Vertical Tire Forces Research Articles

Virtual tyre force sensors: An overview of tyre model-based and tyre model-less state estimation techniques

This paper presents a comprehensive literature review on tyre force estimation and road grip recognition approaches. With the development of modern automotive control systems, a precise estimation of a large number of vehicle states is necessary to guarantee a robust actuation of the controller. Moreover, the estimation of these states must be carried out in a cost-effective and reliable way. The aim of this work is to provide a solid base for the development of automotive virtual sensors, and in particular, virtual tyre force sensors. An initial overview of the tyre force estimation problem is provided in the first section. Tyre and vehicle modelling, as well as observers for vehicle state estimation, are covered in detail in the second section. The third section introduces a brief discussion regarding the main limitations of direct tyre force measurement approaches. In the following sections, relevant works regarding three-axis tyre force estimation and road grip recognition are discussed. The review is structured around longitudinal force estimation, lateral force estimation, combined tyre force estimation, tyre self-alignment torque estimation and vertical tyre force estimation. Within each section, the most significant road grip identification approaches are introduced. An additional section, Road slope and bank angle compensation, describes relevant work on estimation methods for global chassis orientation. A brief summary of the presented approaches is provided in the section Summary of presented approaches. Finally, relevant conclusions and further research steps are given in the last section.

H∞ control of anti-rollover strategy based on predictive vertical tire force

The mainstream rollover evaluation index, lateral load transfer rate (LTR), is commonly used in the rollover control field. However, it is not instant enough to reflect the rollover tendency since it can only reflect the load transfer rate of one side wheels while single rear wheel leaves the ground first during rollover happens. In order to monitor the rollover tendency more instantly and improve the reliability of anti-rollover control system, a new evaluation index called predictive vertical tire force (PVTF) is proposed, which is based on the single vertical tire force and merges both iterative prediction and derivative prediction methods. Meanwhile, an optimization is taken to solve the contradiction between prediction time and deviation. Secondly, using the PVTF as the measurement output, an anti-rollover control system based on active steering is established in this paper. In order to achieve the desired tracking effect and anti-jamming capability, a two-way H∞ controller is adopted in the anti-rollover control system. Lastly, the simulation results of J-turn condition and NHTSA (national highway traffic safety administration) condition are conducted and the results indicate that the anti-rollover control system has strong stability and robustness. Meanwhile, benefit from the pre-warning function of PVTF, the controller is triggered earlier and the vertical tire forces of four wheels are controlled to be positive all the time, which is beneficial for handling stability.

Torques and tyre forces observation by intelligent sensors: case of longitudinal vehicle dynamics

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.

Novel Tire Force Estimation Strategy for Real-Time Implementation on Vehicle Applications

This paper proposes a novel unified structure to estimate tire forces. The proposed structure uses estimation modules to calculate/estimate tire forces by means of nonlinear observers. The novelty in the proposed approach lies in the independence of the estimates from the vehicle tire model, thereby making the structure robust against variations in vehicle mass, tire parameters due to tire wear, and, most importantly, road surface conditions. In the proposed structure, we have a dedicated module to estimate the longitudinal tire forces and another to calculate the vertical tire forces. Subsequently, these forces are fed into a third module that utilizes a nonlinear observer to estimate lateral tire forces. The proposed structure is validated through experimental studies.

Numerical Simulation of Moving Load on Concrete Pavements

Abstract The knowledge of the development with time of the strain and stress states in pavement structures is needed in the solution of various engineering tasks as the design fatigue lifetime reliability maintenance and structure development. The space computing model of the truck TATRA 815 is introduced. The pavement computing model is created in the sense of Kirchhof theory of the thin slab on elastic foundation. The goal of the calculation is to obtain the vertical deflection in the middle of the slab and the time courses of vertical tire forces. The equations of motion are derived in the form of differential equations. The assumption about the shape of the slab deflection area is adopted. The equations of the motion are solved numerically in the environment of program system MATLAB. The dependences following the influence of various parameters (speed of vehicle motion, stiffness of subgrade, slab thickness, road profile) on the pavement vertical deflections and the vertical tire forces are introduced. The results obtained from the plate computing model are compared with the results obtained by the FEM analysis. The outputs of the numerical solution in the time domain can be transformed into a frequency domain and subsequently used to solve various engineering tasks.

