Lateral Tire Research Articles

Speed planning and control in complex road conditions based on vehicle driving capability

In order to solve the problem of vehicle speed planning that meets the constraints of safety and efficiency in complex road environments (large curvature and low adhesion), a differential equation planning method based on vehicle dynamics analysis is proposed. First, the structural parameter expression of the limit speed that meets the lateral tire force constraint during steady-state steering is derived. Secondly, the tire force execution space of the front and rear wheels is combined into an FF diagram, and an implicit differential equation that considers load transfer and driving mode factors is obtained. The differential equation is solved to obtain the limit speed along the path, and a limit speed calculation method for discrete path information is given. Finally, a lateral and longitudinal collaborative model predictive controller is designed, and a CarSim and Simulink joint simulation platform is built. Trajectory tracking simulation experiments are carried out on both continuous and discrete information paths with the planned limit speed. The results show that the limit speed planning method proposed in this paper can complete the trajectory tracking task in complex road environments as quickly as possible while controlling the tire force within the range of the stable friction circle.

Strange nonchaotic attractors and bifurcation of a four-wheel-steering vehicle system with driver steering control

In this paper, a dynamical model is developed for the four-wheel-steering(4WS)vehicles, with nonlinear lateral tyre forces and quasi-periodic disturbances from the steering mechanism and quasi-periodic pavement external deformation. Initially, the stability and Hopf bifurcation of the 4WS vehicle system without disturbance are analyzed employing the central manifold theory and projection method. The effects of parameters on the stability and the types of Hopf bifurcation for the vehicle system are also discussed. It is shown that both Hopf bifurcation and degenerate Hopf bifurcation occur in the vehicle system. The critical speed decreases with increased driver’s perceptual time delay and distance from the vehicle’s center of gravity to the front axles, while it increases with the control strategy coefficient. However, the increase of the frontal visibility distance of the driver leads to an initial increase of the critical speed, decreasing afterwards. Subsequently, the strange nonchaotic dynamical behaviour of the disturbed 4WS system is investigated. Several routes and mechanisms for the birth of strange nonchaotic attractors (SNAs) are identified, including the torus doubling bifurcation, the torus fractalization, and the loss of transverse stability of a torus. Finally, the nonchaotic property is verified through the calculation of the maximum Lyapunov exponent, and the strange property is characterized using power spectra and rational approximation.

Active rack control of steer-by-wire systems for vehicle lateral stability

This paper describes a stability control strategy based on a steer-by-wire system to improve the lateral stability and manoeuvrability of vehicles by integrating individual chassis control modules, such as electronic stability control (ESC) and active front steering (AFS). Because of the uncertainty of cornering stiffness, an adaptive sliding-mode control is implemented without using the cornering stiffness value. An adaptive parameter is used instead of the cornering stiffness in the slip angle estimation and the lateral stability control. An unscented Kalman filter is used to estimate the slip angle and adaptive sliding mode control is used in lateral stability control. An equivalent desired command is calculated in lateral stability control. An integrated AFS and four individual wheel-braking controls were utilised to achieve an optimal distribution of longitudinal and lateral tyre forces, aiming to attain the desired command for lateral stability. Optimal coordination of the control authority for the AFS and the ESC has been chosen to minimise the force of each tyre. Computer simulations and vehicle tests of a closed-loop driver–vehicle–controller system subjected to a double-lane change have been carried out to verify that the proposed control strategy works.

Controllable region analysis of active front steering and differential braking system stability control characterized by additional yaw moment

Active Front Steering (AFS) and Differential Braking System (DBS) are commonly used execution systems for vehicle anti-rollover or handling stability control. They regulate the vehicle’s yaw moment by adjusting the lateral tire force and longitudinal tire force, respectively. However, these two systems differ in terms of control capabilities and regulatory sensitivities. In emergency conditions, it becomes crucial to allocate and coordinate the tasks for the execution systems according to their yaw moment control capability and adjustment sensitivity. This paper proposes a method for calculating the controllable region represented by the additional yaw moment. This method allows for the computation of the control capability of AFS and DBS based on the current state. Additionally, the influence of different vehicle states on the controllable regions of the two execution systems is analyzed. Building upon this analysis, the yaw moment adjustment sensitivities of AFS and DBS systems under the current state are further investigated. Finally, a task coordinated strategy between AFS and DBS is developed based on the analysis of controllable regions and sensitivities of different execution systems. Simulink simulations are conducted on yaw stability and roll stability conditions to comprehensively analyze the working process of the proposed task coordination strategy.

