Nonlinear Tire Force Research Articles

Integrated Control of Steering and Braking for Path Tracking Using Multi-Point Linearized MPC

In this study, we propose an integrated braking and steering model predictive controller for stable and accurate path tracking. To perform model-based longitudinal control and lateral control at the same time, it is necessary to consider nonlinear characteristics caused by changing vehicle speed and nonlinear tire forces. This paper proposes a multipoint linearization method to minimize the linearization error, and a controller with good computational efficiency and accurate consideration of nonlinear vehicle behavior is also introduced. In addition, the proposed model predictive controller (MPC) actively utilizes the road friction limit constraint for each tire force to ensure vehicle stability. Through this, the proposed controller generates optimal braking and steering inputs for situations such as high-speed turns in which braking must be involved. Due to the proposed linearized model, the controller achieves a significant improvement in computational efficiency and good control performance similar to that of the nonlinear MPC. Comparison with other control methods and performance verification for various road conditions are performed through simulations, and the results show very efficient calculation while performing accurate path tracking.

A Model Predictive Control Method for Vehicle Drifting Motions with Measurable Errors

Vehicle drifting control has attracted wide attention, and the study methods are divided into expert-based and theory-based. In this paper, the vehicle drifting control was based on the vehicle drifting state characteristics. The vehicle drifting state parameters were obtained by the theory-based vehicle drifting motion mechanism analysis based on a nonlinear vehicle dynamics model, which was used to express the vehicle characteristics, together with the UniTire model, by considering the vehicle longitudinal, lateral, roll, and yaw motions. A vehicle drifting controller was designed by the model predictive control (MPC) theory and a linear dynamics model with the linearized expressions of nonlinear tire forces based on the consideration of measurable errors. The control targets were the vehicle drifting state parameters obtained by calculation, and the controller performance was proved by simulation in MATLAB/Simulink, demonstrating that the controller is good to realize vehicle drifting motions. The same target drifting motions were realized at different original states, which proved that the vehicle drifting control is possible with the designed controller.

Coordinated longitudinal and lateral vehicle stability control based on the combined-slip tire model in the MPC framework

In extreme driving situations, the coupling between the longitudinal and lateral vehicle motion becomes significant with the highly nonlinear tire forces and influences vehicle overall stability. To address the above problem, a model predictive controller is proposed for four wheels independent motor-drive electric vehicles. Firstly, a LuGre combined-slip tire model is developed to describe the coupling nonlinearity of the tire. The variation of longitudinal velocity is considered a disturbance term in the vehicle dynamics model to consider its effect on vehicle stability. Then, the multiple objectives, including tracking the reference values of the yaw rate and lateral velocity, suppressing the tire slip ratios, and reducing the torque energy consumptions, are balanced by the additional torque generated by the designed model-based controller. The safety and actuator constraints are considered concurrently. Finally, the proposed controller is tested via co-simulation with CarSim and MATLAB/Simulink, and a hardware-in-loop system with extreme maneuvers. The results show that the handling performance, longitudinal and lateral stability are effectively improved under extreme conditions.

Ground maneuver for front-wheel drive aircraft via deep reinforcement learning

The maneuvering time on the ground accounts for 10%–30% of their flight time, and it always exceeds 50% for short-haul aircraft when the ground traffic is congested. Aircraft also contribute significantly to emissions, fuel burn, and noise when taxiing on the ground at airports. There is an urgent need to reduce aircraft taxiing time on the ground. However, it is too expensive for airports and aircraft carriers to build and maintain more runways, and it is space-limited to tow the aircraft fast using tractors. Autonomous drive capability is currently the best solution for aircraft, which can save the maneuver time for aircraft. An idea is proposed that the wheels are driven by APU-powered (auxiliary power unit) motors, APU is working on its efficient point; consequently, the emissions, fuel burn, and noise will be reduced significantly. For Front-wheel drive aircraft, the front wheel must provide longitudinal force to tow the plane forward and lateral force to help the aircraft make a turn. Forward traction effects the aircraft’s maximum turning ability, which is difficult to be modeled to guide the controller design. Deep reinforcement learning provides a powerful tool to help us design controllers for black-box models; however, the models of related works are always simplified, fixed, or not easily modified, but that is what we care about most. Only with complex models can the trained controller be intelligent. High-fidelity models that can easily modified are necessary for aircraft ground maneuver controller design. This paper focuses on the maneuvering problem of front-wheel drive aircraft, a high-fidelity aircraft taxiing dynamic model is established, including the 6-DOF airframe, landing gears, and nonlinear tire force model. A deep reinforcement learning based controller was designed to improve the maneuver performance of front-wheel drive aircraft. It is proved that in some conditions, the DRL based controller outperformed conventional look-ahead controllers.

