Estimation of Vertical, Lateral, and Longitudinal Tire Forces in Four-Wheel Vehicles Using a Delayed Interconnected Cascade-Observer Structure

Many vehicle state parameters will be used in the electronic stability control (ESC) system. ESC system must estimate some important parameters based on a few sensors and help to develop the control strategies. ESC can estimate the work state of vehicle with tire forces based on the estimating of adhesion coefficient and wheel slip ratio, then determine the control strategy on wheels. The tire forces to be estimated include vertical force, lateral force and longitudinal force on tires. In this article, a method of estimating vertical tire force based on vehicle geometric parameters and vehicle working state, a method of estimating tire lateral force based on vehicle yaw rate and the change of tire longitudinal forces caused by the change of vertical forces and lateral forces have researched. Co-simulation shows that the trend of the tire forces changing is correct and small error on high and low adhesive pavement. The ESC system is available on HIL bench and testing vehicle, so the estimates of tire forces are practical methods.

This paper presents a motion control method of 6WD/6WS (6-wheel-drive and 6-wheel-steering) vehicle using optimum tire force distribution method. When we make used of independent driving and steering system, the motion control performance of the 6WD/6WS vehicle can be improved. For example, vehicle's maneuverability is more improved at low speed and vehicle's stability is also improved at high speed. Therefore, it needs to find a control strategy using optimum tire forces. A control strategy must satisfy the driver's command and minimize the energy consumption. When the driver commands vehicle (input steering angle and acceleration/brake pedal stroke), we can obtain the desired yaw moment, the desired lateral force and the desired longitudinal force. Those values are used in the optimum tire force distribution method. The optimum tire force distribution method can find the longitudinal tire force and lateral tire force. That force minimizes the cost function. The cost function is the sum of normalized tire force. The longitudinal tire forces and lateral tire force of each wheel are converted to the reference torque inputs and steering wheel angle inputs. The method was tested on the simulation and effectiveness was verified.

This paper proposes a novel hybrid framework for estimating longitudinal tire forces by combining a model-based observer and a Transformer neural network architecture. A key advantage of the proposed approach is its independence from wheel torque measurements, which are commonly used in vehicle force estimation methods. The proposed framework first employs a model-based observer using the Pacejka tire model to generate preliminary estimates of longitudinal tire forces. These estimates are then refined by a neural network featuring an encoder-only Transformer architecture augmented with dilated convolutions, which effectively captures long-term temporal dependencies in sensor data while compensating for model inaccuracies. Additionally, our hybrid approach is able to estimate the longitudinal velocity and road friction coefficient, which are crucial for observer's preliminary force estimate in extreme road and driving conditions. Experimental validation on an electric Equinox vehicle under diverse driving scenarios-including highslip maneuvers on dry, wet, and icy roads-demonstrates the framework's superior performance compared to model-based and neural network-only approaches. The proposed method achieves robust estimation accuracy even under sensor faults (e.g., biased acceleration signals) and harsh driving conditions, indicating its potential for enhancing vehicle safety systems such as traction and stability control.

Vehicle motion and tire force histories are estimated from an incomplete, noise-corrupted measurement set using an extended Kalman filter. A nine degree-of-freedom vehicle model and an analytic tire force model are used to simulate true vehicle motion, and a five degree-of-freedom vehicle model is used in the estimator. The filtered histories of forces and motion can be used to construct tire force models through off-line analysis, and both tire force estimates and state estimates are available for real time control. No prior knowledge of tire force characteristics or external factors that affect vehicle motion is required for the nonlinear estimation procedure. Simulation of a simple slip control braking system using slip and slip angle estimates for feedback demonstrates the effectiveness of the extended Kalman filter in providing adequate state estimates for advanced control of ground vehicles.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Estimation of Nonlinear Tire Forces and Road Friction for Modeling and Control

The direct yaw moment control system is able to greatly enhance the vehicle stability when driving on challenging road surfaces. This paper introduces a direct control approach for managing the vehicle yaw moment, utilizing terminal sliding mode control and a square root cubature Kalman filter (SRCKF). Initially, the longitudinal and lateral forces acting on the vehicle’s tires are estimated through a sliding mode observer. Subsequently, the SRCKF algorithm and the four-wheel tire force are employed to accurately estimate the yaw rate and sideslip angle. Based on these estimations, additional yaw moments are determined using the terminal sliding mode control algorithm, and a combined control of yaw rate and sideslip angle is achieved through a threshold method. A rule-based braking force distribution strategy is then implemented to ensure vehicle stability control. Simulation results demonstrate that the tire force estimations from the sliding mode observer and the vehicle yaw rate and sideslip angle estimations from the SRCKF algorithm closely align with the output results from Carsim, with an error margin of less than 15%. The braking force distribution strategy, based on the direct yaw moment control using the terminal sliding mode algorithm, effectively tracks the desired yaw rate and sideslip angle.

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.

In order to improve the steering performance of vehicles on low adhesion roads, this paper proposed a drift control method by coordinating the steering angle and the rear wheel slip ratio. Because lateral force of rear wheels is saturated with high longitudinal slip ratio under the drift condition, a vehicle dynamic model considering the coupling of the rear wheels’ longitudinal and lateral force is established. In view of the fact that the lateral tire force is affected by the nonlinearity of sideslip angle and slip ratio, the vehicle dynamic model is complex and makes it difficult for controller design. Due to this, a description method of the nonlinear relationship is presented for simple which introduces a virtual control quantity representing the influence of slip ratio on lateral tire forces based on the function of tire force with sideslip angle and slip ratio. Then, a sliding mode control method is proposed to ensure the stability of the closed-loop system and an off-line two-dimensional map is constructed to convert the virtual control quantity into the actual control quantity. The simulation results in the high-precision vehicle dynamics simulation software show that even if the initial state is far from the equilibrium point of drift, the drift controller also can ensure the stability of the closed-loop system and achieve a good drift performance.

