Accurate Trajectory Tracking Research Articles

Fixed-Time Control with an Improved Sparrow Search Algorithm for Robotic Arm Performance Optimization

This paper presents an innovative approach that integrates a fixed-time control (FTC) algorithm with an improved sparrow search algorithm (ISSA) to enhance the trajectory tracking accuracy of a two-degree-of-freedom (two-DOF) robotic arm. The FTC algorithm, which incorporates barrier Lyapunov function (BLF) and adaptive neural network strategies, ensures rapid convergence, effective vibration suppression, and the robust handling of system uncertainties and input saturation. The ISSA, inspired by the foraging behavior of sparrows, improves search efficiency through dynamic weight adjustments and chaotic mapping, balancing global and local search capabilities. By optimizing control parameters, ISSA minimizes tracking errors. Simulation results demonstrate that the combined FTC and ISSA approach significantly reduces tracking errors and improves response speed compared to the use of FTC alone, underscoring its potential for achieving high-precision control in robotic arms and offering a promising direction for precise robotic control applications.

Adaptive Integral Sliding Mode Control with Chattering Elimination Considering the Actuator Faults and External Disturbances for Trajectory Tracking of 4Y Octocopter Aircraft

This paper presents a control strategy for a 4Y octocopter aircraft that is influenced by multiple actuator faults and external disturbances. The approach relies on a disturbance observer, adaptive type-2 fuzzy sliding mode control scheme, and type-1 fuzzy inference system. The proposed control approach is distinct from other tactics for controlling unmanned aerial vehicles because it can simultaneously compensate for actuator faults and external disturbances. The suggested control technique incorporates adaptive control parameters in both continuous and discontinuous control components. This enables the production of appropriate control signals to manage actuator faults and parametric uncertainties without relying only on the robust discontinuous control approach of sliding mode control. Additionally, a type-1 fuzzy logic system is used to build a fuzzy hitting control law to eliminate the occurrence of chattering phenomena on the integral sliding mode control. In addition, in order to keep the discontinuous control gain in sliding mode control at a small value, a nonlinear disturbance observer is constructed and integrated to mitigate the influence of external disturbances. Moreover, stability analysis of the proposed control method using Lyapunov theory showcases its potential to uphold system tracking performance and minimize tracking errors under specified conditions. The simulation results demonstrate that the proposed control strategy can significantly reduce the chattering effect and provide accurate trajectory tracking in the presence of actuator faults. Furthermore, the efficacy of the recommended control strategy is shown by comparative simulation results of 4Y octocopter under different failing and uncertain settings.

Reproduction and generalization of robot trajectory tracking control method using reinforcement learning and neural network techniques

Abstract. This paper introduces a method for controlling the trajectory of a manipulator robot with uncertainty, using reinforcement learning. The control is designed to work even when there are limitations on the inputs to the system. Reinforcement learning and neural networks are employed alongside standard robust control techniques to enhance the fixed-time convergence of the system state. A novel algorithm is proposed to develop a reinforcement learning-based approach. This approach utilizes radial basis function neural networks and nonsingular fast terminal sliding mode control to ensure error convergence within a predetermined time. This paper presents the task of monitoring the intended path followed by robotic arms in the presence of uncertain and unfamiliar disruptions. The experimental results validate that the suggested approach substantially improves both the stability and accuracy of trajectory tracking, making it more feasible for real-world applications in robotic systems.

Quadrotor Trajectory Tracking using Combined Stochastic Model-Free Position and DDPG-based Attitude Control

This article presents a cascade controller for the quadrotor to track the desired trajectory effectively. Unlike previous approaches, this method avoids simplification and linearization assumptions, making it applicable in a wider range of scenarios. A novel linear quadratic tracking method is utilized, which takes into account both process noise and measurement noise while maintaining a model-free nature. Furthermore, the stability analysis of this stochastic method is thoroughly investigated. In terms of attitude control, a model-free approach is adopted. The Deep Deterministic Policy Gradient (DDPG) algorithm is implemented, leveraging an actor-critic network to handle the nonlinearities associated with attitude control. This model-free approach eliminates the need for an accurate model of the quadrotor's dynamics. Simulations are conducted to evaluate the performance of the proposed controller, and the results demonstrate its ability to effectively control the quadrotor, ensuring accurate trajectory tracking and stability.

