Yaw Rate Tracking Research Articles

Steering control of electric tracked vehicle based on second-order disturbance observer and multiobjective optimization

Autonomous and remote-controlled tracked vehicles are freeing humans from exhausting off-road maneuvers. Advanced motion control is a necessity to achieve high mobility and enhanced safety with less dependence on operator skill. Tracked vehicles may slide laterally or roll over under large centrifugal forces. Precise yaw motion and sideslip prevention are required for steering controller development. A switching control architecture is proposed for the underactuated tracked vehicle in this study. Two control laws for yaw rate tracking and anti-sideslip are proposed respectively based on second-order disturbance observers (DO-2s) with a given bandwidth. The controller is optimized for the two objectives using Nash bargaining method. The proposed steering controller is verified on a small electric track vehicle. Under large disturbance, the optimized DO-2-based controller prevents potential sideslip and reduces the yaw rate tracking error by 42.6% compared with LADRC. The chattering induced by switching is moderate because the estimated disturbances are smoothly switched.

Neural network steering control algorithm for autonomous ground vehicles having signal time delay

An adaptive neural network–based steering control algorithm is proposed for yaw rate tracking of autonomous ground vehicles with in-vehicle signal time delay. The control system consists of two neural networks: the observer neural network and the controller neural network. The observer neural network adapts itself to the system dynamics during the training phase. Once trained, the observer neural network cooperates with the controller neural network, which constantly adapts itself during the control task. In this way, an adaptive and intelligent control structure is proposed. Through simulation studies, it has been shown that while a proportional-integral-derivative type steering controller fails to perform its control task in case of steering signal delay, the proposed control algorithm manages to adapt itself according to the control problem and achieves reference yaw rate tracking. The robustness of the control algorithm according to the signal delay magnitude has been demonstrated by simulation studies. A rigorous Lyapunov stability analysis of the control algorithm is also presented.

Design and comparative study of steering controller for tracked vehicle based on disturbance observation

Tracked vehicles are suitable for rough, low-bearing ground or complex environments because of the large contact area and low pressure between tracks and the ground, and the great obstacle crossing and avoidance capabilities of tracked vehicles. For fast and safe turns, an advanced steering controller is required to achieve precise tracking and stability under system uncertainty. In this study, a steering controller is proposed for tracked vehicles by combining a parameter adaptive law and a second order disturbance observer (DO-2). The friction coefficient between track and ground is estimated online as an uncertain parameter. Random disturbance and function uncertainty are resisted by DO-2. Using Lyapunov’s theory, the input-state stabilities of DO-2 and the closed loop system are proved under random disturbance. A sufficient condition is proposed to check the stability of the system under function uncertainty. Field tests are carried out on rough and slippery grounds using a small-scale electric tracked vehicle. Compared with the controllers based on first order disturbance observer (DO-1) or linear extended state observer (LESO), the optimized DO-2-based steering controller has a smaller root-mean-square error of yaw rate tracking. Adaptive law improves tracking accuracy by 22% on slippery ground.

Path-following and tire loss investigation of a front in-wheel-drive electric vehicle with off-centre CG

Electric Vehicles (EVs) are becoming an inimitable answer to the problem of transport sector pollution. The inherent potential of individual wheels’ control makes in-wheel-drive EVs even more advantageous. This paper investigates the dynamics control of a laterally off-centre CG (Centre of Gravity) electric vehicle as a real-world practice, nevertheless ignored. Apart from dynamic performance, tires’ loss as a representative of their wear and hence TWP (Tire Wear Particle) emission is analysed. In this regard, mathematical modelling of an eight-degree-of-freedom electric vehicle with eccentric CG is pioneered. The model is used to develop a novel control strategy which calculates torque distributions for the front-left and right in-wheel motors. The ideal torque distribution satisfies the torque demand as well as perfect reference yaw rate tracking. Simulation results for two straight and cornering scenarios reveal that while almost removing path-following error, a properly designed torque distribution controller could potentially cancel up to nearly 5% of tires’ wear compared to three other rival strategies.

Data-Driven Feedforward Compensation Tuning in Torque Vectoring Control

In automotive control, torque vectoring enhances a vehicle dynamical characteristic by independently allocating wheel torques. Torque vectoring algorithms are often based on some form of closed-loop yaw rate tracking, whose reference is generated according to the driver's steering input. Thus, unless the vehicle is equipped with steer-by-wire, from the torque vectoring point of view, the driver's input simultaneously acts as a reference and as a disturbance. This paper presents a method to explicitly consider this aspect in the torque vectoring design by means of a feedforward compensation. At first, we identify the plant model highlighting the effects of the driver input steer on the system. Then, we design the compensation term with H∞ techniques based on the identified model. This solution is then refined using a Data-Driven approach based on a Bayesian optimization algorithm. Results show that the compensation term can reduce the tracking error by 40% and the control effort by 35%.

