Tire-road Friction Coefficient Research Articles

Design of ABS sliding mode control system for in-wheel motor vehicle based on road identification

Aiming at the problem that the current Anti-lock Braking System (ABS) control algorithm can not make full use of the ground friction to complete the braking when emergency braking on complex roads, an ABS sliding mode control method based on road surface identification is proposed. Combined with the in-wheel motor of in-wheel motor electric vehicle, a coordinated control method of motor regenerative braking and mechanical friction braking is designed. Based on the neural network control method, the road friction coefficient is estimated to realize the identification of typical roads and dynamically obtain the optimal slip ratio of different roads. The ABS sliding mode controler is designed with the optimal slip ratio and the actual slip ratio as input, and the saturation function is used to replace the symbol function in the traditional sliding mode control to weaken the chattering problem, and then the ABS controller is designed. The research results show that compared with the traditional ABS sliding mode controller, the designed ABS neural network sliding mode controller has the following advantages: 1. Through the identification of tire-road friction coefficient by neural network, the real-time performance and road adaptability of ABS controller are improved; 2. When the braking simulation is carried out at a given speed, the braking time is reduced by about 1.03 % and the braking distance is shortened by about 1.01%; 3. The identification of tire-road friction coefficient is realized, which weakens the chattering problem of traditional sliding mode control and improves the stability and robustness of ABS controller.

Vehicle Sideslip Angle estimation under critical road conditions via nonlinear Kalman filter-based state-dependent Interacting Multiple Model approach

The knowledge of Vehicle Sideslip Angle (VSA) can play an essential role in active safety vehicle control systems. However, due to the high costs of sensing instruments, this information is difficult to be directly measured onboard of series production vehicles, restricting de facto its application in practice. It follows that there is a need for online VSA estimation methods only based on available measurements from low-cost sensors. From this perspective, this work proposes a strategy based on Interacting Multiple Model (IMM) filters, which does not require tyre–road friction coefficient knowledge. By integrating the available onboard sensor data, the IMM estimates relevant information in different driving conditions leveraging a 2-Degrees Of Freedom (DOF) single-track vehicle model embedding a Dugoff tyre representation. Two alternative IMM algorithms based on the Extended (EKF) and Unscented Kalman filter (UKF) are developed. Moreover, while usually the transition probabilities among models in classical IMMs are fixed and set on prior information and/or dedicated analysis, here these conservative hypotheses are relaxed introducing a state-dependent Markov transition matrix based on a novel model switching algorithm. The effectiveness of the new proposed methods is evaluated on extensive non-trivial simulation scenarios through a Monte Carlo analysis exploiting an accurate 15-DOF vehicle model via a purposely designed high-fidelity co-simulation platform embedding the dSPACE software Automotive Simulation Model (ASM). Results provide a meaningful comparative performance analysis between the IMMEKF and IMMUKF solutions, as well as with respect to traditional IMM based on constant probabilities transition matrix, blue in both the EKF and UKF configuration. Finally, the developed IMM-based estimation strategy is tested in two realistic driving scenarios to assess the VSA estimation accuracy in case of abrupt changes in road surface conditions.

Enhanced Vehicle Dynamics and Safety through Tire–Road Friction Estimation for Predictive ELSD Control under Various Conditions of General Racing Tracks

This study focuses on the tire–road friction estimation for the predictive control strategy of electronically limited slip differential (ELSD) to improve the handling and acceleration performance of front-wheel drive cars, which typically suffer from excessive understeer and inner drive wheel spin during acceleration while turning due to reduced vertical load on the wheel. To mitigate this, we propose a control logic for ELSD that enhances course followability and acceleration by pre-transferring the driving torque from the inside to the outside wheel, considering the estimated traction potential for rapid response. It is essential to improve the control accuracy of wheel spin prediction by predicting the friction coefficient of the road surface. Furthermore, this study extends to the analysis of vehicle dynamics during lane-change maneuvers on low-friction surfaces, emphasizing the role of accurate tire–road friction estimation in vehicle safety. A CarSim 2023-based simulation study was conducted to investigate the vehicle response on snowy roads with low friction coefficients (μ = 0.2) and low temperatures (−5 °C). The results demonstrated that even minimal steering input could result in significant side-slip angles, highlighting the nonlinear vehicle behavior and the critical need for robust traction estimation in such challenging conditions of general racing tracks. The proposed friction-estimation method was evaluated through vehicle testing and has been substantiated by patents for its originality in control and friction-estimation approaches. The outcomes of these combined methodologies underline the critical importance of tire–road friction coefficient estimation in both the effectiveness of the ELSD system and the broader context of active safety systems.

