Lateral Tire Research Articles

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.

Coordinated yaw stability control for extreme path tracking of 4WIDEVs based on predictive control

To improve safety and stability of four-wheel independent drive electric vehicles (4WIDEVs) in extreme path tracking maneuvers, a hierarchical yaw stability control scheme based on predictive control is proposed in this work. The upper-level stability control strategy coordinates active front steering (AFS) and direct yaw moment control (DYC), yielding desired front steering angle and longitudinal force of each tire. The control task is formulated into a finite horizon optimal control problem, which is solved by hybrid model predictive control (hMPC) algorithm. The lower-level slip ratio control strategy calculates and tracks the optimal longitudinal slip ratio of each tire for implementation of the longitudinal tire force distributions in a wide range of road friction coefficient. Based on a qualified piecewise affine (PWA) approximation of lateral tire force models, the stable regions of vehicle states under multiple varying inputs are obtained by analyzing trajectories of fixed points. Furthermore, the control modes of the upper-level control strategy with different control inputs and state constraints are determined by judging bifurcation point of system. Finally, the proposed control approach is verified and compared through the dSPACE-based hardware-in-the-loop (HIL) experiments. The results indicate that the proposed yaw stability control strategy can improve yaw stability performance and reduce the tracking error significantly in extreme situations.

ADAPTIVE MODEL PREDICTIVE CONTROLLER FOR TRAJECTORY TRACKING AND OBSTACLE AVOIDANCE ON AUTONOMOUS VEHICLE

Advancement in active steering technology is vital as the autonomous vehicle technology is preparing to enter the commercialization phase. Accurate trajectory tracking and collision free motion have become an active topic being discussed in research field recently. During an emergency obstacle avoidance manoeuvre conditions, tyre force saturation can easily happened when availability of lateral tyre forces is limited by the law of tyre friction circle. This greatly affects the trajectory tracking performance of the vehicle. Existing controllers such as generic model predictive controller (MPC) and geometric controller (Stanley) need a proper gain tuning to cope with this condition. This is due to the control gains were determined by trial and error basis via linearization process at a certain targeted speed. Therefore, the control performance is limited considering the presence of speed variation as well as extreme manoeuvre trajectory. This paper proposes an Adaptive Model Predictive Controller (MPC) controller to solve aforementioned issues. First, optimized weighting gains for the steering control were obtained using PSO algorithm. The optimised weighting gains were then scheduled into the proposed Model predictive Controller via a look-up table strategy. In this work, the proposed adaptive MPC controller was designed by using the linearization of the 7 degree-of-freedom (DOF) non-linear vehicle model. Here, the linearized model for controller design was update based on the instantaneous longitudinal speed of the vehicle system plant.

Estimation of Vehicle–Trailer Hitch-Forces and Lateral Tire Forces Independent of Trailer Type and Geometry

Abstract In this paper, a new approach in estimating the lateral tire forces and hitch-forces of a vehicle–trailer system is introduced. It is shown that the proposed hitch-force estimation is independent of trailer mass and geometry, by utilizing the vehicle velocity, acceleration, torque engine, wheel's speed, and steering angle measurements. The designed lateral tire forces and hitch-force estimations' algorithm can be used for any ball type trailer without any priori information on the trailer parameters. A vehicle–trailer dynamic model is proposed to design an observer for the estimation of the hitch-forces and lateral tire forces. Simulations' studies in carsim along with experimental tests are used to validate the presented method. The results confirm the accuracy of the developed observer, and the experimental tests' results show that there is a good agreement between the estimated and actual lateral tire forces as well as the hitch-forces.

