Proposed Trajectory Tracking Research Articles

Research on trajectory tracking control method for agricultural robot permanent magnet synchronous motor servo system based on improved EMD threshold wavelet filtering

In agricultural robots, trajectory tracking can be affected by disturbances such as road slopes or bumps, leading to sudden changes in path curvature and reduced control accuracy. To address this issue, we propose a servo motor drive control method based on an improved Empirical Mode Decomposition (EMD) threshold. A mathematical model integrating the drive and control of the servo motor is established, and the driving performance of the servo motor is analyzed. By detecting the speed and position of the servo motor, the specified three-phase current values for motor drive control are derived. The actual current of the motor is collected using Hall current sensors and denoised with an improved EMD threshold wavelet filtering method. Within the servo motor drive control model, the system calculates the difference between the given three-phase current values and the actual motor current, and this difference is then used to adjust the motor control via an input linear amplifier, ensuring integrated drive control. Simulation and experimental results show that the proposed trajectory tracking control method for the agricultural robot’s permanent magnet synchronous motor servo system exhibits high control accuracy, strong anti-interference ability, and good performance, making it more suitable for practical applications.

Precise Obstacle Avoidance Movement for Three-Wheeled Mobile Robots: A Modified Curvature Tracking Method

This paper proposes a precise motion control strategy for a three-wheeled mobile robot with two driven rear wheels and one steered front wheel so that an obstacle avoidance motion task is able to be well implemented. Initially, the motion laws under nonholonomic constraints are expounded for the three-wheeled mobile robot in order to facilitate the derivation of its dynamic model. Subsequently, a prescribed target curve is converted into a speed target through the nonholonomic constraint of zero lateral speed. A modified dynamical tracking target that is aligned with the dynamic model is then developed based on the relative curvature of the prescribed curve. By applying this dynamical tracking target, path tracking precision is enhanced through appropriate selection of a yaw motion speed target, thus preventing speed errors from accumulating during relative curvature tracking. On this basis, integral sliding mode control and feedback linearization methods are adopted for designing robust controllers, enabling the accurate movement of the three-wheeled mobile robot along a given path. A theoretical analysis and simulation results corroborate the effectiveness of the proposed trajectory tracking control strategy in preventing off-target deviations, even with significant speed errors.

State-Transform MPC-SMC-Based Trajectory Tracking Control of Cross-Rudder AUV Carrying Out Underwater Searching Tasks

Abstract: In this study, we present a novel dual-loop robust trajectory tracking framework for autonomous underwater vehicles, with the objective of enhancing their performance in underwater searching tasks amidst oceanic disturbances. Initially, a real-world AUV experiment is conducted to validate the efficacy of a cross-rudder AUV configuration in maintaining sailing angle stability during the diving stage, which exhibits a strong capability for straight-line sailing. Building upon the experimental findings, we introduce a state-transform-model predictive guide law to compute the desired velocity for the dynamics loop. This guide law dynamically adjusts the controller across varying depths, thereby reducing model predictive control (MPC) computation while optimizing timing without compromising precision or convergence speed. Subsequently, we incorporate a sliding mode controller with a prescribed disturbance observer into the velocity control loop to concurrently enhance the robustness and convergence rate of the system. This innovative amalgamation of controllers significantly improves tracking precision and convergence rate, while also alleviating the computational burden—a pervasive challenge in AUV MPC control. Finally, various condition simulations are conducted to validate the robustness, effectiveness, and superiority of the proposed method. These simulations underscore the enhanced performance and reliability of our proposed trajectory tracking framework, highlighting its potential utility in real-world AUV applications.

Trajectory Tracking Control for Quadrotor Slung Load System With Unknown Load's Linear Velocity and Cable Length

This paper addresses the trajectory tracking control problem for a quadrotor suspended load system without load's linear velocity measurement and cable length information. Firstly, the cable length is estimated by designing an immersion and invariance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf{I\&amp;I}$</tex-math></inline-formula> )-based adaptive law. Secondly, a virtual thrust force vector is designed for the load position subsystem with the denoted auxiliary variables in the lack of load's linear velocity measurement. Then, through the cable direction subsystem and quadrotor attitude subsystem, the angular velocity input is presented to drive the real thrust input to virtual thrust input via the backstepping method. Thereafter, the uniformly boundedness of the whole closed-loop system is obtained by means of building suitable Lyapunov functions. Ultimately, numerical simulations attest to the performance of the proposed trajectory tracking control law.

