To solve the rust removal planning problem for multiple mobile manipulators on curved surfaces, a novel Gradual-Steepness Recurrent Neural Network (GS-RNN) is proposed in this article. Firstly, the K-means algorithm and ant colony algorithm are used to generate collaborative rust removal paths for multiple manipulators based on the surface and rust removal requirements. Then, considering the end-effector tracking task and velocity constraints, the rust removal task for multiple mobile manipulators on the curved surface is formulated as a time-varying quadratic programming (TVQP) problem with equality and inequality constraints. Secondly, the steepening function is designed, the Karush-Kuhn-Tucker (KKT) condition is improved, and the relevant theories and detailed derivations are given. Finally, the GS-RNN for solving this problem was obtained. Computer simulation experiments verify the effectiveness and feasibility of the proposed method, and the results show that GS-RNN significantly outperforms existing methods in terms of precision and robustness.

For cooperative motion planning of multi-redundant manipulators systems (MRMs) under randomly switching topologies, an adaptive switched time-varying neural network solver (ASTVNN) is developed by integrating Markov processes. To address the challenge of fixed Laplace matrices being incompatible with randomly switching systems, the network topology is constructed by employing two types of Markov random processes (with fully known transition matrices and partially unknown transition matrices). Furthermore, by integrating the coupling relationships among joint positions, velocities, and physical constraints in MRMs, the cooperative motion planning control is formulated as a time-varying quadratic programming problem. The proposed ASTVNN is designed and implemented to solve this problem, where the ASTVNN with error signals exhibits excellent convergence performance. Furthermore, the convergence of the ASTVNN is demonstrated through Lyapunov stability analysis and linear matrix inequality techniques. Finally, simulation results and physical experiment show that the MRMs can realize trajectory cooperative control under two stochastic switching topologies, comparative experiments show that the proposed ASTVNN has better control effects.

In order to enable the mobile parallel manipulator to avoid obstacles and achieve repetitive motion as well as avoid velocity spikes, a bi-criteria obstacle avoidance scheme synthesized by time-varying penalty strategy (BCOA-TVPS) neural network is proposed and designed. To do so, first, the bi-criteria are composed of repetitive motion criterion and infinite norm velocity minimization criterion, and the constraints consider the vector-based obstacle avoidance constraints. Second, the bi-criteria obstacle avoidance scheme is reformulated as a constrained time-varying quadratic programming (QP) problem. Third, a time-varying penalty strategy (TVPS) neural network is adopted to solve the QP problem. Finally, two kinds of trajectory tracking experiments verify the effectiveness and applicability of the proposed BCOA-TVPS scheme.

A novel collaborative position and orientation control scheme (CPOCS) for dual-arm robots is proposed, which is capable of controlling the end-effectors' positions with high precision while preserving their orientations unchanged to some practical tasks (e.g., box handling). To solve the proposed CPOCS in real time while considering key factors such as unknown bounded noise and strict time response constraints in practical engineering environments, this article proposes a novel precisely predefined-time convergent barrier recurrent neural network (PCB-RNN) based on a newly developed piecewise barrier evolution formula. Unlike existing RNNs, the proposed PCB-RNN, owing to its piecewise barrier evolution formula, can achieve precisely predefined-time convergence (PPTC) when addressing the proposed CPOCS under unknown bounded noise conditions. Comprehensive theoretical analysis rigorously proves the PPTC ability of the PCB-RNN under both noise-free and unknown bounded noise conditions. Furthermore, extensive simulation and physical experiments on dual-arm robots validate the effectiveness of the proposed CPOCS and demonstrate the advanced PPTC capability of the proposed PCB-RNN under unknown bounded noises.

To improve the reliability and safety of multirobot manipulator systems (MRMSs) during the execution of cooperative tasks, a distributed neural dynamics fault-tolerance (DNDFT) approach is proposed and implemented. For this reason, combined with the kinematics of the robot manipulator, the performance loss malfunction model of joints is designed and given. Second, the synchronized motion generation constraints of the MRMSs are depicted as equality constraints with coupled variables based on the performance loss malfunction model of joints and the communication topology of leader–follower collaboration. In order to further enhance the reliability of MRMSs, the physical limits of the joints of each robot manipulator are considered and represented as inequality constraints. Then, the problem of reliability-synchronized cooperation of MRMSs is transformed into the quadratic programming form with the minimum velocity norm criterion, and the DNDFT approach is utilized to solve this problem. With the DNDFT approach, the multiple robot manipulators suffering from varying degrees of joint degradation can still satisfactorily perform the end-effector cooperative tracking task. Finally, computer simulations verify that the proposed DNDFT approach can effectively address the synchronized cooperative motion generation problem of MRMSs.

