Path Tracking Research Articles

Intelligent Vehicle Trajectory Tracking Based on Horizontal and Vertical Integrated Control

To address the common issues of accuracy and stability in trajectory tracking tasks for autonomous vehicles, this study proposes an innovative composite control strategy that skillfully integrates lateral and longitudinal dynamic control. For lateral control, model predictive control (MPC) theory is introduced to compute the front wheel steering angle that ensures optimal trajectory following. On the longitudinal control level, the vehicle’s acceleration and deceleration logic are finely tuned to ensure precise adherence to the preset speed trajectory. More importantly, by deeply integrating these two control methods, the comprehensive coordination of the vehicle’s lateral and longitudinal movements is achieved. To validate the effectiveness of the proposed control strategy, simulations were conducted using the CarSim and MATLAB/Simulink platforms. The analysis of the simulation results confirms that the proposed method effectively improves speed tracking stability and significantly enhances path tracking accuracy and overall driving stability.

An actuator space optimal kinematic path tracking framework for tendon-driven continuum robots: Theory, algorithm and validation

Path tracking of continuum robots is a fundamental and crucial problem across various applications. In this article, we address this problem by focussing on three aspects. Firstly, we propose an efficient multi-solution inverse kinematics solver for three-section constant curvature robots by bridging the theoretical reduction and the numerical correction. Secondly, we derive a linear tendon-driven actuation model, establishing the connection between the robot configuration space and the actuator space. With this model, we achieve optimal distance planning and optimal time allocation considering the constraints of actuator velocity and acceleration, generating a continuous trajectory directly in the actuator space. Finally, we present our kinematic path tracking framework, which includes offline optimal trajectory planning and online feedforward and feedback control. Experiments are conducted both in simulations and in the real world on our three-section tendon-driven continuum robot. The experiments validate the increased efficiency, higher success rates, and accessibility of multiple solutions offered by our inverse kinematics solver, as well as the optimality in distance planning and time allocation in the actuator space. Performance improvements in tracking accuracy are demonstrated through comparative experiments and the application of our framework in path tracking tasks with obstacles is presented through a case study.

Path Tracking Control for Four-Wheel Independent Steering and Driving Vehicles Based on Improved Deep Reinforcement Learning

We propose a compound control framework to improve the path tracking accuracy of a four-wheel independent steering and driving (4WISD) vehicle in complex environments. The framework consists of a deep reinforcement learning (DRL)-based auxiliary controller and a dual-layer controller. Samples in the 4WISD vehicle control framework have the issues of skewness and sparsity, which makes it difficult for the DRL to converge. We propose a group intelligent experience replay (GER) mechanism that non-dominantly sorts the samples in the experience buffer, which facilitates within-group and between-group collaboration to achieve a balance between exploration and exploitation. To address the generalization problem in the complex nonlinear dynamics of 4WISD vehicles, we propose an actor-critic architecture based on the method of two-stream information bottleneck (TIB). The TIB method is used to remove redundant information and extract high-dimensional features from the samples, thereby reducing generalization errors. To alleviate the overfitting of DRL to known data caused by IB, the reverse information bottleneck (RIB) alters the optimization objective of IB, preserving the discriminative features that are highly correlated with actions and improving the generalization ability of DRL. The proposed method significantly improves the convergence and generalization capabilities of DRL, while effectively enhancing the path tracking accuracy of 4WISD vehicles in high-speed, large-curvature, and complex environments.

Adaptive Path-Tracking Control Algorithm for Autonomous Mobility Based on Recursive Least Squares with External Condition and Covariance Self-Tuning

This paper introduces an adaptive path-tracking control algorithm for autonomous mobility based on recursive least squares (RLS) with external conditions and covariance self-tuning. The advancement and commercialization of autonomous driving necessitate universal path-tracking control technologies. In this study, we propose a path-tracking control algorithm that does not rely on vehicle parameters and leverages RLS with self-tuning mechanisms for external conditions and covariance. We designed an integrated error for effective path tracking that combines the lateral preview distance and yaw angle errors. The controller design employs a first-order derivative error dynamics model with the coefficients of the error dynamics estimated through the RLS using a forgetting factor. To ensure stability, we applied the Lyapunov direct method with injection terms and finite convergence conditions. Each regression process incorporates external conditions, and the self-tuning of the injection terms utilizes residuals. The performance of the proposed control algorithm was evaluated using MATLAB®/Simulink® and CarMaker under various path-tracking scenarios. The evaluation demonstrated that the algorithm effectively controlled the front steering angle for autonomous path tracking without vehicle-specific parameters. This controller is expected to provide a versatile and robust path-tracking solution in diverse autonomous driving applications.

