Lateral Error Research Articles

Holographic multiplexing metasurface with twisted diffractive neural network

As the cornerstone of AI generated content, data drives human-machine interaction and is essential for developing sophisticated deep learning agents. Nevertheless, the associated data storage poses a formidable challenge from conventional energy-intensive planar storage, high maintenance cost, and the susceptibility to electromagnetic interference. In this work, we introduce the concept of metasurface disk, meta-disk, to expand the capacity limits of optical holographic storage by leveraging uncorrelated structural twist. We develop a physical twisted neural network to describe the optical behavior of the meta-disk and conduct a comprehensive lateral error analysis, where the meta-disk stores large volumes of information through internal structural multiplexing. Two-layer 640 µm x 640 µm meta-disk is sufficient to store over hundreds of high-fidelity images with SSIM of 0.8. By harnessing advanced three-dimensional (3D) printing technology, optical holographic storage is experimentally demonstrated with Pancharatnam-Berry metasurfaces. Our technology provides essential backing for the next generation of optical storage, display, encryption, and multifunctional optical analog computing.

Integrated automatic parking path planning and trajectory tracking optimization method

Current automatic parking systems often separate path planning and trajectory tracking, increasing complexity and failing to meet the parking needs of autonomous cars. Consequently, this study presents an approach based on Multi-stage Nonlinear Model Predictive Control (MSNMPC) for integrated autonomous parking path planning and trajectory tracking optimization. The method represents the evolution of uncertainty parameters over time through a scenario tree, and the MSNMPC controller with a predictive horizon P defines P + 1 phases, each with specific cost and constraint functions that depend only on the vehicle state and control inputs of that phase to satisfy the constraints of all phases of the parking process. In addition, the method integrates path planning and tracking control into one optimization problem, which is solved online to achieve integrated parking control. Simulation confirms that, in comparison to MPC with RRT* hierarchical control, the integrated parking scheme of MSNMPC has less lateral error and offers superior flexibility and tracking performance. To verify the generality of the scheme, it was validated in the diagonal parking scenario and the vertical parking scenario, respectively. The results show that, compared to the control experiments, the parking elapsed time has been reduced by 10.76% and 9.02%, respectively, enhancing parking efficiency. In addition, the parking error has decreased by 30.77% and 38.46%, respectively, thus improving parking accuracy. Moreover, the minimum safe distance in the control scheme for addressing uncertainty factors is 0.7 m greater than that of the control experiments, meeting the driving requirements for driverless vehicles in parking scenarios.

Lateral-Stability-Oriented Path-Tracking Control Design for Four-Wheel Independent Drive Autonomous Vehicles with Tire Dynamic Characteristics under Extreme Conditions

This paper proposes a lateral-stability-oriented path-tracking controller for four-wheel independent drive (4WID) autonomous vehicles. The proposed controller aims to maintain vehicle stability under extreme conditions while minimizing lateral deviation. Firstly, a tiered control framework comprising upper-level and lower-level controllers is introduced. The upper-level controller is a lateral stability path-tracking controller that incorporates tire dynamic characteristics, developed using model predictive control (MPC) theory. This controller dynamically updates the tire lateral force constraints in real time to account for variations in tire dynamics under extreme conditions. Additionally, it enhances lateral stability and reduces path-tracking errors by applying additional yaw torque based on minimum tire utilization. The lower-level controllers execute the required steering angles and yaw moments through the appropriate component equipment and torque distribution. The joint simulation results from CarSim and MATLAB/Simulink show that, compared to the traditional MPC controller with unstable sideslip, this controller can maintain vehicle lateral stability under extreme conditions. Compared to the MPC controller, which only considers lateral force constraints, this controller can significantly reduce lateral tracking errors, with an average yaw rate reduction of 31.62% and an average sideslip angle reduction of 40.21%.