Time-variant-gain zeroing neural networks (TVG-ZNNs) are among the most powerful solvers for time-variant linear matrix-vector inequalities (TVLMVIs). Although TVG-ZNNs with complex nonlinear activation functions achieve effective convergence within finite or predefined time, they incur high computational costs and face challenges in precisely predefining their actual convergence time. In contrast, TVG-ZNNs with linear activation functions offer lower computational costs but struggle to achieve convergence within a finite or predefined time. In addition, the gain values of most existing TVG-ZNNs tend to increase over time, resulting in a significant rise in computational costs. To address these contradictory issues, we propose a novel hybrid-gain ZNN without a nonlinear activation function (HG-ZNN-WNAF) to solve TVLMVIs in both noisy and noise-free environments. Specifically, a new hybrid gain is cleverly designed to construct the HG-ZNN-WNAF activated by a linear activation function, while ensuring that the gain value does not keep increasing over time. Unlike the state-of-the-art TVG-ZNNs with or without nonlinear activation functions, our proposed HG-ZNN-WNAF achieves precisely predefined-time convergence due to the hybrid gain, meaning its actual convergence time can be accurately predefined. Additionally, the piecewise design of the hybrid gain, along with the use of the simple linear activation function, effectively reduces the model's computational cost. Rigorous theoretical analysis demonstrates the precisely predefined-time convergence ability of the HG-ZNN-WNAF in both noisy and noise-free environments. Simulation and physical experiments validate the theoretical analysis and demonstrate that the HG-ZNN-WNAF achieves state-of-the-art performance in terms of convergence speed, robustness, and computational cost.

To solve non-convex nonlinear programming problems, a double center swarm exploring varying parameter neurodynamic network (DCSE-VPNN) is proposed and analyzed. Firstly, a varying parameter neurodynamic network is proposed as a solver for nonlinear programming to seek local optimal solutions. Secondly, a double center particle swarm optimization algorithm is exploited, wherein each neural network serves as a particle. Each particle independently explores a local optimal solution. Through information exchange among particles, the subsequent positions to be explored are updated. As a result, DCSE-VPNN acquires the capability of global search. Computer simulation experiments verify the efficacy of the proposed approach in solving non-convex nonlinear programming problems. In comparison with two existing methods, the results show that the proposed DCSE-VPNN approach has fewer iterations and higher search accuracy.

In this paper, an optimization framework of partial differential neural network combined with divide-space sampling (PDNN-DSS) is proposed to solve the estimation and control problem of 3D diffusion-advection systems. The PDNN-DSS framework contains a divide-space sampling observer, a model prediction estimator, and a partial differential neural network solver. First, the open-loop state of the diffusion-advection system is obtained by designing the division space observer. The observer provides a deployment scheme for sensors so that mobile robots only need to carry actuators not sensors. Then, the control problem is transformed into an optimization problem by designing a model prediction estimator. Subsequently, a novel partial differential neural network is designed. The neural network is based on partial differential equations containing spatial diffusion features and can solve spatio-temporal optimization problems. Finally, the effectiveness of the proposed method in this paper is demonstrated through simulations from multi-dimensional perspectives of 2D and 3D diffusion-advection systems.

This article proposes a novel data-driven distributed recurrent neural network (DDD-RNN) based on neurodynamics principles to address the challenge of precise collaborative motion generation in multimanipulator systems (MMCs) with unknown structural parameters. Unlike traditional methods that rely on precise models and existing data-driven methods with single-order Jacobian estimation, this article designs an improved Jacobian matrix estimation law (IJM). For the first time, it synchronously estimates the first-order and second-order Jacobian matrices online, effectively capturing the time-varying characteristics of robotic manipulators. Furthermore, a recurrent neural network solver is designed based on the neurodynamics criterion, which enables it to take into account the time-varying information of robotic manipulators, thus yielding more accurate motion generation results. Simulations conducted on multiple multimanipulator collaborative systems (MMCs) and experiments performed on the Ufactory XArm6 robots have verified the feasibility of the DDD-RNN method in generating collaborative motions of multiple robotic arms, even when the models of the robotic arms are unknown. Comparisons confirm the superiority of the DDD-RNN in terms of end-effector accuracy and applicability.

