Tire-road Friction Coefficient Research Articles

Driving force coordinated control of an 8×8 in-wheel motor drive vehicle with tire-road friction coefficient identification

Because of the complexities of tire-road interaction, the wheels of a multi-wheel distributed electric drive vehicle can easily slip under certain working conditions. As wheel slip affects the dynamic performance and stability of the vehicle, it is crucial to control it and coordinate the driving force. With this aim, this paper presents a driving force coordination control strategy with road identification for eight-wheeled electric vehicles equipped with an in-wheel motor for each wheel. In the proposed control strategy, the road identification module estimates tire-road forces using an unscented Kalman filter algorithm and recognizes the road adhesion coefficient by employing the recursive least-square method. According to road identification, the optimal slip ratio under the current driving condition is obtained, and a controller based on sliding mode control with a conditional integrator uses this value for acceleration slip regulation. The anti-slip controller obtains the adjusting torque, which is integrated with the driver-command-based feedforward control torque to implement driving force coordination control. The results of hardware-in-loop simulation show that this control strategy can accurately estimate tire-road forces as well as the friction coefficient, and thus, can effectively fulfill the purpose of driving force coordinated control under different driving conditions.

A Super-twisting Controller for Active Control of Ground Vehicles with Lateral Tire-road Friction Estimation and CarSim Validation

In this paper, a ground vehicle equipped with Active Front Steering (AFS) and Rear Torque Vectoring (RTV) is considered. The AFS, actuated through the front tires, adds an incremental steer angle on top of the driver’s input, whereas the RTV, actuated through the rear tires, imposes a yaw torque to the vehicle. These actuators allow the active control of the vehicle chassis, so that a feasible and safe reference trajectory can be tracked. To obtain such a feasible reference generation and an efficient control action, the lateral tire-road friction coefficient has to be estimated. To this aim, in this paper the lateral tire-road friction coefficient is estimated in finite-time by means of a high-order sliding mode differentiator. Then, based on this estimation, a high-order sliding mode controller is designed to track the desired references. The performance of the dynamic controller is evaluated using a CarSim virtual vehicle, and the simulation results highlight the characteristics of the proposed observer-based control.

Comparative assessment of vehicle anti-lock braking system operation using friction brake mechanisms and e-machine in the vehicle with electric drive of traction wheels

Study of the braking process of the vehicle with an electric machine in the traction wheels drive equipped with an anti-lock braking system (ABS), where the actuators are the electric machine and friction brake mechanisms, is a relevant task. This is related to the worldwide trending increase in the share of production of vehicles with an electric machine within the transmission. In this paper, the “traditional” ABS and two systems with different variants of usage of the electric machine and friction brake mechanisms as actuators are compared: 1. The electric machine fulfills the function of the wheel slip regulator; the friction brake mechanisms maintain constant pressure in the brake line, which depends on the tyre-road friction coefficient. 2. The friction brake mechanisms fulfill the function of the wheel slip regulator; the electric machine maintains the set brake torque. According to the study results, usage of the combined actuator system within the ABS allows reducing the braking distance significantly, raising the vehicle deceleration value and improving the driver’s and passengers’ comfort during braking.

Interval Recognition Algorithm of the Pavement Surface Condition Based on Lagrange Interpolation Method

The accurate recognition of road condition is one of the important factors that influence vehicle safety performance. This paper comes up with an original mathematical method of an interval recognition algorithm of the pavement surface condition based on Lagrange interpolation. The ordinate of the peak point is solved by the Lagrange interpolation method, and the pavement surface condition is deduced by the interval identification algorithm. The simulation results from six typical roads and the varied pavement surface show that besides the cobblestone pavement which is not common in the daily road, the estimation error of the initial tire-road friction coefficient by the Lagrange interpolation method is less than 2%, the pavement surface condition can be identified by interval recognition algorithm quickly and accurately, and the response time is less than 0.2 seconds.

