Kinematics of a smart variable caster mechanism for a vehicle steerable wheel

The lateral force of a tyre is a function of the sideslip and camber angles. The camber angle can provide a significant effect on the stability of a vehicle by increasing or adjusting the required lateral force to keep the vehicle on the road. To control the camber angle and hence, the lateral force of each tyre, we can use the caster angle of the wheel. We introduce a possible variable and controllable caster angle ? in order to adjust the camber angle when the sideslip angle cannot be changed. As long as the left and right wheels are steering together according to a kinematic condition, such as Ackerman, the sideslip angle of the inner wheel cannot be increased independently to alter the reduced lateral force because of weight transfer and reduction of the normal load F _z . A variable caster mechanism can adjust the caster angle of the wheels to achieve their top capacity and maximise the lateral force, when needed. Such a system would potentially increase the safety, stability, and maneuverability of the vehicles. Using the screw theory, this paper will examine the kinematics of a variable caster and present the required mathematical equation to calculate the camber angle as a function of suspension mechanism parameters and other relevant variables. Having a steered wheel about a tilted steering axis will change the position and orientation of the wheel with respect to the body of the car. This paper provides the required kinematics of such a suspension and extracts the equations in special practical situations. The analysis is for an ideal situation in which we substitute the tyre with its equivalent disc at the tyre plane.     

Optimisation of active suspension control inputs for improved performance of active safety systems

A collocation-type control variable optimisation method is used to investigate the extent to which the fully active suspension (FAS) can be applied to improve the vehicle electronic stability control (ESC) performance and reduce the braking distance. First, the optimisation approach is applied to the scenario of vehicle stabilisation during the sine-with-dwell manoeuvre. The results are used to provide insights into different FAS control mechanisms for vehicle performance improvements related to responsiveness and yaw rate error reduction indices. The FAS control performance is compared to performances of the standard ESC system, optimal active brake system and combined FAS and ESC configuration. Second, the optimisation approach is employed to the task of FAS-based braking distance reduction for straight-line vehicle motion. Here, the scenarios of uniform and longitudinally or laterally non-uniform tyre–road friction coefficient are considered. The influences of limited anti-lock braking system (ABS) actuator bandwidth and limit-cycle ABS behaviour are also analysed. The optimisation results indicate that the FAS can provide competitive stabilisation performance and improved agility when compared to the ESC system, and that it can reduce the braking distance by up to 5% for distinctively non-uniform friction conditions.     

An ABS control logic based on wheel force measurement

The paper presents an anti-lock braking system (ABS) control logic based on the measurement of the longitudinal forces at the hub bearings. The availability of force information allows to design a logic that does not rely on the estimation of the tyre–road friction coefficient, since it continuously tries to exploit the maximum longitudinal tyre force.

The logic is designed by means of computer simulation and then tested on a specific hardware in the loop test bench: the experimental results confirm that measured wheel force can lead to a significant improvement of the ABS performances in terms of stopping distance also in the presence of road with variable friction coefficient.     

Unscented Kalman filter for vehicle state estimation

Vehicle dynamics control (VDC) systems require information about system variables, which cannot be directly measured, e.g. the wheel slip or the vehicle side-slip angle. This paper presents a new concept for the vehicle state estimation under the assumption that the vehicle is equipped with the standard VDC sensors. It is proposed to utilise an unscented Kalman filter for estimation purposes, since it is based on a numerically efficient nonlinear stochastic estimation technique. A planar two-track model is combined with the empiric Magic Formula in order to describe the vehicle and tyre behaviour. Moreover, an advanced vertical tyre load calculation method is developed that additionally considers the vertical tyre stiffness and increases the estimation accuracy. Experimental tests show good accuracy and robustness of the designed vehicle state estimation concept.     

Stability enhancement and fuel economy of the 4-wheel-drive hybrid electric vehicles by optimal tyre force distribution

In this paper, vehicle stability control and fuel economy for a 4-wheel-drive hybrid vehicle are investigated. The integrated controller is designed within three layers. The first layer determines the total yaw moment and total lateral force made by using an optimal controller method to follow the desired dynamic behaviour of a vehicle. The second layer determines optimum tyre force distribution in order to optimise tyre usage and find out how the tyres should share longitudinal and lateral forces to achieve a target vehicle response under the assumption that all four wheels can be independently steered, driven, and braked. In the third layer, the active steering, wheel slip, and electrical motor torque controllers are designed. In the front axle, internal combustion engine (ICE) is coupled to an electric motor (EM). The control strategy has to determine the power distribution between ICE and EM to minimise fuel consumption and allowing the vehicle to be charge sustaining. Finally, simulations performed in MATLAB/SIMULINK environment show that the proposed structure could enhance the vehicle stability and fuel economy in different manoeuvres.     