Zeroing neural network (ZNN), as a special type of recurrent neural network (RNN), is very competitive in solving time-varying linear matrix-vector equations. Recently, various ZNNs with predefined-time convergence (PTC) capabilities have been reported. Such ZNNs with PTC capabilities can achieve the predefined convergence time via explicitly presetting multiple parameters related to the upper bounds of their convergence time. However, obtaining suitable and robust values for these parameters through reasonable adjustments is a challenging task in many engineering applications. To address this problem, we propose a novel arbitrarily predefined-time convergent RNN (APTC-RNN) with a novel nonlinear piecewise activation-function (NPAF). Unlike most existing ZNNs with PTC capabilities, the proposed APTC-RNN, due to its NPAF, can achieve arbitrarily PTC (APTC) without adjusting any upper bound parameters. Furthermore, due to the piecewise computation form of the NPAF, the proposed APTC-RNN can provide a lower computational cost compared to most existing RNNs. The stability and APTC capability of the proposed APTC-RNN are proven by rigorous theoretical analysis and mathematical derivation. Numerical simulations show that APTC-RNN has faster and more accurate PTC capability than three state-of-the-art RNNs, while having less computational time. Finally, the practicality of the APTC-RNN is verified by applying it to the UR3 robotic arm and multiagent systems.

In this article, a state-coupled neural network (SDNN) is proposed to solve the distributed multiple robotic arms (DMRAs) synchronous collaboration problem. The synchronized collaboration of DMRAs is not only in the Cartesian space of the end-effector but also in the corresponding joint velocity space to keep the joint velocity synchronized. First, the constraints for motion generation of leader and follower robots are obtained based on the desired trajectory and communication topology, respectively. Then, the DMRAs collaboration is transformed into quadratic programming based on the minimum velocity norm index. Second, a novel SDNN is designed based on the communication topology of the DMRAs to solve the quadratic programming problem, and the stability of the SDNN is proved by the Lyapunov method. Finally, simulations and experiments demonstrate that SDNN can solve the synchronized collaboration problem of DMRAs with unique advantages.

A novel binary channel fuzzy self-adjusted neural network (BCF-SANN) is proposed and researched for solving time-changing quadratic programming (QP) problems in this article. Unlike the fixed parameters of the typical zeroing neural network, the main parameters of the proposed BCF-SANN are time-changing, and its errors are adaptively quickly convergent. The biggest advantage of the novel neural network is that it combines a fuzzy self-adjusted controller, which takes the errors and derivatives of errors as fuzzy inputs and neural networks, further improving the convergence and robustness of the neural networks. To design the novel neural network, a time-changing QP problem is first established; then, using Lagrange's law, the time-changing QP problem is transformed into a time-changing matrix equation; and finally, based on the time-changing parameter neural dynamics method, a novel BCF-SANN is proposed. The detailed design process is given in this article, and the convergence and robustness of the proposed BCF-SANN are proved by theoretical analysis. Through comparative experiments, it is demonstrated that the proposed BCF-SANN has a faster convergence rate and stronger robustness than the traditional zeroing neural network and 1-D fuzzy recurrent neural network (RNN).

To avoid the task failure caused by joint breakdown during the collaborative motion planning of dual-redundant robot manipulators, a neural dynamic fault-tolerant (NDFT) scheme is proposed and applied. To do so, a joint fault-tolerant strategy is first designed, and it is formulated as a time-varying equality constraint. Second, combining the robot position and orientation control, joint limit constraint, joint fault-tolerant equality constraint, and considering the repetitive motion optimization criterion, a fault-tolerant framework for the dual-redundant robot manipulators based on quadratic programming (QP) is constructed. Then, a varying-parameter recurrent neural network (VP-RNN) is designed to solve the QP issue. The fault-tolerant framework and the VP-RNN constitute NDFT scheme. With the NDFT scheme, the impact of faulty joints on the whole system can be remedied by healthy joints, thereby the end-effectors of the robot can complete the given end-effector task. Finally, computer simulations and physical experiments are implemented to verify the availability, physical realizability, and accuracy of the proposed NDFT scheme in the collaborative execution of end-effector tasks. Comparative experimental results with conventional repetitive motion planning schemes based on neural networks show higher accuracy and smaller joint angle drift.

The brain signal classification is the basis for the implementation of brain-computer interfaces (BCIs). However, most existing brain signal classification methods are based on signal processing technology, which require a significant amount of manual intervention, such as channel selection and dimensionality reduction, and often struggle to achieve satisfactory classification accuracy. To achieve high classification accuracy and as little manual intervention as possible, a convolutional dynamically convergent differential neural network (ConvDCDNN) is proposed for solving the electroencephalography (EEG) signal classification problem. First, a single-layer convolutional neural network is used to replace the preprocessing steps in previous work. Then, focal loss is used to overcome the imbalance in the dataset. After that, a novel automatic dynamic convergence learning (ADCL) algorithm is proposed and proved for training neural networks. Experimental results on the BCI Competition 2003, BCI Competition III A, and BCI Competition III B datasets demonstrate that the proposed ConvDCDNN framework achieved state-of-the-art performance with accuracies of 100%, 99%, and 98%, respectively. In addition, the proposed algorithm exhibits a higher information transfer rate (ITR) compared with current algorithms.

