MPC-Based Trajectory Tracking Controller for Autonomous Vehicles

<div>Intelligent vehicles can utilize a variety of sensors, computing, and control technologies to autonomously perceive the environment and make decisions to achieve safe, efficient, and automated driving. If the speed planning of intelligent vehicles ignores the vehicle dynamics state, it leads to unreasonable planning speed and is not conducive to improving the accuracy of trajectory tracking control. Meanwhile, trajectory tracking usually does not consider the road and speed information beyond the prediction horizon, resulting in poor tracking precision that is not conducive to improving driving comfort. To solve these problems, this study proposes a new longitudinal speed planning method based on variable universe fuzzy rules and designs the piecewise preview model predictive control (PPMPC) to realize the vehicle trajectory tracking. First, the three-degrees-of-freedom vehicle dynamics model and trajectory tracking model are established and verified. Then, the variable universe fuzzy rules are introduced to design the longitudinal speed planning method, in which the road friction coefficient and road curvature are defined as the input of the speed planning method, and the vehicle lateral deviation is defined as the scaling factor input of the speed variable universe. Based on the dynamics model and trajectory tracking model, the PPMPC method is proposed to improve the accuracy and stability of trajectory tracking. During the PPMPC method design, the reference value of state quantity in the prediction horizon can be updated by using further road information and planning longitudinal speed information. Finally, the results show that the proposed planning algorithm can provide a reasonable longitudinal speed to reduce the tracking lateral error in the tracking control, and the proposed PPMPC can significantly improve the vehicle speed-tracking accuracy and control stability compared with the traditional model predictive control (MPC) method.</div>

This paper explores lane changing trajectory planning and tracking control for intelligent vehicle on curved road. A novel arcs trajectory is planned for the desired lane changing trajectory. A kinematic controller and a dynamics controller are designed to implement the trajectory tracking control. Firstly, the kinematic model and dynamics model of intelligent vehicle with non-holonomic constraint are established. Secondly, two constraints of lane changing on curved road in practice (LCCP) are proposed. Thirdly, two arcs with same curvature are constructed for the desired lane changing trajectory. According to the geometrical characteristics of arcs trajectory, equations of desired state can be calculated. Finally, the backstepping method is employed to design a kinematic trajectory tracking controller. Then the sliding-mode dynamics controller is designed to ensure that the motion of the intelligent vehicle can follow the desired velocity generated by kinematic controller. The stability of control system is proved by Lyapunov theory. Computer simulation demonstrates that the desired arcs trajectory and state curves with B-spline optimization can meet the requirements of LCCP constraints and the proposed control schemes can make tracking errors to converge uniformly.

The objective of this paper is to examine the issues of low accuracy and poor stability in vehicle trajectory tracking under a transverse controller, with a view to investigating the transverse and longitudinal control of vehicle trajectory tracking. Firstly, an MPC transverse controller based on a single-point pre-scan model is constructed. Secondly, a longitudinal controller with PID as the upper layer and vehicle dynamics as the lower layer is constructed. Once more, GA is applied to optimise the parameters of the MPC controller globally offline. Finally, a classical double-shift line trajectory tracking simulation model has been constructed using MATLAB and Carsim software. The results demonstrated that the average deviation of transverse displacement was reduced by 16.76%, and the average transverse angular velocity was reduced by 6.79%, under MPC+PID controllers relative to MPC control. Following the implementation of GA optimization, significant enhancements have been made to the performance of the MPC+PID controllers.

Trajectory tracking and speed control for intelligent vehicles are put forward higher requirements on accuracy by the high traffic density scenario. A standard Model Predictive Control (MPC) algorithm focuses on the trajectory tracking but ignores the speed control. This paper proposes a simultaneous trajectory tracking and speed control algorithm based on MPC approach to address fine control in both space and time dimensions for intelligent vehicles. A threefold cost function including lateral and longitudinal speed as well as comfort has been proposed to improve the control algorithm. The simulations and comparisons demonstrate that the proposed method has a better tracking and speed control performance than the existing method.