Vehicle stability and attitude improvement through the coordinated control of longitudinal, lateral and vertical tyre forces for electric vehicles

Advanced electric vehicles equipped with independent electric driving/braking, steering and active suspension systems provide potential for optimal vehicle performance by accurate and independent control of each longitudinal, lateral and vertical tyre force. However, the lack of an effective method for the optimisation and control of tyre forces has restricted the development of this research field. In this paper, a novel method for the coordinated control of longitudinal/lateral/vertical tyre forces is proposed by solving a non-convex optimisation problem. A unified objective function that combines the tyre workload and the dynamic ratio of the vertical forces is developed. Thirty-six constraints, including driving demands, electric actuator characteristics and tyre friction limitations, are considered. An optimisation algorithm that combines constrained optimisation and feasible region planning is proposed. Finally, simulations and experiments using a driver simulator are conducted, which demonstrate that the proposed coordinated control method simultaneously improves handling stability and controls vehicle attitude effectively.

Effect of Terrain Roughness on the Roll and Yaw Directional Stability of an Articulated Frame Steer Vehicle

Compared to the vehicles with conventional steering, the articulated frame steer vehicles (ASV) are known to exhibit lower directional and roll stability limits. Furthermore, the tire interactions with relatively rough terrains could adversely affect the directional and roll stability limits of an ASV due to terrain-induced variations in the vertical and lateral tire forces. It may thus be desirable to assess the dynamic safety of ASVs in terms of their directional control and stability limits while operating on different terrains. The effects of terrain roughness on the directional stability limits of an ASV are investigated through simulations of a comprehensive three-dimensional model of the vehicle with and without a rear axle suspension. The model incorporates a torsio-elastic rear axle suspension, a kineto-dynamic model of the frame steering struts and equivalent random profiles of different undeformable terrains together with coherence between the two tracks profiles. The simulations are performed to determine the stability limits of the ASV models while operating on different terrains, namely: a perfectly smooth surface, plowed field, pasture, gravel road, and the MVEE random course. The directional stability limits are defined in terms of the static and dynamic rollover thresholds, rearward amplification ratio, and critical speed corresponding to snaking instability under steady and transient steering inputs. The results suggest that the tire interactions with the rough terrains affect the stability limits of both the unsuspended and suspended vehicles in a highly adverse manner. The suspended vehicle responses, however, show less sensitivity to variations in the road roughness profile.

전차륜 독립휠 구동 및 조향 제어 기반 특수목적용 6WD/6WS 차량의 주행제어 알고리즘 연구

This paper discusses the maneuvering control algorithm based on all-wheel independent driving and steering control techniques for special purpose 6WD/WS vehicles. The maneuvering control algorithms considering superior dynamic characteristics of high power in-wheel motors and independent steering system are designed to perform driving, steering, vehicle stability, and fault tolerant control. The maneuvering controller applies sliding and optimal control theories considering optimal torque distribution and friction circle related to the vertical tire force. The fault tolerant control algorithm is applied to obtain the similar maneuverability to that of the non-faulty vehicle. The simulations using the Matlab/Simulink dynamics model and experiments using HIL simulator mounting the real controllers with the designed control algorithms prove the improved performances in terms of vehicle stability and maneuverability.

Designs and Optimizations of Active and Semi-Active Non-linear Suspension Systems for a Terrain Vehicle

This paper introduces a design and optimization procedure for active and semi-active non-linear suspension systems regarding terrain vehicles. The objective of this approach is the ability to quickly analyze vehicles’ suspension performances resulting from passive, active, or semi-active systems. The vehicle is represented by a mathematical model regarding a quarter of it, and equations for motion are derived and solved by using MATLAB/Simulink. In order to verify the reliability of the derived computer program, a comparison is made with one of the comprehensive commercial software packages. The decision parameters of the active damping device are optimized by using the Hooke-Jeeves method, which is based on non-linear programming. The usefulness of the treated active and semi-active systems on a concrete terrain vehicle is presented and compared with the presented passive systems by analyzing the vehicle’s body acceleration, velocity, displacement, and vertical tire force, namely those aspects that directly influence driving comfort and safety.

Road safety: embedded observers for estimation of vehicle's vertical tyre forces

Preventing car accidents using vehicle control systems requires input data concerning vehicle dynamic parameters. Unfortunately, some parameters, like the tyre-road contact forces that have a major impact on vehicle dynamics, are difficult to measure in a car. Therefore, this data must be estimated. In this context, this study presents an estimation process for load transfer and wheel-ground contact vertical forces. The proposed method is based on Kalman filter techniques and on the dynamic response of a vehicle instrumented with currently available standard sensors. Experimental results carried out using an experimental car show the effectiveness of the proposed approach.