Path Tracking Control with Constraint on Tire Slip Angles under Low-Friction Road Conditions

This paper presents a method to design a path tracking controller with a constraint on tire slip angles under low-friction road conditions. On a low-friction road surface, a lateral tire force is easily saturated and decreases as a tire slip angle increases by a large steering angle. Under this situation, a path tracking controller cannot achieve its maximum performance. To cope with this problem, it is necessary to limit tire slip angles to a value where the maximum lateral tire force is achieved. The most commonly used controllers for path tracking, linear quadratic regulator (LQR) and model predictive control (MPC), are adopted as a controller design methodology. The control inputs of LQR and MPC are front and rear steering angles and control yaw moment, which have been widely used for path tracking. The constraint derived from tire slip angles is imposed on the steering angles of LQR and MPC. To fully verify the performance of the path tracking controller with the constraint on tire slip angles, a simulation is conducted on vehicle simulation software. From the simulation results, it is shown that the path tracking controller with the constraint on tire slip angles presented in this paper is quite effective for path tracking on low-friction road surface.

Path tracking of varying-velocity 4WS autonomous vehicles under tire force friction ellipse constraints

In this paper, a control scheme is presented to solve the problem of path tracking for varying-velocity autonomous vehicles with higher robust performance while friction force constraints of vehicle tires and ground are considered to avoid appearing the steering lost situation actively in the limit of the tire friction forces by using four wheel steering. To achieve these goals, a new expression of the tire forces and a new controlled system are proposed for the three degree of freedom vehicle model. A longitudinal input-saturation controller is designed to track the desired longitudinal velocity and attenuate the influence of lateral and yaw motions. The virtual control input method is used to design the input-saturation controller and get the desired steering angles to track the desired path for the lateral and yaw motions while a new control problem with desired forces tracking is considered to autonomously avoid the limit of lateral tire friction forces and the steering lost situation appearing. To test these results, lane changing, U-corner turning and straight-line driving for a varying-velocity vehicle are simulated with external disturbances and model uncertainties. Simulation results show that the higher robustness and precise path tracking performances are obtained.

Research of the elastic properties of a vehicle tire with an tilting wheel rotation axis

The purpose of the study is to develop computational and experimental methods for determining the normal, longitudinal and lateral stiffness of a vehicle tire with an inclined rotation wheel axis. Dimensionless correction factors were obtained to adjust the tire stiffness along the corresponding coordinate when the wheel rotation axis is tilted. It has been established that when the wheel rotation axis is tilted, the tire stiffness changes along different coordinates in different ways. It has been determined that the normal and longitudinal tire stiffness when the wheel rotation axis is tilted always decreases, regardless of the tilt direction. A change in the lateral tire stiffness when the wheel rotation axis is tilted can occur either in the direction of decrease or increase, depending on the combination of the tilt direction and the vector of the wheel lateral force. Keywords vehicle support wheel, rotation axis tilt, tire elastic properties, methods for determining

Vehicle Lateral Control Based on Dynamic Boundary of Phase Plane Based on Tire Characteristics

Lateral control is an essential safety control technology for autonomous vehicles, but the effectiveness of lateral control technology relies heavily on the precision of vehicle motion state judgements. In order to achieve accurate judgements of the vehicle motion state and to improve the control effectiveness of vehicle maneuverability and the stability controller, this paper starts with an analysis of phase plane stability. A simulation analysis is conducted to investigate the effect of the vehicle steering angle of the front wheels, the longitudinal velocity, and the tire–road adhesion coefficient on the boundary of the stability area. The stable area of the phase plane was partitioned using the proposed novel quadrilateral method, and we established a stability area regression model using machine learning methods. We analyzed the inherent connection between the lateral tire forces and the principles of vehicle maneuverability and stability control, indirectly combining the characteristics of tire forces with vehicle maneuverability and stability control. An allocation algorithm for maneuverability and stability control was designed. A co-simulation indicates that the vehicle stability controller not only accurately assesses the motion state of the vehicle but also demonstrates a considerably better performance in maneuverability and stability control compared to a controller using the traditional partitioning method of stable regions. The suggested allocation method enhances vehicle maneuverability and stability by enabling a seamless transition between the two and improving the effectiveness of stability control.

