Tyre–road grip coefficient assessment – Part II: online estimation using instrumented vehicle,extended Kalman filter,and neural network

The main objective of this work is to determine the limit of safe driving conditions by identifying the maximal friction coefficient in a real vehicle. The study will focus on finding a method to determine this limit before reaching the skid, which is valuable information in the context of traffic safety. Since it is not possible to measure the friction coefficient directly, it will be estimated using the appropriate tools in order to get the most accurate information. A real vehicle is instrumented to collect information of general kinematics and steering tie-rod forces. A real-time algorithm is developed to estimate forces and aligning torque in the tyres using an extended Kalman filter and neural networks techniques. The methodology is based on determining the aligning torque; this variable allows evaluation of the behaviour of the tyre. It transmits interesting information from the tyre–road contact and can be used to predict the maximal tyre grip and safety margin. The maximal grip coefficient is estimated according to a knowledge base, extracted from computer simulation of a high detailed three-dimensional model, using Adams^® software. The proposed methodology is validated and applied to real driving conditions, in which maximal grip and safety margin are properly estimated.     

Estimation of the tyre–road maximum friction coefficient and slip slope based on a novel tyre model

In this article, a new approach to estimate the vehicle tyre forces, tyre–road maximum friction coefficient, and slip slope is presented. Contrary to the majority of the previous work on this subject, a new tyre model for the estimation of the tyre–road interface characterisation is proposed. First, the tyre model is built and compared with those of Pacejka, Dugoff, and one other tyre model. Then, based on a vehicle model that uses four degrees of freedom, an extended Kalman filter (EKF) method is designed to estimate the vehicle motion and tyre forces. The shortcomings of force estimation are discussed in this article. Based on the proposed tyre model and the improved force measurements, another EKF is implemented to estimate the tyre model parameters, including the maximum friction coefficient, slip slope, etc. The tyre forces are accurately obtained simultaneously. Finally, very promising results have been achieved for pure acceleration/braking for varying road conditions, both in pure steering and combined manoeuvre simulations.     

Models and methodology for optimal trajectory generation in safety-critical road–vehicle manoeuvres

There is currently a strongly growing interest in obtaining optimal control solutions for vehicle manoeuvres, both in order to understand optimal vehicle behaviour and, perhaps more importantly, to devise improved safety systems, either by direct deployment of the solutions or by including mimicked driving techniques of professional drivers. However, it is non-trivial to find the right combination of models, optimisation criteria, and optimisation tools to get useful results for the above purposes. Here, a platform for investigation of these aspects is developed based on a state-of-the-art optimisation tool together with adoption of existing vehicle chassis and tyre models. A minimum-time optimisation criterion is chosen for the purpose of gaining an insight into at-the-limit manoeuvres, with the overall aim of finding improved fundamental principles for future active safety systems. The proposed method to trajectory generation is evaluated in time-manoeuvres using vehicle models established in the literature. We determine the optimal control solutions for three manoeuvres using tyre and chassis models of different complexities. The results are extensively analysed and discussed. Our main conclusion is that the tyre model has a fundamental influence on the resulting control inputs. Also, for some combinations of chassis and tyre models, inherently different behaviour is obtained. However, certain variables important in vehicle safety-systems, such as the yaw moment and the body-slip angle, are similar for several of the considered model configurations in aggressive manoeuvring situations.     

Tyre friction behaviour under abrupt wheel torque transients on slippery road surfaces: experimental analysis and modelling

The paper shows that, during abrupt wheel torque transients for ice surface and low vehicle speeds, the tyre can develop significantly larger longitudinal force than the peak value of the tyre static curve. This so-called dynamic tyre friction potential (DTFP) effect has many influencing factors such as the rate of change of the wheel torque, the vehicle speed, and the tyre dwell time. The paper presents a detailed analysis of the DTFP behaviour based on the experimental data collected by using an in-wheel motor-based tyre test vehicle. The analysis results and an insight into the brush structure of a tyre model lead to the hypothesis that the different influencing factors may be predominantly explained by the bristle dwell time (BDT) effect. Following this hypothesis, the LuGre model of the tyre friction dynamics is extended with a physical BDT sub-model. The experimental validation results show that the proposed model can accurately capture the low-speed tyre–ice friction behaviour during abrupt wheel torque transients.     

