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The sideslip angle and the yaw rate are the key state parameters for vehicle handling and stability control. To improve the accuracy of the input parameters and the time-varying characteristics of noise covariance in state estimation, a combined method of recursive least squares with a variable forgetting factor and adaptive iterative extended Kalman filtering is proposed for estimation. Based on the established three-degrees-of-freedom nonlinear model of the vehicle, the variable forgetting factor recursive least squares method is used to identify the tire cornering stiffness and serves as an input for vehicle state estimation. An innovative algorithm is used to optimise the uncertain noise covariance in the iterative extended Kalman filter (IEKF) process. Finally, with the help of the joint simulation of CarSim2019 and Matlab/Simulink R2022a, a distributed drive electric vehicle state parameter estimation model is established, and a simulation analysis of typical working conditions is carried out. Furthermore, an experiment is conducted with the pix moving vehicle and the integrated navigation system. The simulation and experimental results show that, compared to the traditional extended Kalman filter algorithm, the proposed algorithm improves the estimation accuracy of the yaw rate, sideslip angle, and longitudinal speed by 58.17%, 57.2%, and 76.47%, respectively, which shows that the algorithm has a higher estimation accuracy and a stronger applicability to provide accurate state information for vehicle handling and stability control. [ABSTRACT FROM AUTHOR]

This paper presents a joint sliding mode control algorithm with fuzzy adaptive gain to address the problem that the lateral stability of distributed drive electric vehicles is affected by system parameter perturbation and external environment disturbances under steering conditions. The control system is designed by considering the influence of road conditions and tire nonlinearity, taking the yaw rate and sideslip angle as control variables. The difference between the expected value and the actual value of the control quantity is taken as the input to obtain the expected front-wheel angle for feedback correction. Aiming at the problem that it is difficult to obtain the critical driving state parameters of vehicles and to directly measure the road adhesion coefficient which affects the vehicle's lateral stability, this paper presents a simplified unscented Kalman filter observer which is designed to dynamically estimate the vehicle state parameters and road adhesion coefficient for the lateral stability controller. Based on CarSim and MATLAB/Simulink, a co-simulation model is developed and verified under different working conditions. The results reveal that the proposed lateral stability control algorithm effectively reduces the front wheel steering angle, improving the vehicle's handling stability while reducing the driver's operating burden and improving driving safety. [ABSTRACT FROM AUTHOR]

For the sake of enhancing the handling and stability of distributed drive electric vehicles (DDEVs) under four-wheel steering (4WS) conditions, this study proposes a novel hierarchical control strategy based on a phase plane analysis. This approach involves a meticulous comparison of the stable region in the phase plane to thoroughly analyze the intricate influence of the front wheel angle, rear wheel angle, road adhesion coefficient, and longitudinal speed on the complex dynamic performances of DDEVs and to accurately determine the critical stable-state parameter. Subsequently, a hierarchical control strategy is presented as an integrated solution to achieve the coordinated control of maneuverability and stability. On the upper control level, a model predictive control (MPC) motion controller is developed, wherein the real-time adjustment of the control weight matrix is ingeniously achieved by incorporating the crucial vehicle stable-state parameter. The lower control level is responsible for the optimal torque allocation among the four wheel motors to minimize the tire load rate, thereby ensuring a sufficient tire grip margin. The optimal torque distribution for the four wheel motors is achieved using a sophisticated two-level allocation algorithm, wherein the friction ellipse is employed as a judgement condition. Finally, this developed control strategy is thoroughly validated through co-simulation utilizing the CarSim 2019 and Simulink 2020b commercial software, demonstrating the validity of the developed control strategy. The comparative results indicate that the presented controller ensures a better tracking capability to the desired vehicle state while exhibiting improved handling stability under both the double lane shifting condition and the serpentine working condition. [ABSTRACT FROM AUTHOR]

To solve the problems of serious buffeting in traditional sliding mode control and difficulty in obtaining the derivative information of the system sliding mode surface, a distributed drive electric vehicles active front steering (AFS) control method based on adaptive super-twisting sliding mode control (ASTSMC) is proposed. Taking the yaw rate deviation as the state quantity, the stable and convergent sliding mode surface is designed to obtain the equivalent control input of the front wheel angle. The sliding mode function information is substituted into the parameters of the super-twisting algorithm; the discontinuous term is kept in the integrand function to keep the control signal continuous and weaken the system chattering; the adaptive control law is added to design the AFS controller. The co-simulation results of Matlab/Simulink and Carsim show that ASTSMC can reduce the yaw rate by 40.59% compared with no control under step steering condition. Compared with the sliding mode controller, ASTSMC has optimized the sideslip angle by 5.41% under the double line shifting condition. [ABSTRACT FROM AUTHOR]