In order to solve the insufficient redundancy problem and slow convergence in multiple end-effector tasks, a piecewise varying-gain dual-criterion optimization (PVDO) method is proposed for motion planning of insufficient redundant manipulators. To achieve this, the convergence coefficients are designed to be piecewise varying, and the end-effector task is divided into two phases. In the initial phase, only the end-effector position task is considered and the fixed coefficient convergence method is adopted, which can take into consideration both end-effector task and secondary task optimization. In the second phase, the end-effector position and orientation are taken into account concurrently, and time-varying coefficients are used for end-effector task. The convergence coefficients are time varying to enhance the convergence speed, particularly when the errors are small in the later phase of task planning. This can ensure the optimization of secondary tasks when the manipulator is insufficient-redundant, and accomplish the end-effector task planning in a relatively fast speed. Finally, experiments are conducted to demonstrate the effectiveness of the proposed PVDO method in obstacle avoidance and joint limits avoidance.

To address the motion generation problem in distributed multimanipulator system operating in obstacles environment, a distributed slack barrier recurrent neural network (DSB-RNN) is proposed in this article. First, the communication topology among the multimanipulator system is summarized using an undirected graph representation. Then, the communication constraints and positions of the multimanipulators collaborative system are formulated as equality constraints with coupling variables. Additionally, nonstrict inequality constraints for obstacle avoidance and bilateral constraints for the manipulator joints are taken into account. Based on minimum velocity norm optimization criterion, the problem of motion generation for distributed multimanipulator system in obstacles environment is transformed into a time-varying quadratic programming problem. Next, a Lagrangian function is established and summarized as the original Karush–Kuhn–Tucker (KKT) conditions. To make this special time-varying problem solvable, barrier parameters and slack parameters are designed to improve the KKT conditions. Based on the improved KKT conditions and neurodynamics formula, a distributed recurrent neural network DSB-RNN is proposed. Experimental results demonstrate the effectiveness and accuracy of the proposed DSB-RNN method, and comparisons with other methods verify its advantages in terms of applicability and precision.

In general, the motion control problem of redundant robot manipulators (RRMs) can be transformed into a constrained time-varying quadratic programming (TVQP) problem. Recently, various recurrent neural networks (RNNs) with predefined time convergence (PTC) abilities have been proposed to solve this constrained TVQP problem in real-time. However, there is still a lack of a unified paradigm to guide researchers and engineers design such RNNs more effectively based on specific requirements. To bridge this gap, we propose a unified paradigm derived from a novel segmentation evolution formula incorporating a special$\mathfrak{B}$–Classfunction. This paradigm enables the construction of various RNNs, collectively referred to as unified arbitrarily predefined-time convergent RNNs (U-APTC-RNNs). Compared with most existing RNNs, the constructed U-APTC-RNN has two significant advantages: 1) it has the arbitrarily PTC (APTC) ability, meaning its actual convergence time can be arbitrarily and precisely predefined without setting other model parameters and 2) using a novel piecewise computation strategy, redundant nonlinear calculations are effectively minimized, leading to a notable reduction in computational costs. The stability and APTC ability of the constructed U-APTC-RNN are demonstrated through detailed theoretical analysis. Numerical simulation experiments confirm the APTC capabilities of various U-APTC-RNNs constructed using the proposed unified paradigm. Comparative experiments show that U-APTC-RNN has more competitive convergence performance and lower computational cost than other state-of-the-art RNNs with PTC abilities. Finally, simulation and physical motion control experiments on the Jaco and UR5 robotic arms demonstrate the superiority and practicality of the proposed U-APTC-RNN.

A swarm-exploring neurodynamic network (SENN) based on a two-timescale model is proposed in this study for solving nonconvex nonlinear programming problems. First, by using a convergent-differential neural network (CDNN) as a local quadratic programming (QP) solver and combining it with a two-timescale model design method, a two-timescale convergent-differential (TTCD) model is exploited, and its stability is analyzed and described in detail. Second, swarm exploration neurodynamics are incorporated into the TTCD model to obtain an SENN with global search capabilities. Finally, the feasibility of the proposed SENN is demonstrated via simulation, and the superiority of the SENN is exhibited through a comparison with existing collaborative neurodynamics methods. The advantage of the SENN is that it only needs a single recurrent neural network (RNN) interact, while the compared collaborative neurodynamic approach (CNA) involves multiple RNN runs.

