Vehicle Sideslip Angle Estimation based on Switched Fuzzy Model

A new tire-road friction coefficient estimation approach based on lateral carcass deflection measurements is proposed. The unique design of the developed wireless piezoelectric sensor decouples lateral carcass deformations from radial and tangential carcass deformations. The estimation of the tire-road friction coefficient depends on the estimation of the slip angle and the lateral tire force. The tire slip angle is estimated as the slope of the lateral deflection curve at the leading edge of the contact patch. The lateral tire force is obtained by using a parabolic relationship with the lateral deflections in the contact patch. The estimated slip angle and lateral force are then plugged into a tire brush model to estimate the tire-road friction coefficient. A specially constructed tire test-rig is used to experimentally evaluate the performance of the tire sensor and the developed approach. Experimental results show that the proposed tire-road friction coefficient estimation approach is quite promising.

This paper presents a method to design a path tracking controller with a constraint on tire slip angles under low-friction road conditions. On a low-friction road surface, a lateral tire force is easily saturated and decreases as a tire slip angle increases by a large steering angle. Under this situation, a path tracking controller cannot achieve its maximum performance. To cope with this problem, it is necessary to limit tire slip angles to a value where the maximum lateral tire force is achieved. The most commonly used controllers for path tracking, linear quadratic regulator (LQR) and model predictive control (MPC), are adopted as a controller design methodology. The control inputs of LQR and MPC are front and rear steering angles and control yaw moment, which have been widely used for path tracking. The constraint derived from tire slip angles is imposed on the steering angles of LQR and MPC. To fully verify the performance of the path tracking controller with the constraint on tire slip angles, a simulation is conducted on vehicle simulation software. From the simulation results, it is shown that the path tracking controller with the constraint on tire slip angles presented in this paper is quite effective for path tracking on low-friction road surface.

This article presents a nonlinear sideslip angle estimation framework that directly incorporates lateral tire force measurements into an observer structure. To address the limitations of conventional approaches that rely on tire models and slip angle approximations, a physically grounded tire model is developed that features load-dependent cornering stiffness, relaxation dynamics, and time-varying parameter adaptation. Cornering stiffness is estimated via a regression-based method using only measurable signals, and a Gaussian process regression (GPR) model is introduced to estimate the front-rear cornering stiffness. The resulting estimates are integrated into an unscented Kalman filter (UKF) observer for robust sideslip angle estimation under nonlinear and transient conditions. The framework is experimentally validated using a full-scale vehicle equipped with in-wheel motors (IWMs) and lateral tire force sensors. Results confirm that the proposed UKF-based observer achieves accurate and stable sideslip angle estimation during aggressive maneuvers and across varying road surfaces. This approach enables high-fidelity, real-time state estimation for advanced driver-assistance and automated driving applications.

SUMMARY This paper discusses two equipment layouts for measuring path data, vehicle sideslip angles and tire slip angles by using a gyrosystem, a vehicle speed-measuring unit with contact or non-contact speed sensor(s), and a computer. Measurement errors are analyzed in detail. A method for eliminating the effect of vehicle roll on measurement is given. Some relations between measurement errors and instrument errors are derived using vector analysis. A practical and effective error correction method for vehicle path measurements is developed.

Estimation of lateral tire–road forces and sideslip angle for electric vehicles using interacting multiple model filter approach

Vehicle dynamics estimation has been the subject of study for some years now. If on-board vehicle control systems can be provided with information such as side slip angle, lateral force etc. then stability of the vehicle can be improved. To estimate these dynamic variables different observers have been used e.g., sliding mode, fuzzy logic, neural networks etc. In this article the authors propose an extended Kalman lter to estimate vehicle side slip angle. Roll angle is estimated using vertical loads as input. First, a linear Kalman lter is used to lter out the vertical forces and estimate roll angle. This information is then used to estimate the vehicle side slip angle. To take into account the nonlinearities concerning lateral vehicle dynamics, Pacejka magic formula is used to model lateral forces. Estimated results are then compared with simulations, showing good accuracy.

This paper proposes a novel adaptive path tracking and stability control strategy for autonomous vehicles based on intelligent tires technology that is introduced to estimate the tire-road contact states based on the in-tire sensor signals. Firstly, a tire finite element model was established based on ABAQUS software. On this basis, the Spearman correlation analysis method was used to acquire the optimal sensitive positions of the in-tire acceleration sensors. The feature values of the inputs of the tire-road contact states estimation model were determined through the PLS-VIP analysis method. Then, the tire slip angle and lateral force estimation models whose inputs are the in-tire sensor signals was constructed using the LSTM neural network. Subsequently, an adaptive MPC path tracking control strategy in which the tire cornering stiffness is calculated in real-time by the intelligent tires model was designed. Finally, an adaptive NFTSM lateral stability control strategy which uses the tire lateral force estimated by the intelligent tires model was designed to determine the direct yaw moment, and an efficient and concise algorithm was then designed to achieve torque distribution. The simulation results indicate that the proposed control strategy provides better path tracking accuracy and stability control effect in emergency lane change and high-speed evasive maneuvers under different road conditions.

