Tracking Error 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.

Robust Control of Motion in Presence of Uncertain Parameters and Control Constraints

The paper describes a novel, simple servo drive position controller, using only knowledge about the structure of the nonlinear model and the constraints met by individual components of the model. The desired behaviour of the position and velocity signals is obtained by imposing a time-varying constraint on the signal aggregating information about position and velocity tracking errors. The method allows you to determine the maximum control (servo drive current) necessary to achieve the control goal under the existing initial conditions and the selected reference trajectory. The control is constrained and consists in appropriate reaction when the trajectory approaches the barrier, the shape of which is responsible for the imposed properties of the transient and quasisteady state tracking error. In addition to the derivation of the control, a discussion of its possible variants and basic properties is presented. Control with time-varying constraints has been introduced, which allows the control objectives to be met with limited conservatism of the imposed constraints. The influence of technical factors related to actual speed and position measurements was discussed and the operation of the real drive on a laboratory stand was presented.

Fault-tolerant control for Markov jump nonlinear systems based on an observer and finite-time fast integral terminal sliding mode control

This paper develops a novel fault-tolerant control based on an observer for underactuated robot manipulators with unknown external disturbances, uncertainties, and actuator faults. First, unlike the traditional approach of treating the robot system as a parameter time-varying system, the underactuated robot manipulator with different drive modes can be considered as one of the classical Markov jump nonlinear systems (MJNSs). Second, an adaptive disturbance observer is designed to estimate the state and disturbances of the system. Finally, based on the observation results, a nonsingular fast integral terminal sliding mode controller (NFITSMC) is utilized to implement fault-tolerant control of the system. Compared with traditional observer and terminal sliding mode controller, the adoption of the novel controller and observer can improve response time and reduce chattering. Especially, in order to eliminate chattering, the integral term is introduced into the nonsingular fast terminal sliding mode controller. Structuring Lyapunov–Krasovskii functional (LKF) and based on linear matrix inequalities (LMIs) techniques, the convergence of control strategy and tracking errors is proved. The simulation results show that the actuator faults can be observed successfully and the error system is finite-time stable.

Neural network-based prescribed performance tracking control for a class of nonlinear systems with mismatched disturbances

This paper addresses the prescribed performance tracking control problem for a class of nonlinear systems subject to mismatched uncertainties. A novel disturbance observer-based control (DOBC) scheme is proposed through combining radial basis function neural network (RBFNN) and prescribed performance function (PPF). In contrast to traditional DOBC, the proposed approach employs RBFNN technology to approximate unknown nonlinear functions in the system, instead of treating them as part of lumped disturbances. A novel disturbance observer is developed to estimate disturbances characterised by a nonlinear exogenous system. To enhance control performance, a PPF that characterises both transient and steady-state behaviour is used for the transformation of tracking errors. It can be proved that all the states of the closed-loop system can be guaranteed to be uniformly ultimately bounded (UUB), and that the tracking error evolves within the prespecified boundaries. Theoretical results are validated and supported by two simulation examples.

Trajectory tracking controller design for wheeled Mobile robot with velocity and torque constraints

This article investigates the trajectory tracking control problem for wheeled mobile robot (WMR) subject to both velocity and torque constraints. Firstly, a more general model is established by considering the displacement between the centre of mass and the midpoint of the driving wheels of the WMR, based on which, a new bounded kinematic controller is proposed by combining the first-order filtering approach to keep the trajectory tracking error asymptotically stable. Then the dynamic controller is designed and the stability of the overall closed-loop system is proved by the Lyapunov stability theory and Barbalat's lemma. Some conditions are given to ensure that both the velocity constraints and torque constraints are satisfied. Finally, some numerical examples are given to show the effectiveness and advantages of the method proposed in this paper.

Adaptive neural network iterative learning control of long-stroke hybrid robots with initial errors and full state constraints

Research on initial errors and constraint restrictions is one of the main research directions in the field of control of uncertain robotic systems. An adaptive iterative learning control (AILC) method based on radial basis function (RBF) neural network is proposed to address the trajectory tracking problem of the long-stroke hybrid robot system with random initial errors and full state constraints. The RBF neural network is used to approximate the unknown nonlinear terms, and the network weights are updated using an iterative learning law that incorporates a projection mechanism. Additionally, a robust learning strategy is used to compensate for both the approximation error of the neural network and the external disturbances that vary with each iteration. To relax the requirement of traditional iterative learning control (ILC) for identical initial condition, an equivalent error function is constructed based on the time-varying boundary layer. The tangent-type barrier Lyapunov function (BLF) is designed to ensure that the joint position and speed of the robot system are bounded within a predetermined range. Through stability analysis based on barrier composite energy function (BCEF), it can be proved that the boundedness of all signals in the closed-loop system and the tracking error of the robot system will converge to an adjustable residual set asymptotically. Finally, through simulation experiments conducted on the MATLAB platform, the results demonstrate that the method overcomes the random initial errors of the system effectively, ensures that the system satisfies the full-state constraints, and realizes high-precision trajectory tracking.