Dynamic Modeling and Robust Trajectory Tracking Control of a Hybrid Propulsion-Based Small Underwater Robot

This paper proposes a hybrid propulsion-based small underwater robot for robust trajectory tracking control in a harsh and complex underwater environment. The robot is equipped with a Coanda-effect jet thruster and a pair of propeller-based reconfigurable magnetic-coupling thrusters, allowing it to traverse safely in confined or cluttered spaces as well as cruise efficiently in the open water. To investigate the robot dynamic modeling, we first formulated its simplified mathematical model and estimated the hydrodynamic coefficients by performing the planar motion mechanism using CFD (computational fluid dynamics) simulation. Then, a double-loop trajectory tracking control architecture was designed considering the model uncertainties and environmental disturbances. Based on Lyapunov theory, the outer-loop kinematic control produces the virtual velocity command, while the inner-loop dynamic control adopts the full-state feedback L1-adaptive control to match the command. The asymptotic convergence of the tracking errors and the stability of the whole closed-loop system are guaranteed. Finally, comparative simulations in the presence of unknown disturbances and the variation of model parameters were carried out to verify the robustness of our proposed trajectory tracking control, which is also suitable for the separated son robots.

Trajectory Tracking Control of Unmanned Surface Vehicles Based on a Fixed-Time Disturbance Observer

In ocean environments with unknown complex disturbances, the control accuracy for an unmanned surface vehicle (USV) is severely challenged with an increase in task complexity. As the foundation for executing complex tasks, it is particularly important to control a USV to navigate along a safe trajectory that has been set. In order to effectively handle the trajectory tracking problem, an innovative USV tracking control strategy with high accuracy is proposed by combining the integral sliding-mode and disturbance observer technologies, and these are effectively extended to a scenario with the cooperative trajectory tracking of multiple USVs in this study. Specifically, unknown disturbances are treated as lumped uncertainties, and a novel fixed-time stable-convergence disturbance observer (FT-DO) is proposed to effectively observe and approximate the lumped uncertainties. Then, in order to quickly reach and steadily navigate along the desired trajectory, an effective fixed-time stable-convergence fast integral sliding mode is modified, and on this basis, an accurate trajectory tracking controller (FTFISM-TTC) for a single USV and a cooperative trajectory tracking controller for multiple USVs are meaningfully proposed. Finally, the stability of FT-DO and FTFISM-TTC was rigorously proven by using the Lyapunov approach, and a comprehensive simulation of current advanced tracking control methods was conducted by using Matlab, which proved the reliability of the proposed trajectory tracking control strategy and further eliminated the impact of the initial state on the tracking accuracy.

Quaternion-Based Adaptive Trajectory Tracking Control of a Rotor-Missile with Unknown Parameters Identification

This paper investigates the adaptive trajectory tracking control problem and the unknown parameter identification problem of a class of rotor-missiles with parametric system uncertainties. First, considering the uncertainty of structural and aerodynamic parameters, the six-degree-of-freedom (6DoF) nonlinear equations describing the position and attitude dynamics of the rotor-missile are established, respectively, in the inertial and body-fixed reference frames. Next, a hierarchical adaptive trajectory tracking controller that can guarantee closed-loop stability is proposed according to the cascade characteristics of the 6DoF dynamics. Then, a memory-augmented update rule of unknown parameters is proposed by integrating all historical data of the regression matrix. As long as the finitely excited condition is satisfied, the precise identification of unknown parameters can be achieved. Finally, the validity of the proposed trajectory tracking controller and the parameter identification method is proved through Lyapunov stability theory and numerical simulations.

Fuzzy adaptive trajectory tracking control of work-class ROVs considering thruster dynamics

Work-class remotely operated vehicles (ROVs) are widely used in oceanic observation and underwater operation, which are driven by hydraulic power. A fuzzy adaptive controller considering thruster dynamics is proposed to improve the trajectory tracking performance of work-class ROVs in this paper. The dynamics of the hydraulic motor driven thruster is much higher than the position and orientation tracking ability of work-class ROVs. Thus, the system is divided into two separate subsystems: out-loop position and orientation control system, and inner-loop hydraulic control system. A fuzzy adaptive algorithm is employed in the out-loop position and orientation controller, which estimates the system parameters and disturbances respectively. A disturbance observer is used in the inner-loop hydraulic controller to attenuate the uncertainties and disturbances. A second order filter is adopted to synthesize these two controllers, which generates a smooth hydraulic motor speed command with appropriate bandwidth and range. The stability of the whole control system is proved through Lyapunov theory. Simulation results demonstrate the effectiveness of the proposed trajectory tracking control strategy under parameter uncertainties and disturbances.

Trajectory Tracking Control of Intelligent X-by-Wire Vehicles

Vehicle intelligence is an effective way to improve driving safety and comfort and reduce traffic accidents. The trajectory tracking control of unmanned vehicles is the core module of intelligent vehicles. As a redundant system, the X-by-wire electric vehicle has the advantage that the turning angles and driving torque of the four wheels can be precisely controlled and it has a higher degree of controllability and flexibility. In this paper, a trajectory tracking control algorithm based on a hierarchical control architecture is designed based on x-by-wire vehicles. The hierarchical control algorithm architecture includes the trajectory tracking layer, tire force distribution layer, and actuator control layer. The trajectory tracking layer uses the longitudinal force, lateral force, and yaw moment as the control variables; the model predictive control algorithm controls the vehicle to follow the desired trajectory. The tire force distribution layer is solved by transforming the tire force distribution problem into a quadratic programming problem with constraints. Based on the expected resultant force and resultant moment, the longitudinal force and lateral force of each tire in the vehicle coordinate system are obtained. The actuator control layer converts the coordinate system to obtain the longitudinal force and lateral force in the tire coordinate system, which uses the arctangent function tire model to solve the desired tire slip angle, and then obtains the vehicle steer angle and driving torque. To verify the effectiveness of the trajectory tracking control algorithm of the hierarchical control architecture, the proposed trajectory tracking control algorithm is simulated and verified through the variable speed double line change condition and the low road friction coefficient double line change condition. The simulation results show that the control algorithm proposed in this paper has the accuracy to follow the desired trajectory.Definition:

Active Lane-Changing Control of Intelligent Vehicle on Curved Section of Expressway

In order to improve the intelligent vehicle lane-changing performance, an active lane-changing control algorithm is proposed considering the changes of road curvature and vehicle speed. Firstly, the vehicle dynamics model considering vehicle speed variation and lane-changing safety distance is established, and the expected lane-changing trajectory model under the curved road is designed simultaneously. Then, taking the yaw rate and longitudinal speed as the control objectives of lateral and longitudinal motions, respectively, the sliding-mode variable structure control method based on Lyapunov stability condition is adopted, and the trajectory tracking controller is designed by combining the inverted method to track the desired lane-changing trajectory. Finally, the lane-changing trajectory model and trajectory tracking controller are verified in simulation platform of CarSim/Simulink and hardware-in-the-loop (HIL) test bench. The results show that the proposed trajectory tracking control method can perform the lane-changing behavior well under different road curvatures and vehicle speeds while maintaining high trajectory tracking control accuracy.

Trajectory tracking under compound noise environments based on weighted total least squares and forney-style factor graph

In compound noise environments, both additive noises and multiplicative noises influence the Time-of-arrival-based (TOA-based) distance measurements, which challenge the source node localization and trajectory tracking in practical sensor networks. In order to realize trajectory tracking under such noise conditions, in this paper, a compound noise parameter estimation algorithm based on Weighted Total Least Squares (WTLS) and a source node tracking algorithm based on Forney-style Factor Graph (FFG) are presented. Four parameters of the compound noise model are estimated based on ranging observations between position-known anchor nodes, and the trajectory tracking is achieved by applying a noise pre-standardized procedure in the FFG. Monte-Carlo simulations evaluate the performance of the proposed system, and the proposed noise parameter estimation algorithm performs better than the traditional Least Square (LS) method and the proposed trajectory tracking algorithm is realizable and robust.

A New Trajectory Tracking Control Method for Fully Electrically Driven Quadruped Robot

To improve the accuracy of tracking the trunk center-of-mass (CoM) trajectory and foot-end trajectory in a fully electrically driven quadruped robot, an efficient and practical new trajectory tracking control method is designed. The proposed trajectory tracking method is mainly divided into trunk balance controller (TBC) and swing leg controller (SLC). In TBC, a quadruped robot dynamics model is developed to find the optimal foot-end force that follows the trunk CoM trajectory based on the model predictive control (MPC) principle. In SLC, the Bessel curve is planned as the desired trajectory at the foot-end, while the desired trajectory is tracked by a virtual spring-damping element driving the foot-end, meanwhile, the radial basis function neural network (RBFNN) is applied for supervisory control to improve the control performance for the system. The experimental results show that the control method can modify the robot’s foot-end trajectory tracking effect, so that the stability error can be eliminated and the robustness of the controller can be improved, meanwhile, the linear and circular trajectory for CoM can be tracked accurately and quickly.

A control architecture to coordinate energy management with trajectory tracking control for fuel cell/battery hybrid unmanned aerial vehicles

Fuel cell/battery hybrid energy storage system (HESS) powered unmanned aerial vehicle (UAV) has the outstanding advantage of long endurance time. Trajectory tracking motion is a commonly used task execution mode of UAVs, especially in autonomous UAVs. This study aims at developing a control architecture to coordinate energy management with trajectory tracking control for fuel cell/battery hybrid UAVs. Its position tracking control adopts model predictive control (MPC) and an extended state observer to eliminate the modeling errors and effect of interference. The attitude tracking control adopts an auto-disturbance rejection controller having a quick response. The obtained control parameters are given as an input to the energy management block. Energy management strategies (EMSs) based on online dynamic programming and hierarchical MPC have been proposed. The results obtained from a simulation show that the proposed trajectory tracking control architecture can track the target trajectory stably with a small tracking error. The tracking performance is stable under interference. Experimental results show that dynamic programming is solved online with good control performance. Compared to ordinary EMSs, dynamic programming and hierarchical MPC can increase endurance time by 2.69% and 1.27%, respectively. The proposed control architecture verifies the coordination of energy management and trajectory tracking control, and prospected the advantages of the combination of fuel cell and autonomous driving for long endurance UAVs in the future.

A TM-Based Adaptive Learning Data-Model for Trajectory Tracking and Real-Time Control of a Class of Nonlinear Systems

In this paper, a Takenaka-Malmquist (TM) basis function based equivalent data-model is established by an adaptive rational decomposition for the finite-time interval trajectory tracking control and real-time control of a class of nonlinear systems in the frequency domain. This data model can adaptively learn and match the control process of nonlinear systems. As a result, the proposed trajectory tracking as well as real-time control method can reflect the feature of adaptive learning in order-by-order decomposition, and the feasibility of the proposed method is guaranteed by the convergence of adaptive decomposition by TM basis function under the maximum selection principle (MSP) in Hardy space H^2(\mathbbD). Compared with the traditional model-free control method, this data learning model which matches the control process has obvious advantages in the system model expression and control accuracy. Simulation results at the end of this paper show the effectiveness of the proposed method.

Event Visualization and Trajectory Tracking of the Load Carried by Rotary Crane.

Tracking the trajectory of the load carried by the rotary crane is an important problem that allows reducing the possibility of its damage by hitting an obstacle in its working area. On the basis of the trajectory, it is also possible to determine an appropriate control system that would allow for the safe transport of the load. This work concerns research on the load motion carried by a rotary crane. For this purpose, the laboratory crane model was designed in Solidworks software, and numerical simulations were made using the Motion module. The developed laboratory model is a scaled equivalent of the real Liebherr LTM 1020 object. The crane control included two movements: changing the inclination angle of the crane’s boom and rotation of the jib with the platform. On the basis of the developed model, a test stand was built, which allowed for the verification of numerical results. Event visualization and trajectory tracking were made using a dynamic vision sensor (DVS) and the Tracker program. Based on the obtained experimental results, the developed numerical model was verified. The proposed trajectory tracking method can be used to develop a control system to prevent collisions during the crane’s duty cycle.

Functional Electrical Stimulation System for Drop Foot Correction Using a Dynamic NARX Neural Network

Neurological diseases may reduce Tibialis Anterior (TA) muscle recruitment capacity causing gait disorders, such as drop foot (DF). The majority of DF patients still retain excitable nerves and muscles which makes Functional Electrical Stimulation (FES) an adequate technique to restore lost mobility. Recent studies suggest the need for developing personalized and assist-as-needed control strategies for wearable FES in order to promote natural and functional movements while reducing the early onset of fatigue. This study contributes to a real-time implementation of a trajectory tracking FES control strategy for personalized DF correction. This strategy combines a feedforward Non-Linear Autoregressive Neural Network with Exogenous inputs (NARXNN) with a feedback PD controller. This control strategy advances with a user-specific TA muscle model achieved by the NARXNN’s ability to model dynamic systems relying on the foot angle and angular velocity as inputs. A closed-loop, fully wearable stimulation system was achieved using an ISTim stimulator and wearable inertial sensor for electrical stimulation and user’s kinematic gait sensing, respectively. Results showed that the NARXNN architecture with 2 hidden layers and 10 neurons provided the highest performance for modelling the kinematic behaviour of the TA muscle. The proposed trajectory tracking control revealed a low discrepancy between real and reference foot trajectories (goodness of fit = 77.87%) and time-effectiveness for correctly stimulating the TA muscle towards a natural gait and DF correction.

A Practical Trajectory Tracking Scheme for a Twin-Propeller Twin-Hull Unmanned Surface Vehicle

Trajectory tracking is a basis of motion control for Unmanned Surface Vehicles (USVs), which has been researched well for common USVs. The twin-propeller and twin-hull USV (TPTH-USV) is a special vehicle for applications due to its good stability and high load. We propose a three-layered architecture of trajectory tracking for the TPTH-USV which explicitly decomposes into trajectory guidance, a motion limitator and controller. The trajectory guidance transforms an expected trajectory into an expected speed and expected course in a kinematic layer. The motion limitator describes some restriction for motion features of the USV in the restriction layer, such as the maximum speed and maximum yaw rate. The controller is to control the speed and course of the USV in the kinetic layer. In the first layer, an adaptive line-of-sight guidance law is designed by regulating the speed and course to track a curved line considering the sideslip angle. In the second layer, the motion features are extracted from an identified speed and course coupled model. In the last layer, the course and speed controller are designed based on a twin-PID controller. The feasibility and practicability of the proposed trajectory tracking scheme is validated in sea experiments by a USV called ‘Jiuhang 490’.

Trajectory tracking method based on the circulation of feasible path planning.

The control method is the central point of the unmanned vehicles. As the core system to guarantee the properties of self-decision and trajectory tracking of the unmanned vehicles, a new kind of trajectory tracking method based on the circulation of feasible path planning for the unmanned vehicles are proposed in this article which considered the dynamics and kinematics characteristics of vehicles. The multi-trace-points cooperative trajectory tracking control strategy on the basis of the circulation of feasible path generation method is proposed and the lateral controller is designed for trajectory tracking. The process of feasible path generation is conducted once the tracking error exceeded. A simulation platform of the trajectory tracking simulation of unmanned vehicles is built considering the mechanical properties of system elements and the mechanical characteristics. Finally, the proposed trajectory tracking method is verified. The tracking error would be reduced to make sure the vehicles move along the pre-set virtual track.

Observer-based adaptive neural sliding mode trajectory tracking control for remotely operated vehicles with thruster constraints

For a class of remotely operated vehicle (ROV) systems with thruster constraints, immeasurable states, and unknown nonlinearities, the trajectory tracking control problem was discussed in this paper. The unknown nonlinear functions were approximated by radial basis function (RBF) neural networks. An adaptive state observer based on neural networks was designed and the immeasurable states were estimated. Considering the problem of thruster saturation constraints, an auxiliary system for saturation compensation was designed and a saturation factor was constructed by the auxiliary system state. By applying the backstepping design method, an adaptive neural sliding mode trajectory tracking controller was developed, in which the saturation factor is contained in adaptive laws. It was proved that the uniformly ultimately bounded (UUB) of trajectory tracking errors can be obtained. Finally, the effectiveness of the proposed trajectory tracking control approach was checked by simulations.

A Dynamic Motion Tracking Control Approach for a Quadrotor Aerial Mechanical System

This paper deals with the reference trajectory tracking problem and simultaneous active disturbance suppression on a class of controlled aerial mechanical systems by processing measurable output signals. A novel dynamic control method for desired motion reference trajectory tracking for quadrotor helicopters is introduced. Measurements of position output signals for efficient and robust tracking of motion profiles specified for the unmanned aerial vehicle are only required. Thus, differentiation of signals and real-time estimation of disturbances affecting the multi-input multioutput, underactuated nonlinear dynamic system are unnecessary. The presented active control approach can be directly extended for a class of vibrating mechanical systems. Analytical, experimental, and numerical results are presented to prove the satisfactory performance of the proposed trajectory tracking control approach for considerably perturbed operating scenarios.