A Real-time Nonlinear Model Predictive Controller for Yaw Motion Optimization of Distributed Drive Electric Vehicles

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 Computationally Efficient Path Following Control Strategy of Autonomous Electric Vehicles with Yaw Motion Stabilization

his 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

Model predictive torque vectoring control with active trail-braking for electric vehicles

In this work we present the development of a torque vectoring controller for electric vehicles. The proposed controller distributes drive/brake torque between the four wheels to achieve the desired handling response and, in addition, intervenes in the longitudinal dynamics in cases where the turning radius demand is infeasible at the speed at which the vehicle is traveling. The proposed controller is designed in both the Linear and Nonlinear Model Predictive Control framework, which have shown great promise for real time implementation the last decades. Hence, we compare both controllers and observe their ability to behave under critical nonlinearities of the vehicle dynamics in limit handling conditions and constraints from the actuators and tyre-road interaction. We implement the controllers in a realistic, high fidelity simulation environment to demonstrate their performance using CarMaker and Simulink

Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars

This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. We present a sparse GP approximation with dynamically adjusting inducing inputs, enabling a real-time implementable controller. The formulation is demonstrated in simulations, which show significant improvement with respect to both lap time and constraint satisfaction compared to an NMPC without model learning

Optimal torque vectoring control strategies for stabilisation of electric vehicles at the limits of handling

The study of chassis control has been a major research area in the automotive industry and academia for more than fifty years now. Among the popular methods used to actively control the dynamics of a vehicle, torque vectoring, the method of controlling both the direction and the magnitude of the torque on the wheels, is of particular interest. Such a method can alter the vehicle’s behaviour in a positive way under both sub-limit and limit handling conditions and has become even more relevant in the case of an electric vehicle equipped with multiple electric motors. Torque vectoring has been so far employed mainly in lateral vehicle dynamics control applications, with the longitudinal dynamics of the vehicle remaining under the full authority of the driver. Nevertheless, it has been also recognised that active control of the longitudinal dynamics of the vehicle can improve vehicle stability in limit handling situations. A characteristic example of this is the case where the driver misjudges the entry speed into a corner and the vehicle starts to deviate from its path, a situation commonly referred to as a ‘terminal understeer’ condition. Use of combined longitudinal and lateral control in such scenarios have been already proposed in the literature, but these solutions are mainly based on heuristic approaches that also neglect the strong coupling of longitudinal and lateral dynamics in limit handling situations. The main aim of this project is to develop a real-time implementable multivariable control strategy to stabilise the vehicle at the limits of handling in an optimal way using torque vectoring via the two independently controlled electric motors on the rear axle of an electric vehicle. To this end, after reviewing the most important contributions in the control of lateral and/or longitudinal vehicle dynamics with a particular focus on the limit handling solutions, a realistic vehicle reference behaviour near the limit of lateral acceleration is derived. An unconstrained optimal control strategy is then developed for terminal understeer mitigation. The importance of constraining both the vehicle state and the control inputs when the vehicle operates at the limits of handling is shown by developing a constrained linear optimal control framework, while the effect of using a constrained nonlinear optimal control framework instead is subsequently examined next. Finally an optimal estimation strategy for providing the necessary vehicle state information to the proposed optimal control strategies is constructed, assuming that only common vehicle sensors are available. All the developed optimal control strategies are assessed not only in terms of performance but also execution time, so to make sure they are implementable in real time on a typical Electronic Control Unit

A hierarchical adaptive nonlinear model predictive control approach for maximizing tire force usage in autonomous vehicles

The ability to reliably maximize tire force usage would improve the safety of autonomous vehicles, especially in challenging edge cases. However, vehicle control near the limits of handling has many challenges, including robustly contending with tire force saturation, balancing model fidelity and computational efficiency, and coordinating inputs with the lower level chassis control system. This work studies Nonlinear Model Predictive Control for limit handling, specifically adapting to changing tire-road conditions and maximally allocating tire force utilization. We present a novel hierarchical framework that combines a single-track model with longitudinal weight transfer dynamics in the predictive control layer, with lateral brake distribution occurring at the chassis control layer. This vehicle model is simultaneously used in an Unscented Kalman Filter for online friction estimation. Comparative experiments on a full-scale vehicle operating on a race track at up to 95% of maximum tire force usage demonstrate the overall practical effectiveness of this approach.Comment: Preprint of accepted paper in Field Robotic

Torque Vectoring Predictive Control of a Four In-Wheel Motor Drive Electric Vehicle

The recent integration of vehicles with electrified powertrains in the automotive sector provides higher energy efficiency, lower pollution levels and increased controllability. These features have led to an increasing interest in the development of Advanced Driver- Assistance Systems (ADAS) that enhance not only the vehicle dynamic behaviour, but also its efficiency and energy consumption. This master’s thesis presents some contributions to the vehicle modeling, parameter estimation, model predictive control and reference generation applied to electric vehicles, paying particular attention to both model and controller validation, leveraging offline simulations and a real-time driving simulator. The objective of this project is focused on the Nonlinear Model Predictive Controller (NMPC) technique developing torque distribution strategies, specifically Torque Vectoring (TV) for a four-in wheel motor drive electric vehicle. A real-time TV-NMPC algorithm will be implemented, which maximizes the wheels torque usage and distribution to enhance vehicle stability and improve handling capabilities. In order to develop this control system, throughout this thesis the whole process carried out including the implementation requirements and considerations are described in detail. As the NMPC is a model-based approach, a nonlinear vehicle model is proposed. The vehicle model, the estimated parameters and the controller will be validated through the design of open and closed loop driving maneuvers for offline simulations performed in a simulation plant (VI-CarRealTime) and by means of a real-time driving simulator (VI-Grade Compact Simulator) to test the vehicle performance through various dynamic driving conditions