Tire Force Estimation Research Articles

Vehicle Sideslip Angle EKF Estimator based on Nonlinear Vehicle Dynamics Model and Stochastic Tire Forces Modeling

This paper presents the extended Kalman filter-based sideslip angle estimator design using nonlinear 5DoF single-track vehicle dynamics model with stochastic modeling of tire forces. Lumped front and rear tire forces have been modeled as first order random walk state variables. The proposed estimator is primarily designed for vehicle sideslip angle estimation ; however it can also be used for estimation of tire forces and cornering stiffness. This estimator design does not rely on linearization of the tire force characteristics and it is robust against the variations of tire parameters and does not require the information on coefficient of friction. The estimator performance has been first analyzed by means of computer simulations using the 10DOF two-track vehicle dynamics model and underlying magic formula tire model, and then validated by running the estimator algorithm off-line on the experimental data sets recorded on the test vehicle.

Estimate Lateral Tire Force Based on Yaw Moment without Using Tire Model

This paper demonstrates the implementation of a model-based vehicle estimator, which can be used for lateral tire force estimation without using any highly nonlinear tire-road friction models. The lateral tire force estimation scheme has been designed, and it consists of the following three steps: the yaw moment estimation based on a disturbance observer, the sum of the lateral tire force of two front tires and two rear tires estimation based on a least-square method, and individual lateral tire force estimation based on a heuristic method. The proposed estimator is evaluated under two typical driving conditions and the estimation values are compared with simulator data from CarSim and experimental data provided by GM. Results to date indicate that this is an effective approach, which is considered to be of potential benefit to the automotive industry.

Estimation of Longitudinal Tire Force Using Nonlinearity Observer

Tire forces are the major forces propelling the road vehicles. They significantly affect the dynamic behavior of the vehicles. Estimation of the tire forces is essential in vehicle dynamics and control. This paper presents an observer-based scheme for estimation of the longitudinal tire force of electric vehicles in real time. The observer is based on a nonlinearity observer method. The pole-placement technique is used for determination of the observer gains. Simulation results demonstrate that the observer is able to estimate the tire force successfully. The experiments are implemented on a single-wheel electric vehicle test rig. The test rig comprises an electric motor driven wheel and a free-rolling drum simulating vehicle-on-road situations. Experimental results confirm the effectiveness of the present scheme.

Progress on Vehicle Dynamics Stability Control System

vehicle dynamics stability control system(DSC) is a key technology of vehicle active safety system, and it has been a hot research issue in vehicle field for a long time. The DSC system which is integrated with anti-lock braking system(ABS), traction control system(TCS) and active yaw control(AYC) can improve the stability and safety of vehicle significantly. The research progress of vehicle dynamics stability control system can be classified into modeling, state observation, control strategy and industrialization. The modeling includes the modeling in simulation and the modeling in control. ADAMS or Carsim can be adopted to build the vehicle model for simulation. Two wheels model or four wheels model usually are used in control. The state observation mainly focuses on the pressure estimation of the wheel cylinder, the estimation of road friction, the estimation of tire forces, the estimation of longitudinal and lateral velocity. After the realization of the basic function of vehicle stability control, the requirement for control is increasing gradually. A new AYC control strategy which is based on the predicted yaw rate is introduced to reduce the hysteresis of control. Meanwhile a new kind of TCS control strategy is introduced to reduce the vehicle vibration on uneven low-adhesion road. Through the unremitting exploration and research, the industrialization of DSC is gradual realizing.

Estimation of Four Individual Tire Forces Using Limited Sensor Signals

This paper suggests two methods of the simultaneous estimation of vehicle lateral and longitudinal tire forces. The two estimation methods based on Kalman filter are presented: The first method utilizes all the sensor signals available in commercial vehicles, including the brake and shaft torque signals, to estimate the vehicle tire forces. The second method uses only the lateral and longitudinal accelerations, and the yaw rate signals with the steering input to extended the usage of the tire force estimator to conventional vehicles with limited sensor signals. The advantages and disadvantages of the two methods are investigated by the various simulation scenarios on different surfaces using Carsim vehicle dynamics software. 

Fuzzy Logic based Modelling and Simulation Approach for the estimation of Tire Forces

Tire modeling is an important aspect of vehicle dynamics as the forces and moments required to control the vehicle's motion are eventually transmitted through the tire and the tire road interface is also an important source for the dynamic excitation of the vehicle. This paper presents a fuzzy logic based approach for estimating tire forces, aligning moment of tire for the different slip ratio and slip angles. Proposed fuzzy logic approach requires slip angle and slip ratio, as the input variables, and estimates the longitudinal force, lateral force, aligning moment as the output variables. Membership functions of input, output variables and fuzzy rules are formulated based on the values obtained using the widely adopted Magic formula for tire model. Simulation values for longitudinal, lateral forces and aligning moment of the tire using the proposed fuzzy model is found to provide good correlation with the magic model. Proposed fuzzy logic frame work does not require the estimation of model parameters used in the Magic formula and it will be useful in developing vehicle control system.

