The trajectory planning problem is a key aspect of underwater robot operations. Most existing studies focus on a single underwater robot and environmental obstacles, with limited research on collision avoidance planning among multiple underwater robots. This paper addresses these issues for multiple underwater robots by performing the simultaneous target tracking (STT) from an optimization perspective. On the basis of the neurodynamic design method, the path tracking, collision avoidance, and communication maintenance are formulated as a series of inequality and equality constraints. By incorporating these constraints, the STT scheme, which is depicted as a unified quadratic program (QP) framework, is thus established for multiple underwater robots with certified safety. Such a QP-type STT scheme is then solved by using the Lagrangian-based recurrent neural network. Computer simulations are performed to further verify the effectiveness and feasibility of the proposed QP-type STT scheme. These results indicate that the multiple underwater robots via the proposed STT scheme can accomplish the assigned target-tracking tasks while maintaining the safe distance to avoid collision and staying within communication range throughout the tracking mission.

Motion planning (MP) is one of fundamental issues in robot manipulators. Various MP schemes at joint velocity and acceleration levels are reported, but the noise impact is usually neglected. This paper presents an enhanced version of the acceleration-level MP (ALMP) method, incorporating additive noise considerations, specifically designed for robotic manipulators. Then, such an improved method, which is based on the pseudoinverse of robots’ Jacobian matrix, is theoretically proven to be robust against different types of noise. As case studies of the improved method, the noise-tolerance repetitive motion planning (NT-RMP) and the noise-tolerance minimum acceleration norm (NT-MAN) scheme are established for robot manipulators. Simulation and experiment results under the UR5 and Panda robot manipulators corrupted by different noises further validate the effectiveness and practicality of such two schemes and the improved ALMP method.

Achieving repetitive motion planning (RMP) is essential in the study of mobile robot manipulators. This paper presents an acceleration-level RMP (ALRMP) scheme for omnidirectional mobile robotic manipulators (OMRMs). Specifically, a new acceleration-level performance index is designed to realize RMP using the gradient-dynamics and neurodynamics methods. Leveraging this index and incorporating physical constraints (i.e., position-level, velocity-level, and acceleration-level limits), a novel ALRMP scheme is proposed and analyzed. The scheme is formulated as a quadratic program (QP) and solved using a neural network solver. Comparative simulations conducted on an OMRM demonstrate the effectiveness and superiority of the proposed ALRMP scheme over the velocity-level RMP scheme. The applicable potential of the proposed ALRMP scheme is further indicated via the real-world experiment on a practical OMRM system.

Infrared maritime object detection is a crucial technology for sea surface monitoring in low-light conditions within maritime Internet of Things (IoT) systems. In practical applications, this task faces significant challenges, including diverse target sizes and stringent real-time processing requirements. To address these challenges, a DEtection TRansformer with Global-Local Adaptive Fusion attention for infrared maritime object detection (GLAF-DETR) is proposed. The Global-Local Adaptive Fusion (GLAF) attention mechanism is designed to capture both global contextual information and fine local details of objects. GLAF dynamically adjusts attention across regions by integrating long-range dependencies with short-range positional information, significantly enhancing detection performance for targets of varying sizes in complex maritime environments. In addition, the Dynamic Adaptive Multiscale Feature Fusion (DAMFF) module is proposed to promote cross-channel interaction among multiscale features. Guided by GLAF, DAMFF dynamically fuses these features, further enhancing the accuracy of multiscale object detection. The lightweight HGNetv2-IRLight backbone is designed to minimize network complexity and ensure real-time performance by reducing redundant information while maintaining strong infrared feature extraction. Extensive experiments conducted on an infrared maritime object dataset show that GLAF-DETR surpasses state-of-the-art methods in both detection accuracy and inference speed. It demonstrates outstanding performance, particularly in detecting objects across different scales, offering enhanced accuracy and robustness in challenging maritime scenarios.