Unscented Kalman filter for vehicle state estimation

Vehicle dynamics control (VDC) systems require information about system variables, which cannot be directly measured, e.g. the wheel slip or the vehicle side-slip angle. This paper presents a new concept for the vehicle state estimation under the assumption that the vehicle is equipped with the standard VDC sensors. It is proposed to utilise an unscented Kalman filter for estimation purposes, since it is based on a numerically efficient nonlinear stochastic estimation technique. A planar two-track model is combined with the empiric Magic Formula in order to describe the vehicle and tyre behaviour. Moreover, an advanced vertical tyre load calculation method is developed that additionally considers the vertical tyre stiffness and increases the estimation accuracy. Experimental tests show good accuracy and robustness of the designed vehicle state estimation concept.     

Tyre–road grip coefficient assessment. Part 1: off-line methodology using multibody dynamic simulation and genetic algorithms

A key factor to understand the vehicle dynamic behaviour is to know as accurately as possible the interaction that occurs between the tyre and the road, since it depends on many factors that influence the dynamic response of the vehicle. This paper aims to develop a methodology in order to characterise the tyre–road behaviour, applying it to obtain the tyre–road grip coefficient. This methodology is based on the use of dynamic simulation of a virtual model, integrated into a genetic algorithm that identifies the tyre–road friction coefficient in order to adjust the response obtained by simulation to real data. The numerical model was developed in collaboration with SEAT Technical Centre and it was implemented in multibody dynamic simulation software Adams®, from MSC®.     

A real-time approach to robust identification of tyre–road friction characteristics on mixed-μ roads

ABSTRACT

The interaction between the tyre and the road is crucial for understanding the dynamic behaviour of a vehicle. The road–tyre friction characteristics play a key role in the design of braking, traction and stability control systems. Thus, in order to have a good performance of vehicle dynamic stability control, real-time estimation of the tyre–road friction coefficient is required. This paper presents a new development of an on-line tyre–road friction parameters estimation methodology and its implementation using both LuGre and Burckhardt tyre–road friction models. The proposed method provides the capability to observe the tyre–road friction coefficient directly using measurable signals in real-time. In the first step of our approach, the recursive least squares is employed to identify the linear parameterisation form of the Burckhardt model. The identified parameters provide, through a T–S fuzzy system, the initial values for the LuGre model. Then, a new LuGre model-based nonlinear least squares parameter estimation algorithm using the proposed static form of the LuGre to obtain the parameters of LuGre model based on recursive nonlinear optimisation of the curve fitting errors is presented. The effectiveness and performance of the algorithm are demonstrated through the real-time model simulations with different longitudinal speeds and different kinds of tyres on various road surface conditions in both Matlab/Carsim environments as well as collected data from real experiments on a commercial trailer.     

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.     

Sliding mode-based lateral vehicle dynamics control using tyre force measurements

In this work, a lateral vehicle dynamics control based on tyre force measurements is proposed. Most of the lateral vehicle dynamics control schemes are based on yaw rate whereas tyre forces are the most important variables in vehicle dynamics as tyres are the only contact points between the vehicle and road. In the proposed method, active front steering is employed to uniformly distribute the required lateral force among the front left and right tyres. The force distribution is quantified through the tyre utilisation coefficients. In order to address the nonlinearities and uncertainties of the vehicle model, a gain scheduling sliding-mode control technique is used. In addition to stabilising the lateral dynamics, the proposed controller is able to maintain maximum lateral acceleration. The proposed method is tested and validated on a multi-body vehicle simulator.     

Noise,vibration, harshness model of a rotating tyre

ABSTRACT

The tyre plays a fundamental role in the generation of acoustically perceptible driving noise and vibrations inside the vehicle. An essential part of these vibrations is induced by the road excitation and transferred via the tyre into the vehicle. There are two basic ways to study noise, vibration, harshness (NVH) behaviour: Simulations in time and frequency domains. Modelling the tyre transfer behaviour in frequency domain requires special attention to the rotation of the tyre. This paper shows the approach taken by the authors to include the transfer behaviour in the frequency range up to 250?Hz from geometric road excitations to resulting spindle forces in frequency domain. This paper validates the derived NVH tyre model by comparison with appropriate transient simulations of the base transient model.     