To enable distributed multiple mobile manipulator systems to complete collaborative tasks safely and stably, this article investigates and presents a motion generation scheme that considers both orientation and position coordination based on a distributed recurrent neural network. Moreover, physical limits are also considered. Specifically, the orientation and position coordination constraints and physical limits are modeled separately as equality and inequality constraints with coupled variables. Subsequently, a motion generation scheme for multiple mobile manipulators based on quadratic programming is established. Finally, a distributed linear variational inequality-based primal-dual neural network is constructed to solve the motion generation scheme and obtain the motion trajectories of all the mobile manipulators. The simulation results demonstrate that the hybrid orientation and position collaboration motion generation scheme effectively addresses the position and orientation coordination problem for multiple mobile manipulator systems. Compared to other schemes, the proposed scheme based on a distributed computing structure greatly enhances the stability of the system. Additionally, the proposed approach introduces orientation coordination and physical limits, which increases the practicality of the system.

Corona virus disease 2019 is an extremely fatal pandemic around the world. Intelligently recognizing X-ray chest radiography images for automatically identifying corona virus disease 2019 from other types of pneumonia and normal cases provides clinicians with tremendous conveniences in diagnosis process. In this article, a deep ensemble dynamic learning network is proposed. After a chain of image preprocessing steps and the division of image dataset, convolution blocks and the final average pooling layer are pretrained as a feature extractor. For classifying the extracted feature samples, two-stage bagging dynamic learning network is trained based on neural dynamic learning and bagging algorithms, which diagnoses the presence and types of pneumonia successively. Experimental results manifest that using the proposed deep ensemble dynamic learning network obtains 98.7179% diagnosis accuracy, which indicates more excellent diagnosis effect than existing state-of-the-art models on the open image dataset. Such accurate diagnosis effects provide convincing evidences for further detections and treatments.

When a robot completes end-effector tasks, internal error noises always exist. To resist internal error noises of robots, a novel fuzzy recurrent neural network (FRNN) is proposed, designed, and implemented on field-programmable gated array (FPGA). The implementation is pipeline-based, which guarantees the order of overall operations. The data processing is based on across-clock domain, which is beneficial for computing units' acceleration. Compared with traditional gradient-based neural networks (NNs) and zeroing neural networks (ZNNs), the proposed FRNN has faster convergence rate and higher correctness. Practical experiments on a 3 degree-of-freedom (DOs) planar robot manipulator show that the proposed fuzzy RNN coprocessor needs 496 lookup table random access memories (LUTRAMs), 205.5 block random access memories (BRAMs), 41384 lookup tables (LUTs), and 16743 flip-flops (FFs) of the Xilinx XCZU9EG chip.

Aiming at solving non-convex nonlinear programming efficiently and accurately, a swarm exploring varying parameter recurrent neural network (SE-VPRNN) method is proposed in this article. First, the local optimal solutions are searched accurately by the proposed varying parameter recurrent neural network. After each network converges to the local optimal solutions, information is exchanged through a particle swarm optimization (PSO) framework to update the velocities and positions. The neural network searches for the local optimal solutions again from the updated position until all the neural networks are searched to the same local optimal solution. For improving the global searching ability, wavelet mutation is applied to increase the diversity of particles. Computer simulations show that the proposed method can solve the non-convex nonlinear programming effectively. Compared with three existing algorithms, the proposed method has advantages in accuracy and convergence time.

Nonlinear inequalities are widely used in science and engineering areas, attracting the attention of many researchers. In this article, a novel jump-gain integral recurrent (JGIR) neural network is proposed to solve noise-disturbed time-variant nonlinear inequality problems. To do so, an integral error function is first designed. Then, a neural dynamic method is adopted and the corresponding dynamic differential equation is obtained. Third, a jump gain is exploited and applied to the dynamic differential equation. Fourth, the derivatives of errors are substituted into the jump-gain dynamic differential equation, and the corresponding JGIR neural network is set up. Global convergence and robustness theorems are proposed and proved theoretically. Computer simulations verify that the proposed JGIR neural network can solve noise-disturbed time-variant nonlinear inequality problems effectively. Compared with some advanced methods, such as modified zeroing neural network (ZNN), noise-tolerant ZNN, and varying-parameter convergent-differential neural network, the proposed JGIR method has smaller computational errors, faster convergence speed, and no overshoot when disturbance exists. In addition, physical experiments on manipulator control have verified the effectiveness and superiority of the proposed JGIR neural network.