This paper studies the stabilization problem of two-dimensional (2D) Markov jump systems (MJSs) with directional communication delays, where delays exist in both states and modes. Based on whether the delay mode can be directly observed, the mode-delayed and asynchronous controllers are designed, respectively. For the mode-delayed case, the closed-loop system with current modes and delayed modes is re-planned as a closed-loop 2D MJS. For the asynchronous case, an extended hidden Markov model is developed to describe the asynchronous modes in controllers. Based on the Lyapunov theory, sufficient conditions are derived to ensure the asymptotic mean square stability of the closed-loop 2D MJSs under these two cases. Finally, two different examples from a representative model of some thermal processes are verified in simulations to demonstrate the effectiveness of the designed approaches. Note to Practitioners—2D systems have found extensive applications in thermal processes, gas absorption, and water stream heating, etc. In these applications, sudden changes in parameters and structures are difficult to avoid, which will result in the system being unable to be described. Fortunately, this problem can be handled by the Markov model, which consists of modes and states. In the control problem of 2D MJSs, delayed states are usually considered in the plant. Consider a more practical case that delays exist in directional communication channels between the plant and the controller, resulting in directional delayed modes and states in the controller. In this case, how to handle these complex modes and state information and stabilize the system is of practical significance. Based on whether the delay mode can be directly observed, the mode-delayed and asynchronous controllers are designed, respectively. Finally, two different examples from a representative model of some thermal processes are verified in simulations to demonstrate the effectiveness of the designed approaches.

The quadratic program (QP) with equality constraint is widely involved in science and engineering fields. Numerous solutions to the equality-constrained QP (ECQP) have been reported, particularly the zeroing neural network (ZNN) for the time-dependent ECQP. However, such solutions can be severely affected by the harmonic noise and may lose their efficacy. This study aims to address the above limitation by proposing the new ZNN model against harmonic noise with the only known frequency. Such a model, called the harmonic noise rejection ZNN (HNR-ZNN) model, is established by incorporating the dynamics of the harmonic signal (from which the unknown information for the signal's amplitude and phase can be eliminated). Theoretical analysis indicates that the proposed HNR-ZNN model effectively determines the optimal solution of time-dependent ECQP under harmonic noise interference. Comparative computer simulations and real-world robot applications further indicate the validity, excellence, and practicality of the presented HNR-ZNN model.

Constrained nonlinear equations (CNEs) are involved in numerous practical applications, and many solutions to CNEs have been reported. In particular, a special neural network called zeroing neural network (ZNN) has recently been developed to solve the time-dependent CNE (TDCNE). In this study, we propose a new discrete-time ZNN (DTZNN) model to determine the numerical solution of the TDCNE. Such a model, which is derived from the discretization of the previous ZNN model via a special difference formula, can achieve excellent performance on computing and solving the TDCNE. Theoretical analysis and comparative numerical results further denote the validity and superiority of the proposed DTZNN model. Finally, the proposed model is used to simulate the dual-arm robot system, which verifies the practicability and feasibility of the DTZNN.

Object detection on unmanned aerial vehicle (UAV) images is an important branch of object detection, belonging to small object detection in a broad sense. Detecting objects in UAV images poses a greater challenge due to the predominance of small objects and dense occlusion caused by UAV capturing images from varying heights and angles. To solve the above problems, we propose Residual Spatial Reduced Transformer based on YOLOv5 (RSRT-YOLOv5). Specifically, Slice Aided Enhancement Module (SAEM) is introduced to enhance the feature quality of small objects. Secondly, a Global attention-based Bi-directional Feature Fusion (GBFF) module is proposed. In the Neck architecture, an efficient Residual Spatial Reduced Transformer (RSRT) module is integrated in order to achieve more efficient feature representation and richer global contextual associations. Finally, our method is evaluated on the Visdrone2019 dataset, and the experimental results show that RSRT-YOLOv5 outperforms the baseline model (yolov5) and successfully improves the detection performance of UAV images.