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Exploring the drift maneuver could extend the dynamic control envelope and application range of autonomous vehicles. This paper presents a novel autonomous drift controller for a distributed drive electric vehicle, whose configuration provides more possibilities for drift. In the upper-level controller, a control channel recombination method transforms the over-actuated system into a standard square system, which is compatible with the proposed fuzzy-integral sliding-mode controller considering the input coupling and uncertain disturbance of the system to bring the vehicle into a marginally stable condition. The operation of the lower-level controller considers the dynamic characteristics of actuators and tires, and distributes the "virtual control input" among each physical actuator. This controller's performance with fast response and strong robustness was proved through the bench test. • A novel autonomous drift controller is proposed. • Redundancy and coupling of control inputs and uncertain disturbance are considered. • Controller effectiveness verified via bench tests with a distributed drive electric vehicle prototype. • Results prove the superiority of the proposed autonomous drift controller. [ABSTRACT FROM AUTHOR]

This article proposes an integrated control strategy of autonomous distributed drive electric vehicles. First, to handle the multi-constraints and integrated problem of path following and the yaw motion control, a model predictive control technique is applied to determine optimal front wheels' steering angle and external yaw moment synthetically and synchronously. For ensuring the desired path-tracking performance and vehicle lateral stability, a series of imperative state constraints and control references are transferred in the form of a matrix and imposed into the rolling optimization mechanism of model predictive control, where the detailed derivation is also illustrated and analyzed. Then, the quadratic programming algorithm is employed to optimize and distribute each in-wheel motor's torque output. Finally, numerical simulation validations are carried out and analyzed in depth by comparing with a linear quadratic regulator–based strategy, proving the effectiveness and control efficacy of the proposed strategy. [ABSTRACT FROM AUTHOR]

In order to fully explore the potential of distributed drive electric vehicle, an integrated coordination control method consists of model predictive control (MPC) and speed tracking control for trajectory tracking is proposed in this paper. Firstly, the vehicle dynamics model including the slip ratio of each wheel is established. Then, a multi-objective function of the MPC controller is established based on the principle of minimum tracking error, control vector, and control increment. And the optimal control sequences are obtained by optimizing the solution and correcting the feedback of the MPC, which satisfy both the actual kinematic constraints and the actuator performance constraints. The steering angle signal is sent to the steering motor directly, and the torque signal of each wheel which is obtained by superimposing the torque value output by the MPC controller and speed tracking controller is sent to the driving motor simultaneously. Finally, the proposed method is validated by using MATLAB/Simulink-Carsim co-simulation on different roads with conventional and severe pavement conditions. The simulation results show that the designed integrated coordination controller has obvious advantages in terms of tracking accuracy and body attitude stability during the course of lane change. [ABSTRACT FROM AUTHOR]

This paper proposes a real-time nonlinear model predictive control (NMPC) strategy for direct yaw moment control (DYC) of distributed drive electric vehicles (DDEVs). The NMPC strategy is based on a control-oriented model built by integrating a single track vehicle model with the Magic Formula (MF) tire model. To mitigate the NMPC computational cost, the continuation/generalized minimal residual (C/GMRES) algorithm is employed and modified for real-time optimization. Since the traditional C/GMRES algorithm cannot directly solve the inequality constraint problem, the external penalty method is introduced to transform inequality constraints into an equivalently unconstrained optimization problem. Based on the Pontryagin's minimum principle (PMP), the existence and uniqueness for solution of the proposed C/GMRES algorithm are proven. Additionally, to achieve fast initialization in C/GMRES algorithm, the varying predictive duration is adopted so that the analytic expressions of optimally initial solutions in C/GMRES algorithm can be derived and gained. A Karush-Kuhn-Tucker (KKT) condition based control allocation method distributes the desired traction and yaw moment among four independent motors. Numerical simulations are carried out by combining CarSim and Matlab/Simulink to evaluate the effectiveness of the proposed strategy. Results demonstrate that the real-time NMPC strategy can achieve superior vehicle stability performance, guarantee the given safety constraints, and significantly reduce the computational efforts. [ABSTRACT FROM AUTHOR]