A Positioning and Tracking Performance–Enhanced Composite Control Algorithm for the Macro–Micro Precision Stage

In the macro–micro composite motion process, the macro stage achieves rapid motion in a large workspace, while the micro stage realizes precise positioning within a small displacement. The large-stroke and high-speed motion of the macro stage is influenced by nonlinear friction, overshooting, and vibrations, making it challenging to achieve rapid stabilization within the travel range of the micro stage, thereby impacting equipment operation efficiency. This paper proposes a composite controller structure designed to solve the fast point-to-point positioning of the macro stage driven by a linear motor and enhance the trajectory tracking performance of the stage. The proposed composite control algorithm (CCA) includes velocity feed-forward, gain-scheduled proportional integral differential (PID) control, and a plug-in repetitive control method. By employing a tracking differentiator, velocity feed-forward, and a gain-scheduled PID controller, the control algorithm can realize rapid stabilization and positioning for the macro stage. Through velocity feed-forward, gain-scheduled PID control, and a plug-in repetitive controller, the control algorithm can reduce the trajectory tracking error of the stage. Simulations and experimental studies of point response and sinusoidal trajectory tracking are carried out on a macro–micro stage to verify the effectiveness of the composite controller for the linear motor. The experimental results demonstrate that the proposed composite controller effectively reduces the macro stage’s settling time and overshoot, and improves the accuracy of sinusoidal trajectory tracking, which lays a foundation for submicron positioning accuracy in high-speed macro–micro motion stages.

Control Design and Implementation of Autonomous Robotic Lawnmower

This paper presents the trajectory tracking control design and implementation of feedback linearization (FL) and robust feedback linearization (RFL), applicable to a robotic lawnmower with four mecanum driving wheels. The RFL control design additionally includes a robust control law. These two nonlinear control laws are developed to enable the controlled robotic lawnmower to accurately follow any specified trajectory. The simulation outcomes illustrate that the suggested control law based on RFL displays superior trajectory tracking accuracy and resilience compared to the FL control method in the case of a robotic lawnmower operating under demanding conditions. These conditions encompass environmental disturbances and uncertainties in modeling. The RFL control method also exhibits lower energy consumption compared to the FL control method. Finally, using the RFL controller derived from this study, the error in trajectory tracking in computer simulations and the actual mowing performance have demonstrated outstanding results.

Adaptive control of an amplified piezoelectric-driven micropositioning stage based on notch filter structure inspiration and neural network online tuning

Abstract Piezoelectric-driven flexure micro/nanopositioning stages often exhibit a low-damping resonance mode, which can easily excite mechanical resonance during high-speed movement, and significantly impact the control system's stability, control bandwidth, and trajectory tracking accuracy. To mitigate the reliance on the precise modeling of stage dynamics inherent in current resonant controllers, an adaptive control method based on a back propagation (BP) neural network was designed to suppress resonance in real-time. First, a piezoelectric-driven flexure micro/nanopositioning stage system was constructed. Next, a feedback controller similar to a notch filter was designed, with bilinear transformation applied based on the system's inherent parameters to determine the initial values. Finally, the designed adaptive control method was tested through trajectory tracking experiments using a triangular wave signal. The experimental results showed that, when tracking the triangular wave signal, the maximum tracking error was reduced by 72.66% compared to proportional-integral (PI) control alone and by 68.66% compared to proportional integral control combined with a traditional notch filter. The tracking results demonstrate a significant improvement in the stage's stability and tracking accuracy.

Trajectory tracking multi-constraint model predictive control of unmanned vehicles based on sideslip stiffness estimation with XGBoost algorithm

When the vehicle is driving at high speed on a slippery road, the sideslip stiffness of the tire which is closely related to the lateral force of the tire, will vary with the change of road conditions, tire inflation pressure, vertical load, and other factors. If the tire sideslip stiffness is set to a fixed value in the control system based on the model design, the uncertainty of the sideslip stiffness will cause a large error with the actual application. Therefore, in order to improve the trajectory tracking accuracy of the vehicle on the slippery road surface under the premise of ensuring the stability of the vehicle, an intelligent vehicle trajectory tracking control strategy considering the influence of sideslip stiffness is designed in this paper. In order to solve the multiple constraints of the vehicle driving on the low-adhesion road surface, a trajectory tracking controller based on the multi-constraint model predictive control algorithm is designed, and then the tire sideslip stiffness estimation strategy is designed based on the XGBoost algorithm, and the estimated sideslip deviation stiffness is added to the trajectory tracking control model. Carsim and MATLAB/Simulink are used to perform co-simulation to verify the accuracy of the proposed tire sideslip stiffness estimation and the tracking performance of the trajectory tracking controller. In order to further verify the reliability of the research content, the relevant working condition tests are carried out on the hardware-in-the-loop platform based on Carsim and LabVIEW, and the effectiveness of the trajectory tracking controller considering the influence of sideslip stiffness is verified.

