Cornering Stiffness Estimation Research Articles

Estimation of States and Cornering Stiffness of a Vehicle by LPV‐MHE

In this paper, we consider an estimation problem of sideslip angle and cornering stiffness of a vehicle from measurements of yaw rate, lateral acceleration and steering angle. Firstly, a vehicle dynamical model is expressed as a linear parameter‐varying system with cornering stiffness as uncertain parameters. Then, we show a method to estimate the parameters and the state based on moving horizon estimation. We provide a simple algorithm to solve the estimation problem. The effectiveness of the estimation method is evaluated through numerical simulations. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Path tracking control of automated vehicles based on adaptive MPC in variable scenarios

AbstractFor complex and dynamic high‐speed driving scenarios, an adaptive model predictive control (MPC) controller is designed to ensure effective path tracking for automated vehicles. Firstly, in order to prevent model mismatch in the MPC controller, a tire cornering stiffness estimation algorithm is designed and a soft constraint on slip angle is added to further enhance the controller's precision in tracking trajectories and the vehicle's driving stability. Secondly, the improved particle swarm optimization (IPSO) method with dynamic weights and penalty functions is suggested to address the issue of insufficient accuracy in solving quadratic programming. Additionally, the standard particle swarm optimization (PSO) algorithm is used to seek the most suitable time horizon parameters offline to obtain the best time horizon data set under different vehicle speeds and adhesion coefficients, and then it is optimized online by an adaptive network‐based fuzzy inference system (ANFIS) to enhance the model predictive controller's adaptability in different operating conditions. Finally, simulation experiments are conducted under three different operating conditions: docked roads, split roads, and variable vehicle speeds. The results indicate that the designed adaptive MPC controller can accurately and stably track the reference trajectory in various scenarios.

Estimation of Lateral Velocity and Cornering Stiffness in Vehicle Dynamics Based on Multi-Source Information Fusion

<div>To address the challenge of directly measuring essential dynamic parameters of vehicles, this article introduces a multi-source information fusion estimation method. Using the intelligent front camera (IFC) sensor to analyze lane line polynomial information and a kinematic model, the vehicle’s lateral velocity and sideslip angle can be determined without extra sensor expenses. After evaluating the strengths and weaknesses of the two aforementioned lateral velocity estimation techniques, a fusion estimation approach for lateral velocity is proposed. This approach extracts the vehicle’s lateral dynamic characteristics to calculate the fusion allocation coefficient. Subsequently, the outcomes from the two lateral velocity estimation techniques are merged, ensuring rapid convergence under steady-state conditions and precise tracking in dynamic scenarios. In addition, we introduce a tire parameter online adaptive module (TPOAM) to continually update essential tire parameters such as cornering stiffnesses, with its effectiveness demonstrated through DLC and slalom simulation tests. Using a dual extended Kalman filter (DEKF) observer, the article allows for joint estimation of vehicle states and tire parameters. Ultimately, we offer a cost-effective estimation method of vital dynamic vehicle parameters to support the motion control module in autonomous driving.</div>

Integrated control method for path tracking and lateral stability of distributed drive electric vehicles with extended Kalman filter–based tire cornering stiffness estimation

Aiming at the lack of adaptability of vehicle parameters under extreme conditions, this paper proposes an integrated control method for path tracking and lateral stability of distributed drive electric vehicles based on tire cornering stiffness adaptive model predictive control (MPC) scheme. The control method integrates active front steering and direct yaw control to improve the path tracking and lateral stability performance of distributed drive electric vehicles. Firstly, considering the influence of vertical load transfer, the tire cornering stiffness is estimated based on the extended Kalman filter (EKF) algorithm. Then, using this online updated tire cornering stiffness value, an adaptive MPC controller for path tracking and lateral motion stability of distributed drive electric vehicles is constructed. Meanwhile, a fuzzy sliding mode control (Fuzzy-SMC)–based longitudinal velocity controller is established to ensure the accuracy of velocity tracking. Also, according to the distributed driving characteristics of the controlled system, a tire torque distributor based on weighted pseudo-inverse (WPI) is designed with the minimum tire load rate as the optimization objective, where the road adhesion condition and the maximum output torque of the motor are considered as constraints. The simulation results show that the proposed integrated control method based on tire cornering stiffness adaptive model predictive control is robust and effective. Compared with constant cornering stiffness model predictive control–based control method, it can improve the vehicle path tracking accuracy and lateral motion stability under extreme conditions.

