Trajectory Tracking Of Vehicle Research Articles

Coupled lateral and longitudinal trajectory tracking control with a modified vehicle kinematics model for autonomous vehicles

Abstract The paper proposes a coupled lateral and longitudinal trajectory tracking control algorithm based on model predictive control (MPC) to enhance the precision and stability of trajectory tracking of autonomous vehicles. The coupled MPC controller is developed based on a modified vehicle kinematics model, which simultaneously takes the steering angle and the longitudinal speed as control variables. The modified vehicle model and the coupled MPC controller are verified by CarSim and MATLAB/Simulink co-simulation experiments. Simulation results demonstrate that, at the cost of 12 percent increase in average computational time, the proposed coupled MPC controller leads to an approximate 48 percent reduction in tracking error compared to the benchmarking coupled lateral and longitudinal MPC controller based on the classic kinematics model.

Trajectory‐tracking control of an unmanned surface vehicle based on characteristic modelling approach: Implementation and field testing

AbstractIn this study, a practical adaptive control scheme is proposed for the trajectory tracking of an unmanned surface vehicle via the characteristic modelling approach. Therefore, accurate tracking control can be achieved in the presence of unknown time‐varying model parameters and environmental disturbances. The control scheme comprises a trajectory guidance module based on the virtual target approach and a tracking control module designed by characteristic modelling theory. Firstly, the ideal control commands of the yaw speed and surge speed are generated using the position errors between the vehicle and the virtual target. Then, a second‐order characteristic model for the heading and surge speed channel is developed. The parameters of the model are updated by a real‐time parameter identification algorithm. Based on this model, an integrated adaptive control law is designed which consists of golden‐section control, feed‐forward control and integral control. Finally, the development processes of the vehicle platform and the control algorithms are described, and the results of simulation and field experiments are presented and discussed.

Research on automatic driving control strategy based on improved model predictive control

As a new technology direction in the automotive industry in recent years, automatic driving technology has played an important role in reducing traffic accidents, promoting energy conservation and emission reduction, and improving the efficiency of high-speed and urban roads. As one of the key technologies of autonomous vehicles, the performance of control algorithm greatly affects the smoothness of vehicle driving and the accuracy of track tracking. In order to consider the lateral control and longitudinal control accuracy at the same time, and ensure that the vehicle travels according to the given trajectory, this paper first establishes the vehicle kinematics model, and improves the traditional model predictive control algorithm, which realizes the high dynamic control of the desired trajectory while ensuring the vehicle stability and comfort. Finally, based on the built real vehicle test platform for automatic driving, the acceleration and deceleration test and the high-speed serpentine test are designed. By analyzing the test data, it can be seen that the control algorithm proposed in this paper can effectively achieve the vehicle trajectory tracking, and the control accuracy is improved.

Three-Dimensional Trajectory Tracking of AUV Based on Nonsingular Terminal Sliding Mode and Active Disturbance Rejection Decoupling Control

This paper presents a nonsingular terminal sliding mode and active disturbance rejection decoupling control (NTSM-ADRDC) scheme for the three-dimensional (3D) trajectory tracking of autonomous underwater vehicles (AUV). Firstly, the AUV model is decoupled into five independent single input–single output (SISO) channels using ADRDC technology. Secondly, the NTSM-ADRDC controller is designed. The linear extended state observer (LESO) is used to observe the AUV state variables, and estimate the total disturbance of the system. In addition, to improve the system error convergence rate, the combination of exponential reaching rate and NTSM constitutes a nonlinear states error feedback control law for the controller. Finally, the stability of the proposed control law is proved using the Lyapunov theory. The simulation results demonstrate the effectiveness and robustness of the designed NTSM-ADRDC trajectory tracking approach.

