A New LTV-MPC Method for Enhancing the Stability of AFS Vehicles

The tire forces of vehicles will fall into the non-linear region under extreme handling conditions, which cause poor path tracking performance. In this paper, a model predictive controller based on a nonlinear tire model is designed. The tire forces are characterized with nonlinear composite functions of the magic formula instead of a simple linear relation model. Taylor expansion is used to linearize the controller, the first-order difference quotient method is used for discretization, and the partial derivative of the composite function is used for matrix transformation. Constant velocity and variable velocity conditions are selected to compare the designed controller with the conventional controller in Carsim/Simulink. The results show that when the tire forces fall in the nonlinear region, two controllers have good stability, and the tracking accuracy of the controller designed in this paper is slightly better. However, after the tire forces become nonlinear, the controller with linear tire force becomes worse, the tracking accuracy is far worse than the controller with the nonlinear tire model, and the vehicle stability is also degraded. In addition, an active steering test platform based on LabVIEW-RT is established, and hardware-in-the-loop tests are carried out. The effectiveness of the designed controller is verified.

Advanced vehicle dynamics control systems, such as integrated chassis control systems, are generally designed in a two layers structure: a tire force determination layer, and a tire force generation layer. The tire force generation layer works as a servo function that follows the force commands from the force determination layer. Therefore, the tire force generation layer should not require a lot of computing resources. This paper presents an inverse tire model that calculates required slip ratios and slip angles when tire forces are commanded. The inverse tire model is based on a nonlinear tire model that is sufficiently complex and, thus, can capture the nonlinear characteristics of tires. Because mathematical inversion of the nonlinear tire model is challenging, recursive methods can be considered for an inverse model. However, recursive methods, such as Newton Raphson method, do not guarantee the fixed time span required for finishing the computation. This paper presents a method for inverse tire model that does not require recursive computations.

Longitudinal and lateral forces acting on tyres are known to be closely related to tractive ability, braking characteristics, handling stability and manoeuvrability of ground vehicles. However, it is not feasible in the operating vehicles to measure the tyre forces directly because of the high cost of sensors, the limitations in sensor technology, interference with tyre rotation and the harsh environment. Another approach is the indirect monitoring technique that can estimate the tyre forces based on remote sensor outputs and vehicle dynamics models. In this paper, in order to develop tyre force-monitoring systems, a monitoring model is proposed utilizing not only the yawing motion but also the roll motion. Based on the monitoring model, a monitoring system is designed to estimate the lateral tyre force acting on each tyre. The monitoring system is constructed on the basis of a new scaled Kalman filter with model error compensator (SKFMEC) technique that is developed in this study to improve the robustness performance of Kalman filter methods. The SKFMEC technique adopts both the well-conditioned observer and the model error compensator concepts. Tyre force estimation performance of the monitoring system is evaluated in the MATLAB simulations where true tyre force data are generated from a 14-degree-of-freedom vehicle model with the combined-slip ‘magic formula’ tyre model.

<div class="htmlview paragraph">Various vehicle dynamic simulation software programs have been developed for use in reconstructing accidents. Typically these are used to analyze and reconstruct preimpact and postimpact vehicle motion. These simulation programs range from proprietary programs to commercially available packages. While the basic theory behind these simulations is Newton's laws of motion, some component modeling techniques differ from one program to another. This is particularly true of the modeling of tire force mechanics. Since tire forces control the vehicle motion predicted by a simulation, the tire mechanics model is a critical feature in simulation use, performance and accuracy. This is particularly true for accident reconstruction applications where vehicle motions can occur over wide ranging kinematic wheel conditions. Therefore a thorough understanding of the nature of tire forces is a necessary aspect of the proper formulation and use of a vehicle dynamics program.</div> <div class="htmlview paragraph">This paper includes a discussion of tire force terminology, tire force mechanics, the measurement and modeling of tire force components and combined tire force models currently used in simulation software for the reconstruction of accidents. The paper discusses the difference between the idealized tire force ellipse and an actual tire friction ellipse. Equations are presented for five tire force models from three different simulation programs. Each model uses a different method for computing tire forces for combined braking and steering. Some experimentally measured light vehicle tire properties are examined.</div> <div class="htmlview paragraph">Some tire force models begin with a specified level of braking force and use the friction ellipse to determine the corresponding steering force; this produces steering forces and a resultant tire force equal in magnitude to full skidding for combined steering and braking. Comparisons are presented of results from simulation programs using different tire models for vehicle motions involving two types of severe yaw. The comparisons in this paper are not of reconstructions where the user seeks initial conditions to match an existing trajectory. The first comparison is a hypothetical postimpact motion with a given initial velocity and initial angular velocity and the other is a sudden steer maneuver. In some cases, the simulations and their tire models predict the vehicle motion closely. In most cases, however, the results differ significantly between simulation programs.</div> <div class="htmlview paragraph">The example simulations presented in this paper are not intended to reflect the way vehicle dynamic simulation programs are used typically in accident reconstruction.</div>

