Unscented Kalman Filter for Real-Time Vehicle Lateral Tire Forces And

Unscented Kalman filter for real-time vehicle lateral tire forces and sideslip angle estimation Moustapha Doumiati, Alessandro Victorino, Ali Charara and Daniel Lechner Abstract— Knowledge of vehicle dynamic parameters is im- trajectories, and to better vehicle control. Moreover, it makes portant for vehicle control systems that aim to enhance vehicle possible the development of a diagnostic tool for evaluating handling and passenger safety. Unfortunately, some fundamen- the potential risks of accidents related to poor adherence or tal parameters like tire-road forces and sideslip angle are difficult to measure in a car, for both technical and economic dangerous maneuvers. reasons. Therefore, this study presents a dynamic modeling and Vehicle dynamic estimation has been widely discussed in observation method to estimate these variables. The ability to the literature. Several studies have been conducted regarding accurately estimate lateral tire forces and sideslip angle is a crit- the estimation of tire-road forces, sideslip angle and the ical determinant in the performances of many vehicle control friction coefficient. For example, in [9], the authors esti- system and making vehicle’s danger indices. To address system nonlinearities and unmodeled dynamics, an observer derived mate longitudinal and lateral vehicle velocities and evaluate from unscented Kalman filtering technique is proposed. The sideslip angle and lateral forces. In [13] and [5], sideslip estimation process method is based on the dynamic response of angle estimation is discussed in detail. More recently, the a vehicle instrumented with easily-available standard sensors. sum of front and rear lateral forces have been estimated in Performances are tested using an experimental car in real [4] and [6]. However, lateral forces at each tire/road level driving situations. Experimental results show the potentiel of the estimation method. were not estimated. Other studies present valid tire/road force observers, but these involve wheel-torque measurements re- I. INTRODUCTION quiring expensive sensors [15]. The goal of this study is to develop an estimation method that Today, automotive electronic technologies are developing uses a simple vehicle model and a certain number of valid for safe and comfortable travelling of drivers and passengers. measurements in order to estimate in real-time the lateral There are a lot of vehicle control system such as Rollover force at each tire-road contact point and the sideslip angle. Prevention System, Adaptive Cruise Control System, Elec- The observation system is highly nonlinear and presents tronic Stability Control (ESC) and so on. These control unmodeled dynamics. For this reason, an observer based on systems installation rate is increasing all around the world. UKF (the Unscented Kalman Filter) is proposed. Vehicle control algorithms have made great strides towards In order to show the effectiveness of the estimation method, improving the handling and safety of vehicles. For example, some validation tests were carried out on an instrumented experts estimate that ESC prevents 27% of loss-of-control vehicle in realistic driving situations. accidents by intervening when emergency situations are The remainder of the paper is organized as follows. Section 2 detected [1]. While nowadays vehicle control algorithms are describes briefly the estimation process algorithm. Section 3 undoubtedly a life-saving technology, they are limited by the presents and discusses the vehicle model and the tire-road available vehicle state information. interaction phenomenon. Section 4 describes the observer Vehicle control systems currently available on production and presents the observability analysis. In section 5 the cars rely on available inexpensive measurements such as results are discussed and compared to real experimental data, longitudinal velocity, accelerations and yaw rate. Sideslip and then in the final section we make some concluding rate can be evaluated using yaw rate, lateral acceleration remarks regarding our study and future perspectives. and vehicle velocity [2]. However, calculating sideslip angle from sideslip rate integration is prone to uncertainty and II. ESTIMATION PROCESS DESCRIPTION errors from sensor bias. Besides, these control systems use unsophisticated, inaccurate tire models to evaluate lateral The estimation process is shown in its entirety by the block tire dynamics. In fact, measuring tire forces and sideslip diagram in figure 1, where ax and aym are respectively the angles is very difficult for technical, physical and economic longitudinal and lateral accelerations, ψ˙ is the yaw rate, θ˙ is reasons. Therefore, these important data must be observed the roll rate, ∆ij (i represents the front(1) or the rear(2) and or estimated. If control systems were in possession of the j represents the left(1) or the right (2)) is the suspension complete set of lateral tire characteristics, namely lateral deflection, wij is the wheel velocity, Fzij and Fyij are forces, sideslip