Tire-road Friction Coefficient Research Articles

Integrated state and parameter estimation for vehicle dynamics control

Most modern day automotive chassis control systems employ a feedback control structure. Therefore, a real-time estimate of the vehicle handling dynamic states and tyre-road contact parameters are invaluable for enhancing the performance of current vehicle control systems, such as anti-lock brake system (ABS) and electronic stability program (ESP). Today's production cars are equipped with onboard sensors (e.g., a 3-axis accelerometer, 3-axis gyroscope, steering wheel angle sensor, and wheel speed sensors) which when used in conjunction with certain model based observers can be used to identify relevant vehicle states for optimal control of comfort, stability and handling. However, some key variables such as the tyre forces, road bank/grade angles, and the tyre-road friction coefficient, which have a significant impact on vehicle handling performance and safety are difficult to measure using sensors already onboard vehicles. This paper introduces an integrated vehicle state estimator comprising a series of model-based and kinematic-based observers for estimating these unmeasurable states. Using an appropriate vehicle model, kinematic equations of motion and vehicle sensor data, the unknown vehicle states as well as the tyre-road contact forces are estimated by implementing a series of observers arranged in a cascade structure. Key estimated signals include the vehicle side slip angle (β), tyre longitudinal/lateral/vertical forces, and the tyre-road friction coefficient (μ). The performance of the proposed estimators has been evaluated via computer simulations conducted using the vehicle dynamics software CarSim®. An effectively designed merging scheme ensures robust estimation performance even during the vehicle manoeuvres which show highly nonlinear tyre characteristics and in the existence of road inclination or bank angle.

Tire-Road Friction Coefficient Estimation under Constant Vehicle Speed Control

Abstract Tire-road friction coefficient (TRFC) is of critical importance for advanced vehicle control systems and autonomous vehicle applications. This paper presents a sequential tire longitudinal stiffness and TRFC estimation method for road vehicles by separate control of the front and rear wheels, for which only standard Kalman filter (KF) and recursive least squares (RLS) techniques are required. While braking torque is actively applied to rear wheels, the proportional-integral-derivative (PID) speed controller dictates the corresponding driving torque to front wheels to compensate the decrease of the vehicle longitudinal speed. Tire force of rear tires are estimated based on the KF, both longitudinal stiffness and TRFC of rear tires are identified using RLS technique. The proposed method has simple structure and the potential of estimating the parameters without severely affecting the vehicle’s desired longitudinal speed. Simulation results from vehicle dynamics software CarSim and Matlab/Simulink validate the effectiveness of the proposed method.

Nonlinear Model Predictive Lateral Stability Control of Active Chassis for Intelligent Vehicles and Its FPGA Implementation

The rapid development of intelligent vehicles has paved the way for active chassis lateral stability, which is a novel issue and critical to vehicle stability and handling performance. To obtain active chassis lateral stability for intelligent vehicles, a nonlinear model predictive control (NMPC) method integrating active front steering and an additional yaw moment is proposed. It adopts the tire sideslip angle to express vehicle lateral stability, and addresses the actuator and security constraints and the nonlinear properties of the tire-road force effectively. Moreover, the hardware implementation, based on the field programmable gate array (FPGA), is presented to satisfy miniaturization and to discuss the computational efficiency of the proposed NMPC method. To verify the effectiveness of the presented NMPC method, offline simulations comparing the NMPC method with the direct yaw moment control (DYC) method under various running conditions and a real-time implementation experiment are carried out. The results indicate that the proposed NMPC method controls better than the DYC-based method. In addition, the presented NMPC method exhibits good robustness when the longitudinal velocity and tire-road friction coefficient vary within a suitable range. Moreover, the computational time of the proposed NMPC controller, implemented using the FPGA, is only 4.994 ms during one sampling period, which can satisfy the real-time requirement of active chassis lateral stability control.

A hybrid controller for ABS based on extended-braking-stiffness estimation

Abstract In the context of antilock braking systems (ABS), we present a two-phase hybrid control algorithm based on the tyre extended braking stiffness (XBS), that is, on the slope of the tyre-road friction coefficient with respect to the wheel slip. Because the XBS cannot be directly measured, a switched observer is used to estimate it. With the proposed hybrid algorithm, the closed-loop trajectories of the system satisfy the conditions required for the observer to correctly estimate the XBS. Moreover, the braking distances are shorter than those obtained using a hybrid algorithm based on wheel deceleration thresholds.