Parallel robots including Gough–Stewart platforms are widely applied in industrial factories and medical fields. This article investigates a kinematically redundant Gough–Stewart robot, designs, and compares three novel zeroing neural networks (ZNNs) to serve as the redundancy-resolution controllers. Unlike the existing ZNN controllers, the newly designed ZNN controllers are endowed with the capability to handle joint constraints by using a nonlinear complementarity problem function without introducing any extra hyperparameters, guaranteeing the safety of the robot. The proposed ZNN controllers are training-free, noniterative, and more accurate, as compared with other typical neural controllers for kinematic control of the Gough–Stewart robot. Theoretically, the convergence analyses of the ZNN controllers are rigorously carried out. Corresponding discrete neural controllers are established and then applied to the kinematically redundant Gough–Stewart robot with two path-tracking tasks exemplified. The path-tracking results comparatively substantiate the effectiveness and superiority of the ZNN controllers for redundancy resolution under joint constraints.

In this article, configuration adjustment (CA) for robot manipulators at the joint-acceleration level is presented. Specifically, a new acceleration-level performance index for achieving CA is designed by employing the neurodynamic method. Thus, based on this performance index, and by incorporating joint physical constraints (i.e., joint-configuration, -velocity, and -acceleration limits), a novel acceleration-level CA (ALCA) scheme for robot manipulators is proposed and investigated. The proposed ALCA scheme is transformed into a quadratic program and calculated using a neural network solver. Comparative simulation results obtained with a four-link robot manipulator are presented to substantiate the effectiveness and superiority of the proposed ALCA scheme compared with those of the velocity-level CA scheme. Moreover, simulations and experiments are conducted on a practical Epson robot manipulator to demonstrate the physical realization of the proposed ALCA scheme.

Repetitive motion planning (RMP) plays a remarkable role in the operation of robotic manipulators. In this article, the RMP of robotic manipulators wherein the high precision of joint angle repeatability and end-effector motion is guaranteed is investigated. In particular, a novel pseudoinverse-based (P-based) RMP scheme is designed and proposed for robotic manipulators by applying a special difference rule to discretize the existing RMP scheme with P-based formulation. Such scheme is theoretically analyzed and proven to simultaneously guarantee joint angle repetitive precision and end-effector motion precision. Comparative simulation results of a five-link robotic manipulator and a universal robotic manipulator are provided to verify the effective performance of the proposed P-based RMP scheme. The physical realizability of the proposed scheme is further substantiated by implementing the scheme on a practical EPSON robotic manipulator.

A typical recurrent neural network (RNN) has been developed for the online solution of a time-varying underdetermined linear system (TVULS) with bound constraint. This article provides a complete investigation by proposing a new discrete-time RNN (DTRNN) model to solve the bound-constrained TVULS. In particular, the continuous-time RNN (CTRNN) model in the existing literature for solving the bound-constrained TVULS is presented. The new DTRNN model is established and investigated by utilizing the Taylor difference formula to discretize the CTRNN model for determining the solution of the TVULS with bound constraint. Theoretical analysis and numerical results are provided to validate the effectiveness and superiority of the proposed DTRNN model. The model applicability is substantiated through the simulations on a PUMA560 robotic manipulator using the proposed DTRNN model.

The Zhang neural network (ZNN) has recently realized remarkable success in solving time-varying problems. Harmonic noise widely exists in industrial applications and can severely affect the solution computed by ZNN models. This article attempts to solve the aforementioned limitations by providing the first ZNN design with an inherent capability to prohibit harmonic noise. Moreover, it opens new opportunities to shift the research on ZNNs in ideal situations to that with theoretical consideration on nonideal working environments. We establish a modified ZNN design formula in a noisy environment by incorporating the dynamics of harmonic signals. Theoretical analysis shows the convergence of the proposed ZNN design. An application case study for the new ZNN model verifies its effectiveness for time-varying matrix inversion in the presence of harmonic noise. The simulation further substantiates the effectiveness, superiority, and application prospects of the proposed ZNN design.

