A Predictive Controller for Autonomous Vehicle Path Tracking

Due to the uncertainty of vehicle model parameters, modeling errors and external disturbances, the performance of path tracking control system is poor, especially under high velocity and large curvature extreme conditions. To address this issue, this paper presents a novel gain-scheduled robust control strategy based on linear parameter varying system with model predictive control (MPC) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> . Firstly, fully considering the influence of the time-varying characteristics of vehicle velocity and tire cornering stiffness on the path tracking system model, a novel linear parameter varying system model is built for path tracking control of autonomous vehicle. Then, a path tracking robust controller is designed based on gain-scheduled approach, and the linear matrix inequality (LMI) is applied to solve optimization problem, in which MPC and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust control theory are applied to the controller design process. Finally, the simulation experiments have verified that the proposed novel robust control strategy can improve the path tracking accuracy and ensure the vehicle lateral and roll stability, especially under high velocity and large curvature extreme conditions. Meanwhile, the proposed robust controller shows superiority to suppress the parameters uncertainty, modeling error and external disturbance.

This paper presents the implementation of an autonomous electric vehicle (EV) project in the National Taiwan University of Science and Technology (NTUST) campus in Taiwan. The aim of this work was to integrate two important practices of realizing an autonomous vehicle in a campus environment, including vehicle positioning and path tracking. Such a project is helpful to the students to learn and practice key technologies of autonomous vehicles conveniently. Therefore, a laboratory-made EV was equipped with real-time kinematic GPS (RTK-GPS) to provide centimeter position accuracy. Furthermore, the model predictive control (MPC) was proposed to perform the path tracking capability. Nevertheless, the RTK-GPS exhibited some robust positioning concerns in practical application, such as a low update rate, signal obstruction, signal drift, and network instability. To solve this problem, a multisensory fusion approach using an unscented Kalman filter (UKF) was utilized to improve the vehicle positioning performance by further considering an inertial measurement unit (IMU) and wheel odometry. On the other hand, the model predictive control (MPC) is usually used to control autonomous EVs. However, the determination of MPC parameters is a challenging task. Hence, reinforcement learning (RL) was utilized to generalize the pre-trained datum value for the determination of MPC parameters in practice. To evaluate the performance of the RL-based MPC, software simulations using MATLAB and a laboratory-made, full-scale electric vehicle were arranged for experiments and validation. In a 199.27 m campus loop path, the estimated travel distance error was 0.82% in terms of UKF. The MPC parameters generated by RL also achieved a better tracking performance with 0.227 m RMSE in path tracking experiments, and they also achieved a better tracking performance when compared to that of human-tuned MPC parameters.

This paper presents the dynamic modeling and predictive control method and the controller design of an electric driven eight-wheeled differential steering autonomous vehicle. First, the dynamic model of autonomous vehicle is built. Then, the model predictive control method is introduced. Consequently, the path tracking controller of autonomous vehicle is designed on the basis of dynamic model and predictive control method. Finally, the real vehicle experiment is performed at a middle speed up to 60km/h on a two kilometers long highway. The experimental results show a mean lateral error less than 0.3m and heading error less than 2 deg when follow the given refer path. The experiment also proofs the controller has certain anti-interference ability, which demonstrates the effectiveness of proposed control method and autonomous vehicle path tracking controller.

This paper presents a method to design a path tracking controller with a constraint on tire slip angles under low-friction road conditions. On a low-friction road surface, a lateral tire force is easily saturated and decreases as a tire slip angle increases by a large steering angle. Under this situation, a path tracking controller cannot achieve its maximum performance. To cope with this problem, it is necessary to limit tire slip angles to a value where the maximum lateral tire force is achieved. The most commonly used controllers for path tracking, linear quadratic regulator (LQR) and model predictive control (MPC), are adopted as a controller design methodology. The control inputs of LQR and MPC are front and rear steering angles and control yaw moment, which have been widely used for path tracking. The constraint derived from tire slip angles is imposed on the steering angles of LQR and MPC. To fully verify the performance of the path tracking controller with the constraint on tire slip angles, a simulation is conducted on vehicle simulation software. From the simulation results, it is shown that the path tracking controller with the constraint on tire slip angles presented in this paper is quite effective for path tracking on low-friction road surface.

This paper presents a method for designing a static output feedback integrated path tracking controller for autonomous vehicles. For path tracking, state–space model-based control methods, such as linear quadratic regulator, H∞ control, sliding mode control, and model predictive control, have been selected as controller design methodologies. However, these methods adopt full-state feedback. Among the state variables, the lateral velocity, or the side-slip angle, is hard to measure in real vehicles. To cope with this problem, it is desirable to use a state estimator or static output feedback (SOF) control. In this paper, an SOF control is selected as the controller structure. To design the SOF controller, a linear quadratic optimal control and sliding mode control are adopted as controller design methodologies. Front wheel steering (FWS), rear wheel steering (RWS), four-wheel steering (4WS), four-wheel independent braking (4WIB), and driving (4WID) are adopted as actuators for path tracking and integrated as several actuator configurations. For better performance, a lookahead or preview function is introduced into the state–space model built for path tracking. To verify the performance of the SOF path tracking controller, simulations are conducted on vehicle simulation software. From the simulation results, it is shown that the SOF path tracking controller presented in this paper is effective for path tracking with limited sensor outputs.