Assessing the influence of the road-tire friction coefficient on the yaw and roll stability of articulated vehicles

This article addresses the yaw stability of articulated vehicles by assessing the influence of the road-tire friction coefficient on the convergence region of a particular equilibrium condition. In addition, the boundaries of this region are compared to the boundaries of the non-jackknife and non-rollover regions to distinguish the instability phenomenon, jackknife or roll-over, responsible for this delimitation. The vehicle configuration considered in this analysis is composed by one tractor unit and one towed unit connected through an articulation point, for instance, a tractor-semitrailer combination. A nonlinear articulated bicycle model with four degrees of freedom is used together with a nonlinear lateral force tire model. To estimate the convergence region, the phase trajectory method is used. The equations of motion of the mathematical model are numerically integrated for different initial conditions in the phase plane, and the state orbits are monitored in order to verify the convergence point and the occurrence of instability events. In all cases, the longitudinal force on each tire, such as traction and braking, is not considered. The results show the existence of convergence regions delimited only by jackknife events, for low values of the friction coefficient, and only by rollover events, for high values of the friction coefficient. Moreover, the transition between these two conditions as the friction coefficient is changed is graphically presented. The main contributions of this article are the identification of the abrupt reduction of the convergence region as the value of the friction coefficient increases and the distinction of the instability events, jackknife or rollover, that define the boundaries of the convergence region.

A real-time approach to robust identification of tyre–road friction characteristics on mixed-μ roads

ABSTRACTThe interaction between the tyre and the road is crucial for understanding the dynamic behaviour of a vehicle. The road–tyre friction characteristics play a key role in the design of braking, traction and stability control systems. Thus, in order to have a good performance of vehicle dynamic stability control, real-time estimation of the tyre–road friction coefficient is required. This paper presents a new development of an on-line tyre–road friction parameters estimation methodology and its implementation using both LuGre and Burckhardt tyre–road friction models. The proposed method provides the capability to observe the tyre–road friction coefficient directly using measurable signals in real-time. In the first step of our approach, the recursive least squares is employed to identify the linear parameterisation form of the Burckhardt model. The identified parameters provide, through a T–S fuzzy system, the initial values for the LuGre model. Then, a new LuGre model-based nonlinear least squares parameter estimation algorithm using the proposed static form of the LuGre to obtain the parameters of LuGre model based on recursive nonlinear optimisation of the curve fitting errors is presented. The effectiveness and performance of the algorithm are demonstrated through the real-time model simulations with different longitudinal speeds and different kinds of tyres on various road surface conditions in both Matlab/Carsim environments as well as collected data from real experiments on a commercial trailer.

Non-linear tyre model–based non-singular terminal sliding mode observer for vehicle velocity and side-slip angle estimation

Vehicle velocity and side-slip angle are important vehicle states for the electronic stability programme and traction control system in vehicle safety control system and for the control allocation method of electric vehicles with in-wheel motors. This paper proposes an innovative side-slip angle estimator based on the non-linear Dugoff tyre model and non-singular terminal sliding mode observer. The proposed estimation method based on the non-linear tyre model can accurately present the tyre’s non-linear characteristics and can show advantages over estimation methods based on the linear tyre model. The utilised Dugoff tyre model has a relatively simple structure with few parameters, and the proposed non-linear observer can be applied in various vehicle tyres and various road conditions. Precise determination of the Dugoff tyre model parameters is not required and the proposed observer can still perform good estimation results even though tyre parameters and the tyre–road friction coefficient are not accurate. The proposed non-singular terminal sliding mode observer can achieve fast convergence rate and better estimation performance than the traditional sliding mode observer. At the end of this paper, simulations in various conditions are presented to validate the proposed non-linear estimator.