Drive control algorithm for an independent 8 in-wheel motor drive vehicle

This paper describes a drive control algorithm based on optimal coordination of drive torque for an independent 8 in-wheel motor drive vehicle. The drive controller improves lateral stability and maneuverability. The drive controller consists of upper level controller and lower level controller. The upper level controller determines front, middle steering angle, additional net yaw moment and longitudinal net force according to the reference velocity and steering commands. The lower level controller coordinates additional tractive and braking forces to guarantee desired longitudinal net force and yaw moment. This controller is based on optimal control theory and takes into consideration the friction circle related to the vertical tire force and friction coefficient acting on the road and tire. Distributed tractive and braking forces are determined as proportional to the size of the friction circle according to the changes at driving conditions. The response of the 8 in-wheel drive vehicle implemented with this drive controller has been evaluated via computer simulations conducted using Matlab/Simulink dynamic model. Computer simulations of an open-loop J-turn maneuver and a closed-loop driver model subjected to double lane change have been conducted to demonstrate improved performance and stability of the proposed drive controller.

Drive control system design for stability and maneuverability of a 6WD/6WS vehicle

This paper describes a drive controller designed to improve the lateral vehicle stability and maneuverability of a 6-wheel drive / 6-wheel steering (6WD/6WS) vehicle. The drive controller consists of upper and lower level controllers. The upper level controller is based on sliding control theory and determines both front and middle steering angle, additional net yaw moment, and longitudinal net force according to the reference velocity and steering angle of a manual drive, remotely controlled, autonomous controller. The lower level controller takes the desired longitudinal net force, yaw moment, and tire force information as inputs and determines the additional front steering angle and distributed longitudinal tire force on each wheel. This controller is based on optimal distribution control and takes into consideration the friction circle related to the vertical tire force and friction coefficient acting on the road and tire. Distributed longitudinal/lateral tire forces are determined as proportion to the size of the friction circle according to changes in driving conditions. The response of the 6WD/6WS vehicle implemented with this drive controller has been evaluated via computer simulations conducted using the Matlab/Simulink dynamic model. Computer simulations of an open loop under turning conditions and a closed-loop driver model subjected to double lane change have been conducted to demonstrate the improved performance of the proposed drive controller over that of a conventional DYC.

Observers for vehicle tyre/road forces estimation: experimental validation

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.

Investigation on dynamical interaction between a heavy vehicle and road pavement

This paper presents a model for three-dimensional, heavy vehicle-pavement-foundation coupled system, which is modelled as a seven-DOF vehicle moving along a simply supported double-layer rectangular thin plate on a linear viscoelastic foundation. The vertical tyre force is described by a single point-contact model, while the pavement-foundation is modelled as a double-layer plate on a linear viscoelastic foundation. Using the Galerkin method and quick direct integral method, the dynamical behaviour of the vehicle-pavement-foundation coupled system is investigated numerically and compared with that of traditional vehicle system and pavement system. The effects of coupling action on vehicle body vertical acceleration, suspension deformations, tyre forces and pavement displacements are also obtained. The investigation shows that the coupling action could not be neglected even on a smooth road surface, such as highway. Thus, it is necessary to investigate the dynamics of vehicle and pavement simultaneously based on the vehicle-pavement-foundation coupled system.

Skid Steering-Based Control of a Robotic Vehicle with Six in-Wheel Drives

This paper describes a driving control algorithm based on a skid steering for a robotic vehicle with articulated suspension (RVAS). The RVAS is a kind of unmanned ground vehicle based on a skid steering using an independent in-wheel drive at each wheel. The driving control algorithm consists of four parts: a speed controller for following a desired speed, a lateral motion controller that computes a yaw moment input to track a desired yaw rate or a desired trajectory according to the control mode, a longitudinal tyre force distribution algorithm that determines an optimal desired longitudinal tyre force, and a wheel torque controller that determines a wheel torque command at each wheel in order to keep the slip ratio at each wheel below a limit value as well as to track the desired tyre force. Longitudinal and vertical tyre force estimators are required for the optimal tyre force distribution and wheel slip control. A dynamic model of the RVAS for simulation study is developed and validated using the vehicle test data. Simulation and vehicle tests are conducted in order to evaluate the proposed driving controller. It is found from simulation and vehicle test results that the proposed driving controller provides a satisfactory motion control performance according to the control mode.