Algorithms for Real-Time Estimation of Individual Wheel Tire-Road Friction Coefficients

It is well recognized in the automotive research community that knowledge of the real-time tire-road friction coefficient can be extremely valuable for active safety applications, including traction control, yaw stability control and rollover prevention. Previous research results in literature have focused on the estimation of average tire-road friction coefficient for the entire vehicle. This paper explores the development of algorithms for reliable estimation of independent friction coefficients at each individual wheel of the vehicle. Three different observers are developed for the estimation of slip ratios and longitudinal tire forces, based on the types of sensors available. After estimation of slip ratio and tire force, the friction coefficient is identified using a recursive least-squares parameter identification formulation. The observers include one that utilizes engine torque, brake torque, and GPS measurements, one that utilizes torque measurements and an accelerometer and one that utilizes GPS measurements and an accelerometer. The developed algorithms are first evaluated in simulation and then evaluated experimentally on a Volvo XC90 sport utility vehicle. Experimental results demonstrate the feasibility of estimating friction coefficients at the individual wheels reliably and quickly. The sensitivities of the observers to changes in vehicle parameters are evaluated and comparisons of robustness of the observers are provided.

Stochastic Models for Tyre Force Estimation: An Overview about Recent Developments and Trends

Friction forces between the road and the tires of a vehicle represent a key technology for modern vehicle control systems. Unfortunately, these forces are difficult to measure, so that these signals have to be estimated by common sensors of series production vehicles (e.g. accelerations, wheel speeds and yaw rate) and tire friction models. A lot of research effort has been done in this area and various analytical and semi-empirical models are proposed in the literature. To reduce the corresponding identification efforts of several specific model parameters, stochastic tire models are proposed as an interesting alternative. In this article, an overview of recent developments and trends in stochastic tire modeling and estimation methods is given. Furthermore, some representive results of two tire-road friction estimation methods (extended Kalman filter (EKF) and unscented Kalman filter (UKF) with field test data are presented.

Robust Observation of Tractor-trailer Vertical Forces Using Inverse Model and Exact Differentiator

In this paper, we are interested in developing a robust tire-force estimator for heavy duty vehicles. We use a combined model of the articulated vehicle : a yaw plane model for the chassis motion and a vertical plane model for the axles. In the proposed method, we make use of the on-board available sensors to which are added lowcost sensors. In order to optimize the sensors configuration, a robust differentiator is used in order to obtain accelerations from the measured velocities. Once the differentiation obtained, the model is inverted to determine the unknown input forces. The approach is validated by comparing the estimation results to those given by the software simulator prosper.

Estimation of Tire Forces for Application to Vehicle Stability Control

Estimated tire forces can be used to implement unified-chassis-control (UCC) systems. This paper presents a scheme for longitudinal/lateral tire-force estimation. The longitudinal and lateral tire-force-estimation scheme has been designed, and this consists of the following five steps: vertical tire-force estimation, shaft torque estimation, longitudinal tire-force estimation based on a simplified wheel-dynamics model, lateral tire-force estimation based on a planar model, and the combined tire-force estimation. The combined tire-force-estimation scheme has been designed to compensate for the longitudinal/lateral tire-force estimator, which uses a random-walk Kalman filter. The proposed estimation scheme has been integrated into a UCC system. The performance of the UCC system, including the estimator, has been evaluated via computer simulations conducted using the vehicle dynamic software CARSIM, the ASM vehicle model, and the UCC system coded with Matlab/Simulink.

Real-time Tire Parameters Observer for Vehicle Dynamics Stability Control

The performance of the vehicle dynamics stability control system(DSC) is dominated by the accurate estimation of tire forces in real-time.The characteristics of tire forces are determined by tire dynamic states and parameters,which vary in an obviously large scope along with different working conditions.Currently,there have been many methods based on the nonlinear observer to estimate the tire force and dynamic parameters,but they were only used in off-line analysis because of the computation complexity and the dynamics differences of four tires in the steering maneuver conditions were not considered properly.This paper develops a novel algorithm to observe tire parameters in real-time controller for DSC.The algorithm is based on the sensor-fusion technology with the signals of DSC sensors,and the tire parameters are estimated during a set of maneuver courses.The calibrated tire parameters in the control cycle are treated as the elementary states for vehicle dynamics observation,in which the errors between the calculated and the measured vehicle dynamics are used as the correcting factors for the tire parameter observing process.The test process with a given acceleration following a straight line is used to validate the estimation method of the longitudinal stiffness;while the test process with a given steering angle is used to validate the estimated value of the cornering stiffness.The ground test result shows that the proposed algorithm can estimate the tire stiffness accurately with an acceptable computation cost for real-time controller only using DSC sensor signal.The proposed algorithm can be an efficient algorithm for estimating the tire dynamic parameters in vehicle dynamics stability control system,and can be used to improve the robustness of the DSC controller.

