Trajectory Tracking Performance Research Articles

Adaptive synchronous sliding control for a robot manipulator based on neural networks and fuzzy logic

Robot manipulators have become important equipment in production lines, medical fields, and transportation. Improving the quality of trajectory tracking for robot hands is always an attractive topic in the research community. This is a challenging problem because robot manipulators are complex nonlinear systems and are often subject to fluctuations in loads and external disturbances. This article proposes an adaptive synchronous sliding control scheme to improve trajectory tracking performance for a robot manipulator. The proposed controller ensures that the positions of the joints track the desired trajectory, synchronize the errors, and significantly reduces chattering. First, the synchronous tracking errors and synchronous sliding surfaces are presented. Second, the synchronous tracking error dynamics are determined. Third, a robust adaptive control law is designed, the unknown components of the model are estimated online by the neural network, and the parameters of the switching elements are selected by fuzzy logic. The built algorithm ensures that the tracking and approximation errors are ultimately uniformly bounded (UUB). Finally, the effectiveness of the constructed algorithm is demonstrated through simulation and experimental results. Simulation and experimental results show that the proposed controller is effective with small synchronous tracking errors, and the chattering phenomenon is significantly reduced.

Optimized Proportional-derivative Feedback-assisted Iterative Learning Control for Manipulator Trajectory Tracking

Optimized Proportional-derivative Feedback-assisted Iterative Learning Control for Manipulator Trajectory Tracking

Robust Fixed-Time Fault-Tolerant Control for USV with Prescribed Tracking Performance

The unmanned surface vessel (USV) is an emerging marine tool with its advantages of automation and intelligence in recent years; the good trajectory tracking performance is an important capability. This paper proposes a novel prescribed performance fixed-time fault-tolerant control scheme for an USV with model parameter uncertainties, unknown external disturbances, and actuator faults, based on an improved fixed-time disturbances observer. Firstly, the proposed observer can not only accurately and quickly estimate and compensate the lumped nonlinearity, including actuator faults, but also reduce the chattering phenomenon by introducing the hyperbolic tangent function. Then, under the framework of prescribed performance control, a prescribed performance fault-tolerant controller is designed based on a nonsingular fixed-time sliding mode surface, which guarantees the transient and steady-state performance of an USV under actuator faults and meets the prescribed tracking performance requirements. In addition, it is proved that the closed-loop control system has fixed-time stability according to Lyapunov’s theory. Finally, upon conducting numerical simulations and comparing the proposed control scheme with the SMC and the finite-time NFTSMC scheme, it is evident that the absolute error tracking performance index of the proposed control scheme is significantly lower, thus indicating its superior accuracy.

Gradient projection-based trajectory tracking control for automatic guided vehicle

In order to solve the problems of long operation time for solving the trajectory tracking controller and low real-time tracking. This paper proposes an improved model predictive control algorithm. By introducing the gradient projection method (GPM), the projection direction is used as the fastest descent direction of the objective function, which is used to reduce the number of iterations of the operation. Meanwhile, this paper adds constraints and relaxation factors to improve the trajectory tracking accuracy and prevent the controller operations from falling into local optimal solutions. Simulation by Simulink, the improved model predictive control algorithm reduces the average operation time by 24.74% and the single maximum operation time by 36.04%, effectively improving the real-time trajectory tracking performance. Finally, the verification experiment of trajectory tracking control is carried out by actual vehicle, proving the method’s effectiveness.

Trajectory tracking of a wheeled mobile robot based on the predefined‐time sliding mode control scheme

AbstractIn this paper, a double‐loop control method is proposed to improve the trajectory tracking performance of a wheeled mobile robot (WMR) with slippage properties and external disturbances. Considering the strong robustness and the ability to enable the system to converge in a short time, the predefined‐time sliding mode control (PTSMC) strategy is applied to the design of a double‐loop controller. Furthermore, a nonlinear disturbance observer (NDO) is adopted to comply with the feedforward compensation of the external disturbances. In turn, the controller only needs to deal with the internal disturbance of the system under the premise of using the NDO, thereby reducing the burden of the sliding mode controller. Based on Lyapunov methods, the stability of the double‐loop controller and the NDO is analyzed. Finally, the feasibility of the double‐loop control strategy is proven by simulations of the WMR operating along circular, sin‐shaped, and eight‐shaped roads.

Fixed-time solution of inequality constrained time-varying linear systems via zeroing neural networks

Zeroing neural network (ZNN) has been explored and applied in a variety of time-varying problems solving. However, ZNN models for inequality constrained time-varying linear equation (ICTVLE) solving are rarely reported. Generally, numerous practical problems can be mathematically modeled as ICTVLE problems. Motivated by the above mentioned issue, a nonlinear tunable activation function activated ZNN (NTAF-ZNN) model is constructed to effectively solve ICTVLE problems. To further improve the performances of NTAF-ZNN model, a fuzzy nonlinear tunable activation function (FNTAF) is also designed. Based on the FNTAF, a fuzzy nonlinear tunable activation function-based ZNN (FNTAF-ZNN) model is realized. Firstly, the fixed-time convergence property and disturbance rejection ability of the NTAF-ZNN and FNTAF-ZNN models are proved by theoretical analysis. Then, comparative simulation results of the two models with other existing ZNN models for solving the ICTVLE problem are provided to further verify their robustness and effectiveness. Additionally, the two models and other existing ZNN models are also employed to realize inequality constrained manipulator trajectory tracking under ideal and noisy environments for further comparisons. Finally, the superior performances of the FNTAF-ZNN model for manipulator trajectory tracking are further verified by physical experiment results.

Compliant variable admittance adaptive fixed-time sliding mode control for trajectory tracking of robotic manipulators

Abstract This paper presents a compliant variable admittance adaptive fixed-time sliding mode control (SMC) algorithm for trajectory tracking of robotic manipulators. Specifically, a compliant variable admittance algorithm and an adaptive fixed-time SMC algorithm are combined to construct a double-loop control structure. In the outer loop, the variable admittance algorithm is developed to adjust admittance parameters during a collision to minimize the collision time, which gives the robot compliance property and reduce the rigid collision influence. Then, by employing the Lyapunov theory and the fixed-time stability theory, a new nonsingular sliding mode manifold is proposed and an adaptive fixed-time SMC algorithm is presented in the inner loop. More precisely, this approach enables rapid convergence, enhanced steady-state tracking precision, and a settling time that is independent of system initial states. As a result, the effectiveness and improved performance of the proposed algorithm are demonstrated through extensive simulations and experimental results.

Deep reinforcement learning and decoupling proportional-integral-derivative control of a humanoid cable-driven hybrid robot

Aiming at the application of robots in service, medical treatment, rehabilitation, and other fields, a humanoid cable-driven hybrid robot by imitating the structure of human arm is designed in this article. The robot is composed of a cable–spool–pulley system, series mechanism, and coaxial spherical parallel mechanism, which can achieve six degrees of freedom movement in space. A challenge with cable driving is that the movement of the rear end joints (such as pitch and roll) can alter the length or tension of the cable driven by the frontend joints, resulting in joint coupling. This interference can lead to a decrease in the motion accuracy of the robotic arm. In addition, it also affects the durability of cables or mechanical components such as bearings and pulleys. Considering the joint motion coupling phenomenon caused by the cable-driven, the decoupling method is proposed, and the kinematic model of the robot is established. To solve the nonlinear coupling characteristics and the uncertainty of the dynamics parameters, a controller is proposed for the humanoid cable-driven hybrid robot, combining proportional-integral-derivative (PID) control based on decoupling method (DC-PID) and the double delay deep deterministic policy gradient (TD3) deep reinforcement learning algorithm. The trajectory tracking of the end-effector position and orientation are controlled by using DC-PID and TD3. And the simulation results show that the proposed control method has good trajectory tracking and convergence performance according to trajectory tracking error and training reward. Finally, the humanoid cable-driven hybrid robot prototype is developed. The experimental results of coupling compensation show that the average maximum error of the joint is reduced by 77.58% after considering the coupling compensation of the joint. The results of the controller validation experiments show that the DC-PID controller reduces the maximum error in each axis by 11.54%, 35.29%, and 40.16%, respectively, compared to the open-loop experiments.

Closed-Loop Subspace Predictive Control of Gyroscope

Control moment gyroscope (CMG) is used in many applications, especially related to spacecraft navigation. Hence, the trajectory tracking problem of the CMG control is important and worth researching. To address this problem, a closed-loop subspace predictive control (CSPC) of the gyroscope is presented in this paper. The proposed control technique constructs an auxiliary variable based on the known controller information. The constructed auxiliary variable assists to handle the inherent correlation between control inputs and noises in the closed-loop system. Additionally, an unbiased prediction of the system output is obtained to calculate the optimal control input. The theoretical analysis of the recursive feasibility and stability of the proposed control technique is also provided. Ultimately, the effectiveness of the proposed control technique is verified on a real-time experimental platform of the CMG. The experimental results demonstrate the improved trajectory tracking and predictive performance of the proposed control technique. Overall, this paper provides a solution for the trajectory tracking problem of the CMG control.

Performance-optimisation-based repetitive trajectory tracking control for autonomous farming vehicle

The high precision trajectory tracking for the autonomous farming vehicle (AFV) is closely related to work quality and crop yield. Farmland operations are usually repetitive tillages, and the farmland soil is relatively soft, slippery, and uneven, which can easily lead to uncertain problems such as slippage, parameter perturbation, and external disturbance. This paper proposes a finite-time repetitive trajectory tracking control strategy integrated with particle swarm optimisation (PSO) and equivalent input disturbance (EID) for the AFV to achieve performance optimisation. The repetitive control framework with finite-time convergence technique can effectively realise the iterative convergence performance of the repetitive trajectory tracking. The PSO algorithm is integrated into determining the control gains to optimise the dynamic and steady-state performances of the trajectory tracking control system. The EID method enhances the tracking precision and robustness to internal and external disturbances. Under MATLAB/Simulink and CarSim co-simulation environment, the effectiveness and advantages of the designed control strategy are illustrated by comparing it with the traditional repetitive control, the EID-based PI control, the active-disturbance-rejection-control-based nonsingular terminal sliding mode control, as well as the sliding-mode-observer-based integral sliding mode control strategies for a farming vehicle.

Disturbance‐observer‐based fault‐tolerant control of robotic manipulator: A fixed‐time adaptive approach

AbstractThe concurrent existence of model uncertainties, external disturbances, and actuator faults in a nonlinear system such as a robotic manipulator can significantly affect the trajectory tracking performance of these systems. Therefore this study is devoted to proposing a control approach based on fixed‐time control theory to improve the trajectory tracking performance of the robotic manipulator in the presence of lumped disturbance, including uncertainties, external disturbances, and actuator faults. The control approach in this paper is designed based on the integration of a fixed‐time adaptive sliding mode observer and a fixed‐time non‐singular fast terminal sliding mode control design strategy. Firstly, a new fixed‐time adaptive sliding mode observer is designed based on fixed‐time theory and adaptive control theory to estimate the lumped disturbance present in the system. Then, using the information from the disturbance observer, the fixed‐time non‐singular fast terminal sliding mode control is devised based on a non‐singular fixed‐time sliding surface and a fixed‐time reaching approach. Furthermore, in the sense of the Lyapunov theorem, through rigorous analysis, it is demonstrated that the tracking errors of the closed‐loop system converge to a small neighbourhood within a fixed time, regardless of the information about the initial conditions of the states of the system. Finally, extensive comparative simulations are performed using the PUMA560 robot to manifest the feasibility and validity of the proposed control strategy in terms of trajectory tracking accuracy and fast convergence in the presence of uncertainties, disturbances, and actuator faults.

A Walking Trajectory Tracking Control Based on Uncertainties Estimation for a Drilling Robot for Rockburst Prevention

A walking trajectory tracking control approach for a walking electrohydraulic control system is developed to reduce the walking trajectory tracking deviation and enhance robustness. The model uncertainties are estimated by a designed state observer. A saturation function is used to attenuate sliding mode chattering in the designed sliding mode controller. Additionally, a walking trajectory tracking control strategy is proposed to improve the walking trajectory tracking performance in terms of response time, tracking precision, and robustness, including walking longitudinal and lateral trajectory tracking controllers. Finally, simulation and experimental results are employed to verify the trajectory tracking performance and observability of the model uncertainties. The results testify that the proposed approach is better than other comparative methods, and the longitudinal and lateral trajectory tracking average absolute errors are controlled in 10.23 mm and 22.34 mm, respectively, thereby improving the walking trajectory tracking performance of the walking electrohydraulic control system for the coal mine drilling robot for rockburst prevention.

Observer-based adaptive tracking control of robotic manipulators with predefined time-guaranteed performance: Theory and experiment

This paper investigates the challenging problem of fixed time trajectory tracking for robotic manipulators under the presence of unavailable model perturbation, external disturbance and from different initial states. Firstly, a novel fixed-time extended state observer (FESO) is designed to estimate and compensate the lumped disturbance, which is analyzed and proved to be stable in the sense of fixed time bounded stability. Secondly, a new type of fixed-time prescribed performance control (FPPC) is constructed to guarantee the system convergences to stable state within a predefined time and enhance transient performance. Furthermore, a novel continuous fixed time nonsingular fast terminal sliding mode variable is established, which addresses singularity obstacle in terminal sliding mode. Together with FESO and FPPC, a new fixed-time adaptive nonsingular fast terminal sliding mode controller (FANFTSMC) is developed. Meanwhile, an adaptive terminal sliding mode reaching law adopted in FANFTSMC promotes the robustness and decreases the chattering phenomenon. Then, the Lyapunov approach is given to clarify the advantages of FANFTSMC in terms of predefined time stabilization and which is demonstrated on a 2-DOF robotic manipulators. Thirdly, theoretical analysis and experiments are presented to illustrate the formulated control strategy owns fine performance and stronger robustness.

Tuning the Proportional-Integral-Derivative Control Parameters of Unmanned Aerial Vehicles Using Artificial Neural Networks for Point-to-Point Trajectory Approach.

Nowadays, trajectory control is a significant issue for unmanned micro aerial vehicles (MAVs) due to large disturbances such as wind and storms. Trajectory control is typically implemented using a proportional-integral-derivative (PID) controller. In order to achieve high accuracy in trajectory tracking, it is essential to set the PID gain parameters to optimum values. For this reason, separate gain values are set for roll, pitch and yaw movements before autonomous flight in quadrotor systems. Traditionally, this adjustment is performed manually or automatically in autotune mode. Given the constraints of narrow orchard corridors, the use of manual or autotune mode is neither practical nor effective, as the quadrotor system has to fly in narrow apple orchard corridors covered with hail nets. These reasons require the development of an innovative solution specific to quadrotor vehicles designed for constrained areas such as apple orchards. This paper recognizes the need for effective trajectory control in quadrotors and proposes a novel neural network-based approach to tuning the optimal PID control parameters. This new approach not only improves trajectory control efficiency but also addresses the unique challenges posed by environments with constrained locational characteristics. Flight simulations using the proposed neural network models have demonstrated successful trajectory tracking performance and highlighted the superiority of the feed-forward back propagation network (FFBPN), especially in latitude tracking within 7.52745 × 10-5 RMSE trajectory error. Simulation results support the high performance of the proposed approach for the development of automatic flight capabilities in challenging environments.

Optimal iterative feedforward parameter tuning for varying trajectory under actuator constraints

AbstractThis paper presents a feedforward control algorithm that combines the benefits of optimal iterative learning control (OILC) and model‐based feedforward control (MFC) using iterative feedforward tuning and input shaping filter (IFT‐ISF) for industrial motion systems. OILC effectively compensates for tracking errors in repeating tasks under actuator constraints. However, its performance deteriorates when the trajectory changes. In contrast, MFC can achieve high performance for varying trajectory tracking tasks, but its performance may degrade for constrained systems if the control force exceeds the actuator saturation boundary. The proposed algorithm aims to overcome these limitations to achieve optimal trajectory tracking performance for varying trajectories under actuator constraints. Simulation and experimental results demonstrate that the proposed algorithm achieves optimal tracking performance while complying with the actuator constraints. The algorithm provides a data‐driven approach without requiring the tedious process of model identification. By combining the benefits of OILC and IFT‐ISF, the proposed algorithm can achieve high‐performance trajectory tracking for both repeating and varying tasks under actuator constraints, making it suitable for industrial motion systems.

Adaptive EKF enhanced fault diagnosis and fault tolerant control for space manipulators with position measurements only

Space manipulators play a critical role in the operation of space robots. However, the failure of these manipulators can affect the control performance and even lead to instability. To improve the safety and robustness of space manipulators, this paper presents an efficient fault diagnosis and fault tolerant control method by integrating adaptive extended Kalman filter (AEKF) and sliding mode control (SMC). The proposed method uses AEKF for system estimation, taking into account uncertainties in the process and measurement noise, as well as sensor limitations. By detecting the failure of angle sensors timely, the trajectory tracking performance can be guaranteed by the robustness of AEKF. In cases where a joint experiences free-swinging, the failure can be identified based on the estimated control effectiveness coefficients from AEKF. Then, once the failure is identified, the joint angle can be regulated by exploiting the motion coupling between the joints. Furthermore, SMC is employed to mitigate the effects of unknown disturbances in the joints. The effectiveness of the proposed method is demonstrated through numerical simulation, which illustrates its ability to diagnose failures and maintain control performance under various failure scenarios. In addition, the robustness of the method is verified through Monte Carlo simulation, demonstrating its reliability in dealing with various uncertainties.

A Multistage Hemiplegic Lower-Limb Rehabilitation Robot: Design and Gait Trajectory Planning.

Most lower limb rehabilitation robots are limited to specific training postures to adapt to stroke patients in multiple stages of recovery. In addition, there is a lack of attention to the switching functions of the training side, including left, right, and bilateral, which enables patients with hemiplegia to rehabilitate with a single device. This article presents an exoskeleton robot named the multistage hemiplegic lower-limb rehabilitation robot, which has been designed to do rehabilitation in multiple training postures and training sides. The mechanism consisting of the thigh, calf, and foot is introduced. Additionally, the design of the multi-mode limit of the hip, knee, and ankle joints supports delivering therapy in any posture and training sides to aid patients with hemiplegia in all stages of recovery. The gait trajectory is planned by extracting the gait motion trajectory model collected by the motion capture device. In addition, a control system for the training module based on adaptive iterative learning has been simulated, and its high-precision tracking performance has been verified. The gait trajectory experiment is carried out, and the results verify that the trajectory tracking performance of the robot has good performance.

Comparison of Two-Wheel and Four-Wheel Steering Using Event-Triggered Predictive Motion Control and Scale Vehicles

Abstract This study compares the trajectory tracking performance of two- and four-wheel steering systems, especially under normal driving conditions. Specifically, the lateral motion is controlled by an event-triggered model predictive control (MPC), which activates either when consecutive control steps surpass the predictive horizon or when tracking error exceeds a predetermined lateral offset. Using a modified 1/10th scale Tamiya TT-02 RC car as a test platform, the tracking performance of both two- and four-wheel systems are evaluated. Results from the experiments highlight the better tracking performance of the four-wheel steering system over the traditional two-wheel systems and demonstrate the benefit of using event-triggered MPC for lateral motion control even under normal driving conditions, contrary to common belief that four-wheel steering systems are beneficial only in tight steering maneuvers.

