Nonlinear Tire Research Articles

非線形モデル予測制御を用いた車両限界域制御と最速走行のための制御

In this paper, we propose a vehicle motion control method considering stability at the limit state using nonlinear model predictive control. In order to consider the vehicle limit state, a vehicle model is defined by using a nonlinear tire model that considers combined slip etc. The steering angle and the slip rates of each wheel at the limit lateral acceleration state are calculated on the numerical simulations. In addition, as an application example of the proposed method, results of running a circuit course at the fastest speed using curvature minimum path generation algorithm is demonstrated. Simulation results show that the proposed method can run at the speed at the lateral acceleration limit according to the course shape and it is able to run on the out-in-out trajectory.

Bifurcation of Lane Change and Control on Highway for Tractor-Semitrailer under Rainy Weather

A new method is proposed for analyzing the nonlinear dynamics and stability in lane changes on highways for tractor-semitrailer under rainy weather. Unlike most of the literature associated with a simulated linear dynamic model for tractor-semitrailers steady steering on dry road, a verified 5DOF mechanical model with nonlinear tire based on vehicle test was used in the lane change simulation on low adhesion coefficient road. According to Jacobian matrix eigenvalues of the vehicle model, bifurcations of steady steering and sinusoidal steering on highways under rainy weather were investigated using a numerical method. Furthermore, based on feedback linearization theory, taking the tractor yaw rate and joint angle as control objects, a feedback linearization controller combined with AFS and DYC was established. The numerical simulation results reveal that Hopf bifurcations are identified in steady and sinusoidal steering conditions, which translate into an oscillatory behavior leading to instability. And simulations of urgent step and single-lane change in high velocity show that the designed controller has good effects on eliminating bifurcations and improving lateral stability of tractor-semitrailer, during lane changing on highway under rainy weather. It is a valuable reference for safety design of tractor-semitrailers to improve the traffic safety with driver-vehicle-road closed-loop system.

Vehicle System State Estimation Based on Adaptive Unscented Kalman Filtering Combing With Road Classification

This paper presents a new method to address issues associated with vehicle system state estimation using an unscented Kalman filter (UKF) with considering full-car system and nonlinear tire force under various international standards organization (ISO) road conditions. Due to the fact that practical road information is complex and noise covariance cannot be treated as a constant, the influence of varying vehicle system process noise variance and measurement noise covariance on the estimation accuracy of the UKF is first discussed. To precisely estimate road information, a novel road classification method using measured signals (vertical acceleration of sprung mass and unsprung mass) of vehicle system is proposed. According to road excitation levels, different road process variances are defined to tune the vehicle system’s variance for application of UKF. Then, road classification and UKF are combined to form an adaptive UKF (AUKF) that takes into account the relationship of different road process noise variances and measurement noise covariances under varying road conditions. Simulation results reveal that the proposed AUKF algorithm has higher accuracy for state estimation of a vehicle system under various ISO road excitation condition.

Tyre modelling for an autonomous articulated wheel loader conducting a V-shape loading cycle simulation

Virtual product developments (VPDs) tools have a great effect on reducing the cost of development, which explains the considerable amount of attention they received lately from researchers. In this work, two different VPD tyre models, restricted fully non-linear and enhanced non-linear transient models, are tested through modelling and simulation. A detailed multibody mechanical system model of a large wheel loader conducting a V-shape loading cycle was used to test the performance differences between the two transient tyre models. VPD simulations show that both tyre models enable the operator (controller) to drive the machine tracking the desired path; however, the enhanced non-linear tyre model shows larger deviation and less operator comfort when compared with the restricted non-linear transient tyre model. Results also show the ability of the restricted tyre model to produce higher forces and moment to keep the machine on track.