Repetitive motion planning (RMP) is a crucial issue encountered in studies on redundant robot manipulators. Numerous RMP schemes have been established in previous studies wherein simulations are assumed to be free of noise. However, noise is ubiquitous and can severely affect RMP schemes to the point of causing failure. This paper attempts address the limitations imposed by noise by providing the first RMP scheme with inherent noise-suppression capability. The new RMP scheme for redundant robot manipulators in a noisy environment is proposed on the basis of an equality criterion that is robust against additive noise. The equality criterion is established by incorporating the proportional and integral information of the desired end-effector path. The proposed scheme is reformulated as a quadratic program and is calculated by using a recurrent neural network. Comparative simulation results obtained with PA10 and four-link robot manipulators illustrate the effectiveness and superiority of the proposed RMP scheme over the traditional RMP scheme.

Neural networks have been generally deemed as important tools to handle kinds of online computing problems in recent decades, which have plenty of applications in science and electronics fields. This paper proposes a novel recurrent neural network (RNN) to handle the perturbed time-varying underdetermined linear system with double bound limits on residual errors and state variables. Beyond that, the bound-limited underdetermined linear system is converted into a time-varying system that consists of linear and nonlinear formulas through constructing a nonnegative time-varying variable. Then, theoretical analyses are conducted to verify the superior convergence performance of the proposed RNN model. Furthermore, numerical experiment results and computer simulations demonstrate the superiority and effectiveness of the proposed RNN model for handling the time-varying underdetermined linear system with double bound limits. Finally, the proposed RNN model is applied to the physically limited PUMA560 robot to show its satisfactory applicabilities.

Recurrent neural network (RNN) has recently been viewed as a significant alternative to online mathematical problem solving. This paper offers important improvements by proposing the first RNN model to solve the time-dependent underdetermined linear system with bound constraint. In particular, by introducing a time-dependent nonnegative vector, the bound-constrained underdetermined linear system is initially transformed into a time-dependent system that comprises linear and nonlinear equations. The newly constructed RNN model can thus zero in on the time-dependent equations. Then, the model is theoretically proven to have convergence properties, and the simulation results further substantiate the efficacy of the proposed RNN model to solve the time-dependent underdetermined linear system with bound constraint. Finally, the proposed RNN model is applied to physically constrained redundant robot manipulators, thereby indicating the applicability of the proposed model.

A typical recurrent neural network called zeroing neural network (ZNN) was developed for time-varying problem-solving in a previous study. Many applications result in time-varying linear equation and inequality systems that should be solved in real time. This paper provides a ZNN model for determining the solution of time-varying linear equation and inequality systems. By introducing a nonnegative slack variable, the time-varying linear equation and inequality systems are transformed into a mixed nonlinear system. The ZNN model is established via the definition of an indefinite error function and the usage of an exponential decay formula. Theoretical results indicate the convergence property of the proposed ZNN model. Comparative simulation results prove the ZNN effectiveness and superiority for time-varying linear equation and inequality systems. Furthermore, the proposed ZNN model is employed to robot manipulators, thus showing the ZNN applicability.

Recently, the approach based on recurrent neural network (RNN) has been considered a powerful alternative to mathematical problem solving. In this study, a new discrete-time RNN (DTRNN) is proposed and investigated to determine an exact solution of dynamic nonlinear equations. Specifically, the resultant DTRNN model is established for solving dynamic nonlinear equations by utilizing a Taylor-type difference rule. This DTRNN model is then theoretically proven to have an O(τ4) error pattern, where τ denotes the sampling gap. Comparative numerical results are illustrated to further substantiate the efficacy and superiority of the proposed DTRNN model in comparison with the existing approach. Finally, the proposed DTRNN model is applied to redundant robot manipulators by solving the system of dynamic nonlinear kinematic equations, indicating the application prospect of the proposed model.