Saturated Sliding Mode Control Scheme for a New Wearable Back-Support Exoskeleton

Low back pain has been torturing people around the world as a common and chronic disease, the main inducement of which is lumbar disc herniation (LDH). To alleviate patients’ pain noninvasively, this paper proposes a new lumbar spinal rehabilitation exoskeleton. This exoskeleton is composed of two bands connected by four motor-driven piston pushrods, where the range of band can be adjusted to adapt to people with different waistlines. The four pushrods provide support forces to hold the upper body to relieve the burden of lumbar. The joints between pushrods and band are universal pairs and spherical pairs. The whole structure can be regarded as a parallel robot, thus the supporting and waist tracking performance can be determined by motion control effect of pushrods. Considering the motor torque of pushrods is limited, in this paper, a saturated sliding mode control scheme is proposed. Meanwhile, an extended state observer (ESO) is employed to estimate the external disturbance and internal uncertainties, then the estimates of perturbations will be compensated by the feedback scheme. Furthermore, to enhance the disturbance-tracking performance of the ESO an integrated sliding mode observer is proposed to compensate the tracking errors of ESO. The stabilities of controller and observers are proved by Lyapunov stability theory. Finally, a simulation and two experiments are conducted to verify the performance of the proposed controller and the new exoskeleton. The simulation results show that the novel/new controller can drive the new exoskeleton to move along with the desirable trajectory to support the upper body so that alleviating the burden of waist. The results of myoelectricity experiments also show favorable effectiveness of exoskeleton on supporting upper body in different postures. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —this article was inspired by the concerns of low back pain that many people are suffering. Most existing rehabilitation robots tend to focus on supporting lower body and arms, while back-support rehabilitation robots are barely seen. Although we can see a few upper-body supporting robots in sporadic papers, these studies have not proposed a good control scheme yet. Besides, it is difficult to find a rehabilitation robot with simple structure as well as conforming to ergonomics. To resolve the shortcomings of the structure of existing robots and control models, we proposed a completely new rehabilitation robot with novel mechanical structure. Meanwhile, a new saturated sliding mode and novel integrated observer are employed in the position-force control system to enhance the stability and controllability of the whole robot control system. Then, some elaborately designed experiments are conducted to test the proposed robot and the control system. Numerical results demonstrate that the proposed method can significantly increase the trajectory tracking performance and alleviate low back pain.

Barrier Function-Based Integral Sliding Mode Controller Design for a Single-Link Rotary Flexible Joint Robot

Abstract This paper proposes and evaluates a novel control approach for trajectory tracking, stability enhancement, and vibration reduction of a flexible joint robot (FJR). The FJR is a 2-degree-of-freedom underactuated nonlinear system that is challenging to control due to vibration, underactuation, uncertainties, and external disturbances. The control objectives are high trajectory tracking performance together with suppressing vibration. The proposed control approach uses integral sliding mode control (ISMC) combined with a barrier function based on back-stepping. This ensures robust and smooth performance by eliminating the reaching phase where sliding mode control (SMC) is typically not robust. Robustness is thus guaranteed from the start. The FJR is modeled as a 4th-order system using Lagrangian mechanics and decomposed into two 2nd-order subsystems for control design. Sliding variables are defined for each subsystem. Using these variables, the proposed control achieves robust trajectory tracking, stability, and vibration reduction. Numerical simulations in MATLAB validate the superior performance of the proposed ISMC-barrier function control compared to conventional ISMC for the FJR. This novel control approach addresses the challenges of controlling this FJR.