Time-varying quadratic programming (TV-QP) is widely used in artificial intelligence, robotics, and many other fields. To solve this important problem, a novel discrete error redefinition neural network (D-ERNN) is proposed. By redefining the error monitoring function and discretization, the proposed neural network is superior to some traditional neural networks in terms of convergence speed, robustness, and overshoot. Compared with the continuous ERNN, the proposed discrete neural network is more suitable for computer implementation. Unlike continuous neural networks, this article also analyzes and proves how to select the parameters and step size of the proposed neural networks to ensure the reliability of the network. Moreover, how to achieve the discretization of the ERNN is presented and discussed. The convergence of the proposed neural network without disturbance is proven, and bounded time-varying disturbances can be resisted in theory. Furthermore, the comparison results with other related neural networks show that the proposed D-ERNN has a faster convergence speed, better antidisturbance ability, and lower overshoot.

To address the real-time motion generation problem of a multimanipulator collaborative system, a novel distributed varying-parameter recurrent neural network (DVP-RNN) is proposed in this article. First, an undirected graph is used to simplify the communication topology of the multimanipulator collaborative system. Then, the communication and coupled constraints of the multimanipulator collaborative system are expressed as equality constraints with coupled variables. The physical limits (i.e., angular limits and angular velocity limits) of the multimanipulator collaborative system are expressed as inequality constraints. Based on the minimum velocity norm optimization criterion, a quadratic programming problem with coupled variables and constraints is employed to formulate the motion generation problem of a multimanipulator collaborative system. Finally, a DVP-RNN is designed to solve the quadratic programming problem with coupled variables and constraints to obtain the joint trajectory of the multimanipulator collaborative system. Simulations show that the proposed DVP-RNN can effectively solve the motion generation problem of a multimanipulator collaborative system. Comparisons confirm the superiority of the DVP-RNN in terms of applicability and precision.

Soft wires of robot operating tools often interfere with end-effector tasks in practical automated production scenarios. In order to avoid soft wires of industrial robot manipulators executing end-effector tasks, a real-time 3-D visual detection-based soft wire avoidance (3D-VDWA) scheme is proposed, which considers the soft wire detection and location, the soft wire avoidance, and the motion planning at the same time. The proposed 3D-VDWA includes three modules: 1) perception module; 2) motion planning module; and 3) soft wire avoidance module. The perception module is based on hue–saturation–value (HSV) range and depth information to detect and locate soft wires. The motion planning module is based on the method of the pseudo-inverse matrix to plan the path of the manipulator to the target position and orientation. The soft wire avoidance module is based on the Jacobian transpose method to dynamically avoid soft wire obstacles in the process of movement. Experiments demonstrate the effectiveness and the feasibility of the proposed scheme to solve the motion planning problem with soft wire avoidance of industrial manipulators for end-effector tasks.

In order to make redundant robot manipulators (RRMs) track the complex time-varying trajectory, the motion-planning problem of RRMs can be converted into a constrained time-varying quadratic programming (TVQP) problem. By using a new punishment mechanism-combined recurrent neural network (PMRNN) proposed in this article with reference to the varying-gain neural-dynamic design (VG-NDD) formula, the TVQP problem-based motion-planning scheme can be solved and the optimal angles and velocities of joints of RRMs can also be obtained in the working space. Then, the convergence performance of the PMRNN model in solving the TVQP problem is analyzed theoretically in detail. This novel method has been substantiated to have a faster calculation speed and better accuracy than the traditional method. In addition, the PMRNN model has also been successfully applied to an actual RRM to complete an end-effector trajectory tracking task.

In this article, a novel approach of utilizing an integral dynamic learning network (IDLN) is presented for addressing a general time-varying Lyapunov matrix equation (TVLME). First, a cost function is defined by designing a variable unbounded vector/matrix-type error function. The goal is to make the cost function approximate to zero. Second, an integral neural dynamic equation with an odd activation function that is monotonically increasing is designed and applied to guarantee that the error function can converge to zero. Third, a novel IDLN with a recurrent topological structure is exploited to find the time-varying theoretical solution. The proposed IDLN with strong robustness to bounded noise with unknown amplitude regardless of the value of hyperparameters, can be implemented through electronic circuits as a method of parallel computing and achieve global convergence from any initial state. In addition, for better convergence rates, the novel linear-arcsine-type and softsign-arcsine-type activation functions are designed and utilized to the proposed IDLN. The effectiveness, stability, and practicability of the proposed IDLN are verified by comparative computer simulations and the application to the analysis of voltage stability in a single-machine infinite bus system.