Integrated model control of brake–wheel system using bond graph method

Brake system is an important actuator of most active safety systems equipped on vehicles. It combines with the wheel to make vehicle decelerate and finally stop it. Moreover, brake system is an electronic, mechanical, and hydraulic hybrid system; it contains some highly nonlinear characters, which is a challenge to system control. In this article, an integrated model of brake system and single-wheel system using bond graph method is developed, in which the nonlinear characters of the volumetric compliance effect of brake fluid and the resistance effect of valves are taken into consideration. The accuracy and reliability of the brake system is verified by experiment. Nonlinear sliding-mode controller as well as sliding-mode observer is proposed. The controller is used to modulate inlet and outlet valves control signals according to the vehicle states, which will lead to cancel the usage of wheel cylinder pressure sensors. The controller is analyzed by different tire–road friction coefficient conditions. The results show that the proposed integrated bond graph model is accurate, and the nonlinear sliding-mode control is reliable on valves control signal regulation.

Robust road friction estimation during vehicle steering

ABSTRACTAutomated vehicles require information on the current road condition, i.e. the tyre–road friction coefficient for trajectory planning, braking or steering interventions. In this work, we propose a framework to estimate the road friction coefficient with stability and robustness guarantee using total aligning torque in vehicle front axle during steering. We first adopt a novel strategy to estimate the front axle lateral force which performs better than the classical unknown input observer. Then, combined with an indirect measurement based on estimated total aligning torque and front axle lateral force, a non-linear adaptive observer is designed to estimate road friction coefficient with stability guarantee. To increase the robustness of the estimation result, criteria are proposed to decide when to update the estimated road conditions. Simulations and experiments under various road conditions validate the proposed framework and demonstrate its advantage in stability by comparing it with the method utilising the wide-spread Extended Kalman Filter.

Dynamics and Control of a Novel Active Yaw Stabilizer to Enhance Vehicle Lateral Motion Stability

In this paper, a novel active yaw stabilizer (AYS) system is proposed for improving vehicle lateral stability control. The introduced AYS, inspired by the recent in-wheel motor (IWM) technology, has two degrees-of-freedom with independent self-rotating and orbiting movements. The dynamic model of the AYS is first developed. The capability of the AYS is then investigated to show its maximum generation of corrective lateral forces and yaw moments, given a limited vehicle space. Utilizing the high-level Lyapunov-based control design and the low-level control allocation design, a hierarchical control architecture is established to integrate the AYS control with active front steering (AFS) and direct yaw moment control (DYC). To demonstrate the advantages of the AYS, generating corrective lateral force and yaw moment without relying on tire–road interaction, double lane change maneuvers are studied on road with various tire–road friction coefficients. Co-simulation results, integrating CarSim® and MATLAB/Simulink®, successfully verify that the vehicle with the assistance of the AYS system has better lateral dynamics stabilizing performance, compared with cases in which only AFS or DYC is applied.

Methodology for determining real time safety margin in a road vehicle

Abstract There are multiple factors that can compromise safety during driving such as the tire-road friction coefficient, an inadequate speed, or an aggressive driving by the driver, leading to dangerous situations for all users of the way. It is difficult to measure quantitatively the level of safety during driving and the change in it, depending, at each instant of time, of the situations that occur, changes in the adherence by a puddle of oil, soil wet from rain, sudden accelerations and brakings, which change the margin of safety available. In this paper presents a methodology that allows to determine the level of safety with which it is circulating through the use of ṙ-β stability regions used for the predictive control of vehicles. The validation of the methodology is carried out through virtual tests carried out with the MSC Adams® multibody dynamic simulation software that allows reproducing the behaviour of the vehicle and knowing the values of the parameters that are necessary, such as longitudinal and lateral accelerations, yaw rate, the slips angles of the wheels, among others.

Estimation of Road Adhesion Coefficient Based on Tire Aligning Torque Distribution

Road adhesion coefficient is an important parameter in vehicle active safety control system. Many researchers estimate road adhesion coefficient by total tire self-aligning torque (SAT, also called front-axle aligning torque), which obtains the average road adhesion coefficient of front wheels, thus leading large estimation error. In this paper, a novel estimation of road adhesion coefficient based on single tire SAT, which is obtained by tire aligning torque distribution, is brought forward. Due to the use of SAT, the proposed estimation method is available in steering only condition. The main idea of the proposed method is that road adhesion coefficient is estimated by single tire SAT instead of total tire SAT. The single tire SAT is closer to real tire torque state, and it can be obtained by aligning torque distribution, which makes use of the ratio for the aligning torque of front-left wheel and front-right wheel. Tire sideslip angle used in torque distribution is estimated by unscented Kalman filter (UKF). Two coefficients, including front-left and front-right tire-road friction coefficients, are estimated by iteration algorithm form single tire SAT. The final road adhesion coefficient is determined by a coefficient identification rule, which is designed to determine which tire-road friction coefficient as the final road adhesion coefficient. Both simulations and tests that use gyroscope/lateral accelerometer/global position system (GPS)/strain gauge are conducted, to validate the proposed methodology that can provide accurate road adhesion coefficient to vehicle active safety control.