On Prediction Model Fidelity in Explicit Nonlinear Model Predictive Vehicle Stability Control

This study discusses vehicle stability control based on explicit nonlinear model predictive control (NMPC) and investigates the influence of prediction model fidelity on controller performance. The explicit solutions are generated through an algorithm using multiparametric quadratic programming (mp-QP) approximations of the multiparametric nonlinear programming (mp-NLP) problems. Controllers with different prediction models are assessed through objective indicators in sine-with-dwell tests. The analysis considers the following prediction model features: 1) nonlinear lateral tire forces as functions of slip angles, which are essential for the operation of the stability controller at the limit of handling. Moreover, a simple nonlinear tire force model with saturation is shown to be an effective alternative to a more complex model based on a simplified version of the Magic Formula; 2) longitudinal and lateral load transfers, playing a crucial role in the accurate prediction of the lateral tire forces and their yaw moment contributions; 3) coupling between longitudinal and lateral tire forces, which has a significant influence on the front-to-rear distribution of the braking forces generated by the controller; and 4) nonlinear peak and stiffness factors of the tire model, with visible yet negligible effects on the results.

A Novel Design of Traction Control Based on a Piecewise-Linear Parameter-Varying Technique for Electric Vehicles With In-Wheel Motors

This paper presents a novel piecewise-linear robust traction controller for electric vehicles with in-wheel motors. Considering the nonlinear tire force and the time-varying wheel and vehicle speeds, a piecewise-linear parameter-varying (PWLPV) slip-ratio model with disturbances is first established. A novel traction controller is then designed. The key of the traction controller proposed in this paper is to separate the traction torque into a feedforward control torque and a PWLPV feedback control torque to track the desired slip ratio. The feedforward controller is calculated through the desired working point of the PWLPV slip-ratio model. The PWLPV controller can guarantee the closed-loop stability and $H_{\infty }$ performance for disturbance rejection. To verify the effectiveness of the proposed traction controller, both simulations and experiments are performed. A high-fidelity vehicle model in veDYNA is employed for simulation studies. Experiments were carried out on an electric vehicle with in-wheel motors. The experimental tests were performed on a brake-measurement track at Nong'an Automotive Proving Ground of the First Automobile Works.

A Piecewise Affine Robust Yaw Stability Control Method for In-wheel Motor Electric Vehicle

Considering the nonlinear tire force and suspension K&C characteristic, this paper presents a piecewise affine robust yaw stability control method for the in-wheel motor electric vehicle. Using the piecewise linear to approximate front and rear tire force, and additional steering angle to describe the suspension K&C characteristic, a piecewise affine lateral dynamics model with uncertainty disturbance is firstly established. And then, by means of analysis of the dynamic behavior of front and rear tire force, the unreachable piecewise partition is neglected such that the lateral dynamics model is simplified. By using LMI technique, the yaw stability controller which can guarantee the closed-loop stability and Hinf disturbance rejection is obtained. Simulation results show that the yaw stability control method proposed in this paper is feasible and effective.

Driver Model-Based Fault-Tolerant Control of Independent Driving Electric Vehicle Suffering Steering Failure

This paper presents a fault-tolerant control (FTC) strategy for a four-wheel independent driving electric vehicle suffering steering failure. The method is based on the functional redundancy of driving and braking actuators to recover the vehicle’s steering ability. A dynamic vehicle model is derived with the function of four-wheel driving. A sliding mode controller with a combined sliding surface is employed as a motion controller, allowing the desired vehicle motion to be tracked by the adaptive driver model. An extended Kalman filter-based state estimator is adopted to virtually measure the sideslip angle while considering the nonlinear tire force. A new allocation strategy, involving two distribution modes of coordination, is designed. In addition, a weight coefficient adjustment strategy is implemented in optimal mode based on the lateral load transfer, thus improving the steering performance. Simulations are conducted to verify the proposed FTC algorithm. The results demonstrate that steering failure can be effectively covered by the functional redundancy of the driving/braking actuators.