A Vehicle Lateral Motion Control Based on Tire Cornering Stiffness Estimation Using In-Wheel Motors

In this paper, a study on vehicle lateral motion control using an in-wheel motor (IWM) based on tire cornering stiffness estimation is presented. The main purpose of this paper is to develop a lateral motion control that can be implemented considering practical issues in real-world vehicle applications such as driver comfort, high availability, and stable control accuracy. The proposed lateral motion controller for yaw rate tracking is intended to improve vehicle cornering agility. In this paper, we develop a model-based controller with a feedforward control term to accomplish this. In particular, a change in tire cornering stiffness according to the size of the tire slip angle is reflected to improve control accuracy. Finally, the Weighted Least Square (WLS) allocation method optimally distributes the IWM torque to each wheel. Simulation studies confirm that some evaluation factors are improved in terms of cornering performance compared to conventional control algorithms.

Coordinated Path Following Control of 4WID-EV Based on Backstepping and Model Predictive Control

A path following control strategy for a four-wheel-independent-drive electrical vehicle (4WID-EV) based on backstepping and model predictive control is presented, which can ensure the accuracy of path following and maintain vehicle stability simultaneously. Firstly, a 2-DOF vehicle dynamic model and a path following error model are built and the desired yaw rate is obtained through backstepping. Then, a model predictive controller is adopted to track the desired yaw rate and obtain the optimal front wheel steering and external yaw moment. Meanwhile, an optimal torque distribution algorithm is carried out to allocate it to each tire. Finally, the effectiveness and superiority of the strategy is validated via CarSim–Simulink joint simulation. Results show that the strategy has higher following accuracy, smaller sideslip angle, and better yaw rate tracking.

Integrated Path Tracking and Lateral Stability Control with Four-Wheel Independent Steering for Autonomous Electric Vehicles on Low Friction Roads

This paper presents a method to design an integrated path tracking and lateral stability controller for an autonomous electric vehicle with four-wheel independent steering (4WIS) on low friction roads. Recent advances in autonomous driving have led to extensive studies on path tracking control. However, path tracking is difficult on low friction roads. In this paper, path tracking control was converted to the yaw rate tracking one to cope with problems caused by low friction roads. To generate a reference yaw rate for path tracking, we present several methods using a driver model and a target path. For yaw rate tracking, we designed a controller with a two-layer control hierarchy, i.e., upper and lower layers. The control yaw moment was calculated using a direct yaw moment controller in the upper layer. In the low layer, a control allocation method was adopted to allocate the control yaw moment into steering angles of 4WIS. To verify the performance of the proposed controller, we conducted a simulation on vehicle simulation software. From the simulation results, it is shown that the proposed controller is effective for path tracking and lateral stability on low friction roads. To analyze path tracking and lateral stability performance of the proposed controller on low friction roads, the effects of the steady-state yaw rate gain are investigated from the simulation results.

Path Tracking Control With Four-Wheel Independent Steering, Driving and Braking Systems for Autonomous Electric Vehicles

This paper presents a method to design a path tracking controller with four-wheel independent braking (4WIB), drive (4WID) and steering (4WIS) systems equipped in in-wheel motor-driven electric vehicles (IWM-EVs). Generally, it is difficult to calculate the steering angles of 4WIS and the braking/traction torques of 4WIB/4WID for path tracking control. Moreover, there have been limitations of an error dynamics-based path tracking controller, which requires assumptions on a target path. To cope with these problems, the path tracking problem on a target path is converted into the yaw rate tracking one with a reference yaw rate in this paper. Two methods are adopted for the purpose of calculating a reference yaw rate. The first is to use a pure pursuit method, which generates a steering angle for path tracking. From the steering angle, a reference yaw rate is calculated. The second is to derive a reference yaw rate from a target path and a current vehicle position. For yaw rate tracking, direct yaw moment control is adopted to generate a control yaw moment. A control allocation method is adopted to distribute a control yaw moment into tire forces, generated by 4WIS, 4WID and 4WIB. Several actuator combinations are represented by various sets of virtual weights in the control allocation method. A simulation with a vehicle simulation program, CarSim®, shows that the proposed path tracking controller is effective in enhancing the path tracking performance with 4WIS, 4WID and 4WIB. From the simulation, effects of actuator combinations on path tracking performance are analyzed.