Research on collision warning strategy considering characteristics of drivers and road conditions

Collision warning strategy considering different characteristics of drivers and complex road conditions is of great importance for active safety control of autonomous vehicles. However,existing estimation methods for Tire-road friction coefficient (TRFC) cannot deal with the problem of estimation accuracy degradation caused by state mutation. Therefore, an adaptive cascaded strong tracking unscented Kalman filter (ACSTUKF) is proposed to estimate TRFC. The proposed algorithm consists of two strong tracking filters, which are connected in series with each other. Fuzzy control is introduced to estimate the reaction time of different drivers. Simulation experiments and real vehicle tests are carried out to demonstrate the effectiveness of the proposed strategy. Results show that the proposed ACSTUKF has a more excellent performance for TRFC than EKF and UKF, which greatly reduces the impact of state mutation. Moreover, ACSTUKF shows a strong robustness to driving conditions and road conditions. The established collision warning strategy is consistent with the actual situation, which realizes the adaptation of human and road.

Modeling and Clamping Force Tracking Control of an Integrated Electric Parking Brake System Using Sliding-Mode-Based Observer

This article proposes a hierarchical control strategy to address semi-ABS control as well as the precise clamping force control problems for an integrated electric parking brake (iEPB) system. To this end, a detailed system model, including modeling of the motor, transmission mechanism, friction and braking torque, is constructed for controller and observer design, and a sliding-mode-based observer (SMO) is proposed to estimate the load torque by using the motor rotational speed without installing a force sensor. In addition, a stable and reliable tire–road friction coefficient (TRFC) estimation method is adopted, and the desired slip ratio (DSR) is observed as the target that the rear wheels cycle around. At the upper level of the hierarchical control structure, the desired clamping forces of the rear wheels are generated using a sliding mode control (SMC) technique, and the control objective is to track the DSR to make full use of the road condition. At the lower level, the motor is controlled to track the desired clamping force generated from the upper controller. The hardware-in-the-loop (HIL) experimental results demonstrate the effectiveness and high tracking precision of the proposed strategy under different road conditions, and the estimation parameters based on the proposed observers are timely and accurate to satisfy the control requirements.

Tire Road Friction Coefficient Estimation for Individual Wheel based on two Robust PMI Observers and a Multilayer Perceptron

Tire Road Friction Coefficient Estimation for Individual Wheel based on two Robust PMI Observers and a Multilayer Perceptron

A Novel Fault-Tolerant Scheme for Multi-Model Ensemble Estimation of Tire Road Friction Coefficient With Missing Measurements

A Novel Fault-Tolerant Scheme for Multi-Model Ensemble Estimation of Tire Road Friction Coefficient With Missing Measurements

Real-time estimation of longitudinal tire stiffness considering dynamic characteristics of tire

To enhance the effectiveness of active safety control, the tire–road friction coefficient (TRFC) must be precisely estimated, and the longitudinal tire stiffness coefficient is an important vehicle dynamic parameter to estimate TRFC. In this research, we present an observer that improves the performance of longitudinal tire stiffness coefficient estimation by applying tire dynamics that were previously applied in the lateral direction to the longitudinal direction. To begin, we model longitudinal tire dynamics using the relaxation length concept and validate the model using vehicle braking tests. We develop an observer that estimates the longitudinal tire stiffness coefficient by integrating the proposed tire dynamics and vehicle dynamics. The observer, which is based on an extended Kalman filter, can be applied to nonlinear systems and successfully removes noise from wheel speed measurement. The observer’s estimation performance is verified using CarSim simulation and vehicle tests, and the results are compared to existing approaches that do not account for longitudinal tire dynamics. Even in the transient section when the vehicle begins accelerating, the difference between the estimate and the reference value is about 0.3% using the proposed method, but if tire dynamics are not taken into account, the estimate is 6.5% lower than the reference value.