Predefined-Time Fault-Tolerant Trajectory Tracking Control for Autonomous Underwater Vehicles Considering Actuator Saturation

This paper presents the design of two predefined-time active fault-tolerant controllers for the trajectory tracking of autonomous underwater vehicles (AUVs) which can address actuator faults without causing actuator saturation. The first controller offers improved steady-state trajectory tracking precision, while the second ensures a nonsingular property. Firstly, a predefined-time sliding mode controller is formulated based on a predefined-time disturbance observer by integrating a novel predefined-time auxiliary system to prevent the control input from exceeding the actuator’s physical limitations. Subsequently, a non-singular backstepping controller is introduced to circumvent potential singularities in the sliding mode controller, guaranteeing that the trajectory tracking error is uniformly ultimately bounded (UUB) within the predefined time. Additionally, theoretical analysis and simulation results are presented to illustrate the advantages of the proposed method.

A Double-Layer Model Predictive Control Approach for Collision-Free Lane Tracking of On-Road Autonomous Vehicles

This paper proposes a double-layer model predictive control (MPC) algorithm for the integrated path planning and trajectory tracking of autonomous vehicles on roads. The upper module is responsible for generating collision-free lane trajectories, while the lower module is responsible for tracking this trajectory. A simplified vehicle model based on the friction cone is proposed to reduce the computation time for trajectory planning in the upper layer module. To achieve dynamic and accurate collision avoidance, a polygonal distance-based dynamic obstacle avoidance method is proposed. A vertical load calculation method for the tires is introduced to design the anti-rollover constraint in the lower layer module. Numerical simulations, with static and dynamic obstacle scenarios, are conducted on the MATLAB platform and compared with two state-of-the-art MPC algorithms. The results demonstrate that the proposed algorithm outperforms the other two algorithms regarding computation time and collision avoidance efficiency.

Neural network optimization algorithm based non-singular fast terminal sliding-mode control for an uncertain autonomous ground vehicle subjected to disturbances

As computer computing capabilities increase, optimization algorithms are becoming more useful for solving engineering problems. Up to now, several metaheuristic algorithms have been exploited in control engineering. However, this effort remains weak in addressing the autonomous ground vehicles (AGVs) trajectory tracking problem. This research presents a novel optimal approach merging the robust non-singular fast terminal sliding-mode control method (NFTSMC) and the neural network optimization algorithm (NNA) for automatic lane changing. First, a reference double lane-change path (DLC) is designed, and the robust non-singular fast terminal sliding-mode steering controller is developed, according to Lyapunov stability theory, to suppress the lateral deviation and ensure the yaw stability. Then, the control strategy is optimized by the NNA algorithm to adjust the steering controller optimally while avoiding local optimums. A comparison, under the same conditions, with the particle swarm optimization algorithm (PSO) revealed the superiority of the control law resulting from the NNA-based optimization. Furthermore, the proposed approach shows its excellent tracking performance versus the integrated backstepping sliding-mode controller (IBSMC) and the adaptive sliding-mode control (ASMC) under severe conditions typical of real-world lane changes.

Adaptive practical prescribed-time fault-tolerant control for autonomous underwater vehicles trajectory tracking

This article investigates the practical prescribed-time trajectory tracking control problem for AUVs with parametric uncertainties under tracking error constraints and velocity constraints. A settling time regulator is combined to construct the performance function, with which we build a new adaptive fault-tolerant control scheme upon the transferred error, ensuring that the tracking error converges to an adjustably small residual set within the prescribed time with a continuous control action. Furthermore, with the specific velocity transformation techniques, the problem of velocity constraints is transformed into the boundedness of new variables, thus the feasibility conditions are eliminated, and the requirements of constrained boundary functions are relaxed. Theoretical analysis shows that the proposed control method is an effective way to achieve pre-given tracking precision within the prescribed time, while avoiding the issue of explosion of complexity. The prescribed time is independent of system initial conditions and other parameters, and the tracking error will converge asymptotically. Simulation results further demonstrate the effectiveness of the proposed approach.

Fuzzy predictive Stanley lateral controller with adaptive prediction horizon

The challenge of trajectory tracking of autonomous vehicles (AVs) is a critical aspect that must be effectively addressed. Recent studies are concerned with maintaining the yaw stability to guarantee the customers’ comfort throughout the journey. Most of the geometrical controllers solve this task by dividing it into consecutive point stabilization problems, limiting the controllers’ ability to handle sudden trajectory changes. One research presented a predictive Stanley lateral controller that uses a discrete prediction model to mimic human behavior by anticipating the vehicle’s future states. That controller is limited in its use, as the parameters must be manually tuned for every change in the maneuver or vehicle velocity. This article presents a novel approach for trajectory tracking in autonomous vehicles, by introducing a fuzzy supervisory controller that automatically adapts to changes in the vehicle’s velocity and maneuver by estimating the prediction horizon’s length and providing different weights for each controller. The proposed method overcomes the limitations of traditional controllers that require manual tuning of parameters, making it ready for real-world experiments. This is the main contribution of the research in this paper. The suggested technique demonstrated an advantage over the Basic Stanley controller and the manually tuned predictive Stanley controller in terms of the total lateral error and the model predictive control (MPC) in terms of computational time. The performance is determined by performing various simulations on V-Rep and hardware-in-the-loop (HIL) experiments on an E-CAR golf bus. A broad selection of velocities is used to validate the behavior of the vehicle while working on different maneuvers (double lane change, hook road, S road, and curved road).

State constrained control strategy for unmanned surface vehicle trajectory tracking based on improved barrier Lyapunov function

This paper addresses the state-constrained control of the symmetric underactuated unmanned surface vehicles (USVs) under unknown dynamics and time-varying interference based on improved Lyapunov function. Inspired by the prescribed performance control (PPC), the improved logarithmic barrier Lyapunov function (BLF) is proposed with a reasonably defined performance function in advance. The tracking errors of position and yaw direction are constrained within the set range. Meanwhile, the symmetric barrier Lyapunov function (SBLF) and dynamic surface control (DSC) are introduced to simplify the controller design and indirectly restrict the yaw velocity. On this basis, the finite-time disturbance observer (FDO) is proposed to estimate the unknown disturbance. The finite-time auxiliary dynamic system is introduced to deal with the input saturation. In addition, the neural network minimum learning parameter (MLP) can reduce the computational complexity while figuring out the unknown dynamics. Finally, numerical simulation verifies the effectiveness of the control system.

Trajectory tracking control considering the transmission backlash of the dual-motor autonomous steering system

In order to solve the tracking error caused by transmission backlash in the dual-motor autonomous steering system, and thus improve the trajectory tracking accuracy of autonomous vehicles, a novel steering control strategy combining sliding model control (SMC) with variable weights and linear quadratic regulator (LQR) is proposed in this paper. Firstly, the vehicle dynamics model is built and the steering system model with contact and backlash modes is established by combining it with the simplified gear backlash system. Secondly, the front wheel angle control based on SMC is designed and the weights of contact mode and backlash mode are optimized by Particle Swarm Optimization (PSO) algorithm. Finally, the results of simulation under typical conditions show that the proposed strategy has better accuracy of angle tracking and stronger adaptability to the change of system load. Furthermore, it is also proved by simulation and Hardware-in-Loop (HiL) test under different trajectory tracking conditions that the LQR controller with proposed strategy has better accuracy of trajectory tracking for autonomous vehicles.

An Integrated Motion Planning Scheme for Safe Autonomous Vehicles in Highly Dynamic Environments

This study proposes a new integrated approach to the motion control of autonomous vehicles, which differs from the conventional method of treating planning and tracking tasks as separate or hierarchical components. By means of the proposed approach we can reduce the side effects on the performance of autonomous vehicles under challenging driving circumstances. To this end, our approach processes both of the aforementioned tasks asynchronously and simultaneously utilizes a multi-threaded architecture to enhance control performance. Meanwhile, the behavior planning feature is integrated into the path-tracking module. Then, a linear parameter-varying model predictive control is deployed for trajectory tracking of autonomous vehicles and compared with the linear model predictive control method. Finally, the control performance of the proposed approach was evaluated through simulation trials on urban roads with placed obstacles. The outcomes revealed that the suggested framework satisfies the processing rate and high-precision criteria, while safely avoiding obstacles, indicating that it is a promising control strategy for real-world applications.

Adaptive fixed-time backstepping control for three-dimensional trajectory tracking of underactuated autonomous underwater vehicles

An adaptive fixed-time backstepping control is proposed to achieve the three-dimensional trajectory tracking control of an underactuated autonomous underwater vehicle (AUV) in the presence of model uncertainty and external disturbances. In this paper, the dynamics of the AUV in terms of five degrees of freedom (DOFs) are discussed. Considering it is an underactuated AUV, a virtual velocity guidance law is derived using the backstepping method. For velocity convergence, an adaptive fixed-time control is derived without model parameters, with adaptive adjusting law tackling system unknows. Theoretical analyses demonstrate that the tracking error converges to a small bounded field within a fixed time in the proposed control scheme. The effectiveness and superiority of the proposed method are verified by simulation results.

Isolating Trajectory Tracking From Motion Control: A Model Predictive Control and Robust Control Framework for Unmanned Ground Vehicles

This letter studies the trajectory tracking and motion control problems of unmanned ground vehicles (UGVs). A model predictive control and robust control (MPC-RC) framework for UGVs is proposed to improve tracking accuracy, yaw stability and robustness in a modular fashion without introducing complexity into controller. The trajectory tracking problem and three-dimensional phase trajectory planning with high stability of a vehicle motion can be performed in the model predictive control design simultaneously. Also, combining the advantages of linear matrix inequality, sliding mode control, and back-stepping control law, three robust motion controllers can track the generated three-dimensional phase trajectory steadily so that the UGV motion stability is guaranteed. The robust performance is guaranteed through considering model uncertainties and terra-aerodynamic disturbances in robust controllers. Sufficient conditions for closed-loop stability under the diverse robust factors are provided by the Lyapunov method analytically, which ensures the series system's feasibility. The results of simulations on MATLAB-Carsim platform demonstrate that the proposed controller can significantly enhance tracking accuracy, motion stability, and robustness compared to the existing methods, which guarantees the feasibility and capability of driving in a nonlinear extreme scenario.

Cooperative Strategy of Trajectory Tracking and Stability Control for 4WID Autonomous Vehicles Under Extreme Conditions

Trajectory tracking and stability control are two essential functions of autonomous vehicles, and there is inevitable mutual interference between them, especially under extreme conditions. Towards addressing this challenge, this paper proposes a novel cooperative strategy of trajectory tracking and stability control for four-wheel independent drive (4WID) autonomous vehicles. An adaptive trajectory tracking controller is designed based on the model predictive control (MPC) theory, in which the tire cornering stiffness is modified in real-time leverages the lateral force estimated by the square-root cubature Kalman filter (SCKF). Then, the vehicle stability controller is designed based on the sliding mode control (SMC), in which the tire force saturation constraint and the relative weight of yaw rate and sideslip angle are considered. Furthermore, a weight adaptive criterion with normalized stability index is defined to develop the cooperative strategy of trajectory tracking and stability control. The feasibility and adaptability of the proposed method to different extreme conditions are verified by hardware-in-the-loop (HIL) test and CarSim-Simulink co-simulation. Finally, an experimental case is presented to demonstrate the realizability of the proposed method.

Realtime wide-area vehicle trajectory tracking using millimeter-wave radar sensors and the open TJRD TS dataset

• A system based on millimeter wave radar is introduced for tracking vehicles. • Trajectory splicing is applied for tracking vehicles in wide-area level. • Validation results show a reliable and stable performance of the system. • The system performs well in detecting speeding fractions through pilot project. • TJRD TS Platform is introduced in sharing wide-area trajectory dataset (open). This paper presented a real-time millimeter wave radar-based system for tracking vehicle trajectories in a wide area (continuously along a roadway with essentially no length limit in practice). The trajectory tracking results were first validated for single vehicle trajectory tracking using the Real-Time Kinematic positioning technology based on the Beidou satellite navigation systems. The validation showed that the vehicle positions were captured with a mean lateral offset of −0.284 m and a mean longitudinal offset of −0.352 m. The mean estimated speeds were found to have a difference of only −0.048 km/h from the ground truths. The trajectory tracking results were also validated through multi-object tracking using video data from an unmanned aerial vehicle (UAV). Compared with the UAV video footage, the millimeter wave-based system was found to correctly capture around 92% of the total number of vehicles. For the correctly captured vehicles, their positions were found to be within 0.99 m (about a quarter of the width of a regular traffic lane) of the ground truth. In this paper, we also would like to share openly the entire validated datasets which has been recently published online as the TJRD TS platform. Additionally, a demonstration in using the dataset to detect aggressive driving behaviors, such as speeding was presented. It is expected that the open dataset will help enable researchers and practitioners to further explore the behaviors of road users, track the dynamics of safety risks and congestion formation, and evaluate incident impacts in a more microscopic but comprehensive way.