Design, implementation, and test of skid steering-based autonomous driving controller for a robotic vehicle with articulated suspension

This paper describes an autonomous driving control algorithm based on skid steering for a Robotic Vehicle with Articulated Suspension (RVAS). The driving control algorithm consisted of four parts: speed controller for following the desired speed, trajectory tracking controller to track the desired trajectory, longitudinal tire force distribution algorithm which determines the optimal desired longitudinal tire force and wheel torque controller which determines the wheel torque command at each wheel to keep the slip ratio below the limit value as well as to track the desired tire force. The longitudinal and vertical tire force estimators were designed for optimal tire force distribution and wheel slip control. The dynamic model of the RVAS is validated using vehicle test data. Simulation and vehicle tests were conducted in order to evaluate the proposed driving control algorithm. Based on the simulation and test results, the proposed driving controller was shown to produces satisfactory trajectory tracking performance.

An investigation into unified chassis control scheme for optimised vehicle stability and manoeuvrability

This paper describes a unified chassis control (UCC) strategy to improve the lateral stability andmanoeuvrability of vehicles by integrating individual chassis control modules such as electronic stability control (ESC), active front steering (AFS) and continuous damping control (CDC). In order to achieve a target lateral vehicle response, an integrated AFS and four individual wheel braking controls have been used for an optimum distribution of longitudinal and lateral tyre forces the desired yaw moment for lateral stability has been designed by the sliding control method using a planar bicycle model and taking into consideration cornering stiffness uncertainties. The desired yaw moment is generated by the coordinated control of AFS and ESC. Optimal coordination of the control authority for the AFS and the ESC has been determined to minimise longitudinal deceleration. Estimated vertical tyre forces have been used for the optimum distribution of the longitudinal and lateral tyre forces. For the improved performance of the lateral stability control system, the damping forces at the four corners have been controlled to minimise roll angle by the CDC system. The response of the vehicle to the UCC system has been evaluated via computer simulations using vehicle dynamic software CarSim and a UCC controller coded with Matlab/Simulink. Computer simulations of a closed-loop driver–vehicle–controller system subjected to double lane change have been carried out to prove the improved performance of the proposed UCC strategy over a conventional ESC.

Design and analysis of an H<SUB align=right>∞ integrated control system consists of active suspension and four wheel steering

In this paper, the integration of vehicle vertical and lateral motion control is investigated via control coordination between active suspension (AS) and four wheel steering (4WS) based on interactions from vehicle vertical and lateral dynamics and tyre force coupling characteristics. An H∞ control algorithm has been applied in the controller design to provide more robust characteristics. Comprehensive simulation results and analysis suggest that by using integrated control strategy, significant performance improvements on both lateral and vertical motion can be achieved. Control coordination, individual subsystems, active suspension and rear wheel steering control each play an indispensable role in this control configuration.

A Parameter Identifying a Kalman Filter Observer for Vehicle Handling Dynamics

The paper presents a method for designing a non-linear (i.e. extended) Kalman filter that is also parameter adaptive and hence capable of online identification of its model. The filter model is deliberately simple in structure and low order, yet includes non-linear, load-varying tyre force calculations to ensure accuracy over a range of test conditions. Shape parameters within the (Pacejka) tyre model are adapted rapidly in real time, to maintain excellent state reconstruction accuracy, and provide valuable real-time lateral and vertical tyre force information. The filter is tested in both simulated and test vehicle environments and provides good results. The paper also provides an illustration of the importance of good Kalman filter design practice in terms of selection and tuning of the noise matrices, particularly in terms of the influence of model/sensor error cross-correlations.

Steering system forces due to local camber in ruts

A driver related area that is difficult to simulate and to reproduce in a driving simulator is the steering feel, especially the sense of longitudinal ruts and the self-steering of the vehicle. The hypothesis that the major contribution to the steering feel is due to the lateral movement of the vertical force due to local camber changes is stated. A tyre measurement rig is developed and described. Measurements are taken of the lateral movement of the vertical tyre force and presented for two different tyres. The original hypothesis is proven to be false by computer simulations using the measurements from the rig. Instead the aligning moment created by the tyre belt stiffness for a cambered tyre is shown to have the largest significance on a steering system of modern layout.