It is a striking fact that the characteristics of parametric uncertainties, external disturbance, time-varying and nonlinearities are available in the constructed model of autonomous independent-drive vehicles; therefore, in this paper, the robust model predictive control (MPC) with the finite time horizon is proposed to realize the coordinated path tracking and direct yaw moment control (DYC) for autonomous four in-wheel motor independent-drive electric vehicles (AMIDEV). Firstly, considering the time-varying and uncertain feature of the tire cornering stiffness and the vehicle velocity in the state space equation constructed by 2 degrees of freedom (DoF) vehicle model and the path tracking preview model, the linear parameter varying (LPV) discrete model with four polytypic vertexes is constructed. Then, based on the linear matrix inequality (LMI) method, the novel robust MPC theory with the finite time horizon is put forward to solve the min-max optimization problem after updating four polytypic vertexes in real time, which could deal with the inevitable model mismatch problem caused by the time-varying, uncertain vehicle dynamic characteristics and external disturbance. Finally, the simulation and experimental results have verified that the proposed novel robust MPC theory could emerge from the stranglehold exercised by the conservativeness of the traditional robust MPC theory with the infinite time horizon, which strengthens the robustness of this control system as well as achieves better path tracking accuracy and handling ability of AMIDEV.

This paper attempts to implement an integrated path planning and tracking controller that generates optimal control inputs guaranteeing a collision-free path. This integrated scheme is achieved by unifying model predictive control (MPC) with a potential field for assigning collision risk. The target vehicle is an electrified autonomous vehicle that is capable of directly controlling traction and braking torques of vehicle. Wheel torque and steering input of vehicle are optimized by receding horizon optimization (RHO) and give us stable and comfort reference trajectories. In the optimization process, control inputs, tracking errors, and collision risk are to be minimized in a single objective function. Collision risk is taken into account by modeling proper potential fields that allow the controller to re-plan the given desired path for avoiding a collision. Simulation is conducted using a high-fidelity vehicle plant model and the control scheme demonstrates promising results by verifying optimal and stable path guaranteeing collision-free.

A hybrid control strategy for path tracking of intelligent vehicles is developed to address the limitations of traditional control algorithms in coordinating the control performance of intelligent vehicles under varying working conditions. The strategy combines error-free kinematic model predictive control (MPC) and no sinusoidal terminal sliding mode control (NTSMC) to account for the distinct system characteristics of intelligent vehicles during high-speed and low-speed steering operations. The control strategy employs error-free kinematic model predictive control for low speed and large curvature conditions and non-singular terminal sliding model control for high speed and small curvature conditions. The path-tracking control mode is determined by the vehicle speed, and the switching coordination controller is designed to achieve smooth switching of the lateral control system. And the yaw stability controller (YSC) is designed to ensure yaw stability during high-speed turns. Finally, based on the hardware-in-the-loop (HIL) platform, the hybrid control strategy for intelligent vehicle path tracking was simulated and verified. The simulation and test results show that the designed hybrid control strategy can ensure the path tracking performance of the intelligent vehicle at any speed with good tracking accuracy, real-time performance, and vehicle driving stability.

Model predictive control (MPC) has become a practical approach for implementing active safety control strategies in autonomous vehicles (AVs). This paper introduces a Fast Iterative MPC (FI-MPC) framework with rule-based iteration convergence criteria to tackle the significant challenges of control precision and solving time discrepancies between linear and nonlinear MPC algorithms within tracking control strategies for AVs. Differing from linear and nonlinear MPC structures, the core concept of FI-MPC involves incorporating the unmodeled nonlinear dynamics of the vehicle or tires into a linear framework to achieve optimal iterative control solutions. The goal is to mitigate the mismatch between linear and high-fidelity nonlinear dynamics models, thus achieving real-time high-precision tracking control of nonlinear vehicle dynamics under challenging conditions. In addition, rule-based convergence criteria are designed to enhance the iteration mechanism of FI-MPC, further conserving the computational resources of the onboard controller by reducing unnecessary iteration steps. To validate the effectiveness of the FI-MPC algorithm, this study investigates the trajectory tracking problem for a four-wheel-drive AV for a weave test scenario. Co-simulation and hardware-in-the-loop testing results at various speeds confirm that FI-MPC enables high-precision control of nonlinear dynamics while ensuring excellent real-time performance.