Analysis and design of control systems via parameter‐based approach

Analysis and design of control systems via parameter‐based approach

Trajectory Tracking of Autonomous Vehicle Using Clothoid Curve

This paper proposes a clothoid-curve-based trajectory tracking control method for autonomous vehicles to solve the problem of tracking errors caused by the discontinuous curvature of the control curve calculated by the pure pursuit tracking algorithm. Firstly, based on the Ackerman steering model, the motion model is constructed for vehicle trajectory tracking, Then, the position of the vehicle after the communication delay of the control system is predicted as the starting point of the clothoid control curve, and the optimization interval of the curve end point is determined. The clothoid control curves are calculated, and their parameters are verified by the vehicle motion and safety constraints, so as to obtain the optimal clothoid control curve satisfying the constraints. Finally, considering the servo system response delay time of the steering system, the steering angle target control value is obtained by previewing the curvature of the clothoid control curve. The field experiment is conducted on the test road, which consists of straight, right-angle turns and lane-change elements under three sets of speed limitations, and the test results show that the proposed clothoid-curve-based trajectory tracking control method greatly improved the tracking accuracy compared with the pure pursuit method; in particular, the yaw deviation is improved by more than 50%.

Adaptive Control Algorithm for Trajectory Tracking of Underactuated Unmanned Surface Vehicle (UUSV)

The ability to track the trajectory or path on the sea surface remains a key measurement in the control system of an unmanned surface vehicle (USV). In this research, the designed algorithm defines the path and minimizes the disturbances to zero. Underactuated USVs are ships or boats, which operate on the water surface without a crew and the underactuated system has low actuators than its degree of freedom (DOF). The adaptive control strategy is applied to the unbounded system as the ocean due to its high performance, while the robust control system attains high performance in the bounded system. To consider the trajectory tracking of UUSV and provide an optimal control strategy for a ship in the presence of external disturbances, the study presents a controller-based on model reference adaptive control with an integrator (MRACI), which guarantees the stability of a closed-loop system. The vehicle experiences variations in the system response due to external disturbance. This abovementioned scheme reduces the variations to nearly equal to zero making the vehicle stable. First, use computer-based simulation to verify the proposed controller under two different scenarios. Then, simulation results show that the designed scheme lowers the errors and performs well.

Intelligent electric vehicle trajectory tracking control algorithm based on weight coefficient adaptive optimal control

The track tracking effect of intelligent vehicle directly affects the safety of vehicle and passengers. In the process of intelligent vehicle track tracking, the track tracking accuracy is related to many factors such as track curvature, road friction coefficient, and longitudinal speed change. In this paper, a new lateral and longitudinal coupling control algorithm is proposed. Based on the vehicle dynamics model and the optimal control theory, combined with the fuzzy control theory, the Fuzzy Linear Quadratic Regulator (FLQR) lateral optimal controller is designed, and feed-forward control and predictive controller are added. According to the real-time tracking lateral error and fuzzy control algorithm fed back by the system, the weight coefficient of the lateral displacement deviation in the cost function is dynamically adjusted; considering the coupling effect of lateral and longitudinal controllers of vehicle trajectory tracking control, a model predictive control (MPC) longitudinal speed controller is designed based on MPC theory, considering acceleration constraint and acceleration variation constraint, and taking lateral stability as evaluation index. A joint simulation platform is built based on CarSim and Simulink. The simulation results show that the designed lateral and longitudinal coupling controller of FLQR + MPC has better track tracking accuracy and can improve the driving stability of the vehicle; finally, the tracking effect of the designed algorithm is verified by real vehicle experiments. The maximum error of the designed controller algorithm in real vehicle tracking is 0.56 m, and the tracking effect is good.