Vehicle side-slip angle estimation on a banked and low-friction road

The effective application of integrated vehicle dynamics control and automatic driving require consistent vehicle state variables and parameters. Considering lateral vehicle dynamics, the yaw rate and (estimated) vehicle side-slip angle are the minimum set of state variables that can give insight into the handling characteristics of a vehicle. Various methods of vehicle side-slip angle (lateral velocity) estimation have been tested in virtual and real world applications, in particular on a horizontal dry road. Vehicle side-slip angle, however, is not only affected by the (steering) commands of the driver, and possibly by a vehicle dynamics controller, but can also arise from a banked road or result from a low-friction surface, changing tyre–road contact. The combined effects require a comprehensive estimation approach, which is less often touched upon in the literature. Based on earlier findings on important aspects of observability, the paper addresses a modular vehicle side-slip angle estimation approach that is particularly focused upon practical aspects of modelling and design. Estimation of the combined vehicle side-slip angle, road bank angle and maximum tyre–road friction coefficient has been broadly tested with a vehicle equipped with an electronic stability control (ESC) and electric power-assisted steering (EPS) sensor configuration, for various road conditions, driving situations and vehicle/tyre setups.

Collision Avoidance via Adaptive Trajectory Control in Case of a Sudden Decrease in the Maximum Road Friction Coefficient

This study analyses an Adaptive Trajectory Control (ATC) system in case of a sudden change in μ-max (maximum tyreroad friction coefficient) during an emergency lane change manoeuvre in order to maintain the driving safety. Autonomous front wheel steering (FWS) systems have been developed for emergency steering situations. The trajectory design is also a part of these systems. Moreover, in this study ATC has been designed by sensing μ-max to complete the emergency steering manoeuvre successfully. Therefore, the originality of this paper arises from the necessity of a trajectory change in case of a sudden change in μ-max to minimize the distance between the desired and the actual path. Suitable cases were designed by using a two-track model in IPG/CarMaker (MATLAB/Simulink). Results show that ATC could be used during an emergency steering manoeuvre in case of a sudden decrease in μ-max as it can be advantageous in certain critical traffic situations. Therefore, ATC could beused as an alternative system instead of Electronic Stability Program.

Continuous monitoring the vehicle dynamics and driver behavior using navigation systems

In all fields cost is very important and the increasing amount of data that are needed for active safety systems, like ADAS, lead to implementation of some complex and powerful unit for processing raw data. In this manner is necessary a cost-effective method to estimate the maximum available tire road friction during acceleration and braking by continuous monitoring the vehicle dynamics and driver behavior. The method is based on the hypothesis that short acceleration and braking periods can indicate vehicle dynamics, and thus the available tire road friction coefficient, and also human behavior and his limits. Support for this hypothesis is found in the literature and is supported by the result of experiments conducted under different conditions and seasons.

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

It is well known that both the tire-road friction coefficient and the absolute vehicle velocity are crucial factors for vehicle safety control systems. Therefore, numerous efforts have been made to resolve these problems, but none have presented satisfactory results in all cases. In this paper, cost-effective observers are designed based on an adaptive scheme and a recursive least squares algorithm without the addition of extra sensors on a production vehicle or modification of the vehicle control system. This paper has three major contributions. First, the front biased braking characteristics of production vehicles such that the front wheel brake torques are saturated first are exploited when estimating the tire-road friction coefficient. Second, the vehicle absolute speed is identified during the friction coefficient estimation process. Third, unlike the conventional method, this paper proposes using already available excitation signals in production vehicles. In order to verify the performance of the proposed observers, experiments based on real production vehicles are conducted, and the results reveal that the proposed algorithm can enhance the performance of any vehicle dynamics control systems.