Development of an Autonomous Measurement System for Estimation of Snow Profile on Road Surfaces

This paper presents the development of a novel prototype system to measure the profile of snow and detect ice on road surfaces. While researchers have previously developed methods to estimate the tire-road friction coefficient, methods to create a high resolution map of snow cover and ice on roads have not been developed. The prototype and data processing methods presented in this study provide a potential solution that would greatly benefit winter road maintenance teams. Having a device capable of creating a detailed map of snow and ice cover on roads would allow for more efficient plowing and salt deployment, better informing of the public about current road conditions, as well as better analysis of current plowing techniques to improve winter road maintenance operations. The measurement of the snow profile is based on the use of two types of inexpensive ranging sensors mounted on a rotationally controlled stepper motor platform. The technical challenges addressed in the development include analysis of the scan path over which the system scans the road, differentiation between asphalt, concrete, and snow surfaces using reflection amplitudes, accurate transformation of raw distance measurements to inertial coordinates, and identification of the Euler angles of the sensors using parameters associated with the scanned surface profile. Extensive experimental results and test data are presented, which show that the system is capable of measuring the snow profile on a road with an accuracy of ±1 cm when a reasonable portion of bare road is visible, and ±2 cm when only small portions of bare road are visible.

A phase plane H∞ controller for distributed drive electric vehicles with stability enhancement based on tire road friction coefficient estimation

An H∞ control strategy based on the phase plane method (phase plane H∞ controller) tracking two degrees of freedom (DOF) ideal vehicle trajectory scheme is designed for distributed drive electric vehicles with stability enhancement. Firstly, an Extended Kalman Filter (EKF) tire road friction coefficient estimation method based on Keras neural network is presented to accurately and efficiently identify the tire road friction coefficient, taking into account the huge influence of the tire road friction coefficient on vehicle equilibrium point and stability region. Secondly, the phase plane method is applied to provide a dynamic stability boundary for the switching control strategy of direct yaw moment for different tire road friction coefficients; Furthermore, based on the dynamic stability boundary, the weighted phase stability is applied to achieve more realistic stability evaluation criteria, and the fuzzy control strategy is adopted to carry out the feedback regulator of the target side slip angle and yaw rate on the purpose of limiting its maximum value max ( β) and max ( ωr). Then the torque of the four-wheel was optimized by the quadratic programming method. Finally, the presented method is verified and the results indicate that: (1) the phase plane H∞ control has the advantage in terms of stability and maneuvering performance. More importantly, under a low tire road friction coefficient, the amplitude of the side slip angle is decreased by 26.52% over the H∞; (2) the designed EKF based on Keras neural network parameter correction has a quick and accurate performance in identifying the tire road friction coefficient, and the steady-state error does not exceed 3.25%.

Tire-Road Friction Coefficient Estimation for Distributed Drive Electric Vehicles Using PMSM Sensorless Control

Many tire-road friction coefficient estimation methods require the wheel angular speed sensor to provide a signal. In this paper, a tire-road friction coefficient estimation algorithm for distributed drive electric vehicles using permanent magnet synchronous motors(PMSM) sensorless control is proposed to reduce the use of wheel angular speed sensors. The wheel angular speed signal is replaced by the rotor speed signal obtained from PMSM sensorless control. First, the three degrees of freedom vehicle dynamics model and the PMSM mathematical model are established, and a strong tracking cubature Kalman filtering algorithm based on orthogonal transformation (T-STCKF) is derived to overcome the problem that the STCKF algorithm is prone to nonlocal sampling when dealing with high dimensional systems. Second, a PMSM sensorless control system based on the adaptive exponent reaching law of sliding mode control and the T-STCKF algorithm is established, and confirmed its validity. Finally, the feasibility of the proposed algorithm is demonstrated through multicase simulation and experiment and the results shows that the T-STCKF algorithm is more accurate than the STCKF algorithm.