A Vehicle Lateral Motion Control Based on Tire Cornering Stiffness Estimation Using In-Wheel Motors

In this paper, a study on vehicle lateral motion control using an in-wheel motor (IWM) based on tire cornering stiffness estimation is presented. The main purpose of this paper is to develop a lateral motion control that can be implemented considering practical issues in real-world vehicle applications such as driver comfort, high availability, and stable control accuracy. The proposed lateral motion controller for yaw rate tracking is intended to improve vehicle cornering agility. In this paper, we develop a model-based controller with a feedforward control term to accomplish this. In particular, a change in tire cornering stiffness according to the size of the tire slip angle is reflected to improve control accuracy. Finally, the Weighted Least Square (WLS) allocation method optimally distributes the IWM torque to each wheel. Simulation studies confirm that some evaluation factors are improved in terms of cornering performance compared to conventional control algorithms.

Vehicle Sideslip Angle Estimation Based on Interacting Multiple Model Kalman Filter Using Low-Cost Sensor Fusion

This study proposes a new method for vehicle sideslip angle estimation utilizing the competitively priced sensor fusion using in-vehicle sensors and low-cost standalone global positioning system (GPS). To estimate unmeasurable vehicle states, vehicle sideslip angle and tire cornering stiffness, an interacting multiple model (IMM) Kalman filter is proposed that combines two extended Kalman filters (EKFs), each including kinematic and dynamic equations of vehicle lateral velocity. To properly combine the outputs of these model-based EKFs, a weighted probability of each model based on the stochastic process is designed, which reflects the characteristics of each of the kinematic and dynamic equations in real-time. Also, the observability of the proposed estimation algorithm is checked by observability functions of nonlinear systems. The estimation performance in various driving scenarios is verified using an experimental vehicle, and its superiority is confirmed through a comparative study. The proposed algorithm makes the following main contributions for estimating the vehicle sideslip angle: 1) the high optimality of estimation results and 2) the accurate estimation of tire cornering stiffness.

Estimation of sideslip angle and cornering stiffness of an articulated vehicle using a constrained lateral dynamics model

In this paper, a constrained lateral dynamics model of articulated vehicles and an algorithm for estimating sideslip angle and cornering stiffness are proposed. The articulated vehicle was modeled using the bicycle model, linear tire model, and modified Dug-off model. The normal force of each axle included in the model was estimated based on the longitudinal load transfer model. Physical constraints were applied to reduce model states. Accurate sideslip angle and cornering stiffness are essential for vehicle control safety and autonomous driving performance. The sideslip angle and cornering stiffness were simultaneously estimated using a dual linear time-varying (LTV) Kalman filter. The observability matrix guaranteed the convergence of the proposed estimation algorithm. The estimation performance was verified by simulation with TruckSim and an experiment using an articulated bus.

Robust sideslip angle observer of commercial vehicles based on cornering stiffness estimation using neural network

Accurate estimation of sideslip angle is essential for vehicle stability control. For commercial vehicles, the estimation of sideslip angle is challenging due to severe load transfer and tire nonlinearity. This paper presents a robust sideslip angle observer of commercial vehicles based on identification of tire cornering stiffness. Since tire cornering stiffness of commercial vehicles is greatly affected by tire force and road adhesion coefficient, it cannot be treated as a constant. To estimate the cornering stiffness in real time, the neural network model constructed by Levenberg-Marquardt backpropagation (LMBP) algorithm is employed. LMBP is a fast convergent supervised learning algorithm, which combines the steepest descent method and gauss-newton method, and is widely used in system parameter estimation. LMBP does not rely on the mathematical model of the actual system when building the neural network. Therefore, when the mathematical model is difficult to establish, LMBP can play a very good role. Considering the complexity of tire modeling, this study adopted LMBP algorithm to estimate tire cornering stiffness, which have simplified the tire model and improved the estimation accuracy. Combined with neural network, A time-varying Kalman filter (TVKF) is designed to observe the sideslip angle of commercial vehicles. To validate the feasibility of the proposed estimation algorithm, multiple driving maneuvers under different road surface friction have been carried out. The test results show that the proposed method has better accuracy than the existing algorithm, and it’s robust over a wide range of driving conditions.

