An Alternate Control Algorithm for the Four-Wheel-Steering Vehicles

In this study, a vehicle state joint estimation method based on lateral stiffness was applied to estimate the running states of electric vehicles driven by rear-drive, in-wheel motors. Different from the estimation methods used in other research, the joint estimator designed in this study uses the least-squares (LS) algorithm to estimate the lateral stiffness of the front and rear axles of the vehicle, deploying the high-degree cubature Kalman filter algorithm to estimate the vehicle state. We establish a three-degree-of-freedom nonlinear vehicle model with longitudinal velocity, lateral velocity, and yaw rate, and the lateral stiffness of the front and rear axles as the principal parameters. For the low-speed running state of the vehicle, a linearized magic tire model with high fitting accuracy was used to calculate the lateral force of the entire vehicle. The LS algorithm with a forgetting factor was used to design a lateral stiffness estimator to assess the front-axle and rear-axle lateral stiffness of the entire vehicle. The generalized high-degree cubature Kalman filter (GHCKF) algorithm was used to design the vehicle state estimator and further improve the GHCKF algorithm. A vehicle state estimator, using the square root generalized high-degree cubature Kalman filter (SRGHCKF), was designed. Therefore, the joint estimator, comprising a lateral stiffness estimator and a vehicle state estimator, adopts the LS-GHCKF/SRGHCKF algorithm and enables the estimation of the lateral stiffness, the longitudinal velocity, the lateral velocity, and the yaw rate of the entire vehicle during the driving process. A double lane change and slalom simulation were performed to analyze the feasibility and accuracy of the joint estimation algorithm and verify the results of the LS-GHCKF algorithm and the LS-SRGHCKF algorithm. Further, a low-speed driving experiment was carried out for electric vehicles driven by rear in-wheel motors. The inertial navigation system (INS), the global positioning system (GPS), the real-time kinematic (RTK), and an angle sensor were used to collect real-time vehicle data. The results were compared to verify the feasibility of the joint estimator and the progressiveness of the algorithm. The experimental verification and simulation both show that the vehicle state joint estimator, designed based on the LS-GHCKF/SRGHCKF algorithm, can accurately estimate the real-time state of the vehicle. Additionally, the LS-SRGHCKF algorithm shows better effectiveness and robustness than the LS-GHCKF algorithm.

In this study, a collision avoidance method with model predictive control is proposed for a nonlinear model of a four-wheeled vehicle. The C/GMRES algorithm is used for solving the nonlinear model predictive control (NMPC) problem within a short sampling period. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. Here, to consider whether it is possible to avoid an obstacle physically, an unavoidable region (UR) is constructed as the region in which the vehicle cannot avoid the obstacle owing to physical limitations. Even if the distance between the vehicle and the obstacle is short, the vehicle is controlled by NMPC not only to avoid the UR but also to stay on the road. A performance index for satisfying the above constraints is proposed, and control responses are investigated through numerical simulations.

<div class="htmlview paragraph">Various systems have been introduced recently in the automotive industry to improve the safety, ride and handling qualities of passenger vehicles, such as anti-lock braking system (ABS), active suspension system, four wheel steering system, traction control system, etc. Although each system has been shown to impose positive effects on the performance of a vehicle, the benefits of integrating various systems is yet to be determined.</div> <div class="htmlview paragraph">A feasibility study was conducted of a new non-linear control law for integration of anti-lock braking system and active suspension system. The control law is based on the use of a candidate Lyapunov function. Lyapunov stability theorem is applied to synthesize the control law and the adaptation law necessary to estimate the unknown parameters of the vehicle/road system. The proposed MIMO non-linear control strategy can maintain desired values of various variables while estimating the unknown parameters of the system. The desired values for various states are obtained by solving an optimal control problem for a simple vehicle model. Simulations of braking maneuvers were conducted using a non-linear vehicle model together with a non-linear tire model. The preliminary study indicates that the controller designed is capable of maintaining desired front and rear wheel longitudinal slip values as well as generating sufficient suspension forces to minimize sprung mass vibrations.</div>

This article presents a hierarchy control strategy for magneto-rheological suspension system integrated with active braking and active front steering subsystems. This is proposed for the improvement of ride comfort and vehicle stability under different kinds of driving conditions. A nonlinear complicated full vehicle model which includes the longitudinal, lateral and vertical motions is established and combined with a modified coupling ‘Magic Formula’ tyre model. Subsequently, the global state identification and task assignment logic are formulated by adopting several driving conditions such as the straight driving and cornering state. A fuzzy control strategy is then used for the suspension system, while a sliding mode control technique is utilised for both braking and steering systems. In order to demonstrate the effectiveness of the proposed control methodology, control performances such as roll angle, yaw rate and vehicle trajectory are evaluated and presented.

This brief presents a nonlinear observer for estimating the longitudinal and lateral velocities based on Dugoff's tire model and vehicle dynamics. The observer has a fixed gain structure and can make full use of information about acceleration measurements and nonlinear vehicle model. A sufficient condition is derived to guarantee the stability of the observer, and the robustness of the observer with respect to additive disturbances is analyzed with the help of input-to-state stability theory. The performance of the observer is compared with that of existing approaches and evaluated experimentally under a variety of maneuvers and road conditions.

This paper studies the application of sliding mode control (SMC) using the nonlinear sliding surface for yaw rate tracking of active front steering (AFS) control. The nonlinear vehicle model is described to simulate the vehicle plant while the linear uncertain vehicle model with uncertainty of cornering stiffness is established for controller design and analysis. The design of nonlinear sliding surface, AFS control law based SMC and its stability is discussed. The preliminary results of desired yaw rate and uncontrolled vehicle response is presented. It is expected that the propose high performance robust control strategy could improve the yaw rate transient performances in presence of uncertainty.

To study the vehicle hunting behavior and its coupling with car body vibrations, a simplified lateral-dynamics-intended railway vehicle model is developed. A two-truck vehicle is modeled as a 17 degrees-of-freedom rigid system, into which the car body flexural vibrations of torsion and bending modes are further integrated. The wheel/rail interaction employs a real-time calculation for the Hertzian normal contact, in which the nonlinear curvatures of wheel and rail profiles are presented as functions of wheelset lateral movement and/or yaw rotation. Then the tangential/creep forces are analytically expressed as the Hertzian contact patch geometry, and lead to a continuous and fast calculation compared to a look-up table interpolation. It is shown that the hunting frequencies of the vehicle model and a truck model differ significantly, which verifies the necessity of the whole vehicle model. In the case of low wheel/rail conicity, the hunting frequency increases linearly with vehicle speed, whereas it rises slowly at high speed for a large conicity. Comparison of hunting frequency and damping ratio between various conicities shows that first hunting (car body hunting) may occur when the vehicle is operated at a low speed in a small conicity case, while a second hunting (truck hunting) appears when the vehicle is operated at a high speed in a large conicity case. Stability analysis of linear and nonlinear vehicle models was carried out through coast down method and constant speed simulations. Results tell that the linear one overestimates the lateral vibrating. Whereas the structural vibrations of car body can be ignored in the stability analysis. Compared to existing simplified models for hunting stability study, the proposed simplified vehicle model released limitations in the nonlinear geometries of wheel/rail profiles, and it is suitable for a frequency-domain analysis by deriving the analytical expressions of the normal and tangential wheel/rail contact forces.

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.

Robust linear control, combined with model-reduction methodologies, is investigated for gust rejection on large, very flexible aircraft using trailing-edge control surfaces. Controllers are designed on linearizations of the nonlinear aeroelastic equations, and the closed-loop response of both the linearized and nonlinear system to discrete gust distributions is compared to the open-loop dynamics. Results show that an controller performs well on a relatively large linearized system, with 9% load alleviation in root bending moments for the critical gust length. When applied to the nonlinear model of the same vehicle, the robust controller gives a good performance in response to short gusts, including the critical length, with even better load reductions than the linear case. However, this performance gap decreases as the gust length is increased. It is also shown how standard model-reduction techniques can provide metrics for the selection of a minimum size of the aeroelastic system. Finally, it is shown that both the full and reduced controllers are capable of stabilizing a large-amplitude phugoid mode on the nonlinear model of the vehicle.

In this paper the systematic development of an integrated braking controller for a vehicle driven by an electric motor on the front axle is presented. The objective is to engage the electric motor only during braking, up to the point at which the vehicle reaches its manoeuvrability and stability limit. The control challenges are to distribute the braking effort correctly between the hydraulic brakes at the four tyres and the electric motor, to handle the tyre saturation and motor constraints effectively and to adapt the control allocation based on the vehicle’s states. The controller is designed using the state-dependent Riccati equation control technique, the vehicle state estimation and the ‘magic formula’ tyre model. The state-dependent Riccati equation control technique is a suboptimal control design technique for non-linear systems. A novel method for constructing the state-dependent coefficient formulation of the system dynamics is proposed. Soft constraints in the state dynamics are described, while an augmented penalty approach is suggested for handling the system’s hard constraints. The performance of the controller was evaluated for different braking scenarios using simulations in a MATLAB/Simulink environment. An eight-degree-of-freedom non-linear vehicle model was utilized. The numerical results show that the controller suboptimizes the regenerative braking effort while considering the tyre force saturation, the motor torque limits, the vehicle yaw rate and the slip angle error. A comparison with a constrained linear quadratic regulator shows the advantages of the proposed controller.

One of the well-known methods for improving the lateral stability of a vehicle is to utilize an active steering controller. Common active steering systems use feedback signals from a yaw rate sensor and side-slip angle estimation. However, in some driving conditions, skilled drivers can prevent vehicle rollover using the steering angle of the vehicle. Hence, the effect of an active front-steering controller on the roll angle of the vehicle is studied in this paper. For this study, a three-degree-of-freedom linear model of a vehicle which has the lateral motion, the yaw motion and the roll motion as the degrees of freedom is derived. The effectiveness of the active steering controller on the roll stability of the vehicle is examined by simulations in a wide range of longitudinal velocities of the vehicle using a linear quadratic regulator controller. The results obtained indicate that the active steering controller increases the roll stability of the vehicle only at low vehicle speeds and also that consideration of the roll degree of freedom in the design of the active steering controller is not effective at high vehicle speeds. Therefore a two-degree-of-freedom bicycle model is sufficient for active steering controller design. Another part of this paper is dedicated to designing a practical active steering controller for a vehicle with time-varying and uncertain parameters. In fact, designing a controller which guarantees the stability of the vehicle with simultaneous uncertainties in the cornering stiffnesses of the tyres and in the time-varying velocity is the main goal of this paper. Another important advantage of the proposed controller is its simplicity and static structure. In fact, this controller design is carried out offline and can be implemented for use in a real vehicle. This simple and powerful controller is a robust linear quadratic regulator controller. For designing a robust linear quadratic regulator controller, a polytopic model of the two-degree-of-freedom vehicle is obtained, which considers the uncertainty in the parameters. In addition, a linear matrix inequality is used to design a linear quadratic regulator controller for an uncertain or parameter-varying system. Finally, the performance of the designed robust linear quadratic regulator controller was studied by simulating the vehicle responses in some manoeuvres. A sport utility vehicle model is used for simulation purposes. This non-linear vehicle model has eight degrees of freedom and its tyres are assumed to be both linear and non-linear. The performance of the robust linear quadratic regulator controller was studied for vehicles with both linear and non-linear Pacejka tyres. The proposed controller guarantees robust stability of the closed-loop system in the presence of 50% variation in the vehicle speed and 20% uncertainty in the stiffnesses of the tyres.

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.

<div class="htmlview paragraph">A control law for integrating 4WS and 4WD systems is presented. It is based upon a non-linear vehicle model in which the lateral force acting on the tires changes according to the tire slip angle, slip ratio and the load. The purpose of the system is to make the actual yaw rate follow the desired yaw rate. A two-degree-of-freedom control structure has been devised and variable transformation is used to linearize the non-linear model so that H∞ control theory can be applied to design the feedback compensator. A new control theory is used to calculate optimum command values for the 4WS and 4WD actuators. Moreover, adaptive logic is added to reduce the desired yaw rate as the tires approach the limits of adhesion. Simulations and experiments prove the system greatly improves stability during cornering.</div>

This paper examines how changes in the tyre and suspension impact the dynamic spindle force response of an automotive tyre rolling over an obstacle in the roadway. The investigation is conducted with a simple vehicle dynamics simulation coupled to a comprehensive 2D dynamic nonlinear finite tyre model. The tyre model uses an inextensible, circular membrane to approximate the shape, and an empirical, nonlinear term to account for forces that result from the elastic deformation of the sidewall. Both the tyre structure and contact between the tyre and roadway are modelled with the finite element method. This approach allows the tyre model to reproduce the tyre response accurately during large deformations in a computationally efficient manner. This paper presents a brief overview of the models and their limited validation of the tyre model. Included in this discussion is a comparison between measured and simulated tyre contact forces for the case of a slowly rolling tyre. The effect of vehicle speed, suspension stiffness, suspension damping, tyre mass, tyre damping, and tyre inflation pressure on the spindle forces is also presented.

<div>With the rapid development of autonomous driving technology, unmanned ground vehicles (UGVs) are gradually replacing humans to perform tasks such as reconnaissance, target tracking, and search in special scenarios. Omnidirectional mobility based on rapid adjustment of vehicle heading posture enhances the applicability of UGVs in specialized scenarios. Omnidirectional mobility signifies the capability for rapid adjustments to the vehicle’s heading angle, longitudinal velocity, and lateral velocity. Traditional vehicles are constrained by the limitations of under-actuation, which prevents active regulation of lateral movement. Instead, they rely on the coordinated regulation of longitudinal and yaw movements, failing to meet the requirements for omnidirectional mobility. Distributed vehicles featuring steering distributed between the front/rear axles and four-wheel independent drive leverage the over-actuation advantages provided by multi-actuator coordinated control, making them particularly suitable for omnidirectional mobility at large sideslip angles. This feature enables the UGVs to achieve rapid adjustment of vehicle heading posture. However, existing control strategies centered on stabilizing yaw rate and suppressing sideslip angles cannot adapt to the decoupling control requirements of such platforms. Additionally, the strong coupling characteristics between actuator subsystems further exacerbate control difficulties. To this end, this article proposes a full-state decoupling motion control strategy, the nonlinear model is locally linearized at each equilibrium point of the vehicle, and a set of equilibrium state models is derived. The validity of this local linearization method is verified through phase diagram analysis and modal analysis. The Bayesian optimization (BO) algorithm is then employed to optimize and identify the cornering stiffness of the front/rear axles at each equilibrium point in these locally linearized models, thereby enhancing the characterization ability of the linear model for the nonlinear dynamic model at the corresponding equilibrium points. Subsequently, a full-state decoupling motion controller is designed by integrating the model predictive control (MPC) algorithm. Finally, the controller presented in this article is employed on the distributed vehicle experiment platform (DVEP). The experimental results demonstrate that in two drift-like scenarios with different sideslip angles, compared with the baseline controller, the path tracking error of this method is reduced by more than 13%, and the sideslip angle tracking error is reduced by more than 12%.</div>