4WS Vehicle Research Articles

An Investigation of Classical Model Predictive Controller Path Tracking Performance of a Two-Wheel and Four-Wheel Steering Vehicle

Studies on self-driving vehicles have become a trend in recent years, and many systems have been developed to enable autonomous manoeuvre. Various methods have been used to improve path-tracking algorithms which increase vehicle performance, including tracking accuracy and stability. Path tracking is one of the primary problems for autonomous vehicles where the vehicle deviates from target paths, which leads to unnecessary counter-correction. Conventional front wheel steering is unable to satisfy the manoeuvre with a high lateral acceleration since the front steering angle is limited in accurately responding to vehicle dynamics. Moreover, the characteristics of front wheel steering vehicles affect handling stability due to the fact that the turning radius is larger than the vehicle itself. This disadvantageous can compromise safety during under-steer and over-steer situations. The main objective of this preliminary study is to investigate the performance of a four-wheel steering system (4WS) in path tracking for autonomous vehicles using a classical model predictive controller (MPC). Conventional two-wheel steering (2WS) tracking performance following the desired driving system with the same MPC controller is compared with 4WS vehicles. The driving system is developed using Driving Scenario Designer to extract the desired yaw angle and lateral position for controller references constructed in Matlab Simulink. Fixed MPC constraint, prediction, control horizon, yaw angle and lateral position weights were used to compare the performance between 2WS and 4WS vehicles. The simulation results show that 4WS is three times better than 2WS vehicles in tracking predetermined paths. 4WS vehicle show 74.55% better performance in lateral position tracking and 68.75% better performance in trailing predetermined yaw angle value. The simulation data from the preliminary study will be used as a guideline to develop an advanced controller of 4WS vehicles.

Strange nonchaotic attractors and bifurcation of a four-wheel-steering vehicle system with driver steering control

In this paper, a dynamical model is developed for the four-wheel-steering(4WS)vehicles, with nonlinear lateral tyre forces and quasi-periodic disturbances from the steering mechanism and quasi-periodic pavement external deformation. Initially, the stability and Hopf bifurcation of the 4WS vehicle system without disturbance are analyzed employing the central manifold theory and projection method. The effects of parameters on the stability and the types of Hopf bifurcation for the vehicle system are also discussed. It is shown that both Hopf bifurcation and degenerate Hopf bifurcation occur in the vehicle system. The critical speed decreases with increased driver’s perceptual time delay and distance from the vehicle’s center of gravity to the front axles, while it increases with the control strategy coefficient. However, the increase of the frontal visibility distance of the driver leads to an initial increase of the critical speed, decreasing afterwards. Subsequently, the strange nonchaotic dynamical behaviour of the disturbed 4WS system is investigated. Several routes and mechanisms for the birth of strange nonchaotic attractors (SNAs) are identified, including the torus doubling bifurcation, the torus fractalization, and the loss of transverse stability of a torus. Finally, the nonchaotic property is verified through the calculation of the maximum Lyapunov exponent, and the strange property is characterized using power spectra and rational approximation.

Trajectory Tracking Control Design for 4WS Vehicle Based on Particle Swarm Optimization and Phase Plane Analysis

With the rapid development of today’s society, the traffic environment has become more and more complex. As an essential part of intelligent vehicles, trajectory tracking has attracted significant attention for its stability and safety. It is prone to poor accuracy and instability in extreme working conditions like high speed. In this paper, a trajectory tracking control strategy to ensure lateral stability at a high speed and low attachment limit conditions is proposed for distributed drive vehicles. The model predictive controller (MPC) was used to control the front wheel angle, and the particle swarm optimization (PSO) algorithm was designed to optimize the MPC control parameters adaptively. The sliding mode controller controls the rear wheel angle, and the vehicle instability degree is judged by analyzing the β − β˙ phase plane. The controllers of different instability degrees are designed herein. Finally, a torque divider is designed to consider the actuation anti-slip. The designed controller is verified by Carsim and MATLAB-Simulink co-simulation. The results show that the trajectory tracking controller designed in this paper effectively improves the tracking accuracy under the premise of ensuring stability.