An Enabling Tire-Road Friction Estimation Method for Four-in-Wheel-Motor-Drive Electric Vehicles

In this paper, a particle filter (PF)-based tire-road friction estimation method is proposed for four-in-wheel-motor-drive electric vehicles by synthetically using the Dual Global Positioning System (DGPS) and three low-cost Inertia Measurement Units (IMUs). In the scheme, two independent PF-based road friction estimators are developed for straight driving and cornering conditions. For straight driving conditions, the longitudinal tire forces are first estimated using the output torque and rotational speed of motor, based on which a tire-road friction estimator is put forward by using a particle filter and the nonlinear relationship between longitudinal tire force and tire-road friction. For cornering conditions, the lateral tire forces and vehicle sideslip angle are estimated by using three IMUs and the DGPS. A PF-based tire-road friction estimator is established based on the nonlinear lateral tire characteristics. An estimation mode decision scheme is developed to determine which of the two PF-based estimators is used to update the tire-road friction estimate by considering both tire dynamics states and tire force characteristics. The accuracy and reliability of the proposed tire-road friction estimation scheme is verified under various maneuvers and road friction conditions through hardware-in-the-loop tests. The results show that the proposed method exhibits high estimation accuracy, robustness, and computational efficiency.

Front wheel angle control for steering system of intelligent commercial vehicle based on model predictive control

AbstractAccurate control of front wheel angle is essential in intelligent vehicle electric‐hydraulic power steering (EHPS) system, because it has a significant impact on the safety, comfort, and reliability of vehicle steering. However, the accurate control of front wheel angle is a challenging problem due to the non‐linearity of hydraulic power in steering system and the uncertainty of steering resistance. In this paper, a model predictive control (MPC) method for front wheel angle based on steering resistance estimation is proposed. Firstly, through theoretical analysis and practical experiment of EHPS system model, the relationship between front wheel angle and steering wheel angle and the non‐linear characteristics of hydraulic power are obtained. Secondly, a sliding mode observer is established to estimate the front axle lateral tyre force and steering resistance, which is verified by MATLAB/TruckSim co‐simulation. Then a controller based on the MPC theory is designed and applied to the accurate control unit of front wheel angle in the EHPS system for real‐time control. Finally, the simulation and test platform results show that the control algorithm proposed in this paper can precisely control the vehicle's front wheel turning angle within a certain frequency range.

Online Detection of Toe Angle Misalignment Based on Lateral Tire Force and Tire Aligning Moment

Online Detection of Toe Angle Misalignment Based on Lateral Tire Force and Tire Aligning Moment

Impact of the tyre dynamics on autonomous vehicle path following control with front wheel steering and differential motor torque

AbstractThis paper investigates the impact of tyre dynamics on autonomous vehicle dynamic control. The commonly used 2 degrees of freedom bicycle model and a detailed vehicle model considering tyre dynamics are built, respectively, to describe the vehicle dynamics. The two models are firstly compared with the response to front wheel steering input and differential motor torque input. The transient vehicle body vibrations are clearly demonstrated by the detailed model but overlooked by the bicycle model. The influence of tyre nonlinearity on path offset is also revealed. Then, the path following control strategy is designed based on the linear quadratic regulator control to compare the two models from the path following performance perspective. The double lane change simulation is conducted. The results show that at low vehicle speed, the path following errors of two models are very close, which proves the rationality of using the bicycle model to represent the vehicle dynamics in mild and moderate driving conditions. However, when the path following is conducted with high vehicle speed, the required lateral tyre force is large, so the tyres work with large slip angles and the tyre nonlinearity generates significant deviation on the path following errors between the two models.

Steady-state comparison of torque vectoring and vehicle tilt influence on narrow car steering characteristics

Article compares the roll-to-curve and torque vectoring impact on a steering characteristics. The comparison is based on an adopted for tilt mathematical model with two DOFs. The lateral tire forces are a function of the tire sideslip angle and the angle of tilt. The first chapter contains a description of the vehicle for which a series of road tests and simulations was carried out. Next chapter contains an experimental verification of the mathematical model of the vehicle and the simulation tests carried out. The paper describes the mathematical model of the vehicle used to perform the simulation. The next chapter contains the description and results of steady-state simulations examining the effect of differentiation of driving forces on the steering characteristics and the impact of tilt angle on the steering characteristics. The article ends with the chapter containing the conclusions.

A novel nonlinear drift control for sharp turn of autonomous vehicles

Under the sharp turn condition, especially on low adhesion coefficient roads, drift motion can improve vehicle agility and ensure safety. During drift motion, the large sideslip angle and rear wheel slip as well as the saturation of lateral tyre force result in the complex nonlinear dynamic behaviour, such as non-unique equilibrium point and unstable vehicle dynamic. Therefore, this paper focuses on the analysis of dynamic characteristics and the design of both the equilibrium point and feedback controller for drift motion. First, a dynamics model, in which the rear wheel slip ratio is treated as a parametric variable and the influence of rear wheel lateral force on the drift motion is explicitly expressed, is established. Then the expression of steady-state yaw rate and the virtual control input is derived, and the error dynamic model is presented furthermore. To design the equilibrium point, in this paper the effect of rear tyre slip angle and slip ratio on the equilibrium point is discussed, and the condition of stable equilibrium point is proposed. In addition, the design of desired rear tyre slip angle by synthesising the cornering performance during drift motion is presented. For the drift controller design, the main idea is to design the stabilisation controller for the nonlinear dynamic system with the stable equilibrium point and to calculate static feedback gain by means of Lyapunov stability theory. To illustrate the characteristics of drift motion, the influence of the vehicle speed and rear wheel slip ratio on the vehicle path and the low damping characteristics of the dynamic system on the control performance are analysed by different simulation conditions. Moreover, the performance and effectiveness of the proposed drift control are verified by simulation.

Integrated Adhesion Coefficient Estimation of 3D Road Surfaces Based on Dimensionless Data-Driven Tire Model

The tire/road peak friction coefficient (TRPFC) is the core parameter of vehicle stability control, and its estimation accuracy significantly affects the control effect of active vehicle safety. To estimate the peak adhesion coefficient accurately, a new method for the comprehensive adhesion coefficient of three-dimensional pavement based on a dimensionless data-driven tire model is proposed. Firstly, in order to accurately describe the contact state between the three-dimensional road surface and the tire during driving, stress distribution and multi-point contact are introduced into the vertical dynamic model and a new tire model driven by dimensionless data is established based on the normalization method. Secondly, the real-time assessment of lateral and longitudinal adhesion coefficients of three-dimensional pavement is realized with the unscented Kalman filter (UKF). Finally, according to the coupling relationship between the longitudinal tire adhesion coefficient and the lateral tire adhesion coefficient, a fuzzy reasoning strategy of fusing the longitudinal tire adhesion coefficient and the lateral tire adhesion coefficient is designed. The results of vehicle tests prove that the method proposed in this paper can estimate the peak adhesion coefficient of pavement quickly and accurately.

A Hierarchical Estimation Method for Road Friction Coefficient Combining Single-Step Moving Horizon Estimation and Inverse Tire Model

To improve the real-time performance of the estimation method of road friction coefficient (RFC) based on moving horizon estimation (MHE), a hierarchical estimation method for RFC combining single-step MHE (S-MHE) and inverse tire model (ITM) based on lateral vehicle dynamics is proposed in this study. Firstly, a hierarchical estimation framework is designed to decouple vehicle and tire systems. Secondly, the S-MHE estimator is designed based on the nonlinear vehicle model to estimate the lateral tire force. Thirdly, the ITM is deduced based on the Pacejka model, and the estimator for the RFC based on the ITM is designed. Finally, the estimation accuracy, convergence speed, and real-time performance of the proposed method and the traditional MHE method are compared and discussed through different tests based on CarSim and Simulink. The results show that compared with the traditional MHE method, the proposed method reduces the average computation time to about 0.125 s and improves the real-time performance by more than 30% while ensuring the estimation accuracy and convergence speed.