Predictive Anti-Jerk and Traction Control for V2X Connected Electric Vehicles With Central Motor and Open Differential

V2X connectivity and powertrain electrification are emerging trends in the automotive sector, which enable the implementation of new control solutions. Most of the production electric vehicles have centralized powertrain architectures consisting of a single central on-board motor, a single-speed transmission, an open differential, half-shafts, and constant velocity joints. The torsional drivetrain dynamics and wheel dynamics are influenced by the open differential, especially in split- scenarios, i.e., with different tire-road friction coefficients on the two wheels of the same axle, and are attenuated by the so-called anti-jerk controllers. Although a rather extensive literature discusses traction control formulations for individual wheel slip control, there is a knowledge gap on: a) model based traction controllers for centralized powertrains; and b) traction controllers using the preview of the expected tire-road friction condition ahead, e.g., obtained through V2X, for enhancing the wheel slip tracking performance. This study presents nonlinear model predictive control formulations for traction control and anti-jerk control in electric powertrains with central motor and open differential, and benefitting from the preview of the tire-road friction level. The simulation results in straight line and cornering conditions, obtained with an experimentally validated vehicle model, as well as the proof-of-concept experiments on an electric quadricycle prototype, highlight the benefits of the novel controllers.

Tire-road friction coefficient estimation for automatic guided vehicle under multiple road conditions

The traditional unscented Kalman filter (UKF) will have the problem of reduced accuracy or even divergence in the estimation process due to state model perturbation, unknown noise of the system, and other factors, which in turn affect the estimation results of the tire-road friction coefficient. By this problem, the paper investigates the tire-road friction coefficient estimation by taking an automatic guided vehicle (AGV) as the research object and proposes an adaptive singular value decomposition unscented Kalman filter (ASVD-UKF) with a noise estimator. Singular value decomposition (SVD) is introduced into the unscented Kalman filter (UKF) for Sigma sampling to suppress the negative definiteness of the state covariance matrix in UFK. The paper considered estimation schemes for joint road, μ-split road, and μ-different road and constructed corresponding ASVD-UKF observers to reduce the dimension of the road estimation model and real-time observation of four tire-road friction coefficients. Results show that the average absolute error of the μ-split road, joint road, and μ-different road proposed in this paper is significantly smaller than that of UFK, and the estimation accuracy is improved by 13.39%, 6.74%, and 5.71%, respectively. A Distributed Drive AGV prototype was developed for a real vehicle verification experiment, with only a 1.14% error between simulation and experiment. It is further proved that the designed observers are practical. The research can provide a theoretical basis and experimental foundation for the tire-road friction coefficient estimation.

Pavement Friction Evaluation Based on Vehicle Dynamics and Vision Data Using a Multi-Feature Fusion Network

The tire–road friction coefficient is a critical evaluation index of the service performance of roads: it governs the stopping distance, traction control, and stability of vehicles. Moreover, friction information is also needed in many function units of modern vehicles. This paper proposes a novel data-driven approach for inference of the maximum tire–road friction coefficient using a combination of vehicle dynamics signal and machine vision data. The approach is aimed at robust road condition perception that can provide frequent measurements over large areas across all weather conditions. Two different neural network architectures were adopted to extract in-depth features behind vehicle dynamics signals and road surface images. Features from these two types of data were then fused in two different levels, namely feature level and decision level, forming a multi-feature fusion neural network. The proposed network performs better than models based only on dynamic signals or vision data. The method proposed was applied to real data obtained from an electric car in a highway driving scenario. For classification of the maximum tire–road friction coefficient, the proposed network can yield F1-score increments of 0.09 and 0.18 from dynamics-based and vision-based sub-models, respectively. For the maximum tire–road friction coefficient value regression, the proposed model also achieves the highest R-square score of 0.71. Of these two types of data collected under highway driving scenarios, the vision data contribute more to the overall performance of the proposed model. Nevertheless, the dynamics data possess excellent potential in poor lighting conditions. With these fused features, the proposed multi-feature fusion network can not only improve the accuracy of maximum tire–road friction coefficient estimation but also is deemed workable for a broader range of scenarios.