Electronic brake system-based hierarchical motion control of commercial vehicle for autonomous obstacle avoidance

As a high-level autonomous driving technology, efficient and safe automatic obstacle avoidance on highway is one of the critical and ongoing topics that requires in-depth research for commercial vehicles. Electronic control air pressure brake system, owing to its fast response and active braking ability, is an effective active-chassis technology to function path tracking and stability control in such condition. Yaw motion stability control problem of autonomous driving commercial vehicle based on active braking control with electronic air brake system for automatic obstacle avoidance is investigated. First, a hierarchical yaw motion dynamics control architecture is introduced after vehicle and brake system modeling. The quintic polynomial curve-based trajectory planning method and a Model Predictive Control based trajectory tracking control strategy are formulated. Second, to evade the possible stability losing issue in this circumstance, Cubature Kalman Filter (CKF) is utilized to estimate the vehicle motion states, and a fuzzy PID control-based differential brake stability control strategy is designed for the electronic brake system composed of front-and-rear two sets of dual-channel pressure regulator and ABS solenoid valve. Finally, the proposed hierarchical yaw stability control strategy for a commercial vehicle in typical obstacle avoidance conditions is comparatively verified based on the joint simulation tools. After the yaw stability control, the peak value of the lateral displacement error of trajectory tracking can be reduced by 44.7%. The yaw stability control strategy based on fuzzy PID control can reduce the yaw rate by 46%–57% and the sideslip angle by 60%–73% under different conditions. The results show that the proposed control strategy can effectively improve the yaw stability of the vehicle while avoiding obstacles at high speed.

Virtual source total focusing method for surface defects using leaky Rayleigh waves

Leaky Rayleigh waves are sensitive to surface defects and beneficial for automated detection due to their non-contact characteristics. However, the amplitude of the leaky Rayleigh waves is low due to the attenuation of waveform conversion and acoustic waves propagation, which limits the imaging quality for long-distance detection. This study introduces a novel method combining leaky Rayleigh waves detection with virtual source total focusing method. The virtual source (VS) technology enhances the emission energy of leaky Rayleigh waves. Then, the total focusing method (TFM) is applied to acquire high-accuracy images of defects. To reduce noise and artifacts, a weighting function based on the coherence factor (CF) is developed to weight the TFM superimposed signals, thereby achieving high-quality image reconstruction. Experimental results show that compared with the conventional TFM method, the proposed method can effectively improve the amplitude of imaging signals while reducing system noise and imaging artifacts. The lateral accuracy of defects is improved, with the average lateral error of defect size being 0.178 mm. The signal-to-noise ratio (SNR) of ultrasound images is increased by 27.59 dB, and the array performance index (API) of ultrasound images is decreased by 33.78 %. The proposed method provides a new and effective approach for quantitatively assessing the surface defects of metal components using leaky Rayleigh waves.

Intelligent vehicle lateral control strategy research based on feedforward + predictive LQR algorithm with GA optimisation and PID compensation

Targeting the lateral motion control problem in the intelligent vehicle autopilot structural system, this paper proposes a feedforward + predictive LQR algorithm for lateral motion control based on Genetic Algorithm (GA) parameter optimisation and PID steering angle compensation. Firstly, based on the vehicle dynamics tracking error model, the intelligent vehicle LQR lateral motion controller as well as the feedforward controller are designed, and upon which the predictive controller is added to eliminate the system lag.Subsequently, exploiting the advantage that the PID algorithm is not model-based, a PID steering angle compensation controller that can directly control and correct the lateral error is designed. Second, a LQR controller based on path tracking deviation is designed by using the parameter rectification method of genetic algorithm (GA), which optimizes the control parameters of the lateral motion controller and improves the adaptivity of the control accuracy. Finally, Based on the Carsim-Simulink co-simulation platform, the simulation validation and analysis of double lane change (DLC) test and circular condition test (CCT) are carried out, and the results indicate that compared with the other two LQR controllers, the optimised controllers improved more than 50% in lateral error and heading error control, and the vehicle sideslip angle and vehicle yaw rate are in the range of −0.05° to 0.05° and − 0.15 rad/s to 0.10 rad/s, and it showed improved performance in tracking accuracy and satisfied vehicle stability constrains.

Model predictive control with real-time variable weight for civil aircraft towing taxi-out control systems

Unlike the traditional method of taxying, where civil aircraft reach the runway by relying on their engines, the new mode of towing taxi-out may become preferred because of its lower energy consumption, lower emissions, and higher efficiency. To improve the tracking accuracy and lateral stability of the towing system, this study used a two-level time-varying weight control method (RMPC) based on model predictive control (MPC) and fuzzy control. The tractor speed and front wheel angle were set as the control variables in the MPC controller, and the real-time lateral displacement error and yaw angle error of the tractor were set as the fuzzy control inputs. The influence of the weight matrix on the accuracy and stability of path tracking was coordinated by online optimization of the MPC objective function weight. The simulations of multiple working conditions were performed using TruckSim software in Simulink, which showed that the proposed control method can limit the lateral displacement error of the tractor and aircraft within 0.4 m, which can be reduced by 70.83% and 77.4% compared with the single MPC, respectively. Additionally, the maximum yaw angle errors of the tractor and aircraft are reduced by 76.11% and 51.31% compared with the single MPC, respectively. Furthermore, the yaw angle error of tractors can be limited to 4° and that of aircraft can be limited to 6.5°, which is an improvement of the lateral stability and driving safety for the civil aircraft towing system. The new controller may provide technical insights and support for the practical development and safe application of the towing taxi-out mode.

MPC-TD3 Trajectory Tracking Control for Electrically Driven Unmanned Tracked Vehicles

To address the trajectory tracking issue of unmanned tracked vehicles, the majority of studies employ the Model Predictive Control (MPC). The MPC imposes high demands on model accuracy. Due to factors such as environmental interference, actuator constraints, and the nonlinearity of vehicles under high-speed conditions, dynamic and kinematic models fail to accurately delineate the motion process of tracked vehicles. Aiming at the problem of insufficient trajectory tracking precision of unmanned tracked vehicles, a trajectory tracking controller jointly controlled by the Twin Delayed Deep Deterministic policy gradient (TD3) algorithm and the MPC algorithm is developed. During offline training, the agent acquires the discrepancies between the model and the environment under various working conditions and optimizes its own network; during online reasoning, the agent adaptively compensates the output of the MPC based on the vehicle state. The experimental results indicate that, compared with the pure MPC algorithm, the MPC algorithm compensated based on the TD3 algorithm reduces the lateral errors by 41.67% and 22.55%, respectively, in circular and double-lane-change trajectory conditions.

Two-stage spatiotemporal cooperative reentry guidance strategy using transformer and improved beluga whale optimization

This research addresses the challenge of insufficient control margin caused by the coupling of multiple constraints in the cooperative precise reentry guidance of hypersonic vehicles. Drawing inspiration from the concept of spatiotemporal decoupling control, a rapid guidance strategy is developed to ensure precise handling of all constraints, including attack time, attack angle, and trajectory constraints. Initially, during the early phase of gliding flight, the adjustment of the heading angle is conceptualized as a single variable root-solving problem, in relation to the entrance width of the lateral azimuth error corridor. Subsequently, a lateral azimuth error corridor with adaptively narrowing entrance width, coupled with a Transformer network-based bank angle predictor, is incorporated to achieve precise fine-tuning of the heading angle under the soft constraint of velocity. In the later phase of gliding flight, the design of a cooperative guidance law under complex multiple constraints is transformed into a nonlinear rapid optimization problem of control commands. An enhanced beluga whale optimization suited to this guidance task is proposed. Finally, numerical simulations are carried out to validate the effectiveness of the proposed strategy under both nominal and uncertain conditions.

Vision-based trajectory generation and tracking algorithm for maneuvering of a paddy field robot

In this study, we propose a novel visual-based autonomous trajectory-tracking control method for steering a wheeled robot following the lines of crop row in paddy field. A rice crop rows detection method, based on the region growth sequential clustering − random sample consensus (RANSAC) algorithm, is developed to generate trajectory. Concurrently, a dynamics predictive controller is employed to compute the command for the desired steering angle. The controller leverages a model that incorporates slip dynamics and operates on a low power consumption industrial computer. Experimental results show that the developed algorithm can successfully obtain the correct trajectory in more than 96.25 % of the cases, with the angle error consistently below 3°. Furthermore, the single-image processing time is notably swift at 13.98 ms, underscoring the commendable adaptability and real-time performance of the proposed methodology. During movement in the paddy field, the robot exhibits maximum lateral deviations of 4.55 cm, 5.65 cm, and 6.41 cm at speeds of 0.3 m/s, 0.6 m/s, and 0.9 m/s, respectively, accompanied by corresponding heading angle errors of 4.59°, 5.63°, and 7.39°. Notably, while adeptly tracking rice crop rows at all three speeds, the robot consistently maintains a maximum lateral error below one-fourth of the inter-row spacing of rice planting. This study assumes significance in enhancing the stability of ground-traversing agricultural robots, serving as a valuable reference for advancing the research and development of intelligent and efficient agricultural robotic systems.

基于H无穷状态反馈控制的插秧机曲线路径跟踪控制器研究

The accuracy of curved path-tracking for headland turning of transplanters is crucial to maintaining the row spacing precision required for rice planting. To address this issue, a method based on H-infinity state feedback control is proposed. In this method, the requirement of robustness is transformed into linear matrix inequalities (LMIs) to optimize the gain coefficients of the control law. The simulation test show that this method outperforms the Linear Quadratic Regulator (LQR) when facing uncertain parameters (longitudinal speed and cornering stiffness) and path curvature disturbance. In addition, the field test results show that when the transplanter tracks a 1/4 circular arc path with a radius of 2 meters, the mean value of the absolute lateral error and the absolute heading angle error using this controller are 0.029 m and 3.69°, respectively. The maximum absolute lateral error is 0.072 m, and 64% of the absolute lateral error are less than 0.04 m, meeting practical requirements. Compared with the LQR controller with feed forward control, the mean value of the absolute lateral error is reduced by 36%. This method meets the accuracy and robustness requirements for unmanned rice transplanter turning at the headland.

Effectiveness of Iterative Learning Control for Vision-Based Tracking in Repeated Tasks Under Varying Lighting Conditions

Among available techniques for lateral tracking in autonomous driving, none possesses the capability to learn from past behaviors and progressively reduce lateral errors. In contrast, our proposed iterative learning control (ILC) scheme significantly enhances tracking performance in vision-based classical control, particularly in challenging environmental conditions. Our vision-based control system incorporates real-time semantic segmentation using the ENet model for unconstructed road area extraction. Linear regression estimates steering adjustments, while a visual PID controller maintains the vehicle’s position at the road’s centerline. This control system’s performance varies with lighting conditions, notably in dense shade, where the vehicle tends to deviate from the desired path. To assess ILC’s potential in error reduction over successive trials, we examined various ILC structures and compared them with a pure PID controller. Despite challenges in directly comparing PID and ILC designs due to changing lighting conditions during experiments, ILC consistently reduced tracking errors and improved path alignment with each iteration. Notably, the degree of error reduction became more pronounced with a greater number of learning gains in the ILC design. Our experimental results underscore the overall effectiveness of ILC in tracking the desired path in autonomous driving scenarios, particularly in varying environmental conditions.

Trajectory-Tracking Control of Unmanned Vehicles Based on Adaptive Variable Parameter MPC

Aiming at the problems of the poor trajectory-tracking performance and low control accuracy of unmanned vehicles under complex working conditions, we first estimate the lateral force of tires using the square root cubature Kalman filter (SRCKF) in order to correct the lateral stiffness of the tires online, which reduces the model bias caused by constant lateral stiffness, and then adopt a Gaussian function-based adaptive time-domain model predictive control method to improve the trajectory-tracking control accuracy of unmanned vehicles under complex working conditions. Finally, the proposed control algorithm is validated via Carsim and MATLAB/Simulink joint simulation. The results show that compared with the classical model predictive control (MPC) algorithm, the proposed control algorithm reduces the average lateral tracking error by 73.07% and the peak beta and the peak yaw rate by 50.89% and 47.51%, respectively, so that the unmanned vehicle is able to maintain good tracking performance and control accuracy.

Investigating the accuracy of machine vision and augmented reality in percutaneous computed tomography-guided interventions: A phantom study.

This study aimed to evaluate the accuracy of percutaneous computed tomography (CT)-guided puncture based on machine vision and augmented reality in a phantom. The surgical space coordinate system was established, and accurate registration was ensured using the hierarchical optimization framework. Machine vision tracking and augmented reality display technologies were used for puncture navigation. CT was performed on a phantom, and puncture paths with three different lengths were planned from the surface of the phantom to the metal ball. Puncture accuracy was evaluated by measuring the target positioning error (TPE), lateral error (LE), angular error (AE), and first success rate (FSR) based on the obtained CT images. A highly qualified attending interventional physician performed a total of 30 punctures using puncture navigation. For the short distance (4.5-5.5 cm), the TPE, LE, AE, and FSR were 1.90 ± 0.62 mm, 1.23 ± 0.70 mm, 1.39 ± 0.86°, and 60%, respectively. For the medium distance (9.5-10.5 cm), the TPE, LE, AE, and FSR were 2.35 ± 0.95 mm, 2.00 ± 1.07 mm, 1.20 ± 0.62°, and 40%, respectively. For the long distance (14.5-15.5 cm), the TPE, LE, AE, and FSR were 2.81 ± 1.17 mm, 2.33 ± 1.34 mm, 0.99 ± 0.55°, and 30%, respectively. The augmented reality and machine vision-based CT-guided puncture navigation system allows for precise punctures in a phantom. Further studies are needed to explore its clinical applicability.

A global and local integrated dynamic path planning algorithm for village roads region

In China, the village roads are characterized by numerous intersections and significant differences in road widths, creating a complex maze-like terrain. This undoubtedly increases the difficulty of path planning for autonomous vehicles. This study proposes an improved bidirectional RRT* algorithm that utilizes the advantages of the rapid random search of the RRT* algorithm. It introduces virtual points to address the irregularity of road networks and creates enveloping circles at expanding nodes to enhance path reachability, thus obtaining the optimal global planning path. To enhance path tracking comfort, a fifth-order B-spline curve is utilized to smooth the global path, and local path planning is performed using Quadratic Programming (QP). The proposed combined global and local path planning method was evaluated through Co-simulation experiments basing on the Matlab/CarSim/PreScan platform. Simulation results demonstrate that the enhanced RRT* algorithm outperforms the traditional RRT* algorithm in the same scenario. Specifically, the improved algorithm reduces the running time by 29.56%, increases node utilization by approximately 15.33%, and decreases the planned path length by 2.8%. Additionally, the vehicle’s final lateral tracking error was controlled within 0–0.04 m, and the longitudinal tracking error was controlled within 0–0.1 m, fully demonstrating the vehicle’s excellent path-tracking performance. The study’s innovative ideas will offer methodological support for researching path planning for autonomous vehicles in specific scenarios.

A Fusion Positioning System Based on Camera and LiDAR for Unmanned Rollers in Tunnel Construction.

As an important vehicle in road construction, the unmanned roller is rapidly advancing in its autonomous compaction capabilities. To overcome the challenges of GNSS positioning failure during tunnel construction and diminished visual positioning accuracy under different illumination levels, we propose a feature-layer fusion positioning system based on a camera and LiDAR. This system integrates loop closure detection and LiDAR odometry into the visual odometry framework. Furthermore, recognizing the prevalence of similar scenes in tunnels, we innovatively combine loop closure detection with the compaction process of rollers in fixed areas, proposing a selection method for loop closure candidate frames based on the compaction process. Through on-site experiments, it is shown that this method not only enhances the accuracy of loop closure detection in similar environments but also reduces the runtime. Compared with visual systems, in static positioning tests, the longitudinal and lateral accuracy of the fusion system are improved by 12 mm and 11 mm, respectively. In straight-line compaction tests under different illumination levels, the average lateral error increases by 34.1% and 32.8%, respectively. In lane-changing compaction tests, this system enhances the positioning accuracy by 33% in dim environments, demonstrating the superior positioning accuracy of the fusion positioning system amid illumination changes in tunnels.

Estimation of the lateral mis-registrations of the GRAVITY+ adaptive optics system

Context. The GRAVITY+ upgrade implies a complete renewal of its adaptive optics (AO) systems. Its complex design, featuring moving components between the deformable mirrors and the wavefront sensors, requires the monitoring and auto-calibrating of the lateral mis-registrations of the system while in operation. Aims. For preset and target acquisition, large lateral registration errors must be assessed in open loop to bring the system to a state where the AO loop closes. In closed loop, these errors must be monitored and corrected, without impacting the science. Methods. With respect to the first requirement, our method is perturbative, with two-dimensional modes intentionally applied to the system and correlated to a reference interaction matrix. For the second requirement, we applied a non-perturbative approach that searches for specific patterns in temporal correlations in the closed loop telemetry. This signal is produced by the noise propagation through the AO loop. Results. Our methods were validated through simulations and on the GRAVITY+ development bench. The first method robustly estimates the lateral mis-registrations, in a single fit and with a sub-subaperture resolution while in an open loop. The second method is not absolute, but it does successfully bring the system towards a negligible mis-registration error, with a limited turbulence bias. Both methods proved to robustly work on a system still under development and not fully characterised. Conclusions. Tested with Shack-Hartmann wavefront sensors, the proposed methods are versatile and easily adaptable to other AO instruments, such as the pyramid, which stands as a baseline for all future AO systems. The non-perturbative method, not relying on an interaction matrix model and being sparse in the Fourier domain, is particularly suitable to the next generation of AO systems for extremely large telescopes that will present an unprecedented level of complexity and numbers of actuators.

Global Navigation Satellite System/Inertial Measurement Unit/Camera/HD Map Integrated Localization for Autonomous Vehicles in Challenging Urban Tunnel Scenarios

Lane-level localization is critical for autonomous vehicles (AVs). However, complex urban scenarios, particularly tunnels, pose significant challenges to AVs’ localization systems. In this paper, we propose a fusion localization method that integrates multiple mass-production sensors, including Global Navigation Satellite Systems (GNSSs), Inertial Measurement Units (IMUs), cameras, and high-definition (HD) maps. Firstly, we use a novel electronic horizon module to assess GNSS integrity and concurrently load the HD map data surrounding the AVs. This map data are then transformed into a visual space to match the corresponding lane lines captured by the on-board camera using an improved BiSeNet. Consequently, the matched HD map data are used to correct our localization algorithm, which is driven by an extended Kalman filter that integrates multiple sources of information, encompassing a GNSS, IMU, speedometer, camera, and HD maps. Our system is designed with redundancy to handle challenging city tunnel scenarios. To evaluate the proposed system, real-world experiments were conducted on a 36-kilometer city route that includes nine consecutive tunnels, totaling near 13 km and accounting for 35% of the entire route. The experimental results reveal that 99% of lateral localization errors are less than 0.29 m, and 90% of longitudinal localization errors are less than 3.25 m, ensuring reliable lane-level localization for AVs in challenging urban tunnel scenarios.

A prior-knowledge-based time series model for heat demand prediction of district heating systems

Time series prediction methods are effective for predicting energy demands of district heating systems. Due to the thermal inertia of systems, historical heat load is usually applied as the most crucial input for prediction. However, it results in lateral errors (phase lags) between actual and predicted heat demand. To address this issue, a hybrid time series model is proposed based on autoregressive integrated moving average model and resistance–capacitance model. To reduce the lateral errors, estimated current and future heat demands are introduced as exogenous inputs of the autoregressive integrated moving average model, and they perform as prior knowledge. To generate estimated heat demand, a piecewise resistance–capacitance model is proposed, which considers various climatic and operating conditions. Lateral error of the hybrid model is decreased by 7.1% compared with conventional autoregressive integrated moving average model. Moreover, the hybrid model retains good post-hoc interpretability, which proves that exogenous inputs can effectively reduce lateral errors.

Model and Parameter Adaptive MPC Path Tracking Control Study of Rear-Wheel-Steering Agricultural Machinery

To further enhance the precision and the adaptability of path tracking control, and considering that most of the research is focused on front-wheel steering, an adaptive parametric model predictive control (MPC) was proposed for rear-wheel-steering agricultural machinery. Firstly, the kinematic and dynamic models of rear-wheel-steering agricultural machinery were established. Secondly, the influence laws of curvature and velocity on the prediction horizon Np, control horizon Nc, and preview value Npre were obtained by simulating and analyzing the factors influencing the MPC tracking effect. The results revealed that raising Npre can improve curve tracking performance. Np was correlated negatively with the curvature change, whereas Nc and Npre were positively connected. Np, Nc, and Npre were correlated positively with the velocity change. Then, the parameters for self-adaptation of Np, Nc, and Npre were accomplished via fuzzy control (FC), and particle swarm optimization (PSO) was utilized to optimize the three parameters to determine the optimal parameter combination. Finally, simulation and comparative analysis were conducted to assess the tracking effects of the manual tuning MPC, the FC_MPC, and the PSO_MPC under U-shaped and complex curve paths. The results indicated that there was no significant difference and all three methods achieved better tracking effects under no disturbance, with the mean absolute value of lateral error ≤0.18 cm, standard deviation ≤0.37 cm, maximum deviation of U-shaped path <2.38 cm, and maximum deviation of complex curve path <3.15 cm. The mean absolute value of heading error was ≤0.0096 rad, the standard deviation was ≤0.0091 rad, and the maximum deviation was <0.0325 rad, indicating that manual tuning can find optimal parameters, but with high uncertainty and low efficiency. However, FC_MPC and PSO_MPC have better adaptability and tracking performance compared to the manual tuning MPC with fixed horizons under variable-speed disturbance and are more able to meet the actual needs of agricultural machinery operations.