This paper investigates the braking stability from the viewpoint of dynamic simulation. Braking stability refers to the abilities of the vehicle to keep straight or the controllability combined with steering wheel during braking. Suspension extra steer/toe angle caused by forces and moments could change the actual wheel angle directly as well as the tire slip angle, since there is a relationship between tire slip angle and lateral force, braking stability will be changed by the change of lateral force. The orientation of kingpin axis will change during braking, and Wheel alignment and the Position and Angle of the Kingpin Axis (PAKA) have a heavy influence on braking stability during emergence braking and braking on ??-split road. This paper analyzes the importance parameters of wheel alignment and PAKA in suspension K&C during braking stability for asymmetry chassis, and point out that ride-steer and Fx-toe are the key factors that affect braking stability. Vehicle dynamic model is built to analyze braking stability, which include precise description of suspension K&C characteristics, steering system model that can reflect the self-adaptive steering capacity of left and the right wheels, and non-linear UniTire model. Braking stability has been validated well using this vehicle model on the asymmetry chassis.

<div class="section abstract"><div class="htmlview paragraph">Tread depth, inflation pressure, tire temperature, and road surface condition are among the most notable factors that have a noticeable effect on the tire force and moment characteristics. They can vary significantly during the operation of a tire and can effectively modify tire (and thus vehicle) performance. This study presents details of an adaptive magic formula (MF) tire model capable of coping with changes to the tire operating condition. More specifically, extensions have been made to the magic formula expressions for tire cornering stiffness and peak grip level, to account for variations in the tire inflation pressure, load, tread-depth and temperature. As a next step, the benefits of using an adaptive tire model for vehicle control system applications is demonstrated through simulation studies for enhanced vehicle control systems using an adaptive tire model in comparison to traditional control systems based on a non-adaptive tire model with fixed model parameters. In particular, this paper investigates the improvements an adaptive tire model would bring into the following vehicle control system strategies: Electronic Stability Control (ESC) system, Brake Torque Vectoring (BTV) system, and Rear Wheel Steer (RWS) system.</div></div>

This paper introduces a methodology for robust control of vehicle dynamics. The vehicle lateral behavior with roll dynamics is described by Takagi-Sugeno (TS) model. A fuzzy observer is first developed to estimate the vehicle sideslip angle as well as the roll parameters using the yaw rate measurement, while taking into account the road bank angle and the unmeasurable premise variables of the TS model. The objective of this study is the design of an observer-based controller to improve the stability and vehicle safety with perturbations related to the nonlinearities of the contact forces, the variations of the adhesion coefficients, the road bank angle. The proposed observer based controller is represented in the linear matrix inequality (LMI) form. The simulation results show the effectiveness of the proposed control method when different cornering maneuvers are applied to the vehicle.

A lateral acceleration is considered to be a significant sensor signal for an estimation of a side slip angle. Due to the fact that a characteristic of a lateral G sensor, the sensor has a technical issue when a road bank angle has presented. In order to resolve the issue, this paper describes a novel method for the real time estimation of a vehicle side slip angle and a road bank angle simultaneously. A Bayesian tracking approach is used to estimate the road bank angle by comparing a measured lateral acceleration with the calculated one in the case of various angle. A Kalman Filter has been implemented through bicycle model using vehicle roll angle, road bank angle and angular velocity of side slip angle. The performance of the proposed estimation method has been evaluated via vehicle tests on a real road.

Embedded unknown input sliding mode observer to estimate the vehicle roll and road bank angles: Experimental evaluation

The lateral tyre force versus slip angle and vertical load is obtained through specific tests on the single tyre or with a theoretical-empirical analysis with physical models. This study is about the possibility to use a third way: Executing a particular handling test, known as Force-Moment test, using a Flat Track Roadway Simulator (the Fiat-Elasis MTS FTRS). The understanding and the project of vehicle handling is strongly based on the knowledge of lateral tyre force response [1, 2, 3, 7].

The term “fuzzy modeling” was used in [30]. After that, pioneer works in the field of fuzzy modeling were done in [26, 31]. In 80’s, several fuzzy modeling techniques were developed (e.g., [24], [25], and [27]). In particular, Takagi and Sugeno [11] proposed a new type of fuzzy model. The model is called “Takagi-Sugeno fuzzy model (T-S fuzzy model)”. Furthermore, they proposed a procedure to identify the T-S fuzzy model from input-output data of systems in [11]. This work has been referred in many papers on fuzzy modeling for a long time. Sugeno and Kang [9, 10] extended the T-S procedure. It consists of parameter identification and structure identification. They stated in [10] that the structure identification is important and the method is better than GMDH1 in prediction problems for complex systems.

A tire-road friction coefficient estimation approach is proposed which makes use of the uncoupled lateral deflection profile of the tire carcass measured from inside the tire through the entire contact patch. The unique design of the developed wireless piezoelectric sensor enables the decoupling of the lateral carcass deformations from the radial and tangential deformations. The estimation of the tire-road friction coefficient depends on the estimation of slip angle, lateral tire force, aligning moment, and the use of a brush model. The tire slip angle is estimated as the slope of the lateral deflection curve at the leading edge of the contact patch. The portion of the deflection profile measured in the contact patch is assumed to be a superposition of three types of lateral carcass deformations, namely, shift, yaw, and bend. The force and moment acting on the tire are obtained by using the coefficients of a parabolic function which approximates the deflection profile inside the contact patch and whose terms represent each type of deformation. The estimated force, moment, and slip angle variables are then plugged into the brush model to estimate the tire-road friction coefficient. A specially constructed tire test rig is used to experimentally evaluate the performance of the developed estimation approach and the tire sensor. Experimental results show that the developed sensor can provide good estimation of both slip angle and tire-road friction coefficient.