Many scientific and engineering applications can be formulated as a time-varying quadratic programming (TVQP) problem, and effectively solving it is an attractive issue. In order to solve the TVQP problem with multiple constraints effectively, a penalty-strategy varying-gain recurrent neural network (PSVG-RNN) combined is proposed, and is implemented with a field-programmable gate array (FPGA) and packaged into a configurable coprocessor. Comparative experiments verify that the coprocessor has at least an order of magnitude better performance than traditional Euler iterative method and Ode45 method embedded in Matlab implemented in digital computer. Experimental results show that the proposed PSVG-RNN only needs 382 lookup table random-access memories (LUTRAMs), 25583 lookup tables (LUTs) and 9549 flip-flops (FFs) of the Xilinx ZCU102 evaluation board.

Nonlinear and nonconvex optimization problems are vital and fundamental problems in science and engineering fields. In this article, a novel finite-time circadian rhythms learning network (called FT-CRLN) is proposed for solving nonlinear and nonconvex optimization problems with periodic noises. Different from the traditional recurrent neural networks, the proposed FT-CRLN can suppress the periodic noise notably and achieve excellent convergence performance in solving nonlinear and nonconvex problems. The theoretical analysis and rigorous mathematical proof verify the superior convergence, high accuracy, and strong robustness of the proposed FT-CRLN. The simulation results demonstrate the effectiveness and robustness of the proposed FT-CRLN in solving nonlinear and nonconvex problems compared with other state-of-art neural networks.

This research first proposes the general expression of Zhanget al.discretization (ZeaD) formulas to provide an effective general framework for finding various ZeaD formulas by the idea of high-order derivative simultaneous elimination. Then, to solve the problem of future equality-constrained nonlinear optimization (ECNO) with various noises, a specific ZeaD formula originating from the general ZeaD formula is further studied for the discretization of a noise-perturbed continuous-time advanced zeroing neurodynamic model. Subsequently, the resulting noise-perturbed discrete-time advanced zeroing neurodynamic (NP-DTAZN) algorithm is proposed for the real-time solution to the future ECNO problem with various noises suppressed simultaneously. Moreover, theoretical and numerical results are presented to show the convergence and precision of the proposed NP-DTAZN algorithm in the perturbation of various noises. Finally, comparative numerical and physical experiments based on a Kinova JACO2robot manipulator are conducted to further substantiate the efficacy, superiority, and practicability of the proposed NP-DTAZN algorithm for solving the future ECNO problem with various noises.

Many scientific research and engineering problems can be converted to time-varying quadratic programming (TVQP) problems with constraints. Thus, TVQP problem solving plays an important role in practical applications. Many existing neural networks, such as the gradient neural network (GNN) or zeroing neural network (ZNN), were designed to solve TVQP problems, but the convergent rate is limited. The recent varying-parameter convergent-differential neural network (VP-CDNN) can accelerate the convergent rate, but it can only solve the equality-constrained problem. To remedy this deficiency, a novel barrier varying-parameter dynamic learning network (BVDLN) is proposed and designed, which can solve the equality-, inequality-, and bound-constrained problem. Specifically, the constrained TVQP problem is first converted into a matrix equation. Second, based on the modified Karush-Kuhn-Tucker (KKT) conditions and varying-parameter neural dynamic design method, the BVDLN model is conducted. The superiorities of the proposed BVDLN model can solve multiple-constrained TVQP problems, and the convergent rate can achieve superexponentially convergence. Comparative simulative experiments verify that the proposed BVDLN is more effective and more accurate. Finally, the proposed BVDLN is applied to solve a robot motion planning problems, which verifies the applicability of the proposed model.

To solve the motion planning problems of redundant manipulators disturbed by the periodic noise from device hardwares or their surroundings, a Taylor-type discrete-time circadian rhythms neural network (TD-CRNN) method is proposed, developed, and studied in this article. First, a representative bicriteria optimization scheme combining torque criterion and acceleration criterion is presented for the redundant manipulator. Second, inspired by a continuous-time circadian rhythms model, the corresponding TD-CRNN model is derived based on the Taylor discrete formulation. Third, the 0-stability, convergence, and consistency of the proposed TD-CRNN model are analyzed theoretically and proved strictly. Finally, to confirm the capacity of the resisting periodic noise in the tracking problem of manipulators, two groups of comparative simulations and experiments conducted by the proposed TD-CRNN model are performed before the conclusion is given.

Via the Euler forward-difference rule, an Euler-type discrete-time circadian rhythms neural network model (E-DTCRNN) is proposed, developed, and investigated for motion planning of the redundant robot manipulator affected by periodic noises. In this article, an Euler-type discrete-time zeroing neural network model (E-DTZNN) is presented as comparison. The E-DTCRNN model is 0-stable, consistent, and convergent. In addition, through a hybrid torque and velocity optimization scheme synthesized by the proposed E-DTCRNN and the traditional E-DTZNN, a tracking trajectory is designed and applied to the motion planning of the redundant robot manipulator. Finally, groups of simulations and physical experiments verify the efficacy and noise suppression ability of the proposed E-DTCRNN model for motion planning of the manipulator.