Path tracking and energy efficiency coordination control strategy for skid-steering unmanned ground vehicle

The skid steering unmanned ground vehicle (SUGV) plays an important role in extremely harsh environments. Improving the autonomous control capability and energy efficiency of SUGV is urgently needed. This article presents a skid steering-based path tracking control strategy. In the upper controller, an improved model-free sliding mode controller (APMS) is used to calculate the yaw moment for tracking control. On the lower controller, the Snow Ablation Optimizer (SAO) is used to distribute the output torque of the drive motors, taking longitudinal force, yaw moment and energy consumption into account. Finally, the designed controller is validated through simulation under different operating conditions. The results show that the proposed coordination controller achieves good control performance, increases energy efficiency and at the same time ensures tracking accuracy.

Longitudinal and Lateral Cooperative Control of Preview Intelligent Vehicles with Stabilization

Aiming at the highly nonlinear and coupled longitudinal and transverse motion control problems of intelligent vehicle path tracking control, a new method of preview MPC path tracking control is proposed by combining visual preview model and model predictive control theory. The method first locally linearizes the nonlinear prediction model and transforms the MPC optimization solution problem into a quadratic programming problem. The longitudinal vehicle speed and the preview distance are then treated as known in each control time domain, an exponential model is applied to characterize the longitudinal vehicle speed, and a transverse angular velocity-center of mass lateral deflection (r-β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r-\\beta $$\\end{document}) phase plane plot is applied to characterize the vehicle stability. Finally, proportional integral differential stability controller is designed to improve vehicle stability. Simulation and test results show that: Compared with the MPC tracking control method, the preview MPC control method proposed in this paper can optimize the vehicle tracking performance on different adhesion coefficient road surfaces and improve the tracking accuracy, and this enhancement effect is more obvious at high speeds.

A Calculation Study on the Escape of Incident Solar Radiation in Buildings with Glazing Facades

More and more modern buildings are using glass curtain walls as their building envelope. The large area of window leads to a significant increase in solar heat gain, resulting in an increase in the cooling load and energy consumption of the building envelope. In the calculation of building cooling load, the thermal performance parameter of windows, the solar heat gain coefficient, is used to calculate the solar radiation heat gain of the windows. The window-to-wall ratio of buildings with glazing facades is large, and the phenomenon of escape of incident solar radiation cannot be ignored. In order to calculate the solar radiation escape rate, a dynamic model of solar radiation escape rate incorporating the solar path tracking model is developed in this research, which can achieve big data simulation analysis based on actual meteorological conditions. The model is programmed and simulated using MATLAB R2024a software. Five representative cities from different climate regions in China are selected and the variation rule of solar radiation escape rate are analyzed on three different time scales: day, month, and year. The influence of building orientation was also calculated and analyzed. The numerical calculation results indicate that the escape solar radiation rate varies with the incident angle of solar radiation at different times. It was found that the smaller the solar azimuth angle and solar altitude angle, the smaller the escape rate of solar radiation. The latitude of a city has a significant impact on the solar radiation escape rate. The weighted average of the solar radiation escape rates for each city were calculated for both summer and winter. Regardless of the season, the city’s location, and the orientation of the room, the value of solar radiation escape rate varies from 8.64% to 10.33%, which indicates that the solar radiation escape phenomenon cannot be ignored in glass curtain wall buildings. The results can be used as a reference value of solar radiation escape rate for the correction of actual solar heat gain of buildings in different climate regions.