Rear-Wheel Steering Control for Enhanced Steady-State and Transient Vehicle Handling Characteristics

This paper presents a rear-wheel steering (RWS) control algorithm to enhance the vehicle handling performance without prior knowledge of tire characteristics. A RWS system is a chassis control module that can effectively improve vehicle maneuverability and stability. Since the tire-road friction coefficient is difficult to obtain in real world application, the proposed RWS control algorithm is designed so that it can be implemented without any tire-road information. The proposed RWS control algorithm consists of steady-state and transient control inputs. The steady-state control input is proportional to the driver's steering input for achieving the desired yaw rate gain. The desired yaw rate gain is obtained through an offline optimization that is aimed to minimize the vehicle lateral velocity. The transient control input consists of feedforward and feedback control inputs. The feedforward input is designed to improve transient responses of the yaw rate. Computer simulation studies have shown that a trade-off relationship between overshoot and response time exists when the RWS control input is a sum of the steady-state and feedforward inputs. To compromise this conflict, a feedback input has been designed. The overshoot can be significantly reduced while the response time is slightly changed via the feedback input. The proposed algorithm has been investigated via computer simulations. The simulation has been conducted for step steer and sine with dwell scenarios under various road friction conditions. The performance of a RWS vehicle was evaluated using objective indices. Simulation results show that the proposed algorithm enhances vehicle handling performance.

Grid Search Based Tire-Road Friction Estimation

The tire-road friction coefficient (μ max ) is an important input for vehicle dynamics control system and automated driving modules. However, reliable and accurate measurement of this parameter is difficult and costly in mass-produced vehicles and thus estimation is necessary. In this research, an innovative optimization based framework to estimate μ max is proposed. The observation problem is formulated as a non-convex optimization. A novelty of the framework is that the μmax can be accurately estimated in real time together with side slip angle as a by-product without requiring a good initial guess for the non-convex optimization. A key observation is that the time derivative of μmax and side slip angle can be assumed as zero and computed based on measurement, respectively. This allows the observed variables to be updated at a relatively low frequency w.r.t. the solution of the optimization problem. During the interval between each two neighbouring updating time, the observer estimates the μ max and side slip angle by integrating sensor information based on the last update. To find the global optima approximately, a grid search method is implemented for solving non-convex optimization. The estimation results from the proposed observer and a linearization based observer (lbo) are finally compared under various tire-road conditions with simulations and experiments. The results showed that 1) the proposed observer can always guarantee stability in a wide range of vehicle operations while lbo cannot. 2) w.r.t. root mean square of estimation error, the proposed observer performs overall better than lbo in μmax estimation.

Path Planning and Tracking for Autonomous Vehicle Collision Avoidance with Consideration of Tire-Road Friction Coefficient

Abstract Autonomous vehicles (AVs) have attracted a lot of attention in recent years and fully-autonomous vehicles are expected on road in the near future. Collision avoidance is one of the key driving tasks for autonomous driving which consists of path planning and tracking control. The main problem discussed in this paper is the development of a path planning and tracking framework based on model predictive control (MPC) with consideration of the estimated tire-road friction coefficient (TRFC). The planned path in terms of lateral position is generated based on the safety distance between the host and the obstacle vehicle, which is related to TRFC and vehicle speed. A new structure of MPC is further designed so that only lateral position is required to track the planned path. Moreover, the adaptive weights on the outputs to a wide range of vehicle speeds have been identified. The effectiveness of the proposed planning and tracking framework is validated through CarSim-MATLAB/Simulink co-simulations on both high- and low-friction roads.

Vehicle Lateral Dynamic Identification Method Based on Adaptive Algorithm

The development of advanced driver assistance systems relies on an accurate estimation of the tire-road friction coefficient and cornering stiffness of the vehicle, which are closely linked to internal and external driving conditions. In this paper, an identification algorithm capable of simultaneously estimate the friction coefficient and cornering stiffness of the front and rear tires is pursued. A nonlinear adaptive law is proposed for the estimation of vehicle parameters under certain excitation conditions. It is shown that, by exploring the lateral dynamic of the vehicle, the convergence of the parameters to their true values can be guaranteed. A comprehensive study has been carried out in order to reveal the necessary conditions for convergence and observability of the parameters. Simulation results with a high fidelity full order Carsim model show a good performance of the proposed identification method.