The performance of the path tracking control system is poor when vehicles navigate under extreme conditions of high speed and large curvature due to the uncertainty of vehicle model parameters, modeling errors and disturbances. To address this issue, this paper introduces a Linear Model Predictive Controller (GP‐SOMPC) based on Gaussian Process (GP) and Snake Optimizer (SO) to achieve high‐performance trajectory tracking control under large curvatures through learning. This algorithm adopts a two‐degree‐of‐freedom vehicle dynamics model and models disturbances and unmodeled dynamics as Gaussian Processes (GP) using collected experimental data. Additionally, an Adaptive Weighting Coefficient Model Predictive Controller based on the Snake Optimizer (SO) method is presented to improve the poor adaptation of vehicle trajectory tracking accuracy according to reference path curvature under fixed weighting coefficients in traditional Model Predictive Control (MPC), which results in inadequate trajectory tracking precision. The simulation experiments have verified that the proposed GP‐SOMPC algorithm can enhance trajectory tracking precision under high‐speed, large curvature conditions and exhibits good adaptability to variations in path curvature.

Multi-vector model predictive control of permanent magnet synchronous motor can effectively overcome the shortcomings of conventional single-vector model predictive control such as large motor current ripples and limited control accuracy, but its control performance is more susceptible to the influence of motor parameter perturbation. To improve the robustness of the multi-vector predictive control algorithm under the motor parameter perturbation, a novel nonparametric three-vector model predictive current control method for permanent magnet synchronous motors is proposed in this paper. Through constructing an ultra-local predictive current model based on the input and output signals of the permanent magnet synchronous motor, the influence of motor parameter perturbation on current prediction is avoided, and a disturbance observer is designed to estimate the non-modeled and perturbed parts of the ultra-local model. In addition, the direct calculation method of vector duty cycles based on current error is introduced to suppress the influence of motor parameter uncertainty on the duty cycle calculation link, which further improves the system robustness. Finally, simulations and experiments of the proposed method are demonstrated to compare with the conventional parametric three-vector model predictive current control, and the results show that the proposed control strategy can effectively suppress the disturbances caused by the motor parameters and ensure the steady-state performance during motor operation.

A novel regional path tracking description is presented in this manuscript, and the moving horizon control method that is model predictive control (MPC) is proposed to discuss the regional path tracking issue which could avoid colliding road boundary when tracking a more complex road effectively. The feasible region for autonomous ground vehicles (AGVs) running is determined first according to the detected road boundaries. Then, in order to keep the actual trajectory of AGVs in the region and satisfy the safety requirements, MPC method is employed to design the path tracking controller considering actuator and road boundary constraints. In order to verify the effectiveness of the proposed method, experiments based on Hongqi AGV HQ430 are carried out, and the results illustrate that the presented method could be successfully applied to Hongqi AGV vehicle HQ 430.

Autonomous driving technology is constantly developing to a higher level of complex scenes, and there is a growing demand for the utilization of end-to-end data-driven control. However, the end-to-end path tracking process often encounters challenges in learning efficiency and generalization. To address this issue, this paper designs a deep deterministic policy gradient (DDPG)-based reinforcement learning strategy that integrates imitation learning and feedforward exploration in the path following process. In imitation learning, the path tracking control data generated by the model predictive control (MPC) method is used to train an end-to-end steering control model of a deep neural network. Another feedforward exploration behavior is predicted by road curvature and vehicle speed, and adds it and imitation learning to the DDPG reinforcement learning to obtain decision-making experience and action prediction behavior of the path tracking process. In the reinforcement learning process, imitation learning is used to update the pre-training parameters of the actor network, and a feedforward steering technique with random noise is adopted for strategy exploration. In the reward function, a hierarchical progressive reward form and a constrained objective reward function referring to MPC are designed, and the actor-critic network architecture is determined. Finally, the path tracking performance of the designed method is verified by comparing various training results, simulations, and HIL tests. The results show that the designed method can effectively utilize pre-training and feedforward prior experience to obtain optimal path tracking performance of an autonomous vehicle, and has better generalization ability than other methods. This study provides an efficient control scheme for improving the end-to-end control performance of autonomous vehicles.

The wide availability of microprocessors with much higher computational power capabilities has encouraged many researchers during the last decade to introduce the predictive control techniques to the field of power electronics and motor drives. One technique of predictive control, which is called model predictive control, is introduced in this paper and its application to control a five-phase induction motor is also presented. The mathematical formulation of both model predictive torque control and model predictive speed control algorithms are explained, which shows that the algorithms' equations are intuitive so they can be easily understood and implemented. Since a load torque estimate is needed in the predictive speed controller, an observer based on the minimal-order Gopinath's method is designed to get the load torque value. A comparison between the two techniques is carried out based on a simulation study. Also, the simulation results show the effectiveness of the predictive control in achieving a high dynamic performance control of multiphase induction motor drives.

Autonomous vehicle control based on receding horizon method