Stability and Maneuverability Guaranteed Torque Distribution Strategy of DDEV in Handling Limit: A Novel LSTM-LMI Approach

Direct yaw moment (DYC) does increase the maneuverability and controllability of distributed driving electric vehicle. However, the additional DYC could also lead to the instability of vehicle in low friction road. Extensive literatures have proposed various methods to tackle this problem. Nevertheless, the conflict between maneuverability and stability in handling limit is difficult to solve. To this end, a novel multimode torque distribution algorithm is developed in this article. The conception of drive stability region is proposed to describe the feasible operations of the driver. Based on the different regions, we define multitorque distribution modes to handle the varying conditions. A linear matrix inequality based mode decision theorem is developed to estimate the boundaries of the drive stability region as well as determine the optimal mode. Considering that the lateral tire force is important for mode decision, a long short-term memory neural network is adopted to make a precise estimation. Finally, we develop multitorque distribution strategies to meet the requirements of each mode. Processor-in-the-loop test is also implemented to verify the real-time performance of the algorithm. Simulation and experiment indicate that, the multimodes torque distribution strategy show a better performance compared with the single mode, which mitigates the conflict of maneuverability and stability as well as ensures the safety of vehicle in handling limit.

A prioritisation model predictive control for multi-actuated vehicle stability with experimental verification

This paper proposes a novel prioritisation model predictive control for improving the handling and stability of all-wheel-drive vehicles configured with an electric motor and an open differential per axle with differential braking capability. The configuration of the powertrain provides a significant handling improvement by optimising front/rear torque distribution. The controller gives a high priority to front/rear torque distribution and, if needed, activates the differential braking. A coupled force prediction model of the vehicle handling dynamics is developed to capture the interaction of longitudinal and lateral tyre forces. Since differential braking causes speed drop, energy waste, and noise, two control actuations are prioritised: (1) front/rear torque shifting, (2) differential braking. Appropriate stability constraints are defined for the vehicle yaw rate and sideslip, dividing the sideslip-yaw rate phase plane into three regions – stable, marginal, unstable – based on which three control objectives are defined. Then, the priorities of the control actuations and the control objectives are combined, and a model predictive control structure is developed for this multi-objective multi-actuation control problem. The predictive controller prioritises the objectives and actuations through the prediction horizon. The performance of the proposed controller is thoroughly evaluated through numerical and full vehicle experimental studies.

Adaptive fault-tolerant control for distributed in-wheel motor drive electric vehicles with unknown brake systems’ faults

We present in this study an adaptive fault-tolerant control (adaptive FTC) strategy to ensure the handling and safety of the distributed in-wheel motor drive electric vehicles (DIMDEVs) against unknown brake systems’ faults. The proposed adaptive FTC derives the constraints about additional lateral tire force and yaw moments to stabilize DIMDEV when the brake systems’ faults occur, which tracks the desired trajectories including the ideal yaw rate and lateral velocity. Then the proper drive torque increments are calculated by the optimization with the derived constraints and applied on DIMDEV to realize the fault-tolerant capacity. The convergence of the whole scheme is proved by the Lyapunov stability theory and Barbalat’s lemma. Finally, the joint simulation of commercial software Carsim and Simulink verifies the effectiveness of the proposed control algorithm, which lays the foundation for the safety of electric vehicle chassis.

Modeling of the Influence of Operational Parameters on Tire Lateral Dynamics.

Tires play a critical role in vehicle safety. Proper modeling of tire–road interaction is essential for optimal performance of active safety systems. This work studies the influence of temperature, longitudinal vehicle speed, steering frequency, vertical load, and inflation pressure on lateral tire dynamics. To this end, a tire test bench that allows the accurate control of these parameters and the measurement of the variables of interest was used. The obtained results made it possible to propose a simple model that allowed the determination of relaxation length as a function of tire vertical load and vehicle linear speed, and the determination of a representative tread temperature. Additionally, a model has been proposed to determine the lateral friction coefficient from the aforementioned temperature. Finally, results also showed that some variables had little influence on the parameters that characterize lateral dynamics.