The torque distribution strategy of distributed drive electric vehicle is only aimed at safety or economy. A multi-target coordinated control method considering stability and economy is proposed to solve the problem of single torque distribution target, which consists of a coordination decision controller, a high-level motion controller, and a low-level allocation controller. The coordination decision controller based on the phase plane method determines whether to adopt a stability or economic control strategy. The high-level motion controller consists of a bicycle model with 2 degree of freedom, a speed tracking controller, a stability controller, and an economic controller to calculate the desired direct yaw moment of the four in-wheel motors. The stability controller based on the fuzzy algorithm tracks the desired vehicle side slip angle and yaw rate calculated by the bicycle model with 2 degree of freedom to control vehicle stability. The economical controller based on a multi-motor loss model optimizes the efficiency of the vehicle's drive system. The low-level allocation controller is presented to provide optimally distributed torques for each wheel. Finally, the simulation and hardware-in-the-loop testing show that the coordinated control strategy can effectively improve the stability and economy of the distributed drive electric vehicle. [ABSTRACT FROM AUTHOR]

Conventional yaw stability strategy of distributed drive electric vehicle (DDEV) is usually realised by torque distribution strategy. However, the instantaneous variations of four independent tyres slip ratio and the effect of disturbance have not been considered sufficiently. Therefore, it is difficult to realise the robustness of yaw stability for DDEV under various operating conditions. To solve this problem, a novel model predictive controller-based compensation control system (MPC-CCS) is proposed in this paper. The proposed MPC-CCS consists of two parts, an MPC based-feedback controller and a Kalman filter based-feedforward controller. In the feedback controller, a dual torque distribution scheme is adopted to obtain optimal torque values derived from the real-time signals of four independent tyres slip ratio, an MPC is designed to realise optimal torque values for vehicle yaw motion. In the feedforward controller, a Kalman filter is employed to attenuate the effect of the disturbance on yaw performance. In this way, the robustness of yaw stability for DDEV can be guaranteed by the proposed MPC-CCS. The proposed MPC-CCS is evaluated on eight degrees of freedom simulation platform and simulation results of different conditions show the effectiveness of the MPC-CCS. [ABSTRACT FROM AUTHOR]

For a distributed drive electric vehicle (DDEV) which is equipped with redundant actuators, allocation control is a key technique. Three different allocation control algorithms are designated with fixed efficiency matrix, dynamic efficiency matrix, and direct yaw moment distribution, respectively. All these algorithms are applied in a vehicle stability control system with hierarchical control structure and evaluated from three aspects, namely, control precision, real-time characteristics, and control energy. Comparison results demonstrate that the algorithm with dynamic efficiency matrix has the best comprehensive performance, which is also validated in field tests based on a DDEV equipped with four motors. [ABSTRACT FROM AUTHOR]

The effect of vehicle active safety systems is subject to the accurate knowledge of vehicle states. Therefore, it is of great importance to develop a precise and robust estimation approach so as to deal with nonlinear vehicle dynamics systems. In this paper, a planar vehicle model with a simplified tire model is established first. Two advanced model-based estimation algorithms, an unscented Kalman filter and a moving horizon estimation, are developed for distributed drive electric vehicles. Using the proposed algorithms, vehicle longitudinal velocity, lateral velocity, yaw rate as well as lateral tire forces are estimated based on information fusion of standard sensors in today's typical vehicle and feedback signals from electric motors. Computer simulations are implemented in the environment of CarSim combined with Matlab/Simulink. The performance of both estimators regarding convergence, accuracy, and robustness against an incorrect initial estimate of longitudinal velocity is compared in detail. The comparison results demonstrate that both estimation approaches have favourable coincidence with the corresponding reference values, while the moving horizon estimation is more accurate and robust, and owns faster convergence. [ABSTRACT FROM AUTHOR]

In this paper, a novel direct yaw control method based on driver operation intention for stability control of a distributed drive electric vehicle is proposed. It was discovered that the vehicle loses its stability easily under an emergency steering alignment (EA) problem. An emergent control algorithm is proposed to improve vehicle stability under such a condition. A driver operation intention recognition module is developed to identify the driving conditions. When the vehicle enters into an EA condition, the module can quickly identify it and transfer the control method from normal direct yaw control to emergency control. Two control algorithms are designed. The emergency control algorithm is applied to an EA condition while the adaptive control algorithm is applied to other conditions except the EA condition. Both simulation results and real vehicle results show that: The driver module can accurately identify driving conditions based on driver operation intention. When the vehicle enters into EA condition, the emergent control algorithm can intervene quickly, and it has proven to outperform normal direct yaw control for better stabilization of vehicles. [ABSTRACT FROM AUTHOR]