Estimation of Tire-road Friction Limit with Low Lateral Excitation Requirement Using Intelligent Tire

<div class="section abstract"><div class="htmlview paragraph">Tire-road friction condition is crucial to the safety of vehicle driving. The emergence of autonomous driving makes it more important to estimate the friction limit accurately and at the lowest possible excitation. In this paper, an early detection method of tire-road friction coefficient based on pneumatic trail under cornering conditions is proposed using an intelligent tire system. The previously developed intelligent tire system is based on a triaxial accelerometer mounted on the inner liner of the tire tread. The friction estimation scheme utilizes the highly sensitive nature of the pneumatic trail to the friction coefficient even in the linear region and its approximately linear relationship with the excitation level. An indicator referred as slip degree indicating the utilization of the road friction is proposed using the information of pneumatic trail, and it is used to decide whether the excitation is sufficient to adopt the friction coefficient estimate. The friction coefficient is estimated by the ratio of the normalized lateral force and the nonlinear adaptation of the slip degree. The tire forces and pneumatic trail are estimated by neural networks. The experimental validation demonstrates that the pneumatic trail has a good potential to precisely predict the friction coefficient at a low excitation under cornering conditions.</div></div>

A model-based method of tire-road friction estimation for articulated steering vehicles

Articulated steering vehicles (ASV) are widely used in many industries for their high efficiency and excellent maneuverability. The autonomous driving and intelligent control of ASV are extremely critical owing to the operation characteristics. As a very important parameter, the tire-road friction coefficient (TRFC) determines the extreme tire force directly in the process of intelligent control. However, it cannot be obtained with the existing methods for the harsh environment and special structure of ASV. This paper proposed a two-layer model-based method of tire-road friction coefficient estimation for ASV. The dynamic models of ASV in the XY plane, including the longitudinal and lateral models of frames, tire forces, and steering system models, are established first. The dynamic models are embedded into the upper layer with a Kalman filter (KF) to estimate the tire forces in longitudinal and lateral directions. During the process, some self-contained sensors, including the state sensors of frames and steering system, are used to provide the observation data. In the lower layer, a recursive least square (RLS) method with a forgetting factor is used to obtain the TRFC and tire stiffness parameters with the aid of the tire model. The simulation and field test are carried out to validate the method under comprehensive conditions, in which different steering commands, velocities, and roads are included. The simulation and field test results show that the forgetting factor has a significant influence on the convergence and robustness of the proposed method. The forgetting factor τ = 0.95 is used in the field test, the estimation result of dry concrete road friction coefficient is around 0.83. The results indicated that the proposed method can obtain the TRFC and tire parameters dynamically for ASVs.

Path Tracking Control of Intelligent Vehicles Considering Multi-Nonlinear Characteristics for Dual-Motor Autonomous Steering System

In the path tracking control of intelligent vehicles, the traditional linear control method is prone to high tracking errors for uncertain parameters of the steering transmission system and road conditions. Therefore, considering the mechanical friction in the dual-motor autonomous steering system and the nonlinearity of tires, this paper proposes a path tracking control strategy of intelligent vehicles for the dual-motor autonomous steering system that considers nonlinear characteristics. First, a dual-motor autonomous steering system considering mechanical friction and the variation of tire cornering stiffness under different tire–road friction coefficients was established based on the structure of an autonomous steering system. Second, a tire–road friction coefficient estimator was designed based on a PSO-LSTM neural network. The tire cornering stiffness under different tire–road friction coefficients was estimated through the recursive least-square algorithm. Then, the control strategy of the dual-motor autonomous steering system was designed by combining the LQR path tracking controller with the adaptive sliding mode control strategy based on field-oriented control. Here, mechanical friction and the variation of tire cornering stiffness were considered. Finally, simulation and HiL tests validated the method proposed in this paper. The results show that the proposed control strategy significantly improves the tracking accuracy and performance of the dual-motor autonomous steering system for intelligent vehicles.

