Tire Force Estimation Research Articles

Vehicle Stability Control Based on Vehicle Motion State and Tire Force Estimation

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

Study on intelligent tyre force estimation algorithm based on strain analysis

The objective of this paper is to propose a novel approach to develop an algorithm for estimating the grounding force between a tyre and the road surface. First, a finite element model of a heavy-duty tyre is developed in this paper, and the validity of the model is verified by load application tests and mechanical vibration tests. When the tyres are operated under various operating conditions, that is, load, side deflection, side tilt and longitudinal slip conditions, the sensitivity analysis is performed by combining the three-directional forces based on the strain curves measured when the tyres are rolling, respectively. In order to achieve accurate estimation of the three-directional forces, this paper establishes a three-directional force estimation model using the support vector machine (SVM) technique, with the tyre force-sensitive eigenvalues as inputs and the tyre forces as outputs, so as to achieve the three-directional force estimation of the tyre-grounded three-directional forces. joint estimation of tyre-road contact force. The results show that the estimation error of vertical force is 1.79%, the estimation error of lateral force is 3%, the estimation error of longitudinal force is 4.65% and in general, the estimation error of grounding force is kept within 5%, and the estimation effect is good.

An Energy Efficient Control Strategy for Electric Vehicle Driven by In-Wheel-Motors Based on Discrete Adaptive Sliding Mode Control

This paper presents an energy-efficient control strategy for electric vehicles (EVs) driven by in-wheel-motors (IWMs) based on discrete adaptive sliding mode control (DASMC). The nonlinear vehicle model, tire model and IWM model are established at first to represent the operation mechanism of the whole system. Based on the modeling, two virtual control variables are used to represent the longitudinal and yaw control efforts to coordinate the vehicle motion control. Then DASMC method is applied to calculate the required total driving torque and yaw moment, which can improve the tracking performance as well as the system robustness. According to the vehicle nonlinear model, the additional yaw moment can be expressed as a function of longitudinal and lateral tire forces. For further control scheme development, a tire force estimator using an unscented Kalman filter is designed to estimate real-time tire forces. On these bases, energy efficient torque allocation method is developed to distribute the total driving torque and differential torque to each IWM, considering the motor energy consumption, the tire slip energy consumption, and the brake energy recovery. Simulation results of the proposed control strategy using the co-platform of Matlab/Simulink and CarSim® demonstrate that it can accomplish vehicle motion control in a coordinated and economic way.

Online Estimation of Three-Directional Tire Forces Based on a Self-Organizing Neural Network

The road friction coefficient and the forces between the tire and the road have a significant impact on the stability and precise control of the vehicle. For four-wheel independent drive electric vehicles, an adaptive tire force calculation method based on the improved Levenberg–Marquarelt multi-module and self-organizing feedforward neural networks (LM-MMSOFNN) was proposed to estimate the three-directional tire forces of four wheels. The input data was provided by common sensors amounted on the autonomous vehicle, including the inertial measurement unit (IMU) and the wheel speed/rotation angle sensors (WSS, WAS). The road type was recognized through the road friction coefficient based on the vehicle dynamics model and Dugoff tire model, and then the tire force was calculated by the neural network. The computational complexity and storage space of the system were also reduced by the improved LM learning algorithm and self-organizing neurons. The estimation accuracy was further improved by using the Extended Kalman Filter (EKF) and Moving Average (MA). The performance of the proposed LM-MMSOFNN was verified through simulations and experiments. The results confirmed that the proposed method was capable of extracting important information from the sensors to estimate three-directional tire forces and accurately adapt to different road surfaces.

A Comprehensive Vehicle Stability Assessment System Based on Enabling Tire Force Estimation

This paper presents an enabling comprehensive vehicle stability assessment system covering vehicle longitudinal, yaw and roll stability. First, the longitudinal, lateral and vertical tire forces are separately estimated using the strong tracking unscented Kalman filter and the conventional Kalman filter based on low-cost on-board sensors. Then, a comprehensive vehicle longitudinal, yaw and roll stability space is established by utilizing the normalized tire friction ellipse and the Load Transfer Ratio value. Finally, the vehicle stability is determined and predicted based on current driver's inputs. The hardware-in-loop experimental results show that the proposed vehicle stability assessment system can accurately estimate the longitudinal, lateral and vertical tire forces with the normalized root mean square errors of 1.87 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> , 1.07 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> and 1.43 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> , and exhibits satisfying performance for vehicle longitudinal, yaw and roll stability evaluation and prediction. This bears significance for the efficient functioning of active control systems to improve vehicle safety under critical driving conditions.

Hierarchical estimation of vehicle state and tire forces for distributed in-wheel motor drive electric vehicle without previously established tire model

In this paper, a hierarchical estimator combined with the nonlinear observer and particle filter (PF) is proposed to accurately estimate the vehicle state and tire forces of distributed in-wheel motor drive electric vehicles (DIMDEVs) when the traditional tire models are not available. The proposed estimator consists of lower and upper layers. The lower layer, i.e. longitudinal tire force nonlinear observer (LTFNO) aims at estimating the longitudinal force based on the available drive/brake torques and rotational speed of wheels. The convergence of LTFNO is proved by the invariant set principle. The upper layer receives these estimated longitudinal tire forces from LTFNO and estimates the vehicle state including lateral tire forces based on an expert model (EM). The designed EM utilizes basic knowledge and rules about tire characteristics to approximate the unknown lateral tire force. The upper estimator combines with EM (EEM) to further improve the accuracy. The EEM takes the modeling errors and disturbances into account and avoids the usage of complex established tire models. Then PF is applied in the upper layer to complete the estimation, which only needs measurable longitudinal/lateral accelerations and yaw rate signals. Finally, the effectiveness of the designed hierarchical estimator is verified by Carsim and Simulink co-simulations. The results show the proposed strategy can accurately estimate the vehicle state and tire forces in real-time.

An observation algorithm for key motion states of skid-steered wheeled unmanned vehicle

With the increasing demand of military and civilian in the intelligent vehicles, the skid-steering theory has been widely used in unmanned ground vehicles, especially in unmanned military vehicles and unmanned surveillance platforms. Due to its driving environment complex and variable, which requires stricter dynamic control system. In order to improve the active safety performance of the skid-steering unmanned vehicle and develop the key technologies such as behavior decision planning technology, path tracking, and dynamic control technology, it is necessary to develop the dynamic state parameter observation system based on skid-steering theory. In this paper, an observation using Strong Track External Kalman Filter theory with noise matrix adaptive is designed to estimate vehicle kinematic parameters based on a 6 × 6 skid-steered unmanned vehicle. First, kinematic and dynamic model is built to analyze the characters of a skid-steered wheeled vehicle. Then a tire force estimation method based on dynamic model is presented to observe the tire longitude and vertical force. The tire force data is also used by Dugoff nonlinear model. Then an External Kalman Filter theory is designed to estimate vehicle kinematic parameters. To increase the accuracy and the robustness of the observer, the Strong Tracking EKF (STEKF) and noise adaptive adjustment is designed. Finally, a combined simulation using TruckSim and Simulink and the experiment using a 6 × 6 skid-steered unmanned vehicle verifies the efficiency of the observer. Results show that the observer is able to estimate the skid-steered wheeled vehicle states, and it also shows that the yaw rate result in the slip angle difference between each tire.

A Universal Approach to Tire Forces Estimation by Accelerometer-Based Intelligent Tire: Analytical Model and Experimental Validation

ABSTRACT Efforts to improve the performance and safety of vehicles include placing active sensing components (e.g., embedded microsensors) within tires result in intelligent tires. One application of intelligent tire is tire force estimation based on accelerometers. However, its development is limited due to the difficulty of relating the tire force to kinematical information by model-based theory. In this manuscript, a universal approach to tire forces estimation by the accelerometer-based intelligent tire is formulated and experimentally validated. First, a microelectromechanical system accelerometer-based intelligent tire prototype is established with the function of on-board monitoring of tire forces. Then, a theoretical rolling kinematics model is proposed for illustrating the mechanisms of acceleration fields, resulting from the coupling effect of rigid body motion and elastic deformation. An analytical model is formulated to estimate the vertical force in real time. Furthermore, the beam model is adopted to describe lateral deformations of the tire belt, directly linking lateral acceleration and lateral force. Finally, the lateral force can be estimated by lateral acceleration and vertical force already estimated. Based on a universal analytical model, the lateral force estimation method realizes high accuracy under different circumstances, even with unified coefficients, by clarifying and eliminating the influence of ply steer. A field test and two bench experiments have been conducted to fully validate the developed model. It can be concluded that the theoretical-analysis-based estimation model realizes an encouraging tire force estimation application with an intelligent tire hardware system.