Sliding Mode-Based Slip Control of Compact Electric Vehicle Truck for Varying Load and Yaw Rate

Vehicle stability is a critical problem, especially for compact electric vehicle (EV) trucks, owing to the impact of the cargo weight and cornering characteristics. In this study, this problem was approached by mathematically formulating the change in the understeer characteristics of an EV truck as variable mass understeer gradient (VMUG) according to the vehicle cargo weight to design the reference yaw rate without the need to consider cornering stiffness. Comparison was made with the conventional methods by applying the VMUG-based slip control while simulating the yaw rate and side-slip tracking performance of the compact EV model for normal loading and overloading conditions. The simulation results demonstrate the superior performance of the proposed method compared to the existing methods. The proposed method has the potential for application for stability enhancement in non-electric and general-purpose vehicles as well.

Wheel torque distribution optimization of four-wheel independent-drive electric vehicle for energy efficient driving

With the help of several in-wheel motors, four-wheel independent-drive electric vehicle (4WIDEV) has tremendous potential to improve vehicle performance. Except for the theme of stability enhancement during the past two decades, energy saving topic becomes more attractive recently. However, it is difficult to achieve stability and economy performance simultaneously. Given the commonly used control method of rigid yaw rate tracking may limit the energy saving potential of 4WIDEV in cornering. Therefore, be different from previous studies which often focus on a sole target, in this paper, a driving energy management strategy for 4WIDEV based on multi-objective online optimization of four-wheel torque distribution is proposed in this paper, which includes weighted yaw rate tracking error into its parameterized control objectives besides electric drive system efficiency, tire slip losses and wheel torque ripple. Meanwhile, for better coordination of stability and economy in different situation, fuzzy logic control is adopted to dynamically adjust the weight of the control objective indexes of the proposed multi-objective online optimization function. Then, a particle swarm optimization algorithm is adopted to solve the optimization function. Finally, the proposed strategy for energy-efficient driving is verified based on the built Simulink and CarSim co-simulation model. The results show that the proposed four-wheel torque distribution strategy based on the multi-objective online optimization is more effective than average distribution strategy and offline optimization strategy.

Experimental Study of Electric Vehicle Yaw Rate Tracking Control Based on Differential Steering

This paper investigates the experimental study of differential steering control of a four-wheel independently driven (FWID) electric vehicle (EV) based on the steer-by-wire (SBW) system. As each wheel of FWID vehicle can be independently driven, differential steering is realized by applying different driven torques to the front-two wheels. Firstly, the principle of the differential steering is analyzed based on the SBW system. When the differential steering is activated, the driver’s steering request is sent to the vehicle’s ECU. Then, the ECU gives different control signals to the front-left and front-right wheels, generating an external steering force on the steering components. The external steering force pushes the steering components to turn corresponding to the driver’s request. Secondly, to test the feasibility of differential steering, a FWID EV is assembled and the vehicle is equipped with four independently driven in-wheel motors. The corresponding control system is designed. Finally, the field test of the vehicle based on the proposed differential steering control strategy is performed. In the experiment, the fixed yaw rate tracking and varied yaw rate tracking maneuvers are employed. In the fixed yaw rate tracking, the vehicle can track the desired yaw rate well with differential steering. In addition, the vehicle can track the varied yaw rate with proposed differential steering. The test results confirm the feasibility and effectiveness of the differential steering. By using the differential steering, a backup steering is established without additional components; thus, the costs can be reduced and the reliability of the vehicle steering system can be enhanced, significantly.

Lateral Stability Control of a 4-Wheel Independent Drive Electric Vehicle Using the Yaw Moment Contour Line Concept

This paper describes a new algorithm that independently manages braking and driving forces to improve the lateral stability of a vehicle equipped with independent drive motors on all wheels. In a similar way to previous research, the proposed algorithm controls yaw rate to improve lateral stability. However, unlike in previous research that only used differential braking, our algorithm controls both driving and braking forces on all four wheels independently to achieve the target yaw rate. The core contribution of this paper is the distribution logic that determines the braking and driving forces to apply at each wheel. To develop this distribution logic, we introduce the concept of yaw moment contour line. Using this concept, the optimal distribution strategy can be derived by considering yaw moment control performance, lateral movement performance, and deceleration minimization performance in eight different driving situations. Based on this strategy, we design a lateral stability control algorithm that is made up of a target yaw rate, a yaw moment controller, and a distributor. Simulations were performed to investigate the performance of the proposed algorithm using MATLAB/Simulink and the CarSim vehicle dynamics software. The simulation results show that the proposed control algorithm improves vehicle motion in terms of yaw rate tracking, lateral movement, and minimization of deceleration.