This paper presents a motion control method of 6WD/6WS (6-wheel-drive and 6-wheel-steering) vehicle using optimum tire force distribution method. When we make used of independent driving and steering system, the motion control performance of the 6WD/6WS vehicle can be improved. For example, vehicle's maneuverability is more improved at low speed and vehicle's stability is also improved at high speed. Therefore, it needs to find a control strategy using optimum tire forces. A control strategy must satisfy the driver's command and minimize the energy consumption. When the driver commands vehicle (input steering angle and acceleration/brake pedal stroke), we can obtain the desired yaw moment, the desired lateral force and the desired longitudinal force. Those values are used in the optimum tire force distribution method. The optimum tire force distribution method can find the longitudinal tire force and lateral tire force. That force minimizes the cost function. The cost function is the sum of normalized tire force. The longitudinal tire forces and lateral tire force of each wheel are converted to the reference torque inputs and steering wheel angle inputs. The method was tested on the simulation and effectiveness was verified.

Under extreme conditions, a vehicle's handling performance and yaw stability can significantly deteriorate. This paper proposes a handling and stability decoupled control strategy for four-wheel independent drive (4WID) and four-wheel independent steering (4WIS) vehicles based on tire force vector control (TFVC). To address the conflicting objectives of handling and stability, the turning curvature is employed as the lateral reference, while the sideslip angle serves as the stability indicator, thereby decoupling handling and stability control. Additionally, a driver intention remapping method is introduced to maximise the preview turning curvature, effectively balancing longitudinal and lateral objectives. A yaw controller is developed using non-singular terminal sliding mode control (NTSMC) to maintain vehicle stability. Pentagon constraints are formulated to integrate all tire force constraints. Deviations from the driver's expectations are incorporated into the objective function to ensure the solvability of tire force allocation. The TFVC is implemented by integrating a UniTire-based inverse tire model and a saturated tire model to accurately regulate tire forces under both combined and saturated conditions. Finally, hardware-in-the-loop (HIL) and real vehicle test results confirm that the proposed handling and stability decoupled control strategy not only ensures vehicle stability but also enhances handling performance under extreme conditions.

Reeds–Shepp (RS) curves are widely employed for path smoothing in path planning algorithms such as Hybrid A* and Rapidly-Exploring Random Trees (RRT). To ensure the stability of autonomous vehicles when traversing RS-curve paths, this paper proposes a velocity prediction and planning algorithm based on vehicle lateral dynamics. Specifically, given the path curvature and initial velocity, the yaw rate and side-slip angle of the vehicle during steady-state steering are derived using the lateral dynamics model. Considering load transfer effects, the lateral tire force is calculated from the rate of change of vertical loads, and the safe driving velocity is predicted through gradient descent with the tire force saturation coefficient as the optimization objective. Subsequently, a velocity planning method that integrates the Gaussian pseudospectral method (GPM) with sequential quadratic programming (SQP) is developed. The problem is formulated as a nonlinear programming model, in which the predicted safe velocity serves as the upper velocity constraint. Joint simulations in MATLAB/Simulink and CarSim are then conducted to evaluate the proposed framework. The results show that the prediction accuracy of the lateral tire force exceeds 94% under different road friction coefficients, confirming the reliability of the proposed prediction model. Furthermore, comparative experiments demonstrate that the velocity planning method can effectively reduce vehicle velocity from unsafe to safe levels, thereby ensuring driving stability and safety when negotiating curves.

This study investigates an integrated wheel slip, yaw rate, and sideslip angle control via torque vectoring to improve both the longitudinal and lateral stability of electric vehicles (EVs) with four in‐wheel motors. The algorithm is developed based on model predictive control (MPC) and thus can optimally reach a balance among different objectives while considering actuation and state constraints. Firstly, to deal with tyre non‐linearity and variations in the lateral tyre forces due to changes in tyre slip ratios, the mechanism of using torque vectoring to improve vehicle stability is analysed. Then, a non‐linear tyre model is introduced into the predictive model to characterise the tyre force coupling relationship. Here, a linear‐parameter‐varying (LPV) model is employed, which is derived by linearising the nonlinear vehicle model online. Moreover, the stability control of EVs with in‐wheel motors is transformed into a constrained online optimisation problem and solved using the proposed LPV‐MPC method. Finally, the proposed LPV‐MPC is compared with some existing well‐established techniques from literature in different test scenarios. The obtained results demonstrate that the LPV‐MPC approach could reduce the computational burden and shows a precise longitudinal control and obviously improves the lateral stability.

Corner-based estimation of tire forces and vehicle velocities robust to road conditions

This study focuses on real-time model predictive control (MPC) implementation for a point-absorber-type wave energy converter (WEC) to achieve maximum wave power extraction. To address the MPC dependence on current and future wave excitation force knowledge, the control framework includes a square-root unscented Kalman filter (SR-UKF) to estimate the wave excitation force, whereas an autoregressive (AR) model forecasts the excitation force over the prediction horizon. The MPC utilizes a linear model of the point absorber, and its cost function is formulated as a quadratic programming (QP) problem with the objective of maximizing the wave energy extraction subject to physical limitations and constraints. A set of Laguerre functions was used to reduce the MPC computational complexity by decreasing the number of decision variables in the QP problem. The MATLAB/Simulink simulation results showed that the embodiment of point absorber nonlinearities by the SR-UKF enhanced the estimation accuracy compared with that of linear Kalman filters in terms of maximum error, root mean square error, and goodness of fit. Moreover, an AR model of order 100 provided satisfactory prediction performance for a 4 s prediction. The MPC strategy was simulated to evaluate its efficiency with respect to the absorbed wave power and generated electrical power under different sea-state conditions and disturbance uncertainties. Depending on sea state, it was found that the proposed MPC strategy generated 27.8% to 80% more electrical power than resistive loading control. Finally, a hardware-in-the-loop experimental setup was used to validate the computational viability of the proposed control framework in real-time WEC applications.

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.

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.

Trajectory tracking capability is important for automatic vehicle guidance. One difficulty for realizing accurate trajectory tracking is the requirement of knowing the tire cornering stiffness under linear tire force range or the nonlinear tire force function when tire force becomes large. In this study, the vehicle trajectory tracking problem is firstly formulated in the vehicle's local frame. Then an adaptive control methodology is adopted here to tune the discretized nonlinear cornering stiffness function. The method also has the advantage of avoiding the direct usage of vehicle's lateral velocity in generating the steering control signal. In the simulation result part, the performance of the method considering the nonlinear tire force effect is compared with a linear one. Simulation results in CarSim® illustrate that the proposed method considering the nonlinear tire force effect can show improved performance over the method only considers the linear tire force model.

Autonomous vehicles hold significant promise for enhancing traffic safety, alleviating urban congestion, and reducing energy consumption. This study proposes an adaptive Model Predictive Control (MPC)-based trajectory tracking controller to address the issue of increased tracking errors caused by vehicle kinematic parameter variations due to changing speeds in autonomous driving. The controller employs polynomial fitting to adaptively adjust control parameters within the prediction horizon based on varying vehicle speeds, ensuring high-precision trajectory tracking in diverse and complex environments. Multi-scenario simulation results on the Carsim, MATLAB, Simulink co-simulation platform demonstrate that the proposed controller effectively improves control performance under different speeds and prediction horizons. Compared to traditional MPC methods, the controller exhibits enhanced stability and accuracy in complex driving scenarios. The experimental results validate the effectiveness of the proposed approach, providing a novel perspective for adaptive control strategies in the field of autonomous driving. Furthermore, this research investigates the impact of varying prediction horizons on controller performance, specifically analyzing the trade-off between tracking accuracy and computational load. The adaptive strategy demonstrates a capability to dynamically adjust the prediction horizon in response to real-time driving conditions, ensuring both robust tracking and efficient computational performance. By minimizing lateral and heading errors, the proposed controller enhances overall vehicle stability and responsiveness. This study contributes to the advancement of autonomous driving by offering a practical and adaptable control solution for trajectory tracking.

Wind energy has been drawing considerable attention in recent years. However, due to the random nature of wind and high failure rate of wind energy conversion systems (WECSs), how to implement fault-tolerant WECS control is becoming a significant issue. This paper addresses the fault-tolerant control problem of a WECS with a probable actuator fault. A new stochastic model predictive control (SMPC) fault-tolerant controller with the Conditional Value at Risk (CVaR) objective function is proposed in this paper. First, the Markov jump linear model is used to describe the WECS dynamics, which are affected by many stochastic factors, like the wind. The Markov jump linear model can precisely model the random WECS properties. Second, the scenario-based SMPC is used as the controller to address the control problem of the WECS. With this controller, all the possible realizations of the disturbance in prediction horizon are enumerated by scenario trees so that an uncertain SMPC problem can be transformed into a deterministic model predictive control (MPC) problem. Finally, the CVaR object function is adopted to improve the fault-tolerant control performance of the SMPC controller. CVaR can provide a balance between the performance and random failure risks of the system. The Min-Max performance index is introduced to compare the fault-tolerant control performance with the proposed controller. The comparison results show that the proposed method has better fault-tolerant control performance.