Design of a Path-Tracking Controller with an Adaptive Preview Distance Scheme for Autonomous Vehicles

This paper presents a method to design a path-tracking controller with an adaptive preview distance scheme for autonomous vehicles. Generally, the performance of a path-tracking controller depends on tire–road friction and is severely deteriorated on low-friction roads. To cope with the problem, it is necessary to design a path-tracking controller that is robust against variations in tire–road friction. In this paper, a preview function is introduced into the state-space model built for better path-tracking performance. With the preview function, an adaptive preview distance scheme is proposed to adaptively adjust the preview distance according to the variations in tire–road friction. Front-wheel steering (FWS) and four-wheel steering (4WS) are adopted as actuators for path tracking. With the state-space model, a linear quadratic regulator (LQR) is adopted as a controller design methodology. In the adaptive preview distance scheme, the best preview distance is obtained from simulation for several tire–road friction conditions. Curve fitting with an exponential function is applied to those preview distances with respect to the tire–road friction. To verify the performance of the adaptive preview distance scheme under variations in tire–road friction, a simulation is conducted on vehicle simulation software. From the simulation results, it was shown that the path-tracking controller with an adaptive preview distance scheme presented in this paper was effective for path tracking against variations in tire–road friction in the peak’s center offset, and the settling delays were reduced by 60% and 23%, respectively.

Path tracking with switchable stability constraints for vehicle collision avoidance based on extended stability region

There is a certain conflict between vehicle stability and the performance of path-tracking under emergency conditions. In this paper, to make full use of the lateral capacity of vehicles, a path tracking method with switchable stability constraints is proposed. First, using the Lyapunov energy equation and Hurwitz’s theorem, the lateral stability region (SR) and the critical steering angle of steady steering at different longitudinal speeds are calculated. Based on this, the extended stability region (ESR) and the extended critical steering angle of the vehicle under the control of an additional yaw moment are obtained. Furthermore, the driving area during collision avoidance is divided into unsafe and safe areas, and based on the model predictive control strategy, a path-tracking controller with switchable stability constraints is established. In the unsafe area, the vehicle states are allowed to break through the SR temporarily, and to ensure path-tracking accuracy, the ESR is taken as the stability constraint. In the safe area, the stability constraint is switched to the SR, and to make the vehicle states quickly return to SR, a regain stability controller is established. Finally, a Simulink-CarSim simulation and a hardware-in-the-loop (HIL) experiment are conducted. The simulation results show that a balance between tracking effect and vehicle stability can be effectively achieved through the proposed path-tracking system under the investigated emergency conditions. The real-time performance of the proposed control strategy is validated through the HIL experiment.

Research on Complete Coverage Path Planning of Agricultural Robots Based on Markov Chain Improved Genetic Algorithm

Due to the limitations of low coverage, high repetition rate, and slow convergence speed of the basic genetic algorithm (GA) in robot complete coverage path planning, the state transition matrix of the Markov chain is introduced to guide individual mutation based on the genetic mutation path planning algorithm, which can improve the quality of population individuals, enhancing the search ability and convergence speed of the genetic algorithm. The proposed improved genetic algorithm is used for complete coverage path planning simulation analysis in different work areas. The analysis results show that compared to traditional genetic algorithms, the improved genetic algorithm proposed in this paper reduces the average path length by 21.8%, the average number of turns by 6 times, the repetition rate by 83.8%, and the coverage rate by 7.76% in 6 different work areas. The results prove that the proposed improved genetic algorithm is applicable in complete coverage path planning. To verify whether the Markov chain genetic algorithm (MCGA) proposed is suitable for agricultural robot path tracking and operation, it was used to plan the path of an actual land parcel. An automatic navigation robot can track the planned path, which can verify the feasibility of the MCGA proposed.