Phase Portrait Trajectory of a Three Degree-of-Freedom Vehicular Dynamic Model

Abstract This article formulates a front-wheel-drive three degree-of-freedom (3DOF) four-wheel planar vehicle model with the Magic Formula tire model. The state variables' evolutions of the model, i.e., trajectories of the model under acceleration and deacceleration conditions, are analyzed. The process of evolution is divided into desirable and undesirable phases based on the response characteristics of the vehicle to the driver input during the process. The trajectories are categorized as unsaturated trajectories and saturated trajectories by the existence of saturated tires during these phases. The response of state variables to driver input under acceleration conditions during undesirable phases are zero or even opposite, while the response of undesirable phases under the deacceleration condition is partially positive. Besides, the existing yaw rate safety envelope is recalibrated by using a longitudinal and lateral tire force coupling model. A more accurate yaw rate safety envelope is obtained from the given driver input. Furthermore, a longitudinal speed safety envelope is proposed according to the relationships among slip angle, yaw rate, and longitudinal speed. These safety envelopes are determined by driver input, tire properties, and grip condition. After overlaying yaw rate and longitudinal speed safety envelopes in the state space, the feasibility of using the safety envelope as trajectory classification criteria is discussed.

Fixed Settling Time Control for Self-Driving Car: Two-Timescales Approach

This article involves the design of a novel path tracking control technique for the self-driving car. Fixed settling time sliding mode control (FSTSMC) with barrier Lyapunov function is implemented to deal with the non-linear lateral dynamics and to ensure stable standard double-lane-change (DLC) maneuver of self-driving cars in the presence of unknown lateral tire forces and parametric uncertainties. A two-time scale-based approach is employed to deal with the slow and fast dynamics of the car separately. The proposed control scheme efficacy is investigated using simulations based on CarSim and Simulink. The simulation results validate the path-tracking ability of the proposed controller for self-driving cars while accomplishing the stable double-lane-change maneuver at various forward speeds.

Contribution to the investigation of the influence of tire non-uniformity on the lateral tire characteristics

Tire models are widely used in research in the field of vehicle dynamics and noise, and especially in the simulation of their movement under the action of forces and moments. In general case, we distinguish theoretical models defined on the basis of tire construction and empirical or semi-empirical models based on experimental tests. In addition, a combination of these two types of models can also produce tire models. In practice, there is a very wide range of mathematical tire models defined using finite element analysis, by approximation of polynomials of different degrees, by approximation of magic formula, etc. In this paper, an attempt is made to calculate non-stationary lateral characteristics of tires on the basis of experimental stationary lateral characteristics, using two-parameter higher level polynomials. This polynomials define the tire lateral characteristics, and take into account their non-uniformity. More specifically, the lateral characteristics are approximated as a function of the dynamic change of the slip angle, radial load due to tire non-uniformity and time.

Research on intervention criterion and stability coordinated control of AFS and DYC

To improve vehicle handling stability, an intervention criterion and a coordinated control method for active front steering (AFS) and direct yaw moment control (DYC) are proposed. First, the intervention criterion of AFS/DYC stability control based on the working state of lateral tyre force is proposed. Next, a 7-DOF (degree-of-freedom) dynamics model is established, and a method for identifying nonlinear pure lateral force model based on onboard sensors and vehicle handling stability experiment is developed. Then, the mapping relationship between lateral tyre force saturation point and wheel angle is constructed to rapidly judge the working state of lateral tire force. Subsequently, a UKF-based state observer, a hierarchical control algorithm and the yaw moment distribution coefficient are designed for the proposed AFS/DYC control system. Finally, a fishhook test and a step input test are carried out on low adhesion coefficient roads to verify the effectiveness of the proposed AFS/DYC coordinated control method.

Finding optimum Ackermann geometry for a car undergoing steady state cornering using tire data

For a car to have minimum lap times across a track it should be able to produce the maximum cornering force or side force in order to complete the corner at the maximum velocity possible. The grip level of a particular tire limits the maximum side/lateral force it can produce. To find the best steering geometry for a car one should know the grip limit of the tire and at which slip angle it is being produced. This paper provides a simple methodology to find the appropriate Ackermann steering geometry, which can produce the maximum lateral tire grip going through different high speed constant radius corners. Hence, reducing the time spent on-track while testing to find out the suitable steering setup and improving the overall cornering ability of the car. The raw tire data from tire testing runs of the tire: Hoosier 18.0 X 6.0 – 10 R25b is used to fit curves to the raw data using two tire models based on the Magic Formula and Data Non-dimensionalization methods respectively. The results from both of the methods are compared. These tire models are then used to find the ideal steer angles of the front tires at various constant radius steady-state turns and thus the Ackermann geometry of a Formula Student car producing the maximum possible grip.