An Alternative Method to Determine the Magic Tyre Model Parameters Using Genetic Algorithms

Summary Tyre behavior plays an important role in vehicle dynamics research. Knowledge of tyre properties is necessary to properly design vehicle components and advance control system. For that purpose mathematical models of the tyre are being used in vehicle simulation models. The Magic Formula Tyre Model is a semi-empirical tyre model which describes tyre behavior quite accurately. The Magic Formula Tyre Model needs a set of parameters to describe the tyre properties; the determination of these parameters is dealt with in this paper. A new method based on genetic techniques is used to determine these parameters. The main advantages of the method are its simplicity of implementation and its fast convergence to optimal solution, with no need of deep knowledge of the searching space. So to start the search, it is not necessary to know a set of starting values of the Magic Formula parameters. The comparison between analytical optimization methods and the method proposed is discussed in this paper.     

Validation of an Articulated Vehicle Simulation

Tests were performed on a typical UK articulated vehicle to measure dynamic tyre forces and sprung mass accelerations. The measured road profile data and vehicle response data are used to determine some of the important characteristics of articulated vehicle vibration behaviour. In particular, roll motions and their effect on dynamic tyre forces are examined. The measured data are used to validate two and three-dimensional computer models of the vehicle. Attention is given to modelling the tandem leaf-spring trailer suspension. The conditions under which a two-dimensional model can accurately simulate vehicle behaviour are examined.     

Identifying tyre models directly from vehicle test data using an extended Kalman filter

Individual tyre models are traditionally derived from component tests, with their parameters matched to force and slip measurements. They are imported into vehicle models which should, but do not always properly provide suspension geometry interaction. Recent advances in Global Positioning System (GPS)/inertia vehicle instrumentation now make full state measurement viable in test vehicles, so tyre slip behaviour is directly measurable. This paper uses an extended Kalman filter for system identification, to derive individual load-dependent tyre models directly from these test vehicle state measurements. The resulting model therefore implicitly compensates for suspension geometry and compliance. The paper looks at two variants of the tyre model, and also considers real-time adaptation of the model to road surface friction variations. Test vehicle results are used exclusively, and the results show successful tyre model identification, improved vehicle model state prediction – particularly in lateral velocity reproduction – and an effective real-time solution for road friction estimation.     

Estimation of longitudinal speed robust to road conditions for ground vehicles

This article seeks to develop a longitudinal vehicle velocity estimator robust to road conditions by employing a tyre model at each corner. Combining the lumped LuGre tyre model and the vehicle kinematics, the tyres internal deflection state is used to gain an accurate estimation. Conventional kinematic-based velocity estimators use acceleration measurements, without correction with the tyre forces. However, this results in inaccurate velocity estimation because of sensor uncertainties which should be handled with another measurement such as tyre forces that depend on unknown road friction. The new Kalman-based observer in this paper addresses this issue by considering tyre nonlinearities with a minimum number of required tyre parameters and the road condition as uncertainty. Longitudinal forces obtained by the unscented Kalman filter on the wheel dynamics is employed as an observation for the Kalman-based velocity estimator at each corner. The stability of the proposed time-varying estimator is investigated and its performance is examined experimentally in several tests and on different road surface frictions. Road experiments and simulation results show the accuracy and robustness of the proposed approach in estimating longitudinal speed for ground vehicles.     

A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations

A sliding-mode observer is designed to estimate the vehicle velocity with the measured vehicle acceleration, the wheel speeds and the braking torques. Based on the Burckhardt tyre model, the extended Kalman filter is designed to estimate the parameters of the Burckhardt model with the estimated vehicle velocity, the measured wheel speeds and the vehicle acceleration. According to the estimated parameters of the Burckhardt tyre model, the tyre/road friction coefficients and the optimal slip ratios are calculated. A vehicle adaptive sliding-mode control (SMC) algorithm is presented with the estimated vehicle velocity, the tyre/road friction coefficients and the optimal slip ratios. And the adjustment method of the sliding-mode gain factors is discussed. Based on the adaptive SMC algorithm, a vehicle's antilock braking system (ABS) control system model is built with the Simulink Toolbox. Under the single-road condition as well as the different road conditions, the performance of the vehicle ABS system is simulated with the vehicle velocity observer, the tyre/road friction coefficient estimator and the adaptive SMC algorithm. The results indicate that the estimated errors of the vehicle velocity and the tyre/road friction coefficients are acceptable and the vehicle ABS adaptive SMC algorithm is effective. So the proposed adaptive SMC algorithm can be used to control the vehicle ABS without the information of the vehicle velocity and the road conditions.     