Estimation of tire–road friction for road vehicles: a time delay neural network approach

The performance of vehicle active safety systems is dependent on the friction force arising from the contact of tires and the road surface. Therefore, an adequate knowledge of the tire–road friction coefficient is of great importance to achieve a good performance of different vehicle control systems. This paper deals with the tire–road friction coefficient estimation problem through the knowledge of lateral tire force. A time delay neural network (TDNN) is adopted for the proposed estimation design. The TDNN aims at detecting road friction coefficient under lateral force excitations avoiding the use of standard mathematical tire models, which may provide a more efficient method with robust results. Moreover, the approach is able to estimate the road friction at each wheel independently, instead of using lumped axle models simplifications. Simulations based on a realistic vehicle model are carried out on different road surfaces and driving maneuvers to verify the effectiveness of the proposed estimation method. The results are compared with a classical approach, a model-based method modeled as a nonlinear regression.

Control of Antilock Braking Systems Using Disturbance Observer With a Novel Nonlinear Sliding Surface

In this article, the problem of control of antilock braking systems under significant uncertainties and unknown relationship between tire-road friction coefficient and wheel slip ratio for a two-axle vehicle model is considered. Two methods based on a disturbance observer and sliding mode control are proposed. In the first method, a conventional sliding surface is used while in the second method a new nonlinear sliding surface is proposed as an improvement over the first method. The performance under the proposed methods is assessed analytically and by MATLAB simulation under different road conditions. The proposed methods are validated further on CarSim platform.

UKF-based State and tire slip estimation for a 4WD electric vehicle

For performance improvement of modern vehicle dynamic control systems, exact knowledge of the vehicle motion state and the road conditions is essential. Addressing this problem, the development and validation of a state observer for a four-wheel drive electric vehicle is examined in this article. In particular, a reliable and accurate estimation of the tire slip in longitudinal and lateral direction at each wheel is desired. For this, an Unscented Filter is used to estimate the vehicle chassis and wheel dynamics. At the same time, the estimator is able to adapt the tire model according to the current road conditions by using wheel-individual tire-road friction coefficients. In the beginning, details on the used vehicle model as well as the estimator tuning and implementation procedure are given. The validation takes place first in a vehicle simulation environment to point out the performance of the observer especially in severe driving situations, like a sudden change of road friction conditions during a slalom manoeuver. Afterwards, driving tests with an electric four-wheel drive vehicle are carried out to proof the presented observer concept under real-world conditions. All performed driving manoeuvers are described and the test results are presented and evaluated.

Vibration energy harvesting technology for smart tire monitoring

A smart tire monitoring system uses tire information, such as temperature, pressure, acceleration, force, tire-road friction coefficient, in real time to monitor the driving safety of cars. A vibration energy harvester for a smart tire monitoring system converts the tire dynamic strain energy into electrical energy which is the power source of the wireless sensor module. The self-powered wireless sensor module consists of an electro-magnetic type energy harvester, a power conversion circuit, an acceleration sensor and a radio communication circuit. This research is focused on achieving high energy conversion efficiency, lightweight design, and long durability of the harvester because it is located at the inner surface of tire where extremely high pressure and acceleration exist. The energy harvester was made in a cylindrical shape with a length of 35 mm. The manufactured harvester was 9.4 g, the casing 10.8 g, the battery 2.6 g, the wireless acceleration sensor module 1.1 g, and the power conversion circuit module 1.2 g. So, the total weight of the wireless sensor module was less than 27 g. The monitoring system receives an acceleration signal from the wireless sensor module which is attached to the inner surface of a tire. An operating test of the monitoring system was carried out by using the tire driving test equipment. The average output power of the energy harvester was measured as about 5.7 mW at 60 km/h. The wireless sensor module was operated during about 11700 km (60 km / h * 6.5 h / day * 30 day). The test results showed that the energy harvester has sufficient power to maintain the operation of the wireless sensor module, and the sensor module has a sufficient durability.

Force-based braking control algorithm for vehicles with electric motors

ABSTRACT Electric motors offer the possibility to control the braking torque in a more precise way than the hydraulic circuit. The applied torque is in fact measured and so it can be used to feedback the controller. Moreover, this information can be used to estimate the tyre–road friction coefficient, before potential friction is reached. The present paper proposes a novel ABS control strategy for electric vehicles with distributed motors. The controller is a six states machine that uses the information on applied braking torque provided by the electric motors. This information is of paramount importance to understand when the wheel reaches the peak of the braking force. Simulation results shows the benefits of the proposed strategy, comparing the results with state of the art acceleration-based controller.