As for time-varying tracking control problems, many neural-dynamics-based control methods have been proposed because of their high efficiency. The varying-parameter convergent neural dynamics design method with the characteristic of super-exponential convergence has been applied to design controllers for unmanned aerial vehicles. Although the varying-parameter convergent neural dynamics controller has a fast convergence speed, it still needs long enough time to achieve tracking theoretically. By combining the finite-time activation function with the varying-parameter convergent neural dynamics design method, a finite-time-gain-adjustment design method is proposed and proved theoretically in this paper. This controller can make state variables of the system converge to their time-varying targets in finite time. Compared with some traditional methods, contrastive experiments and application to a multi-rotor unmanned aerial vehicle system illustrate that the proposed controller has finite convergence time, better anti-noise performance, and faster convergence speed, which enable the multi-rotor unmanned aerial vehicles to track time-varying targets more quickly and accurately, so as to achieve more complex and efficient control tasks.

This article investigates the synchronization of fractional-order multi-weighted complex networks (FMWCNs) with order$\alpha \in (0,1)$. A useful fractional-order inequality${}_{t_{0}}^{C} D_{t}^{\alpha } V(x(t))\leq -\mu V(x(t))$is extended to a more general form${}_{t_{0}}^{C} D_{t}^{\alpha } V(x(t))\leq -\mu V^{\gamma }(x(t)),\gamma \in (0,1]$, which plays a pivotal role in studies of synchronization for FMWCNs. However, the inequality${}_{t_{0}}^{C} D_{t}^{\alpha } V(x(t))\leq -\mu V^{\gamma }(x(t)),\gamma \in (0,1)$has been applied to achieve the finite-time synchronization for fractional-order systems in the absence of rigorous mathematical proofs. Based on reduction to absurdity in this article, we prove that it cannot be used to obtain finite-time synchronization results under bounded nonzero initial value conditions. Moreover, by using feedback control strategy and Lyapunov direct approach, some sufficient conditions are presented in the forms of linear matrix inequalities (LMIs) to ensure the synchronization for FMWCNs in the sense of a widely accepted definition of synchronization. Meanwhile, these proposed sufficient results cannot guarantee the finite-time synchronization of FMWCNs. Finally, two chaotic systems are given to verify the feasibility of the theoretical results.

The brain-computer interface (BCI) P300 speller analyzes the P300 signals from the brain to achieve direct communication between humans and machines, which can assist patients with severe disabilities to control external machines or robots to complete expected tasks. Therefore, the classification method of P300 signals plays an important role in the development of BCI systems and technologies. In this article, a novel ensemble support vector recurrent neural network (E-SVRNN) framework is proposed and developed to acquire more accurate and efficient electroencephalogram (EEG) signal classification results. First, we construct a support vector machine (SVM) to formulate EEG signals recognizing model. Second, the SVM formulation is transformed into a standard convex quadratic programming (QP) problem. Third, the convex QP problem is solved by combining a varying parameter recurrent neural network (VPRNN) with a penalty function. Experimental results on BCI competition II and BCI competition III datasets demonstrate that the proposed E-SVRNN framework can achieve accuracy rates as high as 100% and 99%, respectively. In addition, the results of comparison experiments verify that the proposed E-SVRNN possesses the best recognition accuracy and information transfer rate (ITR) compared with most of the state-of-the-art algorithms.

In order to resist periodic interfere in robot hardware or environment, a Runge–Kutta type discrete-time circadian rhythms neural network (RK-DCRNN) model is proposed, and investigated to plan the motion of redundant robot manipulators. To achieve the optimal control, a quadratic programming-based acceleration-level hybrid tri-criteria (ALHT) scheme is first designed, which simultaneously minimize the acceleration norm, torque norm, and joint-angle shift-free indices. Second, according to the neural dynamic design method, a continuous-time circadian rhythms neural network model is exploited, and then based on the Runge–Kutta numerical differential method, a discrete-time circadian rhythms neural network model is obtained. Third, the convergence of the proposed RK-DCRNN model is proved by detailed mathematical derivation. Fourth, comparative simulations and physical experiments verify that the proposed RK-DCRNN model can suppress the accumulation of position error in the motion planning of manipulators.

In this article, the repetitive motion control of redundant manipulators is investigated. First, a repetitive motion control scheme is presented, