Trajectory Tracking Method Research Articles

Research on Lie Group Dynamics Modeling and Trajectory-Tracking Optimal Control of Intelligent Ground Vehicle

Abstract Aiming at the multi-objective integrated coordination problem of trajectory tracking control accuracy and vehicle stability, a Lie-group-based dynamics modeling and trajectory-tracking optimal control method of intelligent ground vehicle is proposed in this paper. Based on the theory of Lie group and Lie algebra, the kinematic relationship of intelligent ground vehicle was established, and the integral variational dynamic equation expression was established using the variational method and Lagrange principle. A vehicle performance index function that balances energy optimization and efficiency optimization was established by combining the two-degree-of-freedom dynamic equation and stability constraints of intelligent ground vehicle. On this basis, an optimal control method for trajectory tracking of intelligent ground vehicle is proposed based on Legendre interpolation polynomial discretization method and Gauss pseudospectral method. The comparative results show that the proposed optimal control method can balance vehicle motion control accuracy, real-time performance, and optimization solution efficiency, thereby ensuring the lateral stability control effect of vehicle while achieving trajectory tracking accuracy.

Robust super-twisting-based disturbance observer for autonomous underwater vehicles: Design, stability analysis, and real-time experiments

This paper proposes a new observation-based proportional–derivative control method for robust trajectory tracking of autonomous underwater vehicles (AUVs). The proposed control scheme is designed based on a new observation-based nonlinear model that captures the dynamics and uncertainties of the AUV’s behavior. The proposed control method is formulated in such a way that it can handle system nonlinearities and uncertainties, making it robust to external disturbances and model uncertainties. The effectiveness of the proposed control method is demonstrated through extensive real-time experiments in a real-world AUV trajectory tracking scenario. The obtained results show that the proposed control method outperforms other control methods in the literature regarding trajectory tracking accuracy, robustness, and disturbance rejection. Overall, the proposed observation-based proportional–derivative control method can significantly improve the trajectory tracking performance of AUVs in real-world applications.

Line spectrum tracking method in transformed signal space for underwater moving targets in low signal-to-noise ratio environment

Line spectrum tracking is an essential signal-processing method for underwater passive detection. However, its performance is often seriously degraded due to signal fluctuation, especially in low signal-to-noise ratio scenarios. In this paper, based on signal space transformation and hidden Markov model, a signal trajectory tracking method is proposed for underwater moving target detection and parameter estimation. With this method, tracking the varying line spectrum trajectory in three-dimensional frequency-azimuth-time signal space is constrained onto a two-dimensional plane in the transformed signal space. Not only is the computation complexity reduced, but the ability to track weak line spectrums and estimate target parameters is improved. The performance of this method is verified with numerical simulations and experimental data processing.

Research on the trajectory tracking method of aircraft towing systems based on nonlinear control

Abstract In this paper, for the towing problem of wheeled aircraft, an automatic control method is proposed based on the nonlinear control theory, which realizes the trajectory tracking of the aircraft by controlling the velocity of the towing point of the aircraft, so as to realize the aircraft’s outbound and inbound operations. Firstly, based on the nonholonomic constraint theory, the mathematical model of the aircraft towing system is established, and the kinematic relationship between the aircraft towing point and the aircraft is obtained. Then, a controller is designed based on the nonlinear control theory, and the stability analysis is carried out using the Lyapunov method to realize the trajectory tracking of the aircraft traction system. Finally, the effectiveness and accuracy of the control method are verified by the combination of MATLAB simulation analysis and scaled-down model experiment. The results show that the proposed control method can realize the trajectory control of the aircraft towing system.

Optimized Trajectory Tracking for ROVs Using DNN + ENMPC Strategy

This study introduces an innovative double closed-loop 3D trajectory tracking approach, integrating deep neural networks (DNN) with event-triggered nonlinear model predictive control (ENMPC), specifically designed for remotely operated vehicles (ROVs) under external disturbance conditions. In contrast to single-loop model predictive control, the proposed double closed-loop control system operates in two distinct phases: (1) The outer loop controller uses a DNN controller to replace the LMPC controller, overcoming the uncertainties in the kinematic model while reducing the computational burden. (2) The inner loop velocity controller is designed using a nonlinear model predictive control (NMPC) algorithm with its closed-loop stability proven. A DNN + ENMPC 3D trajectory tracking method is proposed, integrating a velocity threshold-triggered mechanism into the inner-loop NMPC controller to reduce computational iterations while sacrificing only a small amount of tracking control performance. Finally, simulation results indicate that compared with the ENMPC algorithm, NMPC + ENMPC can better track the desired trajectory, reduce thruster oscillations, and further minimize the computational load.

Research on the multitarget 3D trajectory tracking method of Thalassodes immissaria in the thermal infrared region based on YOLOX-GMM and SORT-Pest.

Studying the behavioral responses and movement trajectories of insects under different stimuli is crucial for developing more effective biological control measures. Therefore, accurately obtaining the movement trajectories and behavioral parameters of insects in three-dimensional space is essential. This study used the litchi pest Thalassodes immissaria as the research object. A special binocular vision observation system was designed for nighttime movement. A thermal infrared camera was used for video recording of T. immissaria in a lightless environment. Moreover, a multi-object tracking method based on the YOLOX-GMM and SORT-Pest algorithms was proposed for tracking T. immissaria in thermal infrared images. By obtaining the central coordinates of the two T. immissaria in the video, target matching and 3D trajectory reconstruction in the parallel binocular system were achieved. Error analysis of the T. immissaria detection and tracking model, as well as the 3D reconstruction model, showed that the average accuracy of T. immissaria detection reached 89.6%, tracking accuracy was 96.9%, and the average error of the reconstructed 3D spatial coordinates was 15 mm. These results indicate that the method can accurately obtain the 3D trajectory and motion parameters of T. immissaria. Such data can greatly contribute to researchers' comprehensive understanding of insect behavioral patterns and habits, providing important support for more targeted control strategies.

Uncertainty study of two-phase flow distribution characteristics measurement based on bubble trajectory tracking method

Bubbles undergo complex motions such as nonlinear trajectories in two-phase flow, where the position, velocity magnitude, and direction of bubble centers continuously change as they evolve under the influence of forces. The complexity of bubble trajectory increases the difficulty in measuring the flow field distribution characteristics, which has been understudied in the previous. The bubble trajectory tracking model based on the Monte Carlo method is constructed to study the uncertainty of two-phase flow distribution characteristics measurement by the conductivity probe. The Monte Carlo method is adopted to randomly generate the bubble velocity at the initial moment and the bubble force characteristics are embedded to simulate the three-dimensional motion of the bubble. The influence of various factors on the distribution of effective bubble numbers and velocity relative error at the local point is quantitatively analyzed. It is found that the lateral spacing of the sensors has the greatest influence on the measurement results of small-sized bubbles, the accuracy is greatly reduced when the space is larger than the radius of the measured bubbles. Moreover, the measurement accuracy of the probe for medium-sized bubbles is high, and the effect of bubble lateral velocity and aspect ratio on the effective bubble ratio and velocity relative error is negligible. In addition, the maximum measurement range of the probe at local points is investigated which is found to be 4 mm in the lateral direction and 2 mm in the longitudinal direction. Finally, uniformly distributed bubbles are generated in a 20 mm × 10 mm transverse plane and the distribution of the effective bubble ratio of the probe is found to be consistent at different measurement points, which verifies the reliability of the probe measurement.

Towards Autonomous Operation of UAVs Using Data-Driven Target Tracking and Dynamic, Distributed Path Planning Methods

A hybrid real-time path planning method has been developed that employs data-driven target UAV trajectory tracking methods. It aims to autonomously manage the distributed operation of multiple UAVs in dynamically changing environments. The target tracking methods include a Gaussian mixture model, a long short-term memory network, and extended Kalman filters with pre-specified motion models. Real-time vehicle-to-vehicle communication is assumed through a cloud-based system, enabling virtual, dynamic local networks to facilitate the high demand of vehicles in airspace. The method generates optimal paths by adaptively employing the dynamic A* algorithm and the artificial potential field method, with minimum snap trajectory smoothing to enhance path trackability during real flights. For validation, software-in-the-loop testing is performed in a dynamic environment composed of multiple quadrotors. The results demonstrate the framework’s ability to generate real-time, collision-free flight paths at low computational costs.

Three-dimensional positioning and trajectory tracking of pigeons in large indoor spaces

Animal localization and trajectory tracking are of great value for the study of brain spatial cognition and navigation neural mechanisms. However, traditional optical lens video positioning techniques are limited in their scope due to factors such as camera perspective. For pigeons with excellent spatial cognition and navigation abilities, based on the beacon positioning technology, a three-dimensional (3D) trajectory positioning and tracking method suitable for large indoor spaces was proposed, and the corresponding positioning principle and hardware structure were provided. The results of in vitro and in vivo experiments showed that the system could achieve centimeter-level positioning and trajectory tracking of pigeons in a space of 360 cm × 200 cm × 245 cm. Compared with traditional optical lens video positioning techniques, this system has the advantages of large space, high precision, and high response speed. It not only helps to study the neural mechanisms of pigeon 3D spatial cognition and navigation, but also has high reference value for trajectory tracking of other animals.

Trajectory tracking control of vectored thruster autonomous underwater vehicles based on deep reinforcement learning

ABSTRACT Vectored thruster autonomous underwater vehicles (AUVs) offer superior manoeuvrability compared to traditional fin and rudder systems, especially at low or zero velocities. However, controlling these AUVs becomes challenging in the presence of unpredictable interference forces and external water flow velocities. This paper introduces a novel three-dimensional trajectory tracking method for vectored thruster AUVs using reinforcement learning, enabling the system to learn optimal control policies through environmental interaction. A 5-degree of freedom (5-DOF) model is developed from the kinematics and dynamics equations of the underactuated AUV. An extended state observer (ESO) is used to estimate the differential expansion state based on observed variables. A reinforcement learning-based trajectory tracking strategy is then implemented. Simulation experiments demonstrate the method’s effectiveness in precisely controlling AUVs under varying environmental conditions, achieving exceptional tracking accuracy even in the presence of random interference forces and external water flow velocities.

An Asymmetric Independently Steerable Wheel for Climbing Robots and Its Motion Control Method

Climbing robots, with their expansive workspace and flexible deployment modes, have the potential to revolutionize the manufacturing processes of large and complex components. Given that the surfaces to be machined typically exhibit variable curvature, good surface adaptability, load capacity, and motion accuracy are essential prerequisites for climbing robots in manufacturing tasks. This paper addresses the manufacturing requirements of climbing robots by proposing an asymmetric independently steerable wheel (AISW) for climbing robots, along with the motion control method. Firstly, for the adaptability issue of the locomotion mechanism on curved surfaces under heavy load, an asymmetric independently steerable wheel motion module is proposed, which improves the steering difficulty of the traditional independently steerable wheel (ISW) based on the principle of steering assisted by wheels. Secondly, a kinematic model of the AISW chassis is established and, on this basis, a trajectory tracking method based on feedforward and proportional–integral feedback is proposed. Comparative experimental results on large, curved surface components show that the asymmetric independently steerable wheel has lower steering resistance and higher motion accuracy, significantly enhancing the reachability of climbing robots and facilitating their application in the manufacturing of large and complex components.

Mitigating Singularities in Control of Magnetic Capsule Endoscopes Using a Novel Nested Electromagnetic Coil System

Magnetic actuation systems that utilize external electromagnetic coils present a promising approach for controlling untethered small-scale robots, notably in medical applications. However, these systems frequently experience actuation singularities at which robotic control over the agent is lost or severely diminished. Such singularities may lead to excessively large current or rapid current changes that significantly affect the robots’ stability in specific areas of the workspace. In order to effectively mitigate these actuation singularities, this paper introduces a closed-loop control method using a novel nested electromagnetic coil system, leveraging finite element analysis-based magnetic field data and a novel controller combining a singularity solver and optimal current control method. The electromagnetic system has 12 coils nested in four coil units, each having three concentric coils with different outer radius, surrounding a central workspace. We call the 12-coil system Variable Outer Radius Individually Addressable Coil Stacks (VORIACS). Here, we experimentally evaluate the method for closed-loop trajectory tracking of a soft magnetic capsule endoscope (PillCam™) and a permanent magnet robot inside the VORIACS system at different magnetic field orientations. The results demonstrate that the VORIACS system with a singularity solver reduces root mean square (RMS) position tracking errors of the PillCam™by 46% to 50% and orientation tracking errors by 41% to 42% compared to a standard 4-coil system. Moreover, the system can achieve a notable 60.73% reduction in RMS position error, with sub-millimeter precision control when controlling the permanent magnet robot. We further manipulate the PillCam™for tracking a medical application-inspired complex trajectory, showcasing the system’s potential in precise control of magnetic devices for medical use.

Lyapunov-based model predictive control for trajectory tracking of hovercraft with actuator constraints and external disturbances

In this study, a Lyapunov-based model predictive control (LMPC) method is developed to address the trajectory tracking problem of autonomous hovercrafts subjected to unknown complex disturbances from ocean environments and practical constraints of marine surface vessels, such as actuator increment limitations and saturation. Initially, the novel LMPC algorithm is applied to enhance tracking performance through rolling optimization and online optimization. Subsequently, a nonlinear disturbance observer is designed to estimate external disturbances caused by wind and dynamics uncertainties. Furthermore, to theoretically ensure control stability, contraction constraints are established using the nonlinear backstepping control method. This approach provides the essential conditions for the system's robustness and stability. Finally, the superiority and robustness of the designed LMPC trajectory tracking method are demonstrated through numerical simulations conducted in a marine environment.

Optimal trajectory tracking of uncertain nonlinear continuous-time strict-feedback systems with dynamic constraints

A novel method for optimal trajectory tracking of uncertain nonlinear systems by using adaptive dynamic programming (ADP)-based integral reinforcement learning (IRL) and neural networks (NNs) is proposed. The method utilises an actor-critic framework with optimal backstepping to minimise a discounted value function and uses a single-layer NN identifier for estimating the unknown dynamics. For safety assurance, a time-varying barrier Lyapunov function (TVBLF) is used in the control design to handle the constraints. A novel weight-tuning law by using the control input error, integral Bellman error, and the NN identifier is used for the actor-critic framework. A novel lifelong learning (LL)-based method for critic NN is utilised in an optimal framework by incorporating the Bellman error to mitigate catastrophic forgetting in multitasking scenarios. Stability analysis using Lyapunov stability theory is obtained for the overall closed-loop system. Simulations of leader-follower mobile robot formation control show a 25% reduction in the cost in multitasking scenarios.

An improved convex optimization-based guidance for fuel-optimal powered landing

Convex optimization has great potential for onboard trajectory generation which can eliminate large state deviations and improve landing precision. In practical applications, the convex optimization problem is often infeasible under disturbances. In this paper, we analyze the reason for the infeasibility of the fuel-optimal trajectory optimization problem. The analysis result shows that the thrust saturation degrade the anti-disturbance performance and then lead to infeasibility. Based on this analysis, we improved the anti-disturbance performance of convex optimization-based guidance from two aspects: (1) a maximum-thrust regulation strategy is embedded into the original fuel-optimal problem to avoid thrust saturation; (2) a trajectory tracking method with a disturbance compensator is performed to attenuate disturbance effects and to make the initial state of each optimization cycle close to the existing feasible trajectory. Numerical simulations demonstrate that the proposed method can improve the infeasibility and can realize the high-precision landing under disturbances.

Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking

This article introduces an adaptive fault-tolerant control method for non-repetitive trajectory tracking of linear motor-driven gantry platforms under state constraints. It provides a comprehensive solution to real-world issues involving state constraints and actuator failures in gantry platforms, alleviating the challenges associated with precise modeling. Through the integration of iterative learning and backstepping cooperative design, this method achieves system stability without requiring a priori knowledge of system dynamic models or parameters. Leveraging a barrier composite energy function, the proposed controller can effectively regulate the stability of the controlled system, even when operating under state constraints. Instability issues caused by actuator failures are properly addressed, thereby enhancing controller robustness. The design of a trajectory correction function further extends applicability. Experimental validation on a linear motor-driven gantry platform serves as empirical evidence of the effectiveness of the proposed method.

A coordinated trajectory tracking method with active utilization of drag for underwater vehicle manipulator systems

UVMSs suffer severe drag owing to the manipulator while tracking a trajectory at a considerable speed. Drag, considered a negative force by other researchers, can be utilized for UVMS trajectory tracking. To this end, a novel coordinated trajectory tracking method for UVMS is proposed to actively utilize drag, which consists of three parts: a trajectory planner is developed to plan the desired velocity of the vehicle for trajectory tracking; also, a motion planner is designed to schedule the movement of the manipulator to actively utilize drag and the generating turning torque on the vehicle, making the vehicle approach the desired angular velocity; additionally, a computed torque controller (CTC) is developed to control the linear velocity and joint positions and its stability is demonstrated. Different simulations are performed, the results show that drag can be actively utilized for trajectory tracking, and the combination of the proposed method with other actuators can improve the maneuverability and tracking performance of the system. Pool experiments are conducted to verify the effectiveness of the proposed method in tracking yaw angles.

An accurate trajectory tracking method for low-speed unmanned vehicles based on model predictive control

Trajectory tracking on a low-speed vehicle using the model predictive control (MPC) algorithm usually assumes a simple road terrain. This assumption does not correspond to the actual road situation, leading to low tracking accuracy. Therefore, a trajectory tracking method considering road curvature based on MPC is proposed in this paper. In this method, the controller can automatically switch between MPC types. Linear model predictive control (LMPC) is selected for small road curvatures, while nonlinear model predictive control (NMPC) is employed for large road curvatures. In addition, the NMPC algorithm in this work considers the effect of road curvature on tracking accuracy, making it suitable for tracking time-varying curvature roads. To verify the feasibility of the algorithm, simulation comparisons with the basic MPC model were carried out at different testing roads and vehicle longitudinal speeds. The results indicate that the method significantly improves trajectory tracking accuracy, all while ensuring real-time calculations. The intelligent switching capability of control models based on road curvature allows its application to track trajectories on arbitrarily complex roads.

Machine Vision-based Trajectory Tracking of Honey Bee Crawling Motion

With the maturity of machine vision technology in artificial intelligence and the rise of the concept of "smart agriculture", machine vision-based methods are widely interested in studying biological behavior, but the technology for acquiring biological behavior information is still unsound. In this paper, we propose a machine vision-based bee crawling trajectory tracking method, which automatically records the bee crawling trajectory in the video information and obtains the description of bee crawling behavior. The method establishes the description of bee crawling motion through bee target detection, bee crawling motion tracking and bee crawling motion prediction as a method to study bee crawling behavior through artificial intelligence techniques. The method has the advantages of high timeliness and low labor cost, and reduces the problems of traditional research through manual observation records and bioassays methods with high influence of human subjective judgment factors and high application costs.

Trajectory Tracking Control of Mobile Manipulator Based on Improved Sliding Mode Control Algorithm

Research on trajectory tracking control for climbing welding robots holds significant importance in the field of automated welding. However, existing trajectory tracking methods suffer from issues such as jitter and slow speed. In this paper, an improved sliding mode control strategy is proposed based on the self-designed wall-climbing welding mobile manipulator. Firstly, a new adaptive sliding mode control strategy is proposed for the mobile platform based on the kinematic model. By introducing a new approach law, the controller is designed when the distance between the center of mass is unknown. Secondly, regarding the manipulator, we analyze simplified dynamic equations, extract uncertain components, and utilize a CNN for compensation. This compensation strategy is integrated into the sliding mode control law, achieving precise control over the manipulator and effectively resolving issues like slow tracking speeds, large errors, and chattering. The stability of the robot control system is proved by the Lyapunov function. Through simulation analysis and experimental validation, the proposed control method is confirmed to be feasible and superior.