Managing driving disturbances in lateral vehicle dynamics via adaptive integrated chassis control

This paper presents a vehicle stability control method based on a multi-input multi-output (MIMO) model reference adaptive control (MRAC) strategy as an advanced driver assistance system (ADAS) to enhance the handling and yaw stability of the vehicle lateral dynamics. The corrective yaw moment and additive steering angle are generated using direct yaw moment control (DYC) and active front steering (AFS) at the upper control level in the hierarchical control algorithm. A nonlinear term is added to the conventional adaptive control laws to handle parametric uncertainties and disturbances. The desired yaw moment generated by the upper-level controller is converted to the brake forces and is distributed to the rear wheels by an optimal procedure at the lower-level. The major contribution of this study is the introduction of a nonlinear integrated adaptive control method based on a constraint optimization algorithm. To verify the effectiveness of the proposed control strategy, the nonlinear integrated adaptive controller, and linear time-varying MRAC are designed and used for comparison. Simulation results are performed for the J-turn and double lane change (DLC) manoeuvres at high speeds and low tyre-road friction coefficients. The desired performance of the proposed controller exhibited significant improvement compared to the conventional MRAC in terms of yaw rate tracking and handling of sideslip limitation.

On the model-based design of front-to-total anti-roll moment distribution controllers for yaw rate tracking

In passenger cars active suspensions have been traditionally used to enhance comfort through body control, and handling through the reduction of the tyre load variations induced by road irregularities. However, active suspensions can also be designed to track a desired yaw rate profile through the control of the anti-roll moment distribution between the front and rear axles. The effect of the anti-roll moment distribution relates to the nonlinearity of tyre behaviour, which is difficult to capture in the linearised vehicle models normally used for control design. Hence, the tuning of anti-roll moment distribution controllers is usually based on heuristics. This paper includes an analysis of the effect of the lateral load transfer on the lateral axle force and cornering stiffness. A linearised axle force formulation is presented, and compared with a formulation from the literature, based on a quadratic relationship between cornering stiffness and load transfer. Multiple linearised vehicle models for control design are assessed in the frequency domain, and the respective controllers are tuned through optimisation routines. Simulation results from a nonlinear vehicle model are discussed to analyse the performance of the controllers, and show the importance of employing accurate models of the lateral load transfer effect during control design.

An Adaptive Backstepping Sliding Mode Controller to Improve Vehicle Maneuverability and Stability via Torque Vectoring Control

To improve the maneuverability and stability of a vehicle and fully leverage the advantages of torque vectoring technology in vehicle dynamics control, a finite-time yaw rate and sideslip angle tracking controller is proposed by combining a second-order sliding mode (SOSM) controller with the backstepping method in this paper. However, existing research indicates that first-order sliding mode (FOSM) control suffers from the chattering problem, while the traditional SOSM controller requires knowing the bound of the uncertain term in advance to obtain the switching gain, which is difficult in practice. To address these problems, this paper proposes an adaptive second-order sliding mode (ASOSM) controller based on the backstepping method by adding the high-frequency switching term to the first derivative of the sliding mode variable, which implies that the actual control can be acquired after an integration process. The switching gain in the ASOSM controller is obtained by an adaptive algorithm without knowing any information of the uncertainty. The proposed algorithm is compared with FOSM and SOSM in different scenarios to demonstrate its applicability and robustness. Simulation results show that the bandwidth of the vehicle transient response can be improved by 21%. In addition, ASOSM and SOSM controllers are insensitive to vehicle mass and tire type, implying their robustness to such disturbances. Furthermore, ASOSM requires less control action because of the adaptive law when it performs similarly with SOSM and FOSM.

Influence of vehicle parameters on handling characteristics and its control using torque vectoring

Handling characteristics of any vehicle refer to its directional control and stability for given steering input. The vehicle parameters such as mass, mass moment of inertia and location of C.G. play a vital role and decide handling response of vehicle under different scenarios. Safe drive is ensured by vehicle’s responses such as yaw rate, roll rate and vehicle lateral acceleration. This paper presents steady state and transient state simulation of XUV 500 model in accordance with ISO 4138 and ISO 3888 test standards using CarSim-Simulink Co-simulation. Influence of changes in above mentioned parameters on Vehicle response during both tests is investigated. Further, control of power train output using torque vectoring is implemented in both tests and its effect on vehicle response is evaluated. The results show that understeer tendency of the vehicle is reduced in steady state test (Constant radius test: ISO 4138). Critical vehicle responses of yaw rate, roll rate, lateral acceleration and path tracking showed improvement during the DLC manoeuvre (ISO 3888) hence, improving stability at higher lateral accelerations.