Application of Path Planning and Tracking Control Technology in Mower Robots

Path planning and tracking is the most basic technology for mowing robots, among which the performance of algorithms has a great impact on their intelligence and efficiency. Based on the research of relevant references on mower robots, it mainly focuses on complete coverage path planning, path tracking control, and obstacle avoidance path planning. In complete coverage path planning, three methods were introduced, including simple complete coverage planning, optimal complete coverage planning, and hybrid complete coverage planning. In the path tracking control section, the control methods are divided into three types based on whether the control method depends on the robot model and the type of model, namely model free control method, kinematic model-based control method, and dynamic model-based control method. In obstacle avoidance path planning, we introduce the environment detection device and obstacle avoidance planning algorithm. Then the relevant research papers are analyzed in classification, comparing the research and validation methods adopted by the researchers in the form of charts. Finally, we pointed out the limitations of path planning technology in the application of mower robots. Meanwhile, future development trends are predicted.

Unmanned Agricultural Machine Operation System in Farmland Based on Improved Fuzzy Adaptive Priority-Driven Control Algorithm

Autonomous driving technology for agricultural machinery can maximise crop yield, reduce labour costs, and alleviate labour intensity. In response to the current low degree of automation and low tracking accuracy of driving paths in agricultural equipment, this research proposes an unmanned agricultural machinery operating system based on an improved fuzzy adaptive PD control algorithm. Firstly, mechanical kinematic models and fuzzy adaptive control algorithms are introduced to achieve autonomous driving, and parameter settings and speed adjustments are made while considering errors. Secondly, in the autonomous driving operation system, taking a certain rice machine as an example, perception information, trajectory design, dynamic control, operation supervision, and remote control design are carried out. The experimental results show that the improved fuzzy algorithm exhibits smaller deviation results in driving path tracking, with an average error between the actual path and the expected path of less than 0.001 m. In different testing scenarios, compared with the actual control results, the maximum deviation of the control system platform in straight sections is less than 2.8 m, which is more stable. More than 95% of the lateral deviation results in the road sections are within 0.11 m. And the tracking distance error of the proposed method in the straight and curved segments is relatively small, far smaller than other comparative algorithms. The unmanned agricultural machinery operation system proposed in this study can significantly improve the efficiency and accuracy of agricultural machinery work, promote the development of intelligent and modern agricultural machinery, and provide reference value and important contributions to social and economic development as well as the progress and promotion of related technologies.

Efficient Nonlinear Model Predictive Path Tracking Control for Autonomous Vehicle: Investigating the Effects of Vehicle Dynamics Stiffness

Motion control is one of the three core modules of autonomous driving, and nonlinear model predictive control (NMPC) has recently attracted widespread attention in the field of motion control. Vehicle dynamics equations, as a widely used model, have a significant impact on the solution efficiency of NMPC due to their stiffness. This paper first theoretically analyzes the limitations on the discretized time step caused by the stiffness of the vehicle dynamics model equations when using existing common numerical methods to solve NMPC, thereby revealing the reasons for the low computational efficiency of NMPC. Then, an A-stable controller based on the finite element orthogonal collocation method is proposed, which greatly expands the stable domain range of the numerical solution process of NMPC, thus achieving the purpose of relaxing the discretized time step restrictions and improving the real-time performance of NMPC. Finally, through CarSim 8.0/Simulink 2021a co-simulation, it is verified that the vehicle dynamics model equations are with great stiffness when the vehicle speed is low, and the proposed controller can enhance the real-time performance of NMPC. As the vehicle speed increases, the stiffness of the vehicle dynamics model equation decreases. In addition to the superior capability in addressing the integration stability issues arising from the stiffness nature of the vehicle dynamics equations, the proposed NMPC controller also demonstrates higher accuracy across a broad range of vehicle speeds.

Semantic Segmentation Model-Based Boundary Line Recognition Method for Wheat Harvesting