A hierarchical estimation scheme of tire-force based on random-walk SCKF for vehicle dynamics control

The estimation of vehicle dynamics states is crucial for vehicle stability control and autonomous driving, especially tire-force which governs vehicular motion. However, measuring tire-force directly needs expensive measurement instruments, moreover, vehicle non-linear characteristics, vehicle parameter uncertainties, unknown key variables, and sensor noise could cause great challenges in its observation. Therefore, this paper aims to develop an accurate, affordable tire-force estimator to tackle the above-mentioned issues. A novel hierarchical estimation scheme based on random-walk square-root cubature Kalman filter (SCKF) is proposed and it works without a complex tire model and considers vehicle parameter uncertainties. The estimator scheme contains three blocks. The first block estimates related key variables of tire force observation. The second block estimates both vertical tire-force and longitudinal tire-force. The longitudinal tire-force is observed based on effective tire radius identification, and a proportional integral differential (PID) method is derived based on the Lyapunov principle. Then, a random-walk SCKF algorithm is presented to estimates lateral tire-force. To validate the effectiveness of the proposed estimation scheme, CarSim & Matlab/Simulink joint simulation and real car tests are carried out. Results show that the proposed estimation scheme's accuracy performance and its potential as an affordable solution for the tire-force observation.

Tire Force Estimation in Intelligent Tires Using Machine Learning

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

Speed-adaptive motion control algorithm for differential steering vehicle

The differential steering vehicle uses the in-wheel motors to drive the wheels directly and individually. However, in order to deliver the required structural robustness, the differential steering vehicle discarded the mechanical steering system and achieved vehicle steering by applying differential speed between the left and right wheels. This paper presents a novel speed-adaptive motion control algorithm based on the unique chassis configuration to enhance the performance in vehicle handling and lateral stability. The proposed control method first estimates the driver’s driving intention, from which reference wheel speeds are individually generated for each wheel based on their respective slipping and skidding status. Finally, the torque command is automatically adjusted by the speed-tracking controller by proactive adaptation of the wheel spinning resistance to effectively avoid excessive slip on low friction. This method exploits the fact that the torque at the steady state will always be equal to the available longitudinal force, thereby delivering the sophisticated tire force estimation without additional computational efforts, and ultimately helping conserve energy and promote lateral stability. The essential road information collected by this algorithm is also made available to drivers for improved vehicle controllability. The algorithm is subjected to three experimental case scenarios—pivot steering, low-friction driving, and curvilinear driving—through TruckSim–Simulink co-simulations and real vehicle tests, and the results have validated the algorithm in realizing the high-performance steering and maneuvering capabilities for six-wheeled differential steering vehicles.

Fail-Operation Control of In-Wheel Motor Drive Electric Vehicle Based on Wheel Isolation and Yaw Moment Compensation

To improve the trackability of in-wheel motor drive (IWMD) and wheel-individual steer electric vehicles (EVs) when steering actuators fail, the fail-operation control strategy was proposed to correct vehicles in a steering failure situation and avoid losing control of vehicle steering. A linear quadratic regulator (LQR) decides the additional yaw moment of the vehicle according to vehicle state errors. The tire force estimation module estimates the compensating resistance moment generated by the failed wheel according to the tire slip angle and the vertical tire force. By isolating the failed wheel, the optimal torque distribution (OTD) controller allocates the additional yaw moment and the compensating resistance moment to normal wheels to realize the fail-operation control of the IWMD vehicle. The control effect was verified through co-simulation of MATLAB/Simulink and Trucksim. Compared with the uncontrolled and direct torque allocation methods, the proposed OTD method reduces the lateral trajectory error of the vehicle by 86% and 60.5%, respectively, when failure occurs, and achieves better velocity maintaining ability, which proves the effectiveness of the proposed fail-operation control strategy.

Vehicle state and tyre force estimation: demonstrations and guidelines

This paper presents an in-depth analysis of the application of different techniques for vehicle state and tyre force estimation using the same experimental data and vehicle models, except for the tyre models. Four schemes are demonstrated: (i) an Extended Kalman Filter (EKF) scheme using a linear tyre model with stochastically adapted cornering stiffness, (ii) an EKF scheme using a Neural Network (NN) data-driven linear tyre model, (iii) a tyre model-less Suboptimal-Second Order Sliding Mode (S-SOSM) scheme, and (iv) a Kinematic Model (KM) scheme integrated in an EKF. The estimation accuracy of each method is discussed. Moreover, guidelines for each method provide potential users with valuable insight into key properties and points of attention.

Estimation of Tire Forces using Vehicle Linear Accelerations and Yaw Rate

Estimation of Tire Forces using Vehicle Linear Accelerations and Yaw Rate

Real-time estimation and prediction of tire forces using digital map for driving risk assessment

This work aims to develop a driving risk warning system to enhance the road safety. Different from the existing lane departure warning system, speed limit warning system or collision warning system, the warning system proposed in this work focuses on the safety regarding vehicle's dynamics states. Many road accidents are caused by losing control of vehicle dynamics, such as the rollover, car drift and brake failure. First of all, the importance of monitoring vehicle dynamics states, especially the tire forces, is explained. Then the driving risk assessment criteria based on tire forces are developed in this work. The main contribution of this paper is the development of vehicle dynamics models and observers to estimate and predict individual tire forces using only low-cost sensors and ADAS (Advanced Driver Assistance Systems) map. The major new techniques developed in this study can be summarized in three aspects: (1) development of new vehicle dynamics models to estimate vertical, longitudinal, and lateral tire forces, (2) development of new nonlinear observers to minimize the estimation errors caused by sensor noises and model uncertainty, and (3) development of the tire forces prediction algorithm by taking advantage of digital map. The proposed warning system is validated by real vehicle experiments.