Two-Time-Scale Redesign for Antilock Braking Systems of Ground Vehicles

An antilock braking system (ABS) is one of the most effective active safety control systems for ground vehicles, since it can keep the rotational wheel from locking and, consequently, guarantee the braking safety and handling stability. There have been a variety of ABS control schemes proposed by many researchers. However, most of the results employ sundry tire–road friction models, the alleged $\mu\, \text{--}\,\lambda$ curves ( $\mu$ is the tire–road friction coefficient, while $\lambda$ is the tire slip ratio, which is mathematically defined as $\lambda =({v-\omega r})/{v}$ ), making the ABS controller extremely complicated for the highly nonlinear characteristics of the $\mu\, \text{--}\,\lambda$ relationship. Furthermore, the a priori knowledge of road conditions for these ABS controllers restricts their practicability. To circumvent these problems, a two-time-scale ABS control scheme is proposed in this paper, without considering the intricate $\mu\, \text{--}\,\lambda$ relationship, making the a priori knowledge of the road condition no longer a prerequisite; thus, the designed ABS controller is rather simple. In addition, a modified fast-time-scale estimator is involved to estimate the road condition, which is significant in vehicle active dynamics control. The effectiveness of the proposed ABS controller is verified via numerical simulations and CarSim–MATLAB cosimulations.

Identifying Vehicle and Collision Impact by Applying the Principle of Conservation of Mechanical Energy

Abstract Various methodologies and tools applied to identification of vehicle and collision impact seek to present more and more accurate solutions to reproduce, restore, recreate and investigate the casualty. Modern computer technology and software provide the tools to solve specific problems developing mathematical modelling of complex mechanical systems involving vehicles and other objects in a road accident. Scientists generally utilize the Standard Test Method for Impact Testing calculating the energy of deformation of both vehicles, however, one of its limitations is the evaluation of the kinetic energy of the vehicles in post-collision taking into consideration vehicle rotation and linear displacement. To improve the analysis, dynamic traffic simulation is used, taking into account the variations in the coefficient of friction, suspension elasticity and damping. The proposed method is based on a system of two equations derived from two principles: the Principle of Conservation of Mechanical Energy and the Principle of Conservation of Momentum in the impact phase. The new approach is conducted on mathematical modelling and computer simulation of vehicle motion after the impact, wherefrom the linear and angular velocities are analysed. This is achieved by the numerical solution of the differential equations of motion of the cars after the impact, and the given initial conditions that satisfy the solution are used to solve the system of equations. The main findings of the study can be grouped as follows: 1) The positions of the vehicles prior to the moment of first impact and the post-impact orientation of velocity vectors are more precise. 2) The variability of the tire-road friction coefficient is taken into consideration. 3) The value of coefficient of restitution according to Newton’s theory of impact is unnecessarily determined.

Calculation Algorithm of Tire-Road Friction Coefficient Based on Limited-Memory Adaptive Extended Kalman Filter

In this paper, a limited-memory adaptive extended Kalman Filter (LM-AEKF) to estimate tire-road friction coefficient is proposed. By combining extended Kalman filter (EKF) with the limited-memory filter, this algorithm can reduce the effects of old measurement data on filtering and improve the estimation accuracy. Self-adaptive regulatory factors were introduced to weigh covariance matrix of evaluated error. Meanwhile, measured noise covariance matrix was adjusted dynamically by fuzzy inference to accurately track the breaking status of system. Therefore, problems, including large filter error and divergence caused by incorrect model, can be solved. Joint simulation was conducted for the proposed algorithm with Carsim and Matlab/Simulink. Under the different road conditions, real-vehicle road tests were conducted in various working conditions for contrast with traditional EKF results. Simulation and real-vehicle road tests show that this algorithm can enhance the filter stability, improve the estimation accuracy of algorithm, and increase algorithm robustness.