An Alternative Method to Determine the Magic Tyre Model Parameters Using Genetic Algorithms

Summary Tyre behavior plays an important role in vehicle dynamics research. Knowledge of tyre properties is necessary to properly design vehicle components and advance control system. For that purpose mathematical models of the tyre are being used in vehicle simulation models. The Magic Formula Tyre Model is a semi-empirical tyre model which describes tyre behavior quite accurately. The Magic Formula Tyre Model needs a set of parameters to describe the tyre properties; the determination of these parameters is dealt with in this paper. A new method based on genetic techniques is used to determine these parameters. The main advantages of the method are its simplicity of implementation and its fast convergence to optimal solution, with no need of deep knowledge of the searching space. So to start the search, it is not necessary to know a set of starting values of the Magic Formula parameters. The comparison between analytical optimization methods and the method proposed is discussed in this paper.     

The Tyre as a Sensor to Estimate Friction

SUMMARY

Continuously updated knowledge of the friction potential and the friction demand can help to improve manoeuvrability and thereby safety of vehicles under slippery road conditions. An on line friction estimation method is presented using a simple brush type tyre model. First the method is verified by outdoor experiments using a tyre test trailer. Then the setup of a low-cost measurement system in a vehicle is discussed and results from both simulations and outdoor experiments are presented. Neural networks have been used both for modelling and identification of friction potential and friction demand.     

Application of Elementary Neural Networks and Preview Sensors for Representing Driver Steering Control Behaviour

This paper demonstrates the use of elementary neural networks for modelling and representing driver steering behaviour in path regulation control tasks. Areas of application include uses by vehicle simulation experts who need to model and represent specific instances of driver steering control behaviour, potential on-board vehicle technologies aimed at representing and tracking driver steering control behaviour over time, and use by human factors specialists interested in representing or classifying specific families of driver steering behaviour. Example applications are shown for data obtained from a driver/vehicle numerical simulation, a basic driving simulator, and an experimental on-road test vehicle equipped with a camera and sensor processing system.     

基于强化学习DDPG的智能车辆轨迹跟踪控制

针对智能车辆在轨迹跟踪过程中的横向控制问题，提出一种基于强化学习中深度确定性策略梯度算法（Deep Deterministic Policy Gradient，DDPG）的智能车辆轨迹跟踪控制方法。首先，将智能车辆的跟踪控制描述为一个基于马尔可夫决策过程（MDP）的强化学习过程，强化学习的主体是由Actor神经网络和Critic神经网络构成的Actor-Critic框架；强化学习的环境包括车辆模型、跟踪模型、道路模型和回报函数。其次，所提出方法的学习主体以DDPG方法更新，其中采用回忆缓冲区解决样本相关性的问题，复制结构相同的神经网络解决更新发散问题。最后，将所提出的方法在不同场景中进行训练验证，并与深度Q学习方法（Deep Q-Learning，DQN）和模型预测控制（Model Predictive Control，MPC）方法进行比较。研究结果表明：基于DDPG的强化学习方法所用学习时间短，轨迹跟踪控制过程中横向偏差和角偏差小，且能满足不同车速下的跟踪要求；采用DDPG和DQN强化学习方法在不同场景下均能达到训练片段的最大累计回报；在2种仿真场景中，基于DDPG的学习总时长分别为DQN的9.53%和44.19%，单个片段的学习时长仅为DQN的20.28%和22.09%；以DDPG、DQN和MPC控制方法进行控制时，在场景1中，基于DDPG方法的最大横向偏差分别为DQN和MPC的87.5%和50%，仿真时间分别为DQN和MPC的12.88%和53.45%；在场景2中，基于DDPG方法的最大横向偏差分别为DQN和MPC的75%和21.34%，仿真时间分别为DQN和MPC的20.64%和58.60%。     

Validation of an Articulated Vehicle Simulation

SUMMARY

Tests were performed on a typical UK articulated vehicle to measure dynamic tyre forces and sprung mass accelerations. The measured road profile data and vehicle response data are used to determine some of the important characteristics of articulated vehicle vibration behaviour. In particular, roll motions and their effect on dynamic tyre forces are examined. The measured data are used to validate two and three-dimensional computer models of the vehicle. Attention is given to modelling the tandem leaf-spring trailer suspension. The conditions under which a two-dimensional model can accurately simulate vehicle behaviour are examined.