Off-road motorcycle tyre force estimation

To improve the performance of off-road motorcycles, tyre contact forces need to be estimated. Differently to on-road motorcycle contact force estimators where the rider can be considered attached to the chassis, an off-road motorcycles estimator needs to model the rider dynamics, since driving in standing position provides significant isolation from motorcycle motion. In this article, we use a novel simple rider model to approximate the interaction with the motorcycle when no sensing on him is possible. In particular, the novelty is to keep the pitch angle of the rider constant by means of an active torque on the hip. A tyre force estimator is built using this rider model coupled to a five degree-of-freedom motorcycle, which is verified with a virtual experiment performed on Working Model 2D, showing promising results.

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

Knowledge of tire side-slip angle and lateral tire force is crucial to vehicle lateral stability control which can enhance vehicle handling and passenger safety. However, due to high costs of sensors and limitations to sensor technologies, ordinary automobiles cannot measure the tire side-slip angle and lateral tire force directly during vehicle operation. Therefore, the accurate, affordable monitoring of lateral vehicle motion is essential. This paper presents a unified observation algorithm to simultaneously estimate the tire side-slip angle and lateral tire force of all four wheels. Firstly, an adaptive-sliding-mode observer (ASMO) is utilized to estimate the lateral tire force of each wheel. Secondly, the tire side-slip angle of each wheel can be estimated by an adaptive compensation algorithm (ACA). Simulations and real car experiments are used to validate the effectiveness of the proposed approach, and extended kalman filter (EKF) is used to compare with our proposed algorithm. Results show that the designed observer can effectively estimate tire side-slip angles and lateral tire forces of all four wheels, and its performance is better than EKF.

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

The knowledge of tire-ground interaction forces is valuable for intelligent vehicles technologies. However, tire forces transducers are expensive and not suitable for ordinary passenger cars. An alternative is to estimate these forces using less sophisticated sensors. This paper presents a new delayed interconnected cascade-observer structure to reconstruct the forces acting on each tire in all directions. The addition of delayed interconnections overcomes the mutual dependence problem in the cascade estimator. Observers are developed based on nonlinear vehicle dynamic models. The Extended Kalman Filter and the Unscented Kalman Filter algorithms are applied for comparison purposes. Two experimental data are used to validate the estimator: a driving in ordinary urban streets and a high-speed slalom maneuver in a banked road. The results are compared with force measurements obtained with transducers and with an existing estimator from the literature.

Dynamic modeling of aircraft landing gear and multi-objective optimization with simple cell mapping method

To study the dynamic characteristics of aircraft landing gear and carry out successive optimizations, a mathematical model of flexible landing gear is established by the Hamiltonian principle. The dynamic model includes a tire force estimation derived from the impact model. Dynamic analysis with the flexible model is then conducted. Stress distribution is obtained from the dynamic analysis, which can be used for fatigue analysis, optimization design, etc. To achieve better dynamic characteristics in terms of vibration reduction, a multi-objective optimization problem is formulated and solved via a simple cell mapping algorithm. Optimal simulations indicate the quality of optimal structural designs. Compared with the baseline structure, candidate optimal designs can improve dynamic performance of fuselage vibration suppression, shock absorber efficiency, and stress settling time. The proposed multi-objective optimal parameter design provides a fast tuning procedure that saves considerable time compared to finite element method-based optimization. In addition, the optimal parameter set provides useful interface information for detailed landing gear structural modeling that serves other analysis purposes.

Observer-based estimation of velocity and tire-road friction coefficient for vehicle control systems

A novel nonlinear observer for the estimation of vehicle velocity together with the tire-road friction coefficient is presented in this paper. The modular observer is designed based on a longitudinal tire force estimation approach and a lateral tire friction model. Compared to the state-of-art methods, the proposed observer design provides accurate estimation of the longitudinal velocity, lateral velocity, and the tire-road friction coefficient simultaneously. Particularly, the longitudinal tire forces are first estimated based on a filter observer. Then, according to the calculation of lateral tire forces, the nonlinear observer is proposed to estimate vehicle velocity and the tire-road friction coefficient. Moreover, the stability property of the observer is analyzed using a Lyapunov-based method. Simulation results validate the effectiveness of the proposed method.