The wheat harvesting boundary line is vital reference information for the path tracking of an autonomously driving combine harvester. However, unfavorable factors, such as a complex light environment, tree shade, weeds, and wheat stubble color interference in the field, make it challenging to identify the wheat harvest boundary line accurately and quickly. Therefore, this paper proposes a harvest boundary line recognition model for wheat harvesting based on the MV3_DeepLabV3+ network framework, which can quickly and accurately complete the identification in complex environments. The model uses the lightweight MobileNetV3_Large as the backbone network and the LeakyReLU activation function to avoid the neural death problem. Depth-separable convolution is introduced into Atrous Spatial Pyramid Pooling (ASPP) to reduce the complexity of network parameters. The cubic B-spline curve-fitting method extracts the wheat harvesting boundary line. A prototype harvester for wheat harvesting boundary recognition was built, and field tests were conducted. The test results show that the wheat harvest boundary line recognition model proposed in this paper achieves a segmentation accuracy of 98.04% for unharvested wheat regions in complex environments, with an IoU of 95.02%. When the combine harvester travels at 0~1.5 m/s, the normal speed for operation, the average processing time and pixel error for a single image are 0.15 s and 7.3 pixels, respectively. This method could achieve high recognition accuracy and fast recognition speed. This paper provides a practical reference for the autonomous harvesting operation of a combine harvester.

Model predictive control for autonomous vehicle path tracking through optimized kinematics

Tracking performance and stability of path tracking is crucial for unmanned vehicles' navigational tasks. Researches on vehicle path tracking controllers primarily rely on dynamic models. In contrast, there are less designs and researches that focus on path tracking controller based on kinematic model. This scarcity may stem from the perceived inadequacy in the accuracy of vehicle kinematic models. This research introduces a novel method for modifying the traditional vehicle kinematic model by incorporating a front wheel steering angle modification function to enhance tracking performance of path tracking controllers based on kinematic models. In terms of control strategy selection, the study opted for nonlinear model predictive control with terminal cost. A controller which is founded on the modified model was used on a simulated vehicle on CarSim-Simulink platform to assess the tracking performance. The simulation was designed with a double-shift line reference trajectory and the initial speeds of the simulated vehicle are 5 m/s and 10 m/s, respectively. The results of the simulations indicate that employing a controller based on the modified model could reduce the peak tracking error by 76.45 % and 43.06 %, and the root mean square of the tracking error was reduced by 73.29 % and 36.06 %, respectively.

Interactive strategy of shared control vehicle and automated vehicles based on adaptive non-cooperative game

Considering the complex traffic environment in the future, an interactive strategy between human-machine shared control vehicle (HSCV) and automated vehicles (AVs) based on the adaptive non-cooperative game (NCG) theory is proposed to ensure the safety of vehicles interaction control involving drivers with different characteristics. In HSCV, first, considering the environmental risk potential field (ERPF) and the human-machine conflict coefficient, an adaptive weight distribution method is designed to realize the weight distribution between a driver and an automation system. Subsequently, the steering angle command imposed by a driver is introduced into the game solving process between HSCV and AVs, enabling adaptive dynamic game through weight adjustment. During V2V interaction, based on NCG and distributed model predictive control, a motion planning controller (MOPC) is designed to integrate the optimal solution problem of path planning and tracking control and solve the interaction problem with constraints. Two typical interactive scenarios are used to verify the feasibility of the strategy. The results demonstrate that the interaction strategy considering the different drivers’ operating commands not only realizes the interaction between a driver and an ego vehicle but also realizes the interaction between an ego vehicle and nearby vehicles to ensure the safety of vehicles.

A Finite-Time Path Tracking Control Scheme for Unmanned Vehicles Based on Multidimensional Taylor Network and Adaptive Filtering

Aiming at the path tracking control problem of unmanned vehicles under the conditions of model uncertainty and measurement noise, a finite-time path tracking control scheme based on multidimensional Taylor network (MTN) is proposed. The MTN model is used to characterize the uncertainty of the unmanned vehicle model, and the improved back propagation (BP) algorithm is used as its learning algorithm; an adaptive MTN filter is designed to filter out the measurement noise, MTN is used as a filter, and the least mean square (LMS) algorithm is used as its learning algorithm; an MTN finite-time controller is designed to perform precise path tracking control on the unmanned vehicle, which can quickly and accurately track the reference path; according to the finite-time control theory, the convergence proof verifies the effectiveness of the proposed method through unmanned vehicle simulation experiments.

A fault-tolerant algorithm of AUV formation based on reconfiguration map

Aiming at the fault occurrence of AUV formation members during sailing, a fault tolerance algorithm of AUV formation based on reconfiguration was proposed. Firstly, the cost matrix is designed based on the reconfiguration and Hungarian algorithm to solve the problem of assigning target points under the fault condition. Then, based on Bezier curves, the dynamic constraints of AUV are designed parametrically. The nonlinear optimization problem satisfies the constraints through the characteristics of spline curves, and the adaptive particle swarm optimization algorithm is used to solve the tracking trajectory. The comparison and simulation experiment of a particle swarm algorithm based on a reconfiguration map (RMPSO) was carried out. The simulation results show that under the same planned path, the total tracking path of the following AUV is shorter, the turning radius is smaller, and the heading Angle is more stable. Finally, field tests are carried out in Qiandao Lake to verify the effectiveness of the algorithm for formation faults.

Phase-field approach for precise fracture tracking in anisotropic rocks: Integrating orthotropy-based energy decomposition and two-fold symmetric fracture toughness

Rock formations are known to exhibit material anisotropy, both in terms of elastic and fracture properties. This means that the fracture path in such formations is not a priori known but rather a complex unknown that requires robust numerical techniques to predict accurately. In this context, the phase-field model is considered particularly effective, provided that certain physical considerations are carefully adjusted to align with the physics of the problem. While addressing elastic anisotropy is well-established, the tension–compression asymmetry necessary to inhibit crack interpenetration in phase-field fracture models needs to account for the specific material anisotropy. Additionally, to accurately capture crack propagation, it is critical to simultaneously account for orientation-dependent fracture toughness in such materials. To address this, the present study employs an anisotropic phase-field model that integrates the generalized spectral decomposition proposed in the literature for orthotropic materials with a two-fold symmetric fracture toughness, to predict the fracture trajectories in rock-type samples under fixed mixed-mode loading ratios. While each of the two aspects has primarily been applied to model orthotropic plates under simple tensile and shearing loading conditions in the literature, here we study their applicability in complex loading scenarios. To this end, the experimental data from notched semi-circular specimens of Grimsel Granite undergoing complex mixed-mode loading obtained in our previous work is considered. We focus on two given mode-mixity ratios and perform numerical studies. Our results emphasize the importance of considering this generalized decomposition for phase-field modeling of fracturing in rock-type materials, particularly under loading conditions where the crack might otherwise be unrealistically driven into the compressive region. Although certain features are well captured by considering anisotropy in elasticity alone, our findings demonstrate that incorporating a two-fold symmetric fracture toughness proves to be advantageous for more precise tracking of the fracture path.

Coordinated strategy for path tracking and dynamic stability considering extreme obstacle avoidance in distributed drive electric vehicles

PurposeThis research aims to investigate the trajectory tracking problem for a four-wheel independent drive autonomous vehicle (4WID) and propose an integrated, coordinated control strategy to address the mutual interference between trajectory tracking and stability control in extreme cases.Design/methodology/approachThe authors establish an adaptive preview model that modifies the preview distance based on vehicle speed. They utilize a three-degrees-of-freedom vehicle model and employ model predictive control to calculate the necessary front wheel angle for trajectory tracking. In terms of longitudinal control, a longitudinal coordinated control mechanism is established to achieve the two conflicting objectives of trajectory tracking accuracy and dynamic stability through early deceleration. A stability controller based on sliding mode control (SMC) is designed, considering tire constraints and tracking the optimal yaw angle and sideslip angle. Furthermore, a lateral coordinated control strategy is developed, considering the weight coefficient of stability control, and the yaw moment is calculated and distributed based on the vehicle torque requirements.FindingsThe proposed integrated, coordinated control strategy successfully addresses the mutual interference between trajectory tracking and stability control in extreme cases for the 4WID vehicle. The strategy achieves trajectory tracking accuracy, dynamic stability and reduced energy consumption while taking into account tire constraints.Originality/valueWe have proposed a cooperative control strategy for the trajectory tracking problem of autonomous driving vehicles. This strategy is different from previous methods in that we have taken into account the integrated dynamic control in both longitudinal and lateral directions, balancing the conflicting control requirements and reducing energy consumption, improving trajectory tracking accuracy and vehicle dynamic stability. We have verified the feasibility of this strategy through joint simulation under different driving conditions.