Cornering stiffness estimation using Levenberg–Marquardt approach

Study of vehicle dynamics aggregates possibilities to enhance performance, safety and reliability, such as the integration of control systems, usually requiring knowledge on vehicle's states and parameters. However, some critical values are difficult to measure or are not disclosed. For this reason, dynamics and stability analysis of six-wheeled vehicles are compromised, and available information on this matter is limited. In this context, this paper proposes the estimation of the cornering stiffness of a 6x6 vehicle by an inverse problem approach applying the Levenberg–Marquardt (LM) method. The algorithm required data from field experiments and from simulations of a vehicle model during a double-lane change manoeuvre developed using . Experimental and theoretical values for the vehicle yaw rate were combined through LM method for cornering stiffness estimation. The excellent agreement between measured and simulated yaw rate indicates that the proposed model and the estimated parameters properly represent the vehicle dynamics response.

Integrated control of active steering and braking systems with tyre forces and cornering stiffness estimation

Integrated control of active steering and braking systems with tyre forces and cornering stiffness estimation

Integrated control of active steering and braking systems with tyre forces and cornering stiffness estimation

A model-based integrated controller for active steering and active braking systems is proposed to enhance vehicle handling and stability. A hierarchical scheme is adopted, including vehicle layer based on model predictive control (MPC), actuator layer, and observer layer. The MPC controller adopts a predictive model with the lateral force of front axle and yaw moment as inputs, which leaves the nonlinearity and coupling of tyre forces to be solved by the tyre force allocation algorithm in actuator layer, leading to more precise control action. In order to maintain satisfactory control performance with respect to the variation of tyre character, a dual extended Kalman filter (DEKF) is designed in the observer layer to estimate tyre forces and cornering stiffness. The observed results are used to reduce the mismatch of the reference models in vehicle layer and actuator layer. The effectiveness of the proposed controller is demonstrated by simulations in CarSim environment.

Vehicle dynamics estimation via augmented Extended Kalman Filtering

The response of active safety systems of modern cars strongly depends on the estimation accuracy in the key motion states of the vehicle. One common limitation of current systems is the lack of adaptability in the parameters of the vehicle model that are usually treated as time-invariant, although they are not exactly known or are subject to temporal changes. As a direct consequence, time invariant-parameter control systems may achieve sub-optimal performance and/or deteriorate according to the driving conditions.This paper presents a non-linear model-based observer for combined estimation of motion states and tyre cornering stiffness. It is based on common onboard sensors, that is a lateral acceleration and yaw rate sensor, and it works during normal vehicle manoeuvering. The identification framework relies on an augmented Extended Kalman filter to deal with model parameter variability and noisy measurement input. Results are described to evaluate the performance and sensitivity of the proposed approach, showing an improvement in the estimation accuracy that can reach an order of magnitude compared to standard approaches.

Yaw stability control for a rear double-driven electric vehicle using LPV-H∞ methods

This paper presents a new yaw stability controller for a rear double-driven electric vehicle. A linear parameter varying (LPV) model of the vehicle is formulated using longitudinal speed measurement and tire cornering stiffness estimation. The LPV model is then utilized to design a gain-scheduled (H_∞) controller with guaranteed stability. Results from simulations, performed with CarSim, show that the new controller improves the vehicle performance and handling even in extreme maneuvers and that it is robust to model parameter uncertainties.

Relaxed static stability based on tyre cornering stiffness estimation for all-wheel-drive electric vehicle

A novel dynamics control approach for all-wheel-drive electric vehicle (EV), relaxed static stability (RSS) approach is proposed with two advantages. Firstly, it allows vehicle lateral dynamics system to be inherent unstable to improve configuration flexibility. Secondly, handling performance could be improved based on closed-looped pole assignment with additional yaw moment. In this paper, basic control framework of RSS is proposed, including ‘Desired Pole Location’, ‘Pole Assignment’ and ‘Tyre Cornering Stiffness Estimation’ modules. The tyre cornering stiffness is estimated online to improve the robustness of the controller. The experiments based on an EV testbed show the performance and efficiency of RSS.

Application of Novel Lateral Tire Force Sensors to Vehicle Parameter Estimation of Electric Vehicles.

This article presents methods for estimating lateral vehicle velocity and tire cornering stiffness, which are key parameters in vehicle dynamics control, using lateral tire force measurements. Lateral tire forces acting on each tire are directly measured by load-sensing hub bearings that were invented and further developed by NSK Ltd. For estimating the lateral vehicle velocity, tire force models considering lateral load transfer effects are used, and a recursive least square algorithm is adapted to identify the lateral vehicle velocity as an unknown parameter. Using the estimated lateral vehicle velocity, tire cornering stiffness, which is an important tire parameter dominating the vehicle’s cornering responses, is estimated. For the practical implementation, the cornering stiffness estimation algorithm based on a simple bicycle model is developed and discussed. Finally, proposed estimation algorithms were evaluated using experimental test data.

