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.

A supervisory control strategy, including dynamic control supervisor, handling-stability controller, energy efficiency controller, and coordinated torque allocator, is proposed for distributed drive electric vehicles to coordinate vehicle handling, lateral stability, and energy economy performance. In the dynamic control supervisor, first, the phase plane analysis is implemented to accurately define the vehicle stability boundary so that the lookup table of bounds can be established for online applications. Subsequently, based on the feedback drive conditions and vehicle states, the identified boundary is dynamically quantified by the designed varying weight factor (VWF) in real time. In the handling-stability controller, a unified yaw rate reference of VWF is developed to simultaneously guarantee vehicle maneuverability and lateral stabilization. Then, a novel integral triple-step method is proposed to calculate the proper direct yaw moment for the desired vehicle motion. In the energy efficiency controller, the interaxle torque distribution map is optimized for optimal vehicle energy economy. In the coordinated torque allocator, a torque increment allocation problem is formulated and optimized to realize the desired forces, meanwhile, based on VWF to minimize energy consumption and tire workload usage. The validations of the proposed strategy are conducted under various maneuvers, yielding comprehensive improvements in terms of vehicle handling, lateral stability, and energy performance.

A control framework adopting the on-board radar sensor and vehicle-to-vehicle (V2V) communication has been developed to fulfill the automated vehicle following in the longitudinal and lateral directions. First, a linear feedforward and feedback controller constrained by the string stability is designed to follow the velocity of the preceding vehicle and ensure a safe inter-vehicle distance. Then, a path estimation method is proposed to calculate the trajectory of the preceding vehicle based on its historical movement data transmitted by V2V. The model predictive control method is applied to regulate the steering angle of the front wheel. Furthermore, the robustness and adaptability of the proposed method are validated by simulations and tests under several driving conditions. The results indicate that the proposed method shows the reliable performance to realize the longitudinal and lateral vehicle following only by radar and V2V, independent of high-accuracy positioning system and road marking, and is promising to expand available areas of automated vehicle platooning.

This paper proposes a computationally efficient path following control strategy of autonomous electric vehicles (AEVs) with yaw motion stabilization. First, the nonlinear control-oriented model including path following model, single track vehicle model, and Magic Formula tire model, are constructed. To handle the stability constraints with ease, the nonlinear model predictive control (NMPC) technique is applied for path following issue. Here NMPC control problem is reasonably established with the constraints of vehicle sideslip angle, yaw rate, steering angle, lateral position error, and Lyapunov stability. To mitigate the online calculation burden, the continuation/ generalized minimal residual (C/GMRES) algorithm is adopted. The deadzone penalty functions are employed for handling the inequality constraints and holding the smoothness of solution. Moreover, the varying predictive duration is utilized in this paper so as to fast gain the good initial solution by numerical algorithm. Finally, the simulation validations are carried out, which yields that the proposed strategy can achieve desirable path following and vehicle stability efficacy, while greatly reducing the computational burden compared with the NMPC controllers by active set algorithm or interior point algorithm.

Electric vehicles with a distributed drive train configuration provide great possibilities for the improvement of the vehicle dynamics, handling, safety as well as efficiency. In this paper, an energy-efficient torque allocation scheme is proposed for the improvement of traction efficiency and braking energy recovery. In traction conditions, the traction distribution is developed using an objective function of minimizing power loss of four electric motors. In braking conditions, aiming at guaranteeing the braking stability and recapturing the braking energy as much as possible, the changeable distribution of braking torque is obtained based on the ideal front-rear braking force distribution curve, while complying with braking regulations of Economic Commission for Europe. The proposed allocation scheme does not rely on the complex online computation. It is obtained via an offline optimization procedure and utilized for online allocation by simple interpolation. The low calculation effort makes it easy to implement the algorithm on real vehicles. Additionally, a conventional torque allocation is introduced as a contrasting approach. Finally, the simulations are conducted in CarSim and MATLAB/Simulink environment. The results demonstrate that the energy-efficient torque allocation scheme considerably improves the vehicle efficiency and increases the braking energy recovery compared with the conventional approach.