Creation of electric vehicle ABS operation algorithm with possibility of hybrid braking based on slip-slope approach at wheels slip determining

This paper represents an Anti-lock Braking System (ABS) operation algorithm implementing hybrid braking; the paper considers braking with a high deceleration of an electric passenger vehicle during the rectilinear driving on the roads with different friction coefficients; a short analysis of the approaches used for evaluation of the target vehicle wheels slip is also performed. The main ABS task consists in maintenance of the target wheel slip coefficient based on the tyre-road friction coefficient. The tyre-road friction coefficient φx is determined using the algorithm proposed in the papers by Semmler. The algorithm is about finding the curve peak φx−S using the least square method. Based on the calculated target slip coefficient, the braking torque at the electric motor shaft operating in the regeneration mode is determined. The electric motor ensures relatively low braking torque at the vehicle wheels preventing the tyres from a significant slip. Reaching the target slip coefficient is ensured by means of friction brake mechanisms. Virtual tests showed that the values of the wheel slip coefficient are close to the required ones. Thus, this system makes it possible to implement hybrid braking with two sources creating the brake torque.

Energy Management of Hybrid Electric Vehicle Using Vehicle Lateral Dynamic in Velocity Prediction

Accurately predicting the changes in the speed has a significant impact on the quality of the energy management in hybrid vehicles. Many methods for predicting the speed have been proposed in the literature, but few fully consider vehicle dynamics to predict speed changes. To this end, a new method is introduced to predict the vehicle speed and to perform energy management for hybrid vehicles in situations where lateral dynamics plays a significant role. Based on the tire–road friction coefficient and the GPS signal, the maximum cornering speed of the vehicle, in which each tire force does not saturate, is evaluated. Then, the principle of using less friction braking and using more regenerative braking, the vehicle speed prediction controller is designed. In the end, an optimal control method with a new equivalent factor (EF) adaptive algorithm is designed to distribute the torque of the engine and the motor, as well as the shift schedule of the gearbox. A driver-in-the-loop experiment is used to prove that the vehicle installed with the proposed speed prediction controller has an average 29.1% increase in energy efficiency compared to vehicle that do not have speed prediction controller. And, the EF adaptive algorithm keeps the battery SoC at a reasonable interval.

Adaptive Unified Monitoring System Design for Tire-Road Information

Knowledge of the tire-road information is not only very crucial in many active safety applications but also significant for self-driving cars. The tire-road information mainly consists of tire-road friction coefficient and road-tire friction forces. However, precise measurement of tire-road friction coefficient and tire forces requires expensive equipment. Therefore, the monitoring of tire-road information utilizing either accurate models or improved estimation algorithms is essential. Considering easy availability and good economy, this paper proposes a novel adaptive unified monitoring system (AUMS) to simultaneously observe the tire-road friction coefficient and tire forces, i.e., vertical, longitudinal, and lateral tire forces. First, the vertical tire forces can be calculated considering vehicle body roll and load transfer. The longitudinal and lateral tire forces are estimated by an adaptive unified sliding mode observer (AUSMO). Then, the road-tire friction coefficient is observed through the designed mode-switch observer (MSO). The designed MSO contains two modes: when the vehicle is under driving or brake, a slip slope method (SSM) is used, and a recursive least-squares (RLS) identification method is utilized in the SSM; when the vehicle is under steering, a comprehensive friction estimation method is adopted. The performance of the proposed AUMS is verified by both the matlab/simulinkCarSim co-simulation and the real car experiment. The results demonstrate the effectiveness of the proposed AUMS to provide accurate monitoring of tire-road information.

Observer-based estimation of velocity and tire-road friction coefficient for vehicle control systems

A novel nonlinear observer for the estimation of vehicle velocity together with the tire-road friction coefficient is presented in this paper. The modular observer is designed based on a longitudinal tire force estimation approach and a lateral tire friction model. Compared to the state-of-art methods, the proposed observer design provides accurate estimation of the longitudinal velocity, lateral velocity, and the tire-road friction coefficient simultaneously. Particularly, the longitudinal tire forces are first estimated based on a filter observer. Then, according to the calculation of lateral tire forces, the nonlinear observer is proposed to estimate vehicle velocity and the tire-road friction coefficient. Moreover, the stability property of the observer is analyzed using a Lyapunov-based method. Simulation results validate the effectiveness of the proposed method.