Terrain Adaptive Trajectory Planning and Tracking on Deformable Terrains

In this work, a novel single-level adaptive trajectory planner and tracking controller is developed for off-road autonomous vehicles operating on deformable terrains. Trajectory planning and tracking algorithms often rely on a simplified vehicle model to predict future vehicle states based upon control inputs, hence requiring accurate modeling and parameterization. On off-road deformable terrains this is a challenging task due to unknown terrain parameters and the complex interactions at tire-terrain interfaces, which pose issues in continuous differentiability, operating conditions, and computational time. To address these difficulties, in this paper, a neural network deformable terrain terramechanics model and its implementation within a terrain adaptive model predictive control algorithm is presented to improve vehicle safety and performance through more accurate prediction of the plant response. It is shown in simulations that the neural network is able to predict the lateral tire forces accurately and efficiently compared to the Soil Contact Model as a state-of-the-art model and is able to yield accurate bicycle model predictions. It is demonstrated that the implementation of the neural network within model predictive control can outperform both a baseline Pacejka-based and a rapidly exploring random tree controller by improving performance and allowing for more severe maneuvers to be completed that otherwise lead to failure when terrain deformations are not explicitly taken into account. The improved performance achieved through estimating terrain parameters online in an adaptive controller is highlighted against the nonadaptive realization. Finally, it is shown the algorithm is conducive to real-time implementation.

Vehicle Dynamic Control with 4WS, ESC and TVD under Constraint on Front Slip Angles

To enhance vehicle maneuverability and stability, a controller with 4-wheel steering (4WS), electronic stability control (ESC) and a torque vectoring device (TVD) under constraint on the front slip angles is designed in this research. In the controller, the control allocation method is adopted to generate yaw moment via 4WS, ESC and TVD. If the front steering angle is added for generating yaw moment, the steering performance of the vehicle can be further deteriorated. This is because the magnitude of the lateral tire forces are limited and the required yaw moment is insufficient. Constraint is imposed on the magnitude of the front slip angles in order to prevent the lateral tire forces from saturating. The driving simulation is performed by considering the limit of the front slip angle proposed in this study. Compared to the case that uses the existing 4WS, the results of this study are derived from the actuator combination that enhances performance while maintaining stability.

Should a Vehicle Always Deviate to the Tire Blowout Side?—A New Tire Blowout Model With Toe Angle Effects

Abstract As a severe tire failure, tire blowout during driving can significantly threaten vehicle stability and road safety. Tire blowout models were developed in the literature to conclude that a vehicle always deviates to the tire blowout side. However, this conclusion is proved to be inaccurate in this paper, since one important factor was largely ignored in the existing tire blowout models. Toe angle, as a basic and widely applied setup on ground vehicles, can provide preset and symmetric lateral tire forces for normal driving. However, when tire blowout occurs, different toe angle setups can impact vehicle motions in different ways. For the first time, the toe angle is explicitly considered and integrated into a tire blowout model in this paper. For different tire blowout locations, driving maneuvers, and drivetrain configurations, the impacts of different toe angle setups on the variations of tire friction forces and vehicle motions are analyzed. The developed tire blowout model with toe angles is validated through both high-fidelity carsim simulation results and experimental results of a scaled test vehicle. Both simulation and experimental results show that a vehicle may not deviate to the tire blowout side, depending on the toe angle setups and driving maneuvers. Moreover, the experimental results also validate that the proposed tire blowout model can accurately evaluate the tire blowout impacts on vehicle dynamics.