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.

Non-linear skid steering system for 4×4 UGV using fuzzy logic direct yaw moment control

This paper presents a non-linear control system for skid-steered 4×4. Unmanned Ground Vehicles (UGV) with an accurate representation of non-linear tire forces. The vehicle body dynamics is represented by three degrees of freedom (DOF) model namely; forward, lateral and yaw movements. Additionally two DOFs are included to represent the angular rotations of both left and right wheels which are rigidly driven by a separate electric motor for each side. The proposed skid steering system is aimed to control both the driving speed and directional movement of the UGV body in order to follow a desired cornering scenario. Based on direct yaw moment control (DYC) method, a non- linear fuzzy logic controller is designed to regulate both the magnitude and direction of the output torque form each motor in-order to minimize the error between the desired and actual values of both yaw rate and side slip angle of the vehicle body. Several numerical simulations are carried out in MATLAB / Simulink environment to examine the fidelity of the proposed control system. The simulation results show the appropriateness of the proposed skid steering control system for the implementation in UGVs to perform prescribed cornering scenarios.

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.

A saturation-balancing control method for enhancing dynamic vehicle stability

This paper proposes a vehicle stability control method that quantifies and uses the level of lateral force saturation on each axle of a vehicle. The magnitude of the saturation is determined from on-line estimated nonlinear lateral tire forces and their linear projections. Once known, saturation levels are employed in a saturation balancing control structure that biases the drive torque to either the front or rear axles/wheels. The control structure avoids the need for an explicit reference model to generate target responses. The benefits of the proposed approach are demonstrated considering a nominally unstable vehicle in an extreme obstacle avoidance manoeuvre.

Directional Control of a Driver-Heavy-Vehicle Closed-Loop System

A two degree of freedom (DOF) lateral dynamic model for a three-axe heavy vehicle is set up and the vehicle ordinary differential equations of motion are derived. The nonlinear lateral tire forces are obtained by Gim model with vertical loads, slip angles and cornering performances of front and rear tires being input parameters. A revised closed-loop single-point preview method is proposed to model the driver’s directional control performance. In this proposed method, the steering angle of front wheels is calculated in real time according to the track error between a certain point ahead of the vehicle and the required route. Then the steering angle is input into the vehicle model to gain the dynamic responses and position of the vehicle in next time step. Thus the driver-heavy-vehicle closed-loop system is built. The dynamic responses of the system are simulated on the condition of double lane change and the effects of system parameters on the path following behavior of the vehicle are researched. Then the advice on how to improve the vehicle directional control ability can be brought forward.

Bifurcation Analysis of Nose-Landing-Gear Shimmywith Lateral and Longitudinal Bending

This work develops and studies a model of an aircraft nose landing gear with torsional, lateral, and longitudinal degrees of freedom. The corresponding three modes are coupled in a nonlinear fashion via the geometry of the landing gear in the presence of a nonzero rake angle, as well as via the nonlinear tire forces. Their interplay may lead to different types of shimmy oscillations as a function of the forward velocity and the vertical force on the landing gear. Methods from nonlinear dynamics, especially numerical continuation of equilibria and periodic solutions, are used to asses how the three modes contribute to different types of shimmy dynamics. In conclusion, the longitudinal mode does not actively participate in the nose-landing-gear dynamics over the entire range of forward velocity and vertical force.

Vehicle velocity estimation for real-time dynamic stability control

A new approach is proposed for nonlinear asymptotic observers based on the cascade observer system with a fusion of sensor signals. In the observers, the characteristic of the vehicle dynamic system, the nonlinear tire force estimation, load transfer estimation, and road ramp angle compensation are considered. The errors in the observation of vehicle velocity were diminished, and the computation cost was decreased for a real-time microcontroller. Simulation and real vehicle test results validate the higher accuracy of the velocity estimation by the proposed observers under complicated handling maneuver conditions.

Measurement of contact forces and patch features by means of accelerometers fixed inside the tire to improve future car active control

Huge improvements and advances in sensor technology, together with the increasing demand for safety and handling performances, pull research towards new control strategies. Robustness and promptness of sensors used for active control are key requisites. The main idea behind the research presented in this paper is to instrument the tire with appropriate sensors in order to estimate several contact parameters ranging from the kinematic conditions of the tire (the longitudinal slippage and the side slip angle [Fukada, Y., 1999, Slip-angle estimation for vehicle stability control. Vehicle System Dynamics, 32(4–5), 375–388.]) to its dynamic properties (the contact area shape and dimensions as well as the longitudinal, lateral and vertical loads [Cole, D.J. and Cebon, D., 1989, A capacitative strip sensor for measuring dynamic type forces. Proc. of the Second International Conference on Road Traffic Monitoring, London, 38–42; Cole, D.J. and Cebon, D., 1992, Performance and application of a capacitative strip tyre force sensor. Proc of IEE Conference on Road Traffic Monitoring, London, 123–132.]) and to the adhesion characteristics of the road (the surface roughness [Pasterkamp, W.R. and Pacejka, H.B., 1997, The tire as a sensor to estimate friction. Vehicle System Dynamics, 27, 409–422; Pohl, A., Steindl, R. and Reindl, L., 1999, The ‘intelligent tire’ utilizing passive SAW sensorsmeasurement of tire friction. IEEE Transactions on Instrumentation and Measurement, 48(6), 1041–1046; Ray, L.R., 1997, Nonlinear tire force estimation and road friction identification: Simulation and experiments. Automatics, 33(10), 1819–1833.]). Thus, the tire becomes a sensor of tire–road interaction. Clearly, no other measuring device may ever be more robust nor prompt, and anyway closer to the contact area. After a preliminary research in which the pros and cons of the various sensor technologies were taken into account, it was decided to put accelerometers inside the tire. These accelerometers were fixed to the liner and on-board analysis of the acquired data was performed to reduce the amount of data then sent via radio control to a central data processing unit. This unit, through post-elaboration and recombination of the reduced signals coming from the various accelerometers in the tire, estimates some of the above-described contact parameters. In the near future, these contact parameters coming from all four tires and eventually other signals from sensors placed on the vehicle may be used to develop innovative control strategies in order to increase vehicle performances as well as running safety.

Estimation of Nonlinear Tire Forces and Road Friction for Modeling and Control

This paper presents experimental results of applying extended Kalman-Bucy filtering and Bayesian hypothesis selection to estimate motion, tire forces, and road coefficient of friction (μ) of vehicles on asphalt surfaces. The filter estimates motion and tire forces of an eight degree-of-freedom vehicle from vehicle-mounted sensors without requiring a priori knowledge of μ and without requiring a tire force model. Resulting force estimates are compared statistically with those that result from a nominal analytic tire model to select the most likely μ from a set of hypothesized values. The methods have application to off-line construction of tire models, verification of vehicle dynamic models, and development of vehicle control systems that require road friction.

Adaptive Sliding Mode Control in the Presence of Saturating Tire Forces.

The Authors have developed a four wheel steering controller which can handle nonlinear tire forces. A new technique, Intelligent Sliding Surface Control, has been used to prevent control system instability induced by saturated functions. In this paper, unknown tire-road contact conditions are discussed. The robust performance of two types of controllers, a sliding mode controller and an adaptive sliding mode controller, is compared using simulation.

Nonlinear Tire Force Estimation and Road Friction Identification: Simulation and Experiments ,

This paper applies extended Kalman-Bucy filtering (EKBF) and Bayesian hypothesis selection to estimate motion, tire forces, and road coefficient of friction (μ) of vehicles on asphalt surfaces. The EKBF estimates the state and tire forces of an eight-degree-of-freedom vehicle from vehicle-mounted sensors. The filter requires no a priori knowledge of μ and does not require a tire force model. Resulting force, slip, and slip angle estimates are compared statistically with those that result from a nominal analytic tire model to select the most likely μ from a set of hypothesized values. The methods have application to both off-line construction of tire models and development of vehicle control systems that require μ. Both simulation results and results of applying estimation methods to field test data are presented. Simulation results show excellent convergence and accuracy of μ estimates, and results of processing field test data demonstrate the ability to construct useful tire models. Computation and sensor requirements, and robustness of the μ identification algorithm are considered. © 1997 Elsevier Science Ltd.

Digital Simulation for Automobile Maneuvers

A new all-digital simulation of automobile handling allows severe maneuvers involving braking or accel eration and cornering. A novel feature is the in corporation of closed-loop control based on a mathematical model of the human driver. The program is modular and well-documented. The model includes provisions for nonlinear tire and suspension forces and moments; it also allows the user to switch off the nonlinearities and to include an antilock brake system.