The motion of a vehicle is governed by the forces generated between the tyres and the road. Knowledge of these vehicle dynamic variables is important for vehicle control systems that aim to enhance vehicle stability and passenger safety. This study introduces a new estimation process for tyre/road forces. It presents many benefits over the existing state-of-art works, within the dynamic estimation framework. One of these major contributions consists of discussing in detail the vertical and lateral tyre forces at each tyre. The proposed method is based on the dynamic response of a vehicle instrumented with potentially integrated sensors. The estimation process is separated into two principal blocks. The role of the first block is to estimate vertical tyre forces, whereas in the second block two observers are proposed and compared for the estimation of lateral tyre/road forces. The different observers are based on a prediction/estimation Kalman filter. The performance of this concept is tested and compared with real experimental data using a laboratory car. Experimental results show that the proposed approach is a promising technique to provide accurate estimation. Thus, it can be considered as a practical low-cost solution for calculating vertical and lateral tyre/road forces.

Due to the bus characteristics of large quality, high center of gravity and narrow wheelbase, the research of its yaw stability control (YSC) system has become the focus in the field of vehicle system dynamics. However, the tire nonlinear mechanical properties and the effectiveness of the YSC control system are not considered carefully in the current research. In this paper, a novel adaptive nonsingular fast terminal sliding mode (ANFTSM) control scheme for YSC is proposed to improve the bus curve driving stability and safety on slippery roads. Firstly, the STI (Systems Technologies Inc.) tire model, which can effectively reflect the nonlinear coupling relationship between the tire longitudinal force and lateral force, is established based on experimental data and firstly adopted in the bus YSC system design. On this basis, a more accurate bus lateral dynamics model is built and a novel YSC strategy based on ANFTSM, which has the merits of fast transient response, finite time convergence and high robustness against uncertainties and external disturbances, is designed. Thirdly, to solve the optimal allocation problem of the tire forces, whose objective is to achieve the desired direct yaw moment through the effective distribution of the brake force of each tire, the robust least-squares allocation method is adopted. To verify the feasibility, effectiveness and practicality of the proposed bus YSC approach, the TruckSim-Simulink co-simulation results are finally provided. The co-simulation results show that the lateral stability of bus under special driving conditions has been significantly improved. This research proposes a more effective design method for bus YSC system based on a more accurate tire model.

The concept of intelligent tires has drawn attention of researchers in the areas of autonomous driving, advanced vehicle control, and artificial intelligence. The focus of this paper is on intelligent tires and the application of machine learning techniques to tire force estimation. We present an intelligent tire system with a tri-axial acceleration sensor, which is installed onto the inner liner of the tire, and Neural Network techniques for real-time processing of the sensor data. The accelerometer is capable of measuring the acceleration in x,y, and z directions. When the accelerometer enters the tire contact patch, it starts generating signals until it fully leaves it. Simultaneously, by using MTS Flat-Trac test platform, tire actual forces are measured. Signals generated by the accelerometer and MTS Flat-Trac testing system are used for training three different machine learning techniques with the purpose of online prediction of tire forces. It is shown that the developed intelligent tire in conjunction with machine learning is effective in accurate prediction of tire forces under different driving conditions. The results presented in this work will open a new avenue of research in the area of intelligent tires, vehicle systems, and tire force estimation.

A robust method to estimate tire forces for a passenger vehicle with the Unscented Kalman Filter (UKF) is provided. Only standard vehicle sensors were used and no a priori knowledge of tire and road properties was required. The estimator uses the bicycle model and a random walk tire force model. The tire force estimates were compared to a CarSim reference model for combined slip maneuvers. The results showed a good overall tracking performance of the estimator. In addition, the UKF-estimator demonstrated a high convergence rate and good stability properties. The performed robustness studies showed that the estimator performs well even in the presence of disturbances such as changes in tire-road friction. This method enables a cost-effective and robust implementation for future real time vehicle applications.

Simultaneous estimation of tire side-slip angle and lateral tire force for vehicle lateral stability control

Good vehicle handling characteristics are essential to ensure traffic safety. In the integrated system of electric power steering (EPS) and active front steering (AFS), the steering wheel torque may change abruptly with the interference of active steering. The additional front road wheel angle generated by AFS gives rise to the change of tyre lateral force, which results in the change of steering wheel torque finally. Although the tyre forces are difficult to measure, the extended Kalman filter (EKF) algorithm can be used to estimate it. The problem of steering wheel torque change can be resolved by tyre forces estimate based on the EKF observer in nonlinear system. The vehicle nonlinear mathematical model is presented and a nonlinear tyre lateral force estimator is also established basing on EKF. The estimated tyre lateral forces can be applied to compensate the abrupt change of steering wheel torque, which realises the combination of vehicle states estimation and vehicle control. The simulation results in MATLAB/Simulink show the effectiveness of proposed control strategy.

The knowledge of individual torques at each wheel are important intermediate variables for the design of advanced driver assistance systems. A nonlinear high-gain unknown inputs state observer is designed to compute simultaneously longitudinal and vertical tyre forces, resultant torques applied to wheels, and the vehicle speeds with a very simple four wheels model. The necessary measurements are the usual rotation speed of each wheel. Successful simulated experimentations of the method are shown as well as its present limits.