Vehicle velocity estimation for real-time dynamic stability control

A new approach is proposed for nonlinear asymptotic observers based on the cascade observer system with a fusion of sensor signals. In the observers, the characteristic of the vehicle dynamic system, the nonlinear tire force estimation, load transfer estimation, and road ramp angle compensation are considered. The errors in the observation of vehicle velocity were diminished, and the computation cost was decreased for a real-time microcontroller. Simulation and real vehicle test results validate the higher accuracy of the velocity estimation by the proposed observers under complicated handling maneuver conditions.

A novel wireless piezoelectric tire sensor for the estimation of slip angle

This paper introduces a simple approach for the analysis of tire deformation and proposes a new piezoelectric tire sensor for physically meaningful measurements of tire deformations. Tire deformation measurements in the contact patch can be used for the estimation of slip angle, tire forces, slip ratio and tire–road friction coefficient. The specific case of a wireless tire deformation sensor for the estimation of slip angle is taken up in this paper. A sensor in which lateral sidewall deformation can be decoupled from radial deformation is designed. The slope of the lateral deflection curve in the contact patch is used to calculate slip angle. A specially constructed tire test rig is used to experimentally evaluate the performance of the developed sensor. Results show that the developed sensor can accurately estimate slip angles up to values of 5°.

Estimation of vehicle sideslip, tire force and wheel cornering stiffness

This paper presents a process for the estimation of tire–road forces, vehicle sideslip angle and wheel cornering stiffness. The method uses measurements (yaw rate, longitudinal/lateral accelerations, steering angle and angular wheel velocities) only from sensors which can be integrated or have already been integrated in modern cars. The estimation process is based on two blocks in series: the first block contains a sliding-mode observer whose principal role is to calculate tire–road forces, while in the second block an extended Kalman filter estimates sideslip angle and cornering stiffness. More specifically, this study proposes an adaptive tire-force model that takes variations in road friction into account. The paper also presents a study of convergence for the sliding-mode observer. The estimation process was applied and compared to real experimental data, in particular wheel force measurements. The vehicle mass is assumed to be known. Experimental results show the accuracy and potential of the estimation process.

On-board estimation of dynamic tyre forces from optically measured tyre carcass deflections

Active safety systems would benefit from accurate information on tyre forces. A special sensor module has been developed for research purposes to study real-time tyre force estimation from tyre carcass displacements. The forces can be measured in vertical, lateral and longitudinal directions. The sensor measures tyre carcass movement with respect to the rim and transmits the data wirelessly to the chassis. The raw data is analysed and tyre force information is available on a CAN-bus. The sensor is calibrated in a tyre test rig and proving ground measurement results are presented. The lateral and longitudinal force estimates are accurate when compared with the vehicle accelerations, but the vertical force is difficult to estimate during heavy braking manoeuvres.

The Controller Output Observer: Estimation of Vehicle Tire Cornering and Normal Forces

A controller output observer is used for estimating specific outputs from a physical system through the use of alternative outputs that are measured. In most cases these estimated signals can be measured directly using sensors. However, some outputs are either not possible to measure directly or alternative outputs are just easier to measure. This paper focused on a method to estimate immeasurable quantities, in near real time, through the use of physical models and measured quantities. This can be done through the use of classical observers as introduced by Luenberger in 1964 (“Observing the state of a Linear System,” IEEE Trans. Mil. Electron., 8, pp. 74–80) However, since observers estimate the system states, one would have to again estimate the sought after outputs by another method, such as a constitutive relationship. The method proposed here shows that certain signals can be estimated directly by using a controller but without using a constitutive law. These estimated quantities are inputs to a model of the real system. In other words, these inputs drive the observer model. A promising use for the controller output observer is estimation of tire forces in vehicles. This is because tires are very difficult to model accurately, and even if the tire is modeled accurately, the surface conditions of the road must be known to predict tire forces. The controller output observer does not require a model of the tires. The method is tested using a vehicle model. Real measurements from a vehicle are used to show that the method succeeds in estimating quantities from the real vehicle.