This paper presents an acceleration slip regulation strategy for distributed drive electric vehicles with two motors on the front axle. The tasks of the strategy include controlling the slip ratio to make full use of the road grip and controlling the yaw rate to eliminate the lateral movement due to the difference between motor torques. The rate of the slip ratio change can be controlled by controlling the motor torque, so that the slip ratio can be controlled by applying a proportional-integral control strategy to control the rate of the slip ratio change. The yaw rate can be controlled to almost zero by applying torque compensation based on yaw rate feedback. A coordination control strategy for the slip ratio control and yaw rate control is proposed based on analysis of the priorities and features of the two control processes. Simulations were carried out using MATLAB/Simulink, and experiments were performed on a hardware-in-loop test bench with actual motors. The results of the simulations and experiments showed that the proposed strategy could improve the longitudinal driving performance and straight line driving stability of the vehicle. [ABSTRACT FROM AUTHOR]

A vehicle with a four-channel anti-lock braking system (ABS) has poor safety and stability when braking on a low-adhesion road or off-road. In view of this situation, this paper proposes a multi-objective optimization coordinated control method for ABS and AFS based on multi-agent model predictive control (MPC). Firstly, the single-wheel control method is adopted to establish the single-wheel equation based on the slip rate and the stability equation of the centroid yaw based on AFS. The four wheels and the centroid are regarded as agents. The mathematical model of distributed drive electric vehicles based on graph theory and the coordinated control of AFS and ABS is established to reduce the dimension of the model. Secondly, on the basis of the multi-agent theory, an integrated coordinated control method for AFS and ABS based on distributed model predictive control (DMPC) is proposed to realize the ideal values of the vehicle's slip rate, yaw rate, and sideslip angle, and improve the braking safety and handling stability of the vehicle. Then, to solve the problems of high levels of resource consumption, low real-time performance, and complex implementation in the optimization of the DMPC solution, a prediction solution method using a discrete simplified dual neural network (SDNN) is proposed to balance the computational efficiency and system dynamic performance. Finally, a hardware-in-the-loop (HIL) test bench is built to test the effectiveness of the proposed method under the conditions of a low-adhesion road and an off-road. [ABSTRACT FROM AUTHOR]

For tackling the problem of the reduction in longitudinal driving torque and acceleration as well as the occurrence of undesired yaw moment and yaw angular velocity when the driving force control system of distributed drive electric vehicle enters the working mode of acceleration slip regulation, two multi-wheel driving torque coordination control strategies are proposed. Among them the strategy for power performance is aiming at raising longitudinal driving torque and acceleration, while the strategy for stability is targeted at enhancing the lateral stability of vehicle. The results of real vehicle test show that the proposed coordination control scheme effectively achieves the design objectives and improves the performance of vehicle. [ABSTRACT FROM AUTHOR]

This paper proposes a fast model predictive control allocation (MPCA) approach to minimize the tire slip power loss on contact patches for distributed drive electric vehicles (DDEV). In this strategy, two assumptions are set up from a practical focus: (1) the vehicle acceleration and yaw rate are measurable by global position system (GPS)/ inertial navigation system (INS) and inertial measurement unit (IMU), respectively; (2) the longitudinal velocity, road adhesion factor, and vehicle yaw rate are arranged to be "already known" by advanced estimators. For the strategy design, a CarSim-embedded driver model and a linear quadratic regulator (LQR) based direct yaw moment controller, are respectively applied to calculate the desired longitudinal traction and yaw moment as a virtual input first. Then, a MPCA method is proposed to reasonably distribute the virtual input among four in-wheel motors in order to optimize the tire slip power loss and vehicle stability performance. To accurately characterize tire slip power loss in MPCA, a tire slip estimator is established for tire slip information acquirement. Moreover, addressing on the heavily computational challenge in MPCA, a modified continuation/generalized minimal residual (C/GMRES) algorithm is employed. Since the traditional C/GMRES algorithm cannot directly solve the inequality constraint problem, the barrier functions are applied for transforming the inequality constraints to equivalent cost. According to Pontryagin's minimum principle (PMP) conditions, the existence and uniqueness for solution of the modified C/GMRES algorithm are strictly proved. Subsequently, a Karush–Kuhn–Tucker​ (KKT) condition based approach is developed to fast gain the optimally initial solution in C/GMRES algorithm for extending application. Finally, numerical simulation validations are implemented and demonstrate that the proposed MPCA can ensure the compatibility between the tire slip power loss reduction and vehicle stability in a computationally efficient way. • A MPCA method is proposed for DDEVs to save tire slip energy and guarantee vehicle stability. • C/GMRES algorithm is adopted in MPCA for fast solving. • Barrier function method is used to handle inequality constraints in C/GMRES algorithm. • Sufficiency that solution is existent and exclusive in C/GMRES algorithm is proved. • A KKT based approach is applied for fast initialization in C/GMRES algorithm. [ABSTRACT FROM AUTHOR]