Design of tyre force excitation for tyre–road friction estimation

Knowledge of the current tyre–road friction coefficient is essential for future autonomous vehicles. The environmental conditions, and the tyre–road friction in particular, determine both the braking distance and the maximum cornering velocity and thus set the boundaries for the vehicle. Tyre–road friction is difficult to estimate during normal driving due to low levels of tyre force excitation. This problem can be solved by using active tyre force excitation. A torque is added to one or several wheels in the purpose of estimating the tyre–road friction coefficient. Active tyre force excitation provides the opportunity to design the tyre force excitation freely. This study investigates how the tyre force should be applied to minimise the error of the tyre–road friction estimate. The performance of different excitation strategies was found to be dependent on both tyre model choice and noise level. Furthermore, the advantage with using tyre models with more parameters decreased when noise was added to the force and slip ratio.     

Active approach to Electronic Stability Control for front-wheel drive in-wheel motor electric vehicles

Recently, motion control for electric vehicles has gradually gained respect in automotive society due to increased strictness of vehicle safety evaluation over time. Electronic Stability Control (ESC) is the kernel technology, which refers to two-dimensional motion stabilization. Many investigations have demonstrated that Direct Yaw-moment Control (DYC) is an effective and practical way to carry out the ESC of electric vehicles. However, based on the drive train of conventional steering, conventional approaches are using braking to achieve the DYC. This paper proposes a new ESC based on the construction of DYC. The presented approach is based on a core of individual traction control measures for propulsion wheels. This approach not only constrain the longitudinal slip, but also ensure the performance and the effectiveness of two-dimensional motion control. With a proper control, the vehicle can be maintained to a nearly neutral-steering under high speed turning. Hence, the vehicle’s dynamic stability can be enhanced under aggressive driving by yaw-moment control. Evaluation of the entire control system is performed by well-acknowledged software, which demonstrates that the vehicle’s dynamic stability can be enhanced under aggressive driving by the proposed approach.     

Robust cascade control for the horizontal motion of a vehicle with single-wheel actuators

The article presents a cascade control for the horizontal motion of a vehicle with single-wheel actuators. The outer control loop for the longitudinal and lateral accelerations and the yaw rate ensures a desired vehicle motion. By a combination of state feedback control and observer-based disturbance feedforward the inner control loop robustly stabilises the rotating and steering motions of the wheels in spite of unknown frictions between tyres and ground. Since the three degrees of freedom of the horizontal motion are affected by eight tyre forces, the vehicle considered is an over-actuated system. Thus additional control objectives can be realised besides the desired motion trajectory as, for example, a maximum in driving safety. The corresponding analytical tyre force allocation also guarantees real-time capability because of its relatively low computational effort. Provided suitable fault detection and isolation are available, the proposed cascade control has the potential of fault-tolerance, because the force allocation is adaptable. Another benefit results from the modular control structure, because it allows a stepwise implementation. Besides, it only requires a small number of measurements for control purposes. These measurements are the rotational speeds and steering angles of the wheels, the longitudinal and lateral acceleration and the yaw rate of the vehicle.     

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

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

A novel fuzzy logic correctional algorithm for traction control systems on uneven low-friction road conditions

The traction control system (TCS) might prevent excessive skid of the driving wheels so as to enhance the driving performance and direction stability of the vehicle. But if driven on an uneven low-friction road, the vehicle body often vibrates severely due to the drastic fluctuations of driving wheels, and then the vehicle comfort might be reduced greatly. The vibrations could be hardly removed with traditional drive-slip control logic of the TCS. In this paper, a novel fuzzy logic controller has been brought forward, in which the vibration signals of the driving wheels are adopted as new controlled variables, and then the engine torque and the active brake pressure might be coordinately re-adjusted besides the basic logic of a traditional TCS. In the proposed controller, an adjustable engine torque and pressure compensation loop are adopted to constrain the drastic vehicle vibration. Thus, the wheel driving slips and the vibration degrees might be adjusted synchronously and effectively. The simulation results and the real vehicle tests validated that the proposed algorithm is effective and adaptable for a complicated uneven low-friction road.     

Direct tire force generation algorithm based on non-iterative nonlinear inverse tire model

The function of vehicle dynamics control system is adjusting the yaw moment, the longitudinal force and lateral force of a vehicle body through several chassis systems, such as brakes, steering and suspension. Individual systems such as ESC, AFS and 4WD can be used to achieve desired performance by controlling actuator variables. However, integrated chassis control systems that have multiple objectives may not simply achieve the desired performance by controlling the actuators directly. Usually those systems determine the required tire forces in an upper level controller and a lower level controller regulates the tire forces through the actuators. The tire force is controlled in a recursive way based on vehicle state measurement, which may not be sufficient for fast response. For immediate force tracking, we introduce a direct tire force generation method that uses a nonlinear inverse tire model, a pseudo-inverse model of vehicle dynamics and the relationship between longitudinal force and brake pressure.     

Sliding mode-based lateral vehicle dynamics control using tyre force measurements

In this work, a lateral vehicle dynamics control based on tyre force measurements is proposed. Most of the lateral vehicle dynamics control schemes are based on yaw rate whereas tyre forces are the most important variables in vehicle dynamics as tyres are the only contact points between the vehicle and road. In the proposed method, active front steering is employed to uniformly distribute the required lateral force among the front left and right tyres. The force distribution is quantified through the tyre utilisation coefficients. In order to address the nonlinearities and uncertainties of the vehicle model, a gain scheduling sliding-mode control technique is used. In addition to stabilising the lateral dynamics, the proposed controller is able to maintain maximum lateral acceleration. The proposed method is tested and validated on a multi-body vehicle simulator.     

A novel integrated chassis controller for full drive-by-wire vehicles

In this paper, a systematic design with multiple hierarchical layers is adopted in the integrated chassis controller for full drive-by-wire vehicles. A reference model and the optimal preview acceleration driver model are utilised in the driver control layer to describe and realise the driver's anticipation of the vehicle's handling characteristics, respectively. Both the sliding mode control and terminal sliding mode control techniques are employed in the vehicle motion control (MC) layer to determine the MC efforts such that better tracking performance can be attained. In the tyre force allocation layer, a polygonal simplification method is proposed to deal with the constraints of the tyre adhesive limits efficiently and effectively, whereby the load transfer due to both roll and pitch is also taken into account which directly affects the constraints. By calculating the motor torque and steering angle of each wheel in the executive layer, the total workload of four wheels is minimised during normal driving, whereas the MC efforts are maximised in extreme handling conditions. The proposed controller is validated through simulation to improve vehicle stability and handling performance in both open- and closed-loop manoeuvres.     

A combined-slip predictive control of vehicle stability with experimental verification

In this paper, a model predictive vehicle stability controller is designed based on a combined-slip LuGre tyre model. Variations in the lateral tyre forces due to changes in tyre slip ratios are considered in the prediction model of the controller. It is observed that the proposed combined-slip controller takes advantage of the more accurate tyre model and can adjust tyre slip ratios based on lateral forces of the front axle. This results in an interesting closed-loop response that challenges the notion of braking only the wheels on one side of the vehicle in differential braking. The performance of the proposed controller is evaluated in software simulations and is compared to a similar pure-slip controller. Furthermore, experimental tests are conducted on a rear-wheel drive electric Chevrolet Equinox equipped with differential brakes to evaluate the closed-loop response of the model predictive control controller.     

Comparative study of vehicle tyre–road friction coefficient estimation with a novel cost-effective method

This paper qualitatively and quantitatively reviews and compares three typical tyre–road friction coefficient estimation methods, which are the slip slope method, individual tyre force estimation method and extended Kalman filter method, and then presents a new cost-effective tyre–road friction coefficient estimation method. Based on the qualitative analysis and the numerical comparisons, it is found that all of the three typical methods can successfully estimate the tyre force and friction coefficient in most of the test conditions, but the estimation performance is compromised for some of the methods during different simulation scenarios. In addition, all of these three methods need global positioning system (GPS) to measure the absolute velocity of a vehicle. To overcome the above-mentioned problem, a novel cost-effective estimation method is proposed in this paper. This method requires only the inputs of wheel angular velocity, traction/brake torque and longitudinal acceleration, which are all easy to be measured using available sensors installed in passenger vehicles. By using this method, the vehicle absolute velocity and slip ratio can be estimated by an improved nonlinear observer without using GPS, and the friction force and tyre–road friction coefficient can be obtained from the estimated vehicle velocity and slip ratio. Simulations are used to validate the effectiveness of the proposed estimation method.     

Design of safety-oriented control allocation strategies for overactuated electric vehicles

The new vehicle platforms for electric vehicles (EVs) that are becoming available are characterised by actuator redundancy, which makes it possible to jointly optimise different aspects of the vehicle motion. To do this, high-level control objectives are first specified and solved with appropriate control strategies. Then, the resulting virtual control action must be translated into actual actuator commands by a control allocation layer that takes care of computing the forces to be applied at the wheels. This step, in general, is quite demanding as far as computational complexity is considered. In this work, a safety-oriented approach to this problem is proposed. Specifically, a four-wheel steer EV with four in-wheel motors is considered, and the high-level motion controller is designed within a sliding mode framework with conditional integrators. For distributing the forces among the tyres, two control allocation approaches are investigated. The first, based on the extension of the cascading generalised inverse method, is computationally efficient but shows some limitations in dealing with unfeasible force values. To solve the problem, a second allocation algorithm is proposed, which relies on the linearisation of the tyre–road friction constraints. Extensive tests, carried out in the CarSim simulation environment, demonstrate the effectiveness of the proposed approach.     

A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations

A sliding-mode observer is designed to estimate the vehicle velocity with the measured vehicle acceleration, the wheel speeds and the braking torques. Based on the Burckhardt tyre model, the extended Kalman filter is designed to estimate the parameters of the Burckhardt model with the estimated vehicle velocity, the measured wheel speeds and the vehicle acceleration. According to the estimated parameters of the Burckhardt tyre model, the tyre/road friction coefficients and the optimal slip ratios are calculated. A vehicle adaptive sliding-mode control (SMC) algorithm is presented with the estimated vehicle velocity, the tyre/road friction coefficients and the optimal slip ratios. And the adjustment method of the sliding-mode gain factors is discussed. Based on the adaptive SMC algorithm, a vehicle's antilock braking system (ABS) control system model is built with the Simulink Toolbox. Under the single-road condition as well as the different road conditions, the performance of the vehicle ABS system is simulated with the vehicle velocity observer, the tyre/road friction coefficient estimator and the adaptive SMC algorithm. The results indicate that the estimated errors of the vehicle velocity and the tyre/road friction coefficients are acceptable and the vehicle ABS adaptive SMC algorithm is effective. So the proposed adaptive SMC algorithm can be used to control the vehicle ABS without the information of the vehicle velocity and the road conditions.     

Estimation of the tyre–road maximum friction coefficient and slip slope based on a novel tyre model

In this article, a new approach to estimate the vehicle tyre forces, tyre–road maximum friction coefficient, and slip slope is presented. Contrary to the majority of the previous work on this subject, a new tyre model for the estimation of the tyre–road interface characterisation is proposed. First, the tyre model is built and compared with those of Pacejka, Dugoff, and one other tyre model. Then, based on a vehicle model that uses four degrees of freedom, an extended Kalman filter (EKF) method is designed to estimate the vehicle motion and tyre forces. The shortcomings of force estimation are discussed in this article. Based on the proposed tyre model and the improved force measurements, another EKF is implemented to estimate the tyre model parameters, including the maximum friction coefficient, slip slope, etc. The tyre forces are accurately obtained simultaneously. Finally, very promising results have been achieved for pure acceleration/braking for varying road conditions, both in pure steering and combined manoeuvre simulations.     

An adaptive integrated algorithm for active front steering and direct yaw moment control based on direct Lyapunov method

In this article, an adaptive integrated control algorithm based on active front steering and direct yaw moment control using direct Lyapunov method is proposed. Variation of cornering stiffness is considered through adaptation laws in the algorithm to ensure robustness of the integrated controller. A simple two degrees of freedom (DOF) vehicle model is used to develop the control algorithm. To evaluate the control algorithm developed here, a nonlinear eight-DOF vehicle model along with a combined-slip tyre model and a single-point preview driver model are used. Control commands are executed through correction steering angle on front wheels and braking torque applied on one of the four wheels. Simulation of a double lane change manoeuvre using Matlab^®/Simulink is used for evaluation of the control algorithm. Simulation results show that the integrated control algorithm can significantly enhance vehicle stability during emergency evasive manoeuvres on various road conditions ranging from dry asphalt to very slippery packed snow road surfaces.