Cascaded observers to improve lateral vehicle state and tyre parameter estimates

This paper proposes a method to produce high update, accurate, observable estimates of vehicle sideslip, utilising a two antenna GPS system. Measurements are blended with a kinematic Kalman filter to get high update sideslip estimates, which are used to predict the Dugoff tyre parameters. The parameters are then used in a model-based Kalman filter, which can provide more accurate vehicle state estimates even in the event of a GPS outage. Tyre force estimation is tested with experimental data on high and low friction surfaces, and validated by the performance of the model-based Kalman filter using the identified tyre parameters.

Tyre-force estimation by Kalman inverse filtering: applications to off-highway mining trucks

Kalman inverse filtering is used to develop a methodology for real-time estimation of forces acting at the interface between tyre and road on large off-highway mining trucks. The system model formulated is capable of estimating the three components of tyre-force at each wheel of the truck using a practical set of measurements and inputs. Good tracking is obtained by the estimated tyre-forces when compared with those simulated by an ADAMS virtual-truck model. A sensitivity analysis determines the susceptibility of the tyre-force estimates to uncertainties in the truck’s parameters.

Measurement of contact forces and patch features by means of accelerometers fixed inside the tire to improve future car active control

Huge improvements and advances in sensor technology, together with the increasing demand for safety and handling performances, pull research towards new control strategies. Robustness and promptness of sensors used for active control are key requisites. The main idea behind the research presented in this paper is to instrument the tire with appropriate sensors in order to estimate several contact parameters ranging from the kinematic conditions of the tire (the longitudinal slippage and the side slip angle [Fukada, Y., 1999, Slip-angle estimation for vehicle stability control. Vehicle System Dynamics, 32(4–5), 375–388.]) to its dynamic properties (the contact area shape and dimensions as well as the longitudinal, lateral and vertical loads [Cole, D.J. and Cebon, D., 1989, A capacitative strip sensor for measuring dynamic type forces. Proc. of the Second International Conference on Road Traffic Monitoring, London, 38–42; Cole, D.J. and Cebon, D., 1992, Performance and application of a capacitative strip tyre force sensor. Proc of IEE Conference on Road Traffic Monitoring, London, 123–132.]) and to the adhesion characteristics of the road (the surface roughness [Pasterkamp, W.R. and Pacejka, H.B., 1997, The tire as a sensor to estimate friction. Vehicle System Dynamics, 27, 409–422; Pohl, A., Steindl, R. and Reindl, L., 1999, The ‘intelligent tire’ utilizing passive SAW sensorsmeasurement of tire friction. IEEE Transactions on Instrumentation and Measurement, 48(6), 1041–1046; Ray, L.R., 1997, Nonlinear tire force estimation and road friction identification: Simulation and experiments. Automatics, 33(10), 1819–1833.]). Thus, the tire becomes a sensor of tire–road interaction. Clearly, no other measuring device may ever be more robust nor prompt, and anyway closer to the contact area. After a preliminary research in which the pros and cons of the various sensor technologies were taken into account, it was decided to put accelerometers inside the tire. These accelerometers were fixed to the liner and on-board analysis of the acquired data was performed to reduce the amount of data then sent via radio control to a central data processing unit. This unit, through post-elaboration and recombination of the reduced signals coming from the various accelerometers in the tire, estimates some of the above-described contact parameters. In the near future, these contact parameters coming from all four tires and eventually other signals from sensors placed on the vehicle may be used to develop innovative control strategies in order to increase vehicle performances as well as running safety.

Monitoring system design for estimating the lateral tyre force

Longitudinal and lateral forces acting on tyres are known to be closely related to tractive ability, braking characteristics, handling stability and manoeuvrability of ground vehicles. However, it is not feasible in the operating vehicles to measure the tyre forces directly because of the high cost of sensors, the limitations in sensor technology, interference with tyre rotation and the harsh environment. Another approach is the indirect monitoring technique that can estimate the tyre forces based on remote sensor outputs and vehicle dynamics models. In this paper, in order to develop tyre force-monitoring systems, a monitoring model is proposed utilizing not only the yawing motion but also the roll motion. Based on the monitoring model, a monitoring system is designed to estimate the lateral tyre force acting on each tyre. The monitoring system is constructed on the basis of a new scaled Kalman filter with model error compensator (SKFMEC) technique that is developed in this study to improve the robustness performance of Kalman filter methods. The SKFMEC technique adopts both the well-conditioned observer and the model error compensator concepts. Tyre force estimation performance of the monitoring system is evaluated in the MATLAB simulations where true tyre force data are generated from a 14-degree-of-freedom vehicle model with the combined-slip ‘magic formula’ tyre model.