Model-based vehicle stability control with tyre force and instantaneous cornering stiffness estimation

A model-based vehicle stability controller is proposed in this paper. Since a model-based controller highly depends on the model accuracy, the lateral forces of the tyres and the instantaneous cornering stiffnesses of the predictive vehicle model are estimated online in order to deal with the model mismatch. The model-based controller calculates a desired yaw moment according to the prevailing errors in the the yaw rate and the side-slip angles of the vehicle. Then, by using linearization, an optimal braking force allocation algorithm is proposed to allocate the yaw moments to the target slip ratios of each wheel. Simulations are carried out with a full-vehicle model in CarSim software. The effectiveness and the robustness of the proposed control algorithm are evaluated through simulation cases of open-loop and closed-loop manoeuvres.

Vehicle lateral dynamics modelling by subspace identification methods and tyre cornering stiffness estimation

In this paper, subspace identification method is used for vehicle lateral dynamics modelling, which is based on input and output data and describes the vehicle behaviour more accurately. By standard vehicle road tests, the effects of three traditional subspace methods are validated in vehicle modelling. The results show that the MOESP and N4SID methods are effective, and the CVA models have the highest estimated precision. Furthermore, the CVA models from different tests are evaluated in order to obtain a proper vehicle model. By contrast, the CVA-step model and CVA-DLC model provide better estimations on yaw rate and side-slip angle, respectively. Moreover, a tyre cornering stiffness estimation method based on identified model is proposed, which is derived on condition that the vehicle system poles are constant. The result shows that the estimation of Kf and Kr based on CVA models is more accurate.

Reliable vehicle sideslip angle fusion estimation using low-cost sensors

This paper proposes an adaptive hybrid fusion estimation strategy using low-cost sensors to estimate vehicle sideslip angle in a wide driving-maneuver range. First, the kinematics model-based extended Kalman filter (KEKF) is designed as the basic filtering framework. To ensure the KEKF accuracy and observability in a wide range of driving maneuvers, the influence of inertial sensor drift is considered and the estimation from the bicycle dynamics-based extended Kalman filter (DEKF) is introduced as the KEKF measurement. In the DEKF, the cornering stiffness estimation algorithm is developed to adapt to the changes in tire-road conditions. Further, to reduce the adverse impact of the DEKF performance degradation in nonlinear regions caused by severe maneuvers, a fuzzy decision module is proposed to determine the degree that the KEKF utilizes the DEKF estimation as the reliable measurement. Finally, the sequential measurement-update processing algorithm is developed and the adaptive weighted fusion algorithm is executed to realize the global fusion. The results of both intensive simulations and experiments validate the feasibility and effectiveness of the proposed strategy.

Tire–road friction coefficient and tire cornering stiffness estimation based on longitudinal tire force difference generation

A sequential tire cornering stiffness coefficient and tire–road friction coefficient (TRFC) estimation method is proposed for some advanced vehicle architectures, such as the four-wheel independently-actuated (FWIA) electric vehicles, where longitudinal tire force difference between the left and right sides of the vehicle can be easily generated. Such a tire force difference can affect the vehicle yaw motion, and can be utilized to estimate the tire cornering stiffness coefficient and TRFC. The proposed tire cornering stiffness coefficient and TRFC identification method has the potential of estimating these parameters without affecting the vehicle desired motion control and trajectory tracking objectives. Simulation and experimental results with a FWIA electric vehicle show the effectiveness of the proposed estimation method.

Vehicle dynamics control of four in-wheel motor drive electric vehicle using gain scheduling based on tyre cornering stiffness estimation

This paper focuses on the vehicle dynamic control system for a four in-wheel motor drive electric vehicle, aiming at improving vehicle stability under critical driving conditions. The vehicle dynamics controller is composed of three modules, i.e. motion following control, control allocation and vehicle state estimation. Considering the strong nonlinearity of the tyres under critical driving conditions, the yaw motion of the vehicle is regulated by gain scheduling control based on the linear quadratic regulator theory. The feed-forward and feedback gains of the controller are updated in real-time by online estimation of the tyre cornering stiffness, so as to ensure the control robustness against environmental disturbances as well as parameter uncertainty. The control allocation module allocates the calculated generalised force requirements to each in-wheel motor based on quadratic programming theory while taking the tyre longitudinal/lateral force coupling characteristic into consideration. Simulations under a variety of driving conditions are carried out to verify the control algorithm. Simulation results indicate that the proposed vehicle stability controller can effectively stabilise the vehicle motion under critical driving conditions.