Continuous-time and discrete-time forms of Zhang dynamics (ZD) for time-varying nonlinear optimization have been developed recently. In this paper, a novel discrete-time ZD (DTZD) algorithm is proposed and investigated based on the previous research. Specifically, the DTZD algorithm for time-varying nonlinear optimization is developed by adopting a new Taylor-type difference rule. This algorithm is a five-step iteration process, and thus, is referred to as the five-step DTZD algorithm in this paper. Theoretical analysis and results of the proposed five-step DTZD algorithm are presented to highlight its excellent computational performance. The geometric representation of the proposed algorithm for time-varying nonlinear optimization is also provided. Comparative numerical results are illustrated with four examples to substantiate the efficacy and superiority of the proposed five-step DTZD algorithm for time-varying nonlinear optimization compared with the previous DTZD algorithms.

Recently, a new formula with noise-tolerant capability has been designed by Zhang et al., and the resultant Zhang dynamics (ZD) models have been developed to solve different types of time-varying problems. Based on previous research, this paper presents and investigates the application of such a noise-tolerant ZD design formula to kinematic control of redundant robot manipulators via time-varying nonlinear equations solving. Specifically, by exploiting this ZD design formula to solve the system of time-varying nonlinear kinematic equations involved in robot control, the redundancy-resolution scheme is established. Such a scheme contains the proportional, integral, and derivative information of the desired Cartesian path of the robot end-effector and can thus be viewed as a nonlinear proportional-integral-derivative controller for redundant robot manipulators. Then, theoretical results are given to show that the redundancy-resolution scheme has the capability of noise suppressing. Simulation results based on a four-link planar robot manipulator and a PA10 robot manipulator with zero, constant, and bounded time-varying noises further substantiate the efficacy and superiority of the redundancy-resolution scheme, and show the application prospect of the noise-tolerant ZD design formula.

In the previous work, a continuous-time Zhang neural network (CTZNN) has been proposed for online solution of time-varying linear matrix inequality (LMI). For completeness and also for the purposes of potential digital hardware implementation and numerical algorithm development, this paper further develops the discrete-time form of such a CTZNN, which is termed as the discrete-time ZNN (DTZNN). Specifically, in this paper, by utilizing the Taylor-type difference rule, the three-step DTZNN algorithm is proposed and investigated to solve the time-varying LMI. Then, for this DTZNN algorithm, theoretical results are also given to show its excellent computational property. Numerical results further substantiate the efficacy of the proposed three-step DTZNN algorithm for time-varying LMI solving.

In the previous work, Zhang et al. developed a special type of recurrent neural networks called Zhang neural network (ZNN) with continuous-time and discrete-time forms for time-varying matrix inversion. In this paper, a novel discrete-time ZNN (DTZNN) model for time-varying matrix inversion is proposed and investigated. Specifically, a new numerical difference rule based on Taylor series expansion is established in this paper for first-order derivative approximation. Then, by exploiting this Taylor-type difference rule, the novel DTZNN model, which is a five-step iteration algorithm, is thus proposed for time-varying matrix inversion. Theoretical results are also presented for the proposed DTZNN model to show its excellent computational property. Comparative numerical results with three illustrative examples further substantiate the efficacy and superiority of the proposed DTZNN model for time-varying matrix inversion compared with previous DTZNN models.

This paper primarily demonstrates the effectiveness of the Z-type methodology for solving the problem of time-variant matrix inverse (termed Zhang matrix inverse, ZMI). As a case study of ZMI with examples, the online solution of ZMI is investigated in this paper. Specifically, different Zhang functions (ZFs), which lead to different effective Z-type models (i.e., Zhang neural nets), are proposed and implemented as the error basis functions for ZMI. Meanwhile, a specific relationship between the Z-type model and others' model/method [i.e., the Getz and Marsden (G-M) dynamic system] is presented. Eventually, the MATLAB Simulink modeling and simulative verifications with examples using such different Z-type models are further researched. Both theoretical analysis and modeling results demonstrate the efficacy of the proposed Z-type models which originate from different ZFs for ZMI.