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.

Enhancing trajectory tracking accuracy in three-wheeled mobile robots using backstepping fuzzy sliding mode control

The rise in robotics technology has increased interest in ThreeWheeled Mobile Robots (TWMRs) due to their agility and adaptability across various applications. However, effectively controlling TWMRs presents a significant challenge owing to their inherent nonholonomic constraints, which restrict independent movement in all directions. Factors like sensor noise, nonlinear system dynamics, and uncertain system parameters also add to the complexity of controlling TWMRs. This research endeavors to enhance the precision of trajectory tracking in TWMRs. Specifically, it employs Backstepping Fuzzy Sliding Mode Control (BFSMC) with parameters optimized through Particle Swarm Optimization (PSO), coupled with the Extended Kalman Filter (EKF) for state estimation. The study conducts a comprehensive performance comparison between Backstepping Sliding Mode Control (BSMC) and Backstepping Fuzzy Sliding Mode Control(BFSMC) across various trajectory patterns, revealing substantial improvements in trajectory tracking accuracy with BFSMC. BFSMC demonstrates improvements in performance across various trajectory types when considering the integral time absolute error (IAE). Specifically, it achieves a 51.97% improvement for circular trajectories, an 82.09% improvement for infinity trajectories, and an 84.073% improvement for spiral trajectories. Moreover, BFSMC demonstrates superior robustness in the presence of disturbances, noise, parameter variations, and unmodeled dynamics compared to BSMC. Integrating the Extended Kalman Filter further improves accuracy, particularly in noisy conditions.

Adaptive backstepping and sliding mode control of a quadrotor

This article proposes a simple robust adaptive control architecture with minimum parameter estimation laws for trajectory tracking of a quadrotor subjected to parametric variations and environmental disturbances. This simple control architecture aims to achieve highly accurate, robust, and fast trajectory tracking of the quadrotor in a short time with low computational cost. Firstly, the quadrotor model is divided into altitude, attitude, and position subsystems for which appropriate control methods are designed without prior knowledge of the upper bound of external disturbances. A simple adaptive fractional-order sliding mode control (AFSMC) is designed to enhance the tracking of the altitude subsystem and estimate the upper bound of the disturbances. Then, a simple adaptive backstepping control (ABC) is developed for the horizontal position to generate the required roll and pitch orientations. The adaptation laws not only estimate the upper bound of the disturbances but also adjust the controller gains thereby enhancing the robustness of the ABC. A nonsingular fast terminal sliding mode control (NFTSMC) is incorporated with a finite-time disturbance observer (FDO) to accurately suppress the disturbances, and follow the target rotation angles within a short finite-time. Simulation results showed that the compounded control structure ensures accurate, fast, and robust tracking. The AFSMC can achieve the desired altitude with a settling time of 0.31 s and root mean square error (RMSE) of 0.0454 m. The ABC can attain the target horizontal position coordinates with a settling time of (0.47 s, 0.47 s) and RMSE of (0.0370 m, 0.0518 s). The NFTSMC-FDO can achieve the desired attitude angles with a settling time of (0.11 s, 0.13 s, 0.52 s) and RMSE of (0.0098 rad, 0.0092 rad, 0.0935 rad). Performance comparisons with existing control methods in terms of settling time and RMSE demonstrated that the proposed control architecture is superior.

Nonlinear terminal sliding mode trajectory tracking control algorithm for industrial robots based on dung beetle optimizer

Abstract To enhance the precision of trajectory tracking control in industrial robots, a nonlinear end-to-end sliding mode trajectory tracking control algorithm for industrial robots based on the dung beetle algorithm is proposed. By employing nonlinear terminal sliding mode control to resolve the issue of inadequate trajectory tracking control performance in industrial robots, and integrating the dung beetle optimizer (DBO) algorithm for control parameter adjustment, significant enhancements are achieved in trajectory tracking accuracy.

Coupled error super-twisted sliding mode active fault-tolerant control for robotic system with actuator fault.

This paper focuses on a robotic system with actuator fault and presents a sliding mode active fault-tolerant control method based on coupled position error. The actuator fault is first detected by a fault alerter with a predetermined threshold. After the fault is successfully detected, the fault is estimated by a fault observer. Coupling the position error with the weighted position error of different joints, a non-singular fast terminal sliding mode surface is constructed, and a super-twisted algorithm is introduced to design a coupled error super-twisted sliding mode controller (CESSMC). Furthermore, the fault estimation is incorporated with the CESSMC to accomplish the coupled error super-twisted sliding mode active fault-tolerant control. The stability and the finite-time convergence of the system are theoretically proved. Simulations and experiments are conducted to verify the effectiveness of the proposed method. The proposed method can achieve the position error convergence in finite time and reduce chattering in the control input. With the tight coupling between position error and weighted position error, the fault compensation effect and trajectory tracking accuracy can be improved.

ADRC-Based cooperative control for unmanned towing operation by multiple DP tugboats: A comparative study of two cooperative controllers

This paper addresses the challenge of coordinated manipulation of an unactuated floating object by multiple tugboats to execute both positioning and towing operation within complex marine environments. We proposes a multi-layer cooperative control algorithm for the multi-tugboat system, including tugboat control level and cooperative control level. At the individual tugboat control level, the dynamic positioning system (DPS) has been enhanced to match the operational behavior of the tugboat, enabling it to handle cable tension and environmental disturbances during transit. The controller incorporates a simple yet effective linear active disturbance rejection control method (ADRC) to counter external disturbances and ensure accurate trajectory tracking without relying on preset models. Moving to the multi-tugboat collaboration level, two distinct control strategies are proposed for towing operations: formation-based (FB) and force-allocation-based (FAB). The FB strategy involves multiple tugboats forming a coordinated formation, with control focused on the formation center to indirectly manipulate the object. On the other hand, the FAB strategy utilizes model predictive control (MPC) for the object to allocate the necessary towing force for each cable, thereby determining the required actions for each tugboat based on the cable model and the needed towing force. Simulation results demonstrate that both control strategies can effectively maneuver the floating object with high accuracy to perform positioning and towing tasks. Nevertheless, due to the variations in their fundamental mechanisms, there are significant discrepancies in towline tension, tugboat utilization, and energy consumption.

Control Based on Nonlinear Estimators of Parametric Uncertainties Applied to an Agricultural Tractor Equipped with a Towed Implement System

This article presents a nonlinear control strategy designed to address parametric uncertainties in an agricultural tractor system coupled to a towed implement. The controller ensures accurate tracking of lateral and yaw velocities relative to desired reference trajectories, even under the presence of parametric variations and external disturbances. The reference trajectories are derived from an “ideal” tractor model, excluding the effects of the towed implement. A High-Order Sliding Mode (HOSM) estimator is employed to provide an estimation of disturbances, which are subsequently mitigated by the controller to maintain system stability and precision. The effectiveness of the proposed control strategy is validated through Matlab-Simulink simulations, which include a double-step steer maneuver. This maneuver tests the system’s ability to handle abrupt steering changes, providing insight into the controller’s robustness and its capacity to ensure accurate trajectory tracking in demanding conditions.

Upper Limb Rehabilitation Robots Training Analysis based on Multi-sensor Trajectory Data and Human-computer Interaction

Upper limb rehabilitation robots have important practical significance in helping patients recover their motor function, but traditional training methods often lack real-time and accurate evaluation of patient movement status and intention and have low interactive participation. Therefore, the study proposes a training system for upper limb rehabilitation robots based on multi-sensor trajectory data and human-computer interaction. The system is designed from three aspects: inertial sensor trajectory tracking, Kinect sensor image restoration, and interaction system design. A polynomial joint zero value constraint algorithm is introduced to correct errors, and variable parameter pixel filtering combined with a weighted average moving algorithm is used to improve image quality. The training results showed that the robot trajectory tracking accuracy significantly improved, and the improvement in motion trajectory error was greater than 20%. Compared with traditional training methods, interactive training had a recognition accuracy of over 85% in rehabilitation actions, and the system had better stability. This rehabilitation robot can effectively meet the feasibility and effectiveness of improving the interaction system, providing new technological means for intelligent medical services.

Stochastic LPV MPC-based path following control for bevel-tip flexible needle with probabilistic constraints

This paper addresses the path-tracking problem for flexible needle control systems using a stochastic linear parameter varying (LPV) and model predictive control (MPC) strategy. Flexible needles operating in dynamic environments with non-uniform tissue density often deviate from ideal assumptions, resulting in non-standard models. The bicycle kinematics model for flexible needle motion control is transformed into an LPV model, improving accuracy and enabling more efficient control. The proposed stochastic LPV MPC approach aims to mitigate uncertainties arising from modelling errors and dynamic environmental factors, ensuring accurate trajectory tracking for the flexible needle. The sample and removal method is utilized to reformulate the probabilistic-constrained optimization problem for implementation. The contributions of this work lie in the application of stochastic LPV MPC to address the trajectory tracking problem in the presence of uncertainties. The simulation results illustrate the superior robustness of the stochastic LPV MPC approach, as evidenced by significantly smaller tracking errors across various scenarios.

Trajectory tracking control of a four-bar linkage prosthetic knee with magnetorheological damper

In order to improve biomimicry, a four-bar linkage prosthetic knee with magnetorheological (MR) damper was developed in this paper. The principle and structure of four-bar linkage MR prosthetic knee was introduced and its kinetic model was established. A MR damper matching the proposed prosthetic knee was designed, fabricated and tested, and the forward and inverse mechanical model were conducted. In addition, to solve the problems of complex model, poor bionics and low trajectory tracking accuracy in the MR prosthetic knee, a PD-type iterative learning control (ILC) controller was developed. The simulated and experimental test results show that the positive maximum error of the knee joint swing trajectory based on PD-type ILC controller are 2.2°(speed of 0.5 m/s), 4.1°(speed of 1.0 m/s), and 1.9°(speed of 1.5 m/s), respectively, and the negative maximum error of that are −1.4°(speed of 0.5 m/s), −6.7°(speed of 1.0 m/s), and −5.5°(speed of 1.5 m/s), respectively, which effectively tracks the reference swing trajectory.

Trajectory tracking control of a mobile robot using fuzzy logic controller with optimal parameters

Abstract This work investigates the use of a fuzzy logic controller (FLC) for two-wheeled differential drive mobile robot trajectory tracking control. Due to the inherent complexity associated with tuning the membership functions of an FLC, this work employs a particle swarm optimization algorithm to optimize the parameters of these functions. In order to automate and reduce the number of rule bases, the genetic algorithm is also employed for this study. The effectiveness of the proposed approach is validated through MATLAB simulations involving diverse path tracking scenarios. The performance of the FLC is compared against established controllers, including minimum norm solution, closed-loop inverse kinematics, and Jacobian transpose-based controllers. The results demonstrate that the FLC offers accurate trajectory tracking with reduced root mean square error and controller effort. An experimental, hardware-based investigation is also performed for further verification of the proposed system. In addition, the simulation is conducted for various paths in the presence of noise in order to assess the proposed controller’s robustness. The proposed method is resilient against noise and disturbances, according to the simulation outcomes.

Adaptive Nonsingular Fast Terminal Sliding Mode Control for Shape Memory Alloy Actuated System

Due to its high power-to-weight ratio, low weight, and silent operation, shape memory alloy (SMA) is widely used as a muscle-like soft actuator in intelligent bionic robot systems. However, hysteresis nonlinearity and multi-valued mapping behavior can severely impact trajectory tracking accuracy. This paper proposes an adaptive nonsingular fast terminal sliding mode control (ANFTSMC) scheme aimed at enhancing position tracking performance in SMA-actuated systems by addressing hysteresis nonlinearity, uncertain dynamics, and external disturbances. Firstly, a simplified third-order actuator model is developed and a variable gain extended state observer (VGESO) is employed to estimate unmodeled dynamics and external disturbances within finite time. Secondly, a novel nonsingular fast terminal sliding mode control (NFTSMC) law is designed to overcome singularity issues, reduce chattering, and guarantee finite-time convergence of the system states. Finally, the ANFTSMC scheme, integrating NFTSMC with VGESO, is proposed to achieve precise position tracking for the prosthetic hand. The convergence of the closed-loop control system is validated using Lyapunov’s stability theory. Experimental results demonstrate that the external pulse disturbance error of ANFTSMC is 8.19°, compared to 19.21° for the comparative method. Furthermore, the maximum absolute error for ANFTSMC is 0.63°, whereas the comparative method shows a maximum absolute error of 1.03°. These results underscore the superior performance of the proposed ANFTSMC algorithm.