Tire-road friction coefficient estimation method design for intelligent tires equipped with PVDF piezoelectric film sensors

Intelligent tires, as an emerging technology, have great potential in real-time monitoring of tire-road contact information and new automotive active safety design. In this paper, a tire-road friction coefficient estimation method is proposed based on intelligent tire technology. First, an intelligent tire finite element model with the use of five PVDF piezoelectric film sensors attached to the inner liner of the tire is built using ABAQUS software, and the validity of the finite element model is verified by a piezoelectric intelligent tire test platform. Then, through the finite element analysis method and control variable method, the influence of sideslip angle on the voltage signal of each piezoelectric film under the rolling state of tire is analyzed, and when the sideslip angle is 4°, the influence of load, tire pressure, vehicle speed and slip ratio on the voltage signal of each piezoelectric film under the rolling state of tire is analyzed. Finally, based on the signal response analysis of the piezoelectric film sensors, the response mechanism of the predicted object and the linear correlation analysis, the input eigenvalues of each prediction model are extracted. The longitudinal contact patch length estimation model based on the numerical method and the sideslip angle, vertical force, lateral force and aligning moment estimation model based on the neural network algorithm are built, and the predicted parameters are input into the brush tire model to solve the tire-road friction coefficient. The result shows that the estimation error percentage of the friction coefficient estimation method without genetic algorithm optimization is 16.98%, and the estimation error percentage of the friction coefficient estimation method with genetic algorithm optimization is 5.14%, indicating that the genetic algorithm optimization effect is ideal, and the friction coefficient estimation method is practical. ● Developing an intelligent tire finite element model equipped with PVDF sensors ● Real vehicle test verifies the validity of the intelligent tire finite element model ● Analyzing the signal response of PVDF sensors under different working conditions ● Estimating the tire-road friction coefficient using intelligent tire system and brush tire model

Path following control for 4WID-EV based on extended state observer and sliding mode control considering yaw stability

Automatic driving technology has developed over time and the path-following problem for four-wheel independent drive electric autonomous vehicles (4WID-EV) is a topic of increasing interest. During the path-following process, a consideration of uncertainties in vehicle modeling including parameter variation, modeling error, and external disturbances is made, which have an important effect on path-tracking performance. As so, we proposed a new path following control strategy that can be applied to robotics applications. First, it was determined to establish a 2 DOF dynamic model and path following error model, and were then converted to yaw angle tracking problems. Therefore, the desired control input of steering angle was obtained via yaw angle tracking controller. To estimate and compensate the uncertainties associated with systems, the nonlinear extended state observer (NESO) was designed while the NTSM controller was used to realize yaw angle tracking. Next, considering the system stability, a sliding mode controller with modified reaching law was used to obtain the desired additional yaw moment. Then, the optimized torque distributor was designed for allocating optimal tire forces. Finally, the simulation experiments were carried out in Matlab/Simulink and Carsim joint simulation platform. In conclusion, the proposed control scheme exhibits highly accurate path following as well as strong robustness to speed, tire-road friction coefficient and external disturbance.

Tire-Road Friction Coefficient Estimation Based on Fusion of Model- and Data-Based Methods

Abstract The tire-road interaction generates vehicle driving forces, which affect vehicle performance such as maximum acceleration and stability. Sequential extended Kalman filter (S-EKF) integrated with a slope method has been used for tire-road friction coefficient estimation with its own limitations, along with several “cause-based” and “effect-based” methods. This research proposes a new stochastic-based evaluation criterion using existing vehicle sensor signals with the help of the data-driven Kriging model. The proposed estimation method is validated by both CarSim™ simulation and experimental studies, respectively, under different road conditions. The results show that the proposed novel criterion has a strong correlation with the road friction coefficient and provide an improved tire-road friction coefficient estimation. A signal fusion estimation scheme based on both S-EKF and proposed evaluations is developed to improve estimation robustness.