A New Torque Distribution Control for Four-Wheel Independent-Drive Electric Vehicles

Torque distribution control is a key technique for four-wheel independent-drive electric vehicles because it significantly affects vehicle stability and handling performance, especially under extreme driving conditions. This paper, which focuses on the global yaw moment generated by both the longitudinal and the lateral tire forces, proposes a new distribution control to allocate driving torques to four-wheel motors. The proposed objective function not only minimizes the longitudinal tire usage, but also make increased use of each tire to generate yaw moment and achieve a quicker yaw response. By analysis and a comparison with prior torque distribution control, the proposed control approach is shown to have better control performance in hardware-in-the-loop simulations.

Modular estimation of lateral vehicle dynamics and application in optimal AFS control

The paper introduces a novel modular estimation approach for lateral vehicle and tire dynamics using a simplified vehicle model and a non-linear estimation algorithm. A dynamics-oriented representation of lateral tire forces with a single track lateral vehicle model (STVM) has been introduced. Subsequently, extended Kalman filter (EKF) based distributed observer modules for each dynamical parameter has been designed and combined into a Unified Estimation Scheme (UES). Finally, a linear quadratic regulator (LQR) based Active Front Steering (AFS) control system has been designed using the estimated parameters. The accuracy and computational efficiency of the designed scheme has been analyzed and compared to non-modular UKF, EKF, and Particle Filter (PF) algorithms, through Monte-Carlo Simulations using the CarSim dataset for both high and low [Formula: see text] surfaces, followed by further validation using real-time dataset. The results show that the proposed system significantly improve the accuracy and speed of estimation, as well as stable performance in closed loop control.

Nonlinear Model Predictive Control for Integrated Energy-Efficient Torque-Vectoring and Anti-Roll Moment Distribution

This study applies nonlinear model predictive control (NMPC) to the torque-vectoring (TV) and front-to-total anti-roll moment distribution control of a four-wheel-drive electric vehicle with in-wheel-motors, a brake-by-wire system, and active suspension actuators. The NMPC cost function formulation is based on energy efficiency criteria, and strives to minimize the power losses caused by the longitudinal and lateral tire slips, friction brakes, and electric powertrains, while enhancing the vehicle cornering response in steady-state and transient conditions. The controller is assessed through simulations using an experimentally validated high-fidelity vehicle model, along ramp steer and multiple step steer maneuvers, including and excluding the direct yaw moment and active anti-roll moment distribution actuations. The results show: 1) the substantial enhancement of energy saving and vehicle stabilization performance brought by the integration of the active suspension contribution and TV; 2) the significance of the power loss terms of the NMPC formulation on the results; and 3) the effectiveness of the NMPC with respect to the benchmarking feedback and rule based controllers.

A coupled force predictive control of vehicle stability using front/rear torque allocation with experimental verification

This paper investigates the handling control and stability of an all-wheel-drive vehicle whose axles are individually equipped with an electric motor connected to an open differential. This could offer a potential configuration for the mass production of electric all-wheel-drive vehicles because of reduced cost and complexity. Although there is no torque vectoring or direct yaw moment control in this configuration, considerable handling improvement can be achieved by optimised front/rear torque distribution due to the longitudinal and lateral tire force coupling. In this study, a model predictive control design is presented with a coupled force prediction model for vehicle handling dynamics. The controller optimises the front/rear torque allocation to track the desired handling response and ensure vehicle stability. This study also compensates for actuator delay by incorporating the actuator dynamics into the control design. The performance of the proposed controller is evaluated through software simulations and experimental tests conducted on an electric all-wheel-drive Chevrolet Equinox.