On the experimental analysis of single input single output control of yaw rate and sideslip angle

Electric vehicles with individually controlled drivetrains allow torque-vectoring, which improves vehicle safety and drivability. This paper investigates a new approach to the concurrent control of yaw rate and sideslip angle. The proposed controller is a simple single input single output (SISO) yaw rate controller, in which the reference yaw rate depends on the vehicle handling requirements, and the actual sideslip angle. The sideslip contribution enhances safety, as it provides a corrective action in critical situations, e.g., in case of oversteer during extreme cornering on a low friction surface. The proposed controller is experimentally assessed on an electric vehicle demonstrator, along two maneuvers with quickly variable tire-road friction coefficient. Different longitudinal locations of the sideslip angle used as control variable are compared during the experiments. Results show that: i) the proposed SISO approach provides significant improvements with respect to the vehicle without torque-vectoring, and the controlled vehicle with a reference yaw rate solely based on the handling requirements for high-friction maneuvering; and ii) the control of the rear axle sideslip angle provides better performance than the control of the sideslip angle at the centre of gravity.

SVM Classification and Kalman Filter Based Estimation of the Tire-Road Friction Curve

An estimation method is proposed for the maximum tire-road friction coefficient µMAX and its corresponding wheel-slip λpeak. After a preliminary analysis of Burckhardt’s model analytic properties, a machine learning approach involving Support Vector Machines is used to classify the curves representing different road surfaces. A metric to evaluate the misclassification risk is used to determine boundaries for the curve coefficients. These boundaries are then used to form linear inequality constraints for two recursive parameter estimation algorithms based on the Kalman Filter, in its Extended and Unscented forms. Finally, the proposed method is evaluated via simulations in Matlab environment.

Optimisation of active suspension control inputs for improved performance of active safety systems

ABSTRACTA collocation-type control variable optimisation method is used to investigate the extent to which the fully active suspension (FAS) can be applied to improve the vehicle electronic stability control (ESC) performance and reduce the braking distance. First, the optimisation approach is applied to the scenario of vehicle stabilisation during the sine-with-dwell manoeuvre. The results are used to provide insights into different FAS control mechanisms for vehicle performance improvements related to responsiveness and yaw rate error reduction indices. The FAS control performance is compared to performances of the standard ESC system, optimal active brake system and combined FAS and ESC configuration. Second, the optimisation approach is employed to the task of FAS-based braking distance reduction for straight-line vehicle motion. Here, the scenarios of uniform and longitudinally or laterally non-uniform tyre–road friction coefficient are considered. The influences of limited anti-lock braking system (ABS) actuator bandwidth and limit-cycle ABS behaviour are also analysed. The optimisation results indicate that the FAS can provide competitive stabilisation performance and improved agility when compared to the ESC system, and that it can reduce the braking distance by up to 5% for distinctively non-uniform friction conditions.

Optimal $\mu $ -Estimation-Based Regenerative Braking Strategy for an AWD HEV

Braking force distribution (BFD) for electrified vehicles with the aim of maximizing energy regeneration has been a challenging research topic, due to the complex operating conditions and tradeoff among different vehicle performance measures. It is known that the level of tire-road friction has a significant impact on the braking force boundaries that define the locking conditions of front and rear wheels, and therefore, on the allowable set of BFD’s where the vehicle’s stability and controllability are maintained. However, previously developed BFD strategies for regenerative braking have not considered the changing boundaries of braking limits due to varying tire-road friction levels and introduce conservative BFD constraints to ensure stability and controllability. This paper proposes a BFD strategy for an all-wheel-drive electrified vehicle with a single electric motor, based on the estimation of the tire-road friction coefficient ( $\mu $ ) using a fuzzy logic estimation approach. The proposed strategy takes into consideration the motor efficiency and available speed reduction ratios in order to find the optimal BFD, which maximizes the regenerative power during braking, for a given vehicle speed and deceleration demand. Simulation analyses demonstrate the effectiveness of the proposed tire-road friction estimation-based BFD optimization strategy that significantly improves braking energy recovery. Preliminary test results with a prototype vehicle provide additional validation of the benefits of the proposed method.