This paper proposes and investigates a weighted velocity and acceleration minimization scheme to prevent the occurrence of high joint velocity and joint acceleration caused by the minimum acceleration norm (MAN) scheme in redundant robot manipulators. The proposed scheme considers minimum kinetic energy (MKE) and MAN criterions via two weighting factors, thus guaranteeing the final joint velocity of motion to be near zero, which is acceptable for engineering applications. Joint physical constraints (i.e., joint angle limits, joint velocity limits, and joint acceleration limits) are incorporated in the formulation of the proposed scheme. The proposed scheme is reformulated as a quadratic program and then calculated by using a numerical algorithm based on linear variational inequality. Computer simulation results of a PUMA560 robot manipulator verify the efficacy and flexibility of the proposed scheme for redundancy resolution in robot manipulators. Experimental verifications conducted on a six-link planar robot manipulator demonstrate the effectiveness and physical realizability of the proposed scheme.

In this paper, for online solution of time-varying linear matrix inequality (LMI), such an LMI is first converted to a time-varying matrix equation by introducing a time-varying matrix, of which each element is greater than or equal to zero. Then, by employing Zhang et al.'s neural dynamic method, a special recurrent neural network termed Zhang neural network (ZNN) is proposed and investigated for solving online the converted time-varying matrix equation as well as the time-varying LMI. Such a ZNN model showed in an explicit dynamics exploits the time-derivative information of time-varying coefficients. In addition, theoretical analysis and results of the proposed ZNN model are discussed and presented to show its excellent performance on solving the time-varying LMI. Computer simulation results further demonstrate the efficacy of the proposed ZNN model for online solution of the time-varying LMI and the converted time-varying matrix equation.

In this paper, two simple-structure neural networks based on the error back-propagation (BP) algorithm (i.e., BP-type neural networks, BPNNs) are proposed, developed, and investigated for online generalized matrix inversion. Specifically, the BPNN-L and BPNN-R models are proposed and investigated for the left and right generalized matrix inversion, respectively. In addition, for the same problem-solving task, two discrete-time Hopfield-type neural networks (HNNs) are developed and investigated in this paper. Similar to the classification of the presented BPNN-L and BPNN-R models, the presented HNN-L and HNN-R models correspond to the left and right generalized matrix inversion, respectively. Comparing the BPNN weight-updating formula with the HNN state-transition equation for the specific (i.e., left or right) generalized matrix inversion, we show that such two derived learning-expressions turn out to be the same (in mathematics), although the BP and Hopfield-type neural networks are evidently different from each other a great deal, in terms of network architecture, physical meaning, and training patterns. Numerical results with different illustrative examples further demonstrate the efficacy of the presented BPNNs and HNNs for online generalized matrix inversion and, more importantly, their common natures of learning.

This paper proposes a new inequality-based criterion/constraint with its algorithmic and computational details for obstacle avoidance of redundant robot manipulators. By incorporating such a dynamically updated inequality constraint and the joint physical constraints (such as joint-angle limits and joint-velocity limits), a novel minimum-velocity-norm (MVN) scheme is presented and investigated for robotic redundancy resolution. The resultant obstacle-avoidance MVN scheme resolved at the joint-velocity level is further reformulated as a general quadratic program (QP). Two QP solvers, i.e., a simplified primal-dual neural network based on linear variational inequalities (LVI) and an LVI-based numerical algorithm, are developed and applied for online solution of the QP problem as well as the inequality-based obstacle-avoidance MVN scheme. Simulative results that are based on PA10 robot manipulator and a six-link planar robot manipulator in the presence of window-shaped and point obstacles demonstrate the efficacy and superiority of the proposed obstacle-avoidance MVN scheme. Moreover, experimental results of the proposed MVN scheme implemented on the practical six-link planar robot manipulator substantiate the physical realizability and effectiveness of such a scheme for obstacle avoidance of redundant robot manipulator.