Conflict and Sensitivity Analysis of Vehicular Stability Using a Two-State Linear Bicycle Model

Vehicle parameters and operation conditions play a critical role in vehicular handling and stability. This study aimed to evaluate vehicle stability based on cornering tire stiffness integrated with vehicle parameters. A passenger vehicle is considered in which a two-state linear bicycle model is developed in the Matlab/Simulink. The effect of the vehicle parameters on lateral vehicle stability has been investigated and analyzed. The investigated parameters included CG longitudinal position, wheelbase, and tire cornering stiffness. Furthermore, the effects of load variation and vehicle speed were addressed. Based on a Fishhook steering maneuver, the lateral stability criteria represented in lateral acceleration, yaw rate, vehicle sideslip angle, tire sideslip angles, and the lateral tire force were analyzed. The results demonstrated that the parameters that affect the lateral vehicle stability the most are the cornering stiffness coefficient and the CG longitudinal location. The findings also indicated a positive correlation between vehicle properties and lateral handling and stability.

A cascaded scheme for high-performance estimation of vehicle states

Vehicle active safety control is bonded tightly with the accurate acquirement of vehicle states. This paper presents a cascaded scheme to realize high-performance estimation of vehicle states. To achieve the estimation with good performance, an adaptive sliding mode observer is designed for determining four longitudinal tire forces independently, and the Kalman filter is used for alleviating the inherent chattering effect. On this basis, lateral tire forces are calculated via a simplified formula based on the Dugoff tire model. Lastly, utilizing the obtained tire force information, the key states of vehicle motion are estimated through the smooth variable structure filter. Numerical experiments are conducted to testify the effectiveness of the presented estimation scheme. The results of performance comparison in different case studies show that the chattering effect can be suppressed to a great extent, and the accuracy, robustness and real-time performance to modeling uncertainty and unexpected measurements can be effectively guaranteed for vehicle state estimation by means of the proposed scheme.

New Integrated Vehicle Stability Control of Active Front Steering and Electronic Stability Control Considering Tire Force Reserve Capability

To address the problem of the mutual interference and control distribution in the integrated stability control of active front steering (AFS) and electronic stability control (ESC), this study proposes a new integrated stability controller of AFS and ESC based on holistic control framework. A distribution rule of longitudinal and lateral tire force based on equal reserve capacity of tire force is designed to distribute the control right of steering and braking. A UniTire model with combined slip condition is also designed for the integrated control of steering and braking. Model predictive control (MPC) is adopted to address the constrained multi-objective control problem. To reduce the complexity of the system and improve the real-time performance of the system, a linear time-varying MPC controller is designed by linearizing the nonlinear system, and then the constrained MPC control problem is transformed into a quadratic programming problem for solving. Finally, the proposed method is validated on the basis of Matlab/Simulink and CarSim co-simulation platform. Results show that the proposed method has obvious effects on solving the mutual interference and control right distribution of steering and braking and improving vehicle stability.

A hierarchical framework of emergency collision avoidance amid surrounding vehicles in highway driving

Collision avoidance is a key issue for high-speed vehicles in emergency situations, particularly as it pertains to surrounding vehicles. Accordingly, a hierarchical framework for human-driven or autonomous vehicles is proposed that ensures the safe operation of vehicles in emergency driving scenarios while considering surrounding vehicles. The developed emergency collision-avoidance system consists of an estimator module, a prediction module, a manoeuvre decision-making module, and a manoeuvre control module. The core module for manoeuvre decision making uses finite state machine (FSM) technology to determine the appropriate manoeuvre for avoiding collisions. In particular, a collision risk model is developed in this module, taking into account risk related to surrounding vehicles in the overlapping region, road adhesion, and stabilization performance of vehicle. In the manoeuvre control module, accounting for safe gaps to surrounding vehicles in an adjacent lane, the longitudinal manoeuvre is generated by a model predictive-control algorithm. A yaw stability controller is designed using lateral tire force estimate-based sliding mode control, accounting for both the collision and vehicle stabilization. To mediate the demands of yaw stabilization and collision risk, particularly for reducing the loss of velocity, an integrated controller with propulsion is developed. Modeling vehicles driving under different road conditions with various road adhesion and surrounding-vehicle settings, the results of experiments in a hardware-in-the-loop (HIL) system have successfully demonstrated the effectiveness of the proposed collision avoidance system.