Controllability of the powerslide motion of vehicles with different drive concepts

The steady-state powerslide of an automobile (large side slip angle, negative steering angle, large rear driving torque) is considered as a manoeuvre characterized by nonlinear tyre characteristics and saturated horizontal tyre forces. Due to its typically unstable nature, the powerslide motion has to be stabilized either by the driver or an active system by controlling the steering angle and/or the accelerator (and braking) pedal. Consequences, and an appropriate driver model have already been presented in literature. However, different powertrain configurations, such as rear-wheel drive (RWD), all-wheel drive (AWD), with open, locked and limited slip differentials have not yet been addressed in more detail. Also the effectiveness of redundant inputs, either from the driver or from a driver assist system, is discussed. An appropriate vehicle, powertrain and tyre model is introduced to analyse regular and powerslide steady-state cornering. Then a measure of joint controllability and observability of the modes of these steady-state, and locally linearized motions, is evaluated.It turned out that basically the powerslide motion can be more easily stabilized by controlling the longitudinal tyre forces in particular at vehicles with limited slip differential, for instance with respective throttle commands (by the driver) when utilising the yaw rate measurement only, but also steering angles of the front wheels may (additionally) be applied. In contrast, at regular cornering, the steering inputs are superior to throttle commands to control the lateral motion variables of the vehicle.

Synthetic method to investigate self-loosening of suspension fasteners considering nonlinear tire characteristics at the adhesion limit

AbstractA synthetic test method is described which is capable of investigating various suspension fasteners on a dynamic half-axle test rig. This test method is advantageous compared to an expensive and time-consuming driving cycle. In advance vehicle specific measured values that serve as input parameters for the test rig experiments are required. This study shows how the adhesion limit influences the interdependencies between vertical load, side slip angle and longitudinal slip. By means of multibody systems and in consideration of the determined nonlinear tire characteristics, this method can be applied to investigate suspension fasteners of vehicles without expensive and time-consuming test drives. Validation results of different vehicles are given which demonstrate that the method is appropriate to a wide range of vehicles.

비선형 타이어모델 기반 MPC를 이용한 차량 안정화

Recent research suggests the various applications of Model Predictive Control on vehicle systems. In numerous cases, nonlinear tire models such as the Magic Formula, which are highly complex and are more detailed than necessary, are used. This paper presents a nonlinear tire model that excludes the region of negative slope but expresses the nonlinear properties of tire well enough for tracking the lane of a racing course. The proposed inverse tire model can also be used to calculate the slip angle from the tire force. Thus, the model can be utilized to design the Model Predictive Controller.

Investigation of the tyre characteristics under non-steady-state conditions on the basis of road tests

This paper presents a method of identifying the dynamic characteristics of tyres for non-steady-state conditions on the basis of road measurements on a vehicle. The side force acting on the tyre is presented as a function of not only the slip angle but also the slip angle derivative (i.e. the velocity of the change in the slip angle). Hence, the influence of the manoeuvre dynamics on the tyre characteristics and the difference between the characteristics obtained for steady-state conditions and the characteristics for non-steady-state conditions are shown. Also the results of computer simulations prepared for different types of tyre characteristics are presented in this paper. It is evident from the presented graphs that applying dynamic non-linear tyre characteristics for computer simulations instead of steady-state characteristics enables us to describe the real motion of a vehicle better.

Vehicle position estimation using nonlinear tire model for autonomous vehicle

To achieve technical perfection of the Advanced driver assistant system (ADAS), accurate analysis of the vehicle’s position is essential. For this, conventionally, sensor fusion has been carried out using a general GPS and general Inertial measurement unit (IMU), but the position accuracy decreases because of inertial sensor accumulation. Furthermore, because a vehicle tire model is analyzed by linearization and using a bicycle model, the position error increases. To solve this, in this study, a fusion algorithm was proposed by using an extended Kalman filter based on the non-linear tire model for the vehicle state information and by using the general GPS position information provided by the electric stability program of the vehicle. The fusion algorithm proposed in this study allowed us to suggest a position error correction method corresponding to a high precision Differential global positioning system (DGPS) within 1 m.