angle and the tire-road friction coefficient, respectively the normal and lateral tire-road forces, β is the they could greatly enhance vehicle handling and increase sideslip angle at the center of gravity (cog). The estimation passenger safety. process consists of two blocks, and its role is to estimate As the motion of a vehicle is governed by the forces sideslip angle, normal and lateral forces at each tire/road generated between the tires and the road, knowledge of contact point, and consequently evaluate the used lateral the tire forces is crucial when predicting vehicle motion. friction coefficient. The following measurements are needed: Accurate data about tire forces and sideslip angle leads to • yaw and roll rates measured by gyrometers, a better evaluation of road friction and the vehicles possible • longitudinal and lateral accelerations measured by ac- celerometers, M. Doumiati, A. Victorino and A. Charara are with Heudi- asyc Laboratory, UMR CNRS 6599, Universite´ de Technologie de • suspension deflections using suspension deflections sen- Compiegne,` 60205 Compiegne,` France [email protected], sors, [email protected] and [email protected] • steering angle measured by an optical sensor, D. Lechner is with Inrets-MA Laboratory, Departement of Accident Mechanism Analysis, Chemin de la Croix Blanche, 13300 Salon de • rotational velocity for each wheel given by magnetic Provence, France [email protected] sensors. 978-1-4244-3504-3/09/$25.00 ©2009 IEEE 901 Suspension ∆ij vehicle. Assuming front-wheel drive, rear longitudinal forces deflection are neglected relative to the front longitudinal forces; we sensors Block 1 assume that Fx1 = Fx11 + Fx12. Roll plane model + . The lateral dynamics of the vehicle can be obtained by θ coupling longitudinal/lateral summing the forces and moments about the vehicle’s center Inertial ax, aym dynamics of gravity. Consequently, the simplified FWVM is formulated sensors as the following dynamic relationship: . ψ F β δ F β δ Fzij ax, ay 1 x1 cos( − ) + y11 sin( − )+ V˙g = , m Fy12 sin(β − δ) + (Fy21 + Fy22) sin β Block 2 L F δ F δ F δ Magnetic wij 1[ y11 cos + y12 cos + x1 sin ]− sensor Four wheel vehicle ¨ 1 L [F + F ]+ ψ = I 2 y21 y22 , model + Dugoff tire z E " [Fy11 sin δ − Fy12 sin δ] # model 2 δij Optical 1 −Fx1 sin(β − δ) + Fy11 cos(β − δ)+ sensor β˙ = − ψ,˙ mVg Fy12 cos(β − δ) + (Fy21 + Fy22) cos β Fyij β 1 ay = [Fy11 cos δ + Fy12 cos δ + (Fy21 + Fy22) + Fx1sinδ], Fig. 1. Process estimation diagram m 1 ax = m [−Fy11 sin δ − Fy12 sin δ + Fx1 cos δ], (1) where m is the vehicle mass, and Iz the yaw moment of The first block aims to provide the vehicle’s weight, lateral inertia. load transfer, normal tire forces and the corrected lateral The tire slip angle (αij ), as shown in figure 2, is the acceleration ay (by canceling the gravitational acceleration difference between the tire’s longitudinal axis and the tire’s component that distorts the accelerometer signal aym). We velocity vector. The tire velocity vector can be obtained have looked in detail at the first block in a previous study from the vehicle’s velocity (at the cog) and the yaw rate. [11]. This article focuses only on the second block, whose Assuming that rear steering angles are approximately null, main role is to estimate lateral tire forces and sideslip angle. the direction or heading of the rear tires is the same as that The second block makes use of the estimations provided by of the vehicle. The heading of the front tires includes the the first block. In fact, it is of major importance to include steering angle (δ). The front steering angles are assumed to the impact of accurate normal forces in the calculation of be equal (δ11 = δ12 = δ). The vehicle velocity Vg, steering lateral forces. ˙ One specificity of this estimation process is the use of blocks angle δ, yaw rate ψ and the vehicle body slip angle β are in series. By using cascaded observers, the observability then used to calculate the tire slip angles αij , where: problems entailed by an inappropriate use of the complete Vg β+L1ψ˙ α11 = δ − arctan , modeling equations are avoided, enabling the estimation Vg −Eψ/˙ 2 process to be carried out in a simple and practical way. h i Vg β+L1ψ˙ α12 = δ − arctan , Vg +Eψ/˙ 2 III. VEHICLE-ROAD MODEL h i (2) ˙ α = − arctan Vg β−L2ψ , This section presents the vehicle model and tire-road 21 V −Eψ/˙ 2 interaction dynamics, especially the lateral tire forces. Since g h i the quality of the observer largely depends on the accuracy of Vg β−L2ψ˙ α22 = − arctan . the vehicle and tire models, the underlying models must be Vg +Eψ/˙ 2 precise. Taking real-time calculation requirement, the models h i should also be simple. B. lateral tire-force model A. Four-wheel vehicle model The model of tire-road contact forces is complex because a wide variety of parameters including environmental factors The Four-Wheel Vehicle model (FWVM) is chosen for and pneumatic properties (load, tire pressure, etc.) impact this study because it is simple and corresponds sufficiently the tire-road contact interface.

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