Robust Shared Control for Four-Wheel Steering Considering Driving Comfort and Vehicle Stability

Although the four-wheel steering system expands the flexibility of vehicle control, it also brings the problem of difficult coordination between driver comfort and vehicle stability. To this end, this paper proposes robust coordinated control for a four-wheel steering (4WS) vehicle considering driving comfort and vehicle stability. First, the vehicle dynamics model is constructed to reflect the lateral motion characteristics of a 4WS vehicle. Then, the driver model is coupled into the 4WS vehicle model to describe the driver’s handling characteristics. To suppress the system perturbation caused by the uncertainties of driver behavior and vehicle states, the Takagi-Sugeno fuzzy robust control method is developed to design the human-machine co-driving system. Moreover, the robust positive invariant set theory is used to guarantee the stability and safety constraints of the vehicle. Finally, the proposed human-machine shared robust control for 4WS vehicle is verified through the driving simulator platform. The results indicate that the fuzzy robust shared control approach comprehensively improves the driving comfort, vehicle stability, and path tracking.

Control of four-wheel steering vehicles based on composite model free observer

Four-wheel steering (4WS) is an advanced technology for automotive chassis, which is more flexible and redundant than conventional front wheel steering. For a 4WS vehicle, the accuracy and stability of steering control must be guaranteed, so the main difficulty is the model nonlinearity during driving. To deal with the problems, a novel composite model free observer (CMFO) is designed. The nominal parameters are used to model the 4WS vehicles, and the data-driven method is used to improve observation accuracy. Then a CMFO based controller is designed to control the lateral dynamics of 4WS vehicles. The stability of the proposed control scheme is proved by theoretical derivation, and experiments are carried out to compare the performance between the CMFO based controller, model free adaptive controller (MFAC) and linear quadratic regulator (LQR). The mean absolute error (MAE) values of CMFO are reduced by 75.56% and 44.49% compared with those of LQR and MFAC, respectively.

Stability and Bautin bifurcation of four-wheel-steering vehicle system with driver steering control.

In this paper, the stability and Bautin bifurcation of a four-wheel-steering (4WS) vehicle system, by considering driver steering control, are investigated. By using the central manifold theory and projection method, the first and second Lyapunov coefficients are calculated to predict the type of Hopf bifurcation of the vehicle system. The topological structure of Bautin bifurcation, a degenerate Hopf bifurcation of the 4WS vehicle system, is presented in parameter space, and it reveals the dynamics of the vehicle system of different choices of control parameters. The influences of system parameters on critical values of the bifurcation parameter are also analyzed. It is shown that with the increase in the frontal visibility distance of the driver control strategy coefficient and the cornering stiffness coefficients of rear wheels, the critical speed increases. Nevertheless, the critical speed decreases with the increase in the distance from the center of gravity of the vehicle to the front axles, Driver's perceptual time delay, and cornering stiffness coefficients of the front wheels.

The bicycle model of a 4WS car lateral dynamics for lane change controller

The article shows the validity of four-wheel steering (4WS) bicycle model. At the beginning it is presented in which tasks, connected with 4WS vehicles, the bicycle model is applied. Then the equations in local coordinate system and their forms in global coordinate system are presented. The research tested the response of the model to a lane change manoeuvre, using transfer functions and a “bang-bang” control signal. The transfer functions was connected with static ratio characteristic to construct full four-wheel steering model. A reference signal generator and vehicle model were constructed in analytical form and checked in Matlab&Simulink using sample vehicle’s data from another literature item. One example of simulations was shown. The results presented led to interesting conclusions and indicated directions for further research. This research will include the issue of regulators derivation. This will allow for the construction of a fully functioning control system. The effects of this activities will be tested again in simulation environment.

Optimal Control Method of Path Tracking for Four-Wheel Steering Vehicles

Path tracking is a key technique for intelligent electric vehicles, while four-wheel steering (4WS) technology is of great significance to improve its accuracy and flexibility. However, the control methods commonly used in path tracking for a 4WS vehicle cannot take full advantage of the additional steering freedom of the 4WS vehicle, because of restricting the relationship between the front and rear wheels steering angle. To address this issue, we derive a kinematic model without the restriction based on the small-angle assumption. Then, the objective function and constraints of system control quantity optimization are designed based on the tracking error model. After the optimization problem is solved in the form of quadratic programming with constraints, the control sequence with the smallest performance index is obtained through rolling optimization. The proposed method is tested on a high-fidelity Carsim/Simulink co-simulation platform and an experimental vehicle. The results show that the standard deviation of the lateral error and the yaw angle error of the algorithm is less than 0.1 m and 3.0°, respectively. Compared with the other two algorithms, the control of the front and rear wheels angle of this method is more flexible and the tracking accuracy is higher.

