [x1', x 2 ', x 3'] = [β , ∆C a1 , ∆C a2 ], (22) Y' = [y1',y 2 ', y 3 '] = [Fy1 , Fy2 ,a y ]. Fig. 7 Vehicle trajectory, accelerations diagram 5. VEHICLE WEIGHT IDENTIFICATION METHOD In this study, we will show some of the estimation process results. Figure 8 presents the one side lateral load transfer and the vertical forces on the front and rear wheels, figure 9 presents the lateral forces (sum for front and rear axles), while figure 10 illustrates the rear sideslip angle evolution (computed at the point where the sensor is located) during the vehicle trajectory. We can deduce that for this test the performance of the different observers is satisfactory and the estimations are close to measurements (A statistical study shows that the observers’ normalized error is less than 7 %). However, some small differences appear between estimation and measurements. As presented in the above sections, the vehicle's mass is an important parameter in developing vehicle dynamic equations. Moreover, knowing the load distribution when the vehicle is at rest is essential for initializing observers O1N and O2N (section 2). The vehicle weight identification method applied in this study is that presented in [5]. 6. EXPERIMENTAL RESULTS 537 AVEC '08 7. CONCLUSION This study deals with four vehicle dynamic observers constructed for use in a three-block estimation process. Block 1 mainly estimates vertical tire-forces, block 2 calculates lateral tireforces (without an explicit tire-force model), while block 3 estimates sideslip angle and corrects cornering stiffnesses (with an adaptive tire-force model). The experimental evaluations in real-time embedded estimation processes yielded good estimations close to the measurements. The estimation process potential demonstrates that it may be possible to replace expensive sensors by software observers that can work in real time while the vehicle is in motion. Future studies will improve vehicle-road models, and take into account road irregularities and road bank angle, which can significantly impact vehicle dynamics. Moreover, experimental tests will be performed, notably on different road surfaces and in critical driving situations (strong understeering and oversteering). Fig. 8 Observers O1L and O1N evaluation 8. ACKNOWLEDGEMENTS This study was sponsored by the RADARR theme of the SARI Project, in the PREDIT framework. 9. REFERENCES [1] Ray. L, “Nonlinear Tire Force Estimation and Road Friction Identification: Simulation and Experiments”, Automatica, Vol.33, pp. 1819-1833, 1992. [2] Canudas-De-Wit, C. et al., “Dynamic friction models for road/tire longitudinal interaction”, Vehicle System Dynamics, Vol.39, 189-226, 2003. [3] Baffet, G. et al., “Vehicle Sideslip Angle and Lateral Tire-Force Estimations in Standard and Critical Driving Situations: Simulations and Experiments”, AVEC’06, pp 41-45, Taipei Taiwan, 2006. [4] Baffet, G et al., “Experimental evaluation of tire-road forces and sideslip angle observers”, European Control Conference, ECC’07, KOS, 2007. [5] Doumiati, M. et al., “An estimation process for vehicle wheel-ground contact normal forces”, 17th IFAC WC, Seoul, Korea, 2008. [6] Lakehal-ayat, M. et al., “Disturbance Observer for Lateral Velocity Estimation”, AVEC’06, pp 889-894, Taipei Taiwan, 2006 [7] Kiencke U. et al., “Automotive control system”, Springer, 2000. [8] Milliken, W.F et al., “Race car vehicle dynamics », Society of Automotive Engineers, Inc, U.S.A, 1995. [9] Mohinder, S.G. et al. ”Kalman filtering theory and practice”, Prentice hall, 1993. Fig. 9 Observer O2N evaluation It can be due to model simplification such as suspension dynamics and camber angle which act hugely on vehicle dynamics especially in critical situations, and to the fact that the road lateral slope is not taken into consideration. Fig. 10 Observer O3N evaluation 538