Performance comparison of electric-vehicle drivetrain architectures from a vehicle dynamics perspective

Recent electric vehicle studies in literature utilize electric motors within an anti-lock braking system, traction-control system, and/or vehicle-stability controller scheme. Electric motors are used as hub motors, on-board motors, or axle motors prior to the differential. This has led to the need for comparing these different drivetrain architectures with each other from a vehicle dynamics standpoint. With this background in place, using MATLAB simulations, these three drivetrain architectures are compared with each other in this study. In anti-lock braking system and vehicle-stability controller simulations, different control approaches are utilized to blend the electric motor torque with hydraulic brake torque; motor ABS, torque decomposition, and optimal slip-tracking control strategies. The results for the anti-lock braking system simulations can be summarized as follows: (1) Motor ABS strategy improves the stopping distance compared to the standard anti-lock braking system. (2) In case the motors are not solely capable of providing the required braking torque, torque decomposition strategy becomes a good solution. (3) Optimal slip-tracking control strategy improves the stopping distance remarkably compared to the standard anti-lock braking system, motor anti-lock braking system, and torque decomposition strategies for all architectures. The vehicle-stability controller simulation results can be summarized as follows: (1) higher affective wheel inertia of the on-board and hub motor architecture dictates a higher need of wheel torque in order to generate the tire force required for the desired yaw rate tracking. A higher level of torque causes a higher level of tire slip. (2) Optimal slip-tracking control strategy reduces the tire slip trends drastically and distributes the traction/braking action to each tire with the control-allocation algorithm specifying the reference slip values. This reduces reference tire slip-tracking error and reduces vehicle sideslip angle. (3) Tire slip trends are lower with the hub motor architecture, compared to the other architectures, due to more precise slip control.

Applied nonlinear control of vehicle stability with control and state constraints

For the vehicle dynamic control system, to guarantee directional stability in risky maneuvers, the side-slip angle should be restricted to the admissible range when the yaw rate tracks the proposed desired response for enhanced steerability. Meanwhile, the control input of the external yaw moment produced by asymmetric braking forces should be calculated in the practical range according to the capacity of tire forces. In the present study, a novel constrained controller with input and state constraints is developed. To this aim, a cost function consisting of predicted continuous response of yaw rate tracking error is expanded in terms of current control signal. Concurrently, the state constraint of side slip is transformed to the equivalent constraint of control signal by a novel nonlinear prediction approach. After that, the expanded performance index is analytically minimized in the presence of all input constraints to obtain the control law. The computed yaw moment is optimally distributed to asymmetric braking forces by designing a wheel slip control system. Simulation studies are conducted to evaluate the performance of proposed constrained controller compared with the unconstrained controller and a conventional nonlinear model predictive controller developed in the recent papers using a 14-degree-of-freedom vehicle model which includes suspension system dynamics. The results show that the proposed controller is much faster and easy to solve and implement.

Four-wheel independent brake control to limit tire slip under unknown road conditions

This paper presents a four-wheel independent brake control method for vehicle stability under various road conditions without any tire–road friction information. For safety reasons, it is important to guarantee vehicle stability under unknown road conditions. The proposed algorithm is based on analysis of vehicle dynamic behavior on a tire slip force plane, and consists of three parts, Lateral stability decision, Desired motion governor, and Brake allocation. Lateral stability decision identifies whether vehicle is stable or unstable based on ‘Peak slip line’. The desired motion governor determines both target yaw moment and deceleration to stabilize the vehicle. The brake allocation decides brake inputs of four wheels to achieve desired motions. The proposed algorithm has been evaluated via both computer simulations and vehicle tests. The performance evaluation has been conducted on dry asphalt and wet pebble road using E-segment car. It has been shown via both computer simulations and vehicle tests that the proposed algorithm can successfully maintain the vehicle stability under various road conditions. The performance of the proposed algorithm has been compared to previously developed reference yaw rate and side slip angle tracking algorithm at simulation level and built-in Electronic Stability Control(ESC) logic in the vehicle tests. It has been also shown that the proposed control law provides improved performance compared to others.