Fixed-time trajectory tracking control of a quadrotor UAV under time-varying wind disturbances: theory and experimental validation

This paper adopts a fixed-time method to study the trajectory tracking issue of a quadrotor unmanned aerial vehicle (UAV) under time-varying wind disturbances. Firstly, in order to address the impact of time-varying wind disturbances on UAV, a fixed-time disturbance observer is constructed to accurately estimate wind disturbances. Secondly, to improve control accuracy and convergence rate, a robust fixed-time controller is designed for the position and attitude system by combining the sliding mode control theory with fixed-time techniques. Furthermore, it is rigorously analyzed that the tracking error of the observer and controller can converge to zero via Lyapunov criterion, and the convergence time is independent of the initial state. Finally, the effectiveness and robustness of the designed control strategy are verified by numerical simulations and actual flight experiments, providing an effective connection between control theory and practical applications.

Indoor AR Navigation Framework Based on Geofencing and Image-Tracking with Accumulated Error Correction

This study presents a novel framework for improving indoor augmented reality (AR) navigation with modern smartphone technology, which is achieved by addressing two major challenges: managing large absolute coordinate spaces and reducing error accumulation in camera-based spatial tracking. Our contribution is significant in two ways. First, we integrate geofencing with indoor navigation by considering spatial tracking errors, timing for audio guidance, and dynamic 3D arrow visualization for effective local-to-global spatial coordinate transformation. This method achieves precise local positioning and seamlessly integrates with larger spatial contexts, overcoming the limitations of current AR systems. Second, we introduce a periodic image-based calibration approach to minimize the inherent error accumulation in camera-based tracking, enhancing accuracy over longer distances. Unlike prior studies focusing on individual technologies, our work explores the software architecture of indoor AR navigation by providing a comprehensive framework for its design and practical use. The practicality of our approach is validated through the implementation of a smartphone application at the Mineral Industry Museum of Akita University, highlighting the limitations of component technologies and demonstrating our framework’s effectiveness.

Product Design Interaction and Experience Based on Virtual Reality Technology

Artificial intelligence involves imitating human thought, consciousness, and other aspects. This is similar to having machine with human brain that can think, produce independently. However, unlike human brain, it has a speed, memory advantage. A virtual reality interactive glove is built using a nine-axis inertial sensor, an artificial intelligence deep learning algorithm. In this research work, Product Design Interaction and Experience Based on Virtual Reality Technology (PDIE-VRT-SCGAN) were proposed. Initially, input gestures data are gathered from the Virtual Reality Experiences (VRE) dataset. The input gestures data is then pre-processed using Multi-Window Savitzky-Golay Filter (MWSGF) to reduce noises, increase overall quality of the gestures data. In order to improving overall user engagement in product design interactions on virtual reality (VR) technology, the pre-processed gestures data are then fed into an adversarial network called a Semi-Cycled Generative Adversarial Network (SCGAN). In general, SCGAN does not express some adaption of optimization strategies for determining optimal parameters to promise exact to improving overall user engagement in product design interactions using VR technology. Therefore, FOX-inspired Optimization (FIO) is proposed to enhance weight parameter of SCGAN method, which precisely improving the user experience in product design interaction. The efficacy of PDIE-VRT-SCGAN method is assessed using a number of performance criteria, including tracking accuracy, frame rate, latency, rendering time, error rate, and user error. The proposed PDIE-VRT-SCGAN method attains 22.36%, 25.42% and 18.17% higher tracking accuracy, 21.26%, 15.42% and 19.27% higher latency, 28.36%, 25.32% and 28.27% higher frame rate compared with existing methods, such as design and implementation of virtual reality interactive product software depend on artificial intelligence deep learning algorithm(DVRI-PS-AI-DL), virtual evaluation system for product designing utilizing virtual reality (VES-PD-VR), and analysis of unsatisfying user experiences with unmet psychological needs for virtual reality exergames utilizing deep learning approach (AUUE-UP-VRE-DLA) respectively.

Prescribed Performance Fault-Tolerant Attitude Tracking Control for UAV with Actuator Faults

This paper proposes a prescribed performance fault-tolerant control based on a fixed-time extended state observer (FXTESO) for a carrier-based unmanned aerial vehicle (UAV). First, the attitude motion model of the UAV is introduced. Secondly, the proposed FXTESO is designed to estimate the total disturbances including coupling, actuator faults and external disturbances. By using the barrier Lyapunov function (BLF), it is proved that under prescribed performance control (PPC), the attitude tracking error is stable within the prescribed range. The simulation results for tracking the desired attitude angle show that the average overshoot and stabilization time of PPC-FXTESO is 0.00455rad and 6.2s. Comparatively, the average overshoots of BSC-ESO and BSC-FTESO are 0.035rad and 0.027rad, with stabilization times of 14.97s and 12.56s, respectively. Therefore, the control scheme proposed in this paper outperforms other control schemes.

Integral reinforcement learning‐based optimal tracking control for uncertain nonlinear systems under input constraint and specified performance constraints

AbstractThis article addresses the optimal tracking control problem with prescribed performance for uncertain nonlinear systems subject to input constraint and unknown disturbances. First, a fixed‐time monotonic convergence function is introduced to restrain tracking error, and a nonlinear mapping technique is employed to transform the constrained error into an unconstrained variable, then the fixed‐time output tracking issue is boiled down to the boundedness problem of the transformed variable. With the aid of a nonquadratic cost function, the input constraint is encoded into the optimization problem. To solve the unknown disturbances, an auxiliary system and an auxiliary disturbance policy are constructed, and the optimal control problem is formulated as a two‐player zero‐sum game. Moreover, a Hamilton–Jacobi–Isaacs (HJI) equation associated with this nonquadratic zero‐sum game is established to give the optimal control and the worst‐case disturbance policy solution. Subsequently, to avoid using knowledge of the system dynamics, three neural network approximators, namely, actor, critic, and disturbance, which are tuned online and simultaneously for approximating the solution of HJI, are constructed based on the integral reinforcement learning algorithm. Theoretical analysis shows that the reconstructed error system states and the weight estimation errors are semi‐globally uniformly ultimately bounded. Finally, the simulation study further tests the availability of the proposed control strategy.

Adaptive command filtered control for a class of nonlinear time delay systems with extreme learning machine

AbstractIn this paper, an extreme learning machine (ELM)‐based adaptive command filtered control method is investigated for a class of strict feedback nonlinear systems with unknown external disturbances and time delay. To begin with, the original system state equation is transformed into a new form on account of coordinate transformation. Subsequently, an ELM is adopted to approximate unknown functions which exist in the whole system states, without any prior knowledges of the ideal weight vectors and approximation errors. Secondly, a command filter is developed for the system under consideration, which can avoid the probem of “explosion of complexity” caused by repeated derivation of virtual control signals in traditional backstepping control. Meanwhile, error compensation signals are designed to conquer the shortcoming of a dynamic surface control (DSC) method. The combination of ELM and command filter technique has been used to construct corresponding controllers and adaptive laws. Effective handling of the impact of time delay terms is ensured through designing a novel Lyapunov–Krasovskii functional. The proposed strategy guarantees boundedness of all signals in the closed‐loop system and the tracking error asymptotically converges to a compact set around the origin. In the end, two continuous stirred tank reactors (CSTRs) are taken as example to further verify the efficiency of the put forward control method.

Research on layered control of path tracking for unmanned industrial vehicles based on fully hydraulic steering leakage compensation

Industrial vehicles work in complex terrain, the variable centre of mass position, leakage nonlinearity of full hydraulic steering and other issues lead to poor path tracking stability and accuracy. In this paper, an intelligent hierarchical controller for industrial vehicles’ path tracking is designed with full hydraulic steering leakage compensation, including an upper decision layer and a lower execution layer. The upper decision layer observes the pavement-tyre adhesion coefficients through an extended Kalman filter algorithm, and uses the real-time observations of the adhesion coefficients to establish a variable constraint control for the linear time-varying MPC, and thus performs the path tracking control. The lower actuator layer receives the upper layer’s target steering wheel angle output and performs steering operations. Based on the establishment of a mathematical model of full hydraulic steering considering the leakage characteristics, it analyses the leakage disturbance factors and constructs a fuzzy feed-forward steering leakage compensation controller to compensate for the leakage disturbances in real time for path tracking steering. Simulation and experimental results show that the lateral acceleration, sideslip angle, tyre side slip angle and tracking error of intelligent industrial vehicles under different loads and working conditions are improved by more than 32.4%, 35.8%, 40.2% and 45.8% respectively, and the designed hierarchical controller for the path tracking of intelligent industrial vehicles, which considers the compensation of all-hydraulic steering leakage, can effectively improve the path tracking stability and tracking accuracy of intelligent industrial vehicles under different loads and working conditions.

Decentralized Output-Feedback Adaptive Event-Triggered Control for Interconnected Nonlinear Delay Systems with Actuator Failures

This paper investigates decentralized adaptive event-triggered fault-tolerant control for interconnected nonlinear delay systems with actuator failures. The actuator failures suffered include loss of effectiveness and bias faults. A control scheme based on the K-filter is proposed, which effectively compensates for the effects of unknown actuator failures. A hyperbolic tangent function and neural network are introduced to approximate the unknown interconnection function and nonlinear delay function. By introducing the dynamic surface control method, the “explosion of complexity” issue is addressed. Furthermore, our proposed controller can ensure that all states of the corresponding closed-loop system are semi-globally uniformly ultimately bounded and that the tracking error can converge to a small neighborhood of zero. Meanwhile, Zeno behavior can be effectively avoided. Finally, the validity of the proposed control scheme is verified using a simulation example.

Critic learning control via zero-sum differential game for affine formation maneuver of multi-agent systems with cyber-attacks

The affine formation maneuver (AFM) control problem using the zero-sum differential game is studied for a second-order multi-agent system (MAS) against cyber-injection attacks on the actuators. First and foremost, the distributed control signals and the cyber-injected attack signals are viewed as two competing teams. Then, the leader-follower tracking error system is established where the followers aim to track the AFMs of the leaders. The leader-follower distributed optimal control policies and the cyber-attack attenuation policies are derived from the Nash equilibrium solution of the Hamilton-Jacobi-Isaac (HJI) equation. The solution of the HJI equation is estimated with the aid of the critic neural network. The weights of the critic system are learned online based on the adaptive dynamic programming (ADP) scheme. The uniformly ultimately bounded stability of the closed-loop system under the formulated zero-sum differential game control strategy has been proven by the Lyapunov stability theorem. A simulation example illustrates that the presented control method can attenuate cyber-injection attacks on the actuators and maintain the AFMs of the agents.

Self-supervised learning for interventional image analytics: toward robust device trackers.

The accurate detection and tracking of devices, such as guiding catheters in live X-ray image acquisitions, are essential prerequisites for endovascular cardiac interventions. This information is leveraged for procedural guidance, e.g., directing stent placements. To ensure procedural safety and efficacy, there is a need for high robustness/no failures during tracking. To achieve this, one needs to efficiently tackle challenges, such as device obscuration by the contrast agent or other external devices or wires and changes in the field-of-view or acquisition angle, as well as the continuous movement due to cardiac and respiratory motion. To overcome the aforementioned challenges, we propose an approach to learn spatio-temporal features from a very large data cohort of over 16million interventional X-ray frames using self-supervision for image sequence data. Our approach is based on a masked image modeling technique that leverages frame interpolation-based reconstruction to learn fine inter-frame temporal correspondences. The features encoded in the resulting model are fine-tuned downstream in a light-weight model. Our approach achieves state-of-the-art performance, in particular for robustness, compared to ultra optimized reference solutions (that use multi-stage feature fusion or multi-task and flow regularization). The experiments show that our method achieves a 66.31% reduction in the maximum tracking error against the reference solutions (23.20% when flow regularization is used), achieving a success score of 97.95% at a faster inference speed of 42 frames-per-second (on GPU). In addition, we achieve a 20% reduction in the standard deviation of errors, which indicates a much more stable tracking performance. The proposed data-driven approach achieves superior performance, particularly in robustness and speed compared with the frequently used multi-modular approaches for device tracking. The results encourage the use of our approach in various other tasks within interventional image analytics that require effective understanding of spatio-temporal semantics.

Adaptive Fuzzy Fixed-Time Control for Nonlinear Systems with Unmodeled Dynamics

This article concentrates on the problem of fixed-time tracking control for a certain class of nonlinear systems with unmodeled dynamics. Unmodeled dynamics are prevalent in practical engineering systems, such as axially symmetric systems like robotic arms, spacecraft, and missiles. In this paper, the fuzzy-logic systems (FLSs) are implemented to address the challenge of accurately approximating the unknown nonlinear terms that arise during the derived control algorithm process. By employing fixed-time command filters (FTCF), the “explosion of complexity” issues encountered in traditional backstepping methods will be effectively resolved. Moreover, error compensation mechanisms are derived to effectively mitigate the filtering errors that may arise from the FTCFs. The computational burden associated with FLSs is reduced through the utilization of the weight vector estimation method based on the maximal norm and an adaptive approach. A fixed-time adaptive fuzzy tracking controller is developed within the backstepping control framework to ensure the boundedness of all signals and achieve fixed-time convergence of the tracking error for the controlled system. Illustrative examples are conducted to illustrate the viability of the derived controller.

Accelerated Gradient Approach For Deep Neural Network-Based Adaptive Control of Unknown Nonlinear Systems.

Recent connections in the adaptive control literature to continuous-time analogs of Nesterov's accelerated gradient method have led to the development of new real-time adaptation laws based on accelerated gradient methods. However, previous results assume that the system's uncertainties are linear-in-the-parameters (LIP). To compensate for non-LIP uncertainties, our preliminary results developed a neural network (NN)-based accelerated gradient adaptive controller to achieve trajectory tracking for nonlinear systems; however, the development and analysis only considered single-hidden-layer NNs. In this article, a generalized deep NN (DNN) architecture with an arbitrary number of hidden layers is considered, and a new DNN-based accelerated gradient adaptation scheme is developed to generate estimates of all the DNN weights in real-time. A nonsmooth Lyapunov-based analysis is used to guarantee the developed accelerated gradient-based DNN adaptation design achieves global asymptotic tracking error convergence for general nonlinear control affine systems subject to unknown (non-LIP) drift dynamics and exogenous disturbances. A comprehensive set of simulation studies are conducted on a two-state nonlinear system, a robotic manipulator, and a complex 20-D nonlinear system to demonstrate the improved performance of the developed method. Our simulation studies demonstrate enhanced tracking and function approximation performance from both DNN architectures and accelerated gradient adaptation.

Do socially responsible indices outperform conventional indices? Evidence from before and after the onset of Covid‐19

AbstractAccording to traditional portfolio theories constraints, restrictions, and screens applied in portfolio selection reduces the diversification opportunities which can impact financial performance. Is this true in the case of socially responsible investment (SRI)? To answer this, present study analyzes the performance of Socially Responsible (SR) indices in comparison to conventional indices in an emerging economy. The uniqueness of the study is that it analyses the performance of Shariah, ESG, and thematic indices in a single study. Further, the study measures the impact of Covid‐19 on them. Comparative performance evaluation was conducted by using absolute return analysis and risk‐adjusted measures namely, Sharpe ratio, Treynor ratio, tracking error, information ratio, capital asset pricing model (CAPM), Fama–French three‐factor, and Carhart's four‐factor models. The Structural break was identified, hence analysis was conducted for the total period (January 2017–March 2023) and two sub‐periods, that is, pre and post‐Covid‐19 period. No significant difference was found between the returns of SR indices and conventional indices as against the benchmark index on the basis of absolute return analysis. Sharpe ratio and Treynor ratio both were having negative values for all the SR and conventional indices. Tracking error for all the SR and Conventional indices were very low. The CAPM and both multi‐factor models univocally pointed toward the underperformance of all the SR (except S&P BSE 100 ESG index which had equal performance) and both conventional indices against the benchmark index. Noteworthy point is that only Shariah indices gave the highest returns during post‐Covid period. This research will help in deepening the SRI in the capital market. Companies should increase their ESG scores and make efforts to be listed on the SR indices. Policymakers should announce some kind of rebates, or recognition for star‐performing companies in the field of sustainability to encourage other companies to adopt SR practices in their business operations. The novelty of the current study is that it adds to the socially responsible literature by analyzing the performance of Shariah, ESG, and Thematic indices and conventional indices in a single study in the fastest‐growing economy of India and analyses the impact of Covid‐19 on this performance.

Event‐triggered obstacle avoidance control for autonomous surface vehicles with actuator faults

AbstractThe article addresses the event‐triggered obstacle avoidance control problem for autonomous surface vehicles subject to actuator faults. In order to tackle the challenges presented by unknown actuator faults, internal model uncertainties, and external disturbances, we propose a fault‐tolerant control scheme that relies on an extended state observer to estimate the unknown parameters. In addition, considering the occurrence of actuator faults, a novel event‐triggered mechanism is developed to reduce wear of actuator and ensures the performance of system. On this basis, we employ backstepping technique and an improved artificial potential function methods to develop an event‐triggered obstacle avoidance control scheme with the capability of fault tolerance. This proposed control strategy ensures the uniform ultimate boundedness of tracking errors. In contrast to existing results, the presented control strategy simultaneously holds the performance of obstacle avoidance and fault tolerance and reduce the update frequency of actuators. The effectiveness of the provided control scheme has been confirmed through simulation.