Study of the problem and the idea of operation of four-wheel-steering cars

The article takes the form of a review paper and focuses on the control problems of four wheel steering vehicles. The main issues related to the control of four wheel steering (4WS) vehicles, the historical development, the current state and the approach to the construction of 4WS vehicles have been discussed. The whole of theoretical issues related to the control of the car direction (including elements related to mathematical modelling and simulation studies of the vehicle motion, issues of synthesis and analysis of the 4WS control algorithms) were presented systemically. The presented collection of literature is based on a rather extensive review relating to 4WS cars and on considerations shaping the concept of development of the topic of control algorithms in 4WS cars. A preliminary concept of control in autonomous cars is also presented and will be explain what type of road manoeuvres it is going to analyse. The authors have also shown an example of the computational apparatus used.

Research on automobile four-wheel steering control system based on yaw angular velocity and centroid cornering angle

In order to improve the handling stability of four-wheel steering (4WS) cars, a two-degree-of-freedom 4WS vehicle dynamics model is constructed here, and the motion differential equation of the system model is established. Based on the quadratic optimal control theory, the optimal control of 4WS system is proposed in this paper. When running at low speed and high speed, through yaw rate feedback control, state feedback control, and optimal control, the 4WS cars are controlled based on yaw rate and centroid cornering angle with MATLAB/Simulink simulation. The result indicates that 4WS control based on the optimal control can improve the displacement of the cars. And, the optimal control of 4WS proposed in this paper can eliminate centroid cornering angle completely compared with other two traditional optimal control methods. Besides, the optimal control enjoys faster response speed and no overshoot happens. In conclusion, the optimal control method proposed in the paper represents better stability, moving track and stability, thereby further enhancing the handling property of cars.

Optimal path tracking control for intelligent four-wheel steering vehicles based on MPC and state estimation

Four-wheel steering (4WS) vehicles have better stability control and path following performance than front-wheel steering (FWS) vehicles. Aiming at this characteristic, a new four-wheel active steering control strategy is proposed. For intelligent vehicle path tracking and nonlinear vehicle system state estimation, a path tracking control algorithm based on the MPC algorithm is designed to analyze the stability of the vehicle and set up constraints to achieve accurate tracking of the reference path. Automotive dynamic control systems require information on system variables. For example, the sideslip angle of electric vehicles cannot be measured directly. Based on UKF theory and the information input of low-cost sensors on the vehicle, an estimator is designed to estimate vehicle sideslip angle and yaw rate. According to the difference between the estimated value and the ideal value of the vehicle state, the LQR optimal controller is designed to realize the optimal control of the front and rear steering. And compared with the dynamic simulation results of front-wheel steering, proportional control four-wheel steering and yaw rate feedback four-wheel steering. The experimental results of the simulation platform show that the path tracking 4WS state feedback optimal control method has good lateral control stability and path tracking accuracy.

Trajectory planning and tracking for four‐wheel steering vehicle based on differential flatness and active disturbance rejection controller

SummaryTo address the difficulties of under‐actuation, nonlinearity, strong coupling, disturbances and measurement noise in four‐wheel steering (4WS) vehicle tracking control, this paper presents an innovative control strategy based on differential flatness and linear active disturbance rejection controller (LADRC). The flatness property of 4WS vehicle is derived from a simplified dynamic model that ignores some complicated dynamics and external disturbances. The impact of these neglected components on the system is treated as part of the total‐disturbance, which is estimated by the observer and compensated by LADRC. Three flatness‐based control schemes, including feedback linearization controller with PID corrective term, traditional LADRC and LADRC with robust generalized proportional integral observer (RGPIO), are designed and investigated in this paper. Moreover, an overtaking scenario is selected as an application example for the tracking controllers, and the corresponding trajectory planner is designed. The tracking performances of these schemes for the overtaking trajectory are simulated on a three‐degree‐of‐freedom dynamic model and a more complete dynamic model of the 4WS vehicle, respectively. Results show the effectiveness of these schemes, especially the excellent tracking performance of LADRC with RGPIO in the presence of strong external disturbances and measurement noise.