Cloud-based Intelligent Connected Vehicle (CICV) provide a new solution for realising autonomous driving. The openness of the wireless communication network between the vehicle and the cloud makes it vulnerable to cyber-attacks, and cyber-attacks intruding into the vehicle system tamper with or interrupt the original control signals, which poses a serious threat to the security of the vehicle's control. In order to avoid the degradation of trajectory tracking accuracy and driving stability of CICVs under hybrid cyber-attacks, this paper proposes an output feedback resilient control method. Firstly, the energy-constrained hybrid cyber-attack model and the error-constrained vehicle trajectory tracking control model are established, and the trajectory tracking closed-loop control system of CICV is constructed by combining the \(H\infty\) output feedback controller with the parameters to be determined. Secondly, the closed-loop trajectory tracking control system is analysed for stability based on the Lyapunov stability theory, and a quantitative stability evaluation index is proposed. Then, the linear matrix inequality (LMI) constraints for solving the \(H\infty\) output feedback controller are derived based on the results of the system stability analysis. Finally, the simulation is performed under typical conditions, and the results show that the designed controller can effectively maintain the stability of the vehicle and reduce the vehicle trajectory tracking error under the hybrid cyber-attacks.

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.

To resolve the problem of high-precision trajectory tracking control under interference conditions in a missile’s mid-guidance phase, according to the constructed nominal trajectory, an improved adaptive high-order sliding mode trajectory tracking controller (AHSTC) is proposed. In this method, the open-loop nominal trajectories are established according to the nonlinear programming and Gaussian pseudospectra method. A high-precision trajectory tracking controller is developed by designing a nonlinear sliding mode surface and an adaptive high-order sliding mode approaching law combined with the trajectory tracking nonlinear error model. To verify the effectiveness and superiority of the proposed method, analysis and simulation are carried out through the example of a missile mid-guidance phase tracking control. Compared to the linear quadratic regulator (LQR) and active disturbance rejection controller (ADRC) method, the simulation results show that the proposed AHSTC method shows faster convergence and improved tracking effect. Therefore, the proposed AHSTC method has a good results and engineering application value.

To improve the stability and accuracy of quintic polynomial trajectory tracking, an MPC (model predictive control) and fuzzy PID (proportional‐integral‐difference)‐ based control method are proposed. A lateral tracking controller is designed by using MPC with rule‐based horizon parameters. The lateral tracking controller controls the steering angle to reduce the lateral tracking errors. A longitudinal tracking controller is designed by using a fuzzy PID. The longitudinal controller controls the motor torque and brake pressure referring to a throttle/brake calibration table to reduce the longitudinal tracking errors. By combining the two controllers, we achieve satisfactory trajectory tracking control. Relative vehicle trajectory tracking simulation is carried out under common scenarios of quintic polynomial trajectory in the Simulink/Carsim platform. The result shows that the strategy can avoid excessive trajectory tracking errors which ensures a better performance for trajectory tracking with high safety, stability, and adaptability.

Traditional models of vehicle dynamics engineered from physical principles are usually simplified and assumed, resulting in the model cannot accurately reflect the actual dynamic characteristics of the vehicle under some working conditions, affecting the control accuracy and even safety. In view of this, inspired by the single-track model, this paper uses the data-driven methods to establish a new high-performance time-delay feedback neural network vehicle dynamics model. The feedback connection of a network can describe complex dynamics. The multi-time-step input of the state and control can include highly nonlinear and strong coupling characteristics of a vehicle. The test results of modeling accuracy show that the proposed model can achieve higher vehicle dynamics prediction accuracy than nonlinear vehicle model. Different from the traditional vehicle dynamics model, the proposed model has long-term memory cells, which can implicitly predict coefficient of friction and can be applied to different road conditions. Then, the trajectory tracking control algorithm is designed based on the proposed vehicle model. According to the steady-state steering assumption, the feedforward front wheel steering angle is calculated, and the steady-state sideslip angle is integrated into the steering feedback according to the reference path to realize the reference trajectory tracking control. Finally, Simulink/CarSim is used to conduct the simulation analysis under the double lane change conditions to evaluate the proposed control algorithm. The analysis results show that the control algorithm based on the proposed model can achieve an accurate tracking control effect of a vehicle at medium and high speeds, providing high-accuracy track tracking and good lateral stability of intelligent vehicles.

Autonomous underwater vehicles (AUVs) have been widely used to perform underwater tasks. Due to the environmental disturbances, underactuated problems, system constraints, and system coupling, AUV trajectory tracking control is challenging. Thus, further investigation of dynamic characteristics and trajectory tracking control methods of the AUV motion system will be of great importance to improve underwater task performance. An AUV controller must be able to cope with various challenges with the underwater vehicle, adaptively update the reference model, and overcome unexpected deviations. In order to identify modeling strategies and the best control practices, this paper presents an overview of the main factors of control-oriented models and control strategies for AUVs. In modeling, two fields are considered: (i) models that come from simplifications of Fossen’s equations; and (ii) system identification models. For each category, a brief description of the control-oriented modeling strategies is given. In the control field, three relevant aspects are considered: (i) significance of AUV trajectory tracking control, (ii) control strategies; and (iii) control performance. For each aspect, the most important features are explained. Furthermore, in the aspect of control strategies, mathematical modeling study and physical experiment study are introduced in detail. Finally, with the aim of establishing the acceptability of the reported modeling and control techniques, as well as challenges that remain open, a discussion and a case study are presented. The literature review shows the development of new control-oriented models, the research in the estimation of unknown inputs, and the development of more innovative control strategies for AUV trajectory tracking systems are still open problems that must be addressed in the short term.

Many plants can be modelled as lumped LTI‐systems and described by Differential‐Algebraic‐Equations (DAEs). Systems with m ≥ 1 control inputs are investigated in the frequency domain. It is proved that there exist m basis variables, whose trajectories may be chosen arbitrarily. Then, the trajectories of all system signals including the control signals are entirely determined. In case of unstable plants, trajectory tracking controllers must be added. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Design and experimental validation of a robust model predictive control for the optimal trajectory tracking of a small-scale autonomous bulldozer

This article studies the trajectory tracking of an underactuated unmanned surface vehicle. The trajectory tracking controller is divided into two parts: the kinematics controller and the dynamic controller. Taking the hull coordinate system of the unmanned surface vehicle as the datum plane, the kinematics controller is designed based on the backstepping method, and the virtual control input of the speed and the heading deviation of the ship are obtained. A dynamic controller is designed through an exponential sliding surface to stabilize the error of speed and heading deviation, thereby stabilizing the position error. In the process of designing the controller, the stability of the entire closed-loop control system is analyzed using Lyapunov stability theory. Finally, the designed numerical simulation experiment is carried out. The proposed exponential sliding mode controller is compared with the global integral sliding mode controller, and it is verified that the proposed controller has better effectiveness and robustness in the trajectory tracking of the underactuated unmanned surface vehicle.

The centroid of the whole vehicle moves when the automatic guided vehicle (AGV) loads and unloads goods between stations in the intelligent factory, which reduces the trajectory tracking accuracy. To this end, the dynamics and kinematics models of a four-wheel steering AGV were established, and the Lyapunov direct method was used to construct a trajectory tracking controller with global asymptotic stability in this study. Based on the adaptive learning factor and inertia weight, an adaptive particle swarm optimization algorithm was designed to optimize the control parameters of the controller, and an adaptive global asymptotic tracking control (AGATC) controller was proposed. Under simulated working condition of moving centroid, the AGATC controller was compared with adaptive model predictive control (AMPC) controller, and the trajectory tracking simulation was carried out. The results show that the position deviation of the AGATC controller was 23.97% lower than that of the AMPC controller, and the trajectory tracking control accuracy is higher under the condition of moving centroid. Moreover, a prototype of AGV was developed, and the trajectory tracking control verification experiment was carried out. The results show that the error between simulation and experiment was less than 9.03%, which proves the authenticity and effectiveness of the AGATC controller. This study provides theoretical and experimental basis for intelligent factory to realize precision and intelligent handling technology.

For four-wheel independent drive intelligent vehicle, the Model Predictive Control (MPC) is adopted to design the trajectory tracking controller through active steering and four-wheel independent drive/brake. The control objective is to follow a desired trajectory while taking into account the control actuator constraints and vehicle dynamic stability constraints. To reduce the computational complexity, a linear time-varying model predictive controller is designed to linearize the nonlinear vehicle model locally at each sampling point. The co-simulation of CarSim/Simulink shows that the designed controller has high tracking accuracy on the basis of ensuring vehicle stability and strong robustness to vehicle velocity and road adhesion coefficient. The trajectory tracking accuracy based on MPC is better than that of the preview driver model (PDM).