Investigation on cornering brake stability of a heavy-duty vehicle based on a nonlinear three-directional coupled model

A nonlinear three-directional coupled lumped parameters (TCLP) model is proposed for a heavy-duty vehicle to investigate the longitudinal, lateral and vertical dynamics of vehicles simultaneously. The nonlinear property of suspension damping is described by a fitted exponent model from experimental data. The nonlinear tire forces in different directions are modeled by the nonlinear Gim model and the vertical single dot contact model with square nonlinearity. The system responses are calculated by numerical integration and compared with the Functional Virtual Prototyping (FVP) model and the test data, so as to verify the validity of this new vehicle model. With Lateral-Load Transfer Ratio (LTR) and yaw rate as evaluation indexes, the influences of system parameters on cornering brake stability are analyzed. The critical vehicle speed table is also obtained. The study shows that high vehicle running speed, large front wheel steering angle, large tire cornering stiffness or small braking moment is harmful to yaw stability and roll stability. Road surface frictional coefficient mainly influences yaw stability, and vertical tire stiffness and road surface roughness mainly influence roll stability.

Vehicle Ego-Localization in Autonomous Lane-Keeping Evasive Maneuvers

This paper presents a method for precise and reliable vehicle ego-localization required for autonomous vehicle guidance in highly dynamic lane-keeping evasive maneuvers. It combines the measurements of a low-cost mono-camera used for lane detection with the information of standard vehicle sensors. The proposed data-fusion concept uses an advanced vehicle model based Extended Kalman Filter that takes into account the nonlinear tire characteristics at the limits of driving physics. Extensions of the fusion concept are derived which compensate the application-related limitations of the camera. The experimental results of a pedestrian collision avoidance maneuver demonstrate the accuracy and robustness of the method.

Lateral roll control of vehicle based on UKF and sliding model control

A 3-DOF dynamical model of vehicle is built in this paper by using MATLAB/Simulink. Considering nonlinear tyre performance, the magic formula tyre model is used to improve the accuracy of the model. For the difficulty of measuring the roll angle and roll rate, an observer for the roll angle and roll rate based on the dynamical model of vehicle and kinematic relations is designed in this paper, tracking the roll angle and roll rate in the process of driving based on the easily measured status parameters, using unscented Kalman filter. Then, this method is tested through experiments. Finally, based on the estimated roll angle and roll rate, a roll stability controller based on the sliding model variable structure control theory is designed.

Vehicle Lateral Dynamics Control Through AFS/DYC and Robust Gain-Scheduling Approach

In this paper, we investigate the combined active front-wheel steering/direct yaw-moment control for the improvement of vehicle lateral stability and vehicle handling performance. A more practical assumption in this work is that the longitudinal velocity is not constant but varying within a range. Both the nonlinear tire model and the variation of longitudinal velocity are considered in vehicle system modeling. A linear-parameter-varying model with norm-bounded uncertainties is obtained. To track the system reference, a generalized proportional-integral (PI) control law is proposed. Since it is difficult to get the analytic solution for the PI gains, an augmented system is developed, and the PI control is then converted into the state-feedback control for the augmented system. Both the stability and the energy-to-peak performance of the augmented system are explored. Based on the analysis results, the controller-gain tuning method is proposed. The proposed control law and controller design method are illustrated via an electric vehicle model.

Estimation of the inertial parameters of vehicles with electric propulsion

More accurate information about the basic vehicle parameters can improve the dynamic control functions of a vehicle. Methods for online estimation of the mass, the rolling resistance, the aerodynamic drag coefficient, the yaw inertia and the longitudinal position of the centre of gravity of an electric hybrid vehicle is therefore proposed. The estimators use the standard vehicle sensor set and the estimate of the electric motor torque. No additional sensors are hence required and no assumptions are made regarding the tyre or the vehicle characteristics. Consequently, all information about the vehicle is available to the estimator. The estimators are evaluated using both simulations and experiments. Estimations of the mass, the rolling resistance and the aerodynamic drag coefficient are based on a recursive least-squares method with multiple forgetting factors. The mass estimate converged to within 3% of the measured vehicle mass for the test cases with sufficient excitation that were evaluated. Two methods to estimate the longitudinal position of the centre of gravity and the yaw inertia are also proposed. The first method is based on the equations of motion and was found to be sensitive to the measurement and parameter errors. The second method is based on the estimated mass and seat-belt indicators. This estimator is more robust and reduces the estimation error in comparison with that obtained by assuming static parameters. The results show that the proposed method improves the estimations of the inertial parameters. Hence, it enables online non-linear tyre force estimators and tyre-model-based tyre–road friction estimators to be used in production vehicles.

UIO를 이용한 선회 시 등판각 추정

Availability of the climbing angle information is crucial for the intelligent vehicle system. However, the climbing angle information can't be measured with the sensor mounted on the vehicle. In this paper, climbing angle estimation system is proposed. First, longitudinal acceleration obtained from gyro-sensor is compared with the actual longitudinal acceleration of the vehicle. If the vehicle is in yawing motion, actual longitudinal acceleration can't be approximated from time derivative of wheel speed, because lateral velocity and yaw rate affect actual longitudinal acceleration. Wheel speed and yaw rate can be obtained from the sensors mounted on the vehicle, but lateral velocity can't be measured from the sensor. Therefore, lateral velocity is estimated using unknown input observer with nonlinear tire model. Simulation results show that the compensated results using lateral velocity and yaw rate show better performance than uncompensated results.

A novel vehicle dynamics stability control algorithm based on the hierarchical strategy with constrain of nonlinear tyre forces

Direct yaw moment control (DYC), which differentially brakes the wheels to produce a yaw moment for the vehicle stability in a steering process, is an important part of electric stability control system. In this field, most control methods utilise the active brake pressure with a feedback controller to adjust the braked wheel. However, the method might lead to a control delay or overshoot because of the lack of a quantitative project relationship between target values from the upper stability controller to the lower pressure controller. Meanwhile, the stability controller usually ignores the implementing ability of the tyre forces, which might be restrained by the combined-slip dynamics of the tyre. Therefore, a novel control algorithm of DYC based on the hierarchical control strategy is brought forward in this paper. As for the upper controller, a correctional linear quadratic regulator, which not only contains feedback control but also contains feed forward control, is introduced to deduce the object of the stability yaw moment in order to guarantee the yaw rate and side-slip angle stability. As for the medium and lower controller, the quantitative relationship between the vehicle stability object and the target tyre forces of controlled wheels is proposed to achieve smooth control performance based on a combined-slip tyre model. The simulations with the hardware-in-the-loop platform validate that the proposed algorithm can improve the stability of the vehicle effectively.

Generalized internal model robust control for active front steering intervention

Because of the tire nonlinearity and vehicle’s parameters’ uncertainties, robust control methods based on the worst cases, such as H ∞, µ synthesis, have been widely used in active front steering control, however, in order to guarantee the stability of active front steering system (AFS) controller, the robust control is at the cost of performance so that the robust controller is a little conservative and has low performance for AFS control. In this paper, a generalized internal model robust control (GIMC) that can overcome the contradiction between performance and stability is used in the AFS control. In GIMC, the Youla parameterization is used in an improved way. And GIMC controller includes two sections: a high performance controller designed for the nominal vehicle model and a robust controller compensating the vehicle parameters’ uncertainties and some external disturbances. Simulations of double lane change (DLC) maneuver and that of braking on split-µ road are conducted to compare the performance and stability of the GIMC control, the nominal performance PID controller and the H ∞ controller. Simulation results show that the high nominal performance PID controller will be unstable under some extreme situations because of large vehicle’s parameters variations, H ∞ controller is conservative so that the performance is a little low, and only the GIMC controller overcomes the contradiction between performance and robustness, which can both ensure the stability of the AFS controller and guarantee the high performance of the AFS controller. Therefore, the GIMC method proposed for AFS can overcome some disadvantages of control methods used by current AFS system, that is, can solve the instability of PID or LQP control methods and the low performance of the standard H ∞ controller.

Comparative study of autonomous path-following vehicle control via model predictive control and linear quadratic control

This paper describes a comparative study of steering and yaw moment control manoeuvres in the model predictive control and linear quadratic control approaches for path-following control of an autonomous vehicle. We present the effectiveness of the model predictive control and linear quadratic control approaches for stability control of the vehicle’s lateral position and yaw angle for different control manoeuvres: two-wheel steering, four-wheel steering and direct yaw moment control. We then propose model predictive control with a feedforward controller to minimize the tracking errors of the lateral position and the yaw angle in an active front steering manoeuvre, and these are compared with the results from linear quadratic control that has a feedforward controller. Model predictive control is designed on the basis of the simple yaw–lateral motions of a single-track vehicle with a linear tyre model (i.e. a bicycle model), which is an approximation of the more realistic model of a vehicle with double-track yaw–roll motion with a non-linear tyre model (i.e. the Pacejka model). The linear quadratic controller is designed on the basis of the same approach as adopted for the model predictive controller to achieve a fair comparison. On the basis of a given trajectory, we simulate the manoeuvre of the vehicle at a low speed, a middle speed and a high speed because load transfer effects will influence the roll dynamics especially at a high speed. We also perform simulations on low-road-friction surfaces in a double-lane-change scenario with the aim of following the desired trajectory as closely as possible while maintaining the vehicle stability. The simulation results show that model predictive control through two-wheel steering and four-wheel steering with direct yaw moment control performed better in terms of trajectory tracking at a high forward speed and low road surface variation. The proposed model predictive control with a feedforward controller is shown to be effective in minimizing the trajectory tracking errors. For all control manoeuvres, model predictive control gives a better tracking performance than linear quadratic control does. In addition, when the roll dynamics are considered, model predictive control significantly improves the vehicle stability and the trajectory along the desired path.

LPV-based Variable-Geometry Suspension Control Considering Nonlinear Tyre Characteristics

The paper proposes a method for the LPV-based (Linear Parameter-Varying) control design of the variable-geometry suspension system. The tilting actuation of the front wheel improves the lateral dynamics of the vehicle and assists for the driver in avoiding critical situations. The novelty of the method is the consideration of the nonlinearities in the tyre characteristics. The tyre forces are approximated by polynomials, which are used in the linearizing of the vehicle model. A parameter-varying vehicle model is derived, on which a robust LPV control is designed. The proposed method improves the performances of vehicle dynamics, and handles the critical maneuvers caused by e.g. a skidding car and high velocities. The proposed method is illustrated through CarSim simulation examples.

Enhancing Path Following Control Performance of Autonomous Ground Vehicle through Coordinated Approach under Disturbance Effect

This study proposes the model predictive control (MPC) with proportional-integral (PI) controller for coordination of active front steering (AFS) and direct yaw moment control (DYC) maneuvers for path following control in an unmanned ground vehicle system. A single-track mode of lateral-yaw motions based on a linearized vehicle model with linear tire characteristics is used for controller design, while the vehicle model used includes roll dynamic motion for the double-track model with a nonlinear tire model. Based on a known trajectory, we tested the vehicle at high forward speed due the fact that the roll dynamic motion will be influenced at high vehicle speed for a double lane change scenario in order to follow the desired trajectory as close as possible, while rejecting the effects of a wind gust. We compared two different controllers; i) MPC with PI of an AFS and, ii) MPC with PI for coordination of AFS and DYC. The simulation results show the proposed coordinated control yielded better tracking performance through high speed maneuvers than AFS maneuvers only. It also demonstrates that the proposed control methods are useful to maintain and enhance vehicle stability along the desired path, and has the ability to eliminate the effect of crosswind.