Rear-Steering Based Decentralized Control of Four-Wheel Steering Vehicle

In order to improve the lateral and directional performance of vehicles, this paper proposes a novel rear-steering based decentralized control (RDC) algorithm for four-wheel-steering (4WS) vehicles. Based on a linearized single-track vehicle model, a prototype of the RDC algorithm for linear conditions is derived. Linear analysis in frequency domain shows that the RDC can significantly reduce the magnitude and increase the phase lag of sideslip response as well as enlarge the bandwidth of yaw response in a broad frequency range. Through the incorporation of a novel sliding mode controller, the RDC algorithm is further extended for nonlinear applications. Analysis based on nonlinear model shows that, the RDC can guarantee the performance of the closed-loop (CL) system in the presence of uncertainties in system parameters and state feedback values. Moreover, the RDC is robust to arbitrary lateral disturbances and can guarantee that the vehicle converges to reference yaw rate and zero sideslip. Simulation results show that the RDC can effectively improve the lateral and directional performance of the vehicle in comparison with previous control methods. Excellent robustness to external disturbance and road friction variation is reported as well.

Research on Curved Path Tracking Control for Four-Wheel Steering Vehicle considering Road Adhesion Coefficient

Curved path tracking control is one of the most important functions of autonomous vehicles. First, small turning radius circular bends considering bend quadrant and travel direction restrictions are planned by polar coordinate equations. Second, an estimator of a vehicle state parameter and road adhesion coefficient based on an extended Kalman filter is designed. To improve the convenience and accuracy of the estimator, the combined slip theory, trigonometric function group fitting, and cubic spline interpolation are used to estimate the longitudinal and lateral forces of the tire model (215/55 R17). Third, to minimize the lateral displacement and yaw angle tracking errors of a four-wheel steering (4WS) vehicle, the front-wheel steering angle of the 4WS vehicle is corrected by a model predictive control (MPC) feed-back controller. Finally, CarSim® simulation results show that the 4WS autonomous vehicle based on the MPC feed-back controller can not only significantly improve the curved path tracking performance but also effectively reduce the probability of drifting or rushing out of the runway at high speeds and on low-adhesion roads.

Double-layer Dynamic Decoupling Control System for the Yaw Stability of Four Wheel Steering Vehicle

The four-wheel steering (4WS) is an efficient method to improve the manoeuvrability of electric vehicle with the tendency of understeer, by providing the sufficient steering angles. Because of the various kinds of driving environments, the inner coupling between the active front and rear wheels of the 4WS vehicle is a challenging problem, which usually results in unstable yaw stability of the vehicle. In order to solve this coupling problem, this paper presents a double-layer dynamic decoupling control system (DDDCS), which consists of an upper part-dynamic decoupling unit (DDU) and a lower part-steering control unit (SCU). The DDU is presented to solve the dynamic coupling problem between the active front and rear wheels, and separately establishes two decoupled models by the diagonal decoupling method. The SCU is designed to obtain the decoupled control signals by the model predictive controller, then, the yaw stability of 4WS vehicle can be guaranteed. The results of the simulation show that the proposed DDDCS has good decoupling performance and stable yaw performance for 4WS vehicle.

Improving Handling Stability Performance of Four-Wheel Steering Vehicle Based on the H2/H∞ Robust Control

Considering the demand for vehicle stability control and the existence of uncertainties in the four-wheel steering (4WS) system, the mixed H2/H∞ robust control methodology of the 4WS system is proposed. Firstly, the linear 2DOF vehicle model, the nonlinear 8DOF vehicle model, the driver model, and the rear wheel electrohydraulic system model were constructed. Secondly, based on the yaw rate tracking strategy, the mixed H2/H∞ controller was designed with the optimized weighting functions to guarantee system performance, robustness, and the robust stability of the 4WS vehicle stability control system. The H∞ method was applied to minimize the effects of modeling uncertainties, sensor noise, and external disturbances on the system outputs, and the H2 method was used to ensure system performance. Finally, numerical simulations based on Matlab/Simulink and hardware-in-the-loop experiments were performed with the proposed control strategy to identify its performance. The simulation and experimental results indicate that the handling stability of the 4WS vehicle is improved by the H2/H∞ controller and that the 4WS system with the H2/H∞ controller has better handling stability and robustness than those of the H∞ controller and the proportional controller.

Hierarchical Control of Nonlinear Active Four-Wheel-Steering Vehicles

A new type of hierarchical control is proposed for a four-wheel-steering (4WS) vehicle, in which both the sideslip angle and yaw rate feedback are used, and the saturation of the control variables (i.e., the front and rear steering angles) is considered. The nonlinear three degrees of freedom (3DOF) 4WS vehicle model is employed to describe the uncertainties originating from the operating situations. Further, a normal front-wheel-steering (2WS) vehicle with a drop filter of the sideslip angle is selected as the reference model. The inputs for the rear and front steering angles of the linear 2DOF 4WS, required to achieve the performances described by the reference model, are obtained and controlled by the upper controller. Further, the lower controller is designed to eliminate the state error between the linear 2DOF and nonlinear 3DOF 4WS vehicle models. The simulation results of several vehicle models with/without the controller are presented, and the robustness of the hierarchical control system is analyzed. The simulation results indicate that using the proposed hierarchical controller yields the same performance between the nonlinear 4WS vehicle and the reference model, in addition to exhibiting good robustness.

Fractional Control of An Active Four-wheel-steering Vehicle

A four-wheel-steering (4WS) vehicle model and reference model with a drop filter are constructed. The decoupling of 4WS vehicle model is carried out. And a fractional PIλDμ controller is introduced into the decoupling strategy to reduce the effects of the uncertainty of the vehicle parameters as well as the unmodelled dynamics on the system performance. Based on optimization techniques, the design of fractional controller are obtained to ensure the robustness of 4WS vehicle during the special range of frequencies through proper choice of the constraints. In order to compare with fractional robust controller, an optimal controller for the same vehicle is also designed. The simulations of the two control systems are carried out and it reveals that the decoupling and fractional robust controller is able to make vehicle model trace the reference model very well with better robustness.

Improving The Manoeuvrability of Electric Vehicle with Four-Wheel Drive and Four-Wheel Steering – A Nonlinear Model Vehicle Dynamics Approach

The dynamics motion of a vehicle is inherently a nonlinear dynamics system especially at high speed. Majority of past researches on four-wheel steering (4WS) vehicle adopt easier way of modelling a control system based on vehicle with linear dynamic equation of motion. This paper study on the vehicle dynamics of an electric vehicle with 4WD and 4WS based on nonlinear vehicle dynamic approach. A numerical simulation was performed to analyse the variance of a linear model and nonlinear model during cornering at various constant speed. The results show that during low speed cornering at 10 km/h, the linear and nonlinear model produced similar steady state cornering based on the trajectory and yaw rotational speed. However, the variants of linear and nonlinear started to appear as the vehicle speed increase. By obtaining the steady state cornering speed, another numerical simulation was performed to analyse the characteristics of the 4WD and 4WS electric vehicle. A passive control of the rear wheels’ steer angle was implement in the simulation. The results show that the parallel steering mode decreased the yaw rotational speed which broaden the trajectory of the cornering, while the opposite steering mode increased the yaw rotational speed that led to a tighter trajectory during cornering.

Study on mixed H2/H∞ robust control strategy of four wheel steering system

Four wheel steering (4WS) technology can effectively improve the vehicle handling stability and driving safety. In order to fully consider the influence of the rear wheel steering, the vehicle dynamics model of 4WS vehicle, including the rear wheel steering by wire and two degrees of freedom vehicle model of 4WS vehicle, is established in this paper. The desired yaw rate is obtained according to the variable transmission ratio strategy. The yaw rate tracking strategy is applied to 4WS vehicle and rear wheel steering resistance moment is taken into account. Based on the robust control theory, H2/H∞ mixed robust controller design is carried to research the stability control of 4WS vehicle. Finally, the closed-loop simulation added driver model based on preview theory is carried out. The simulation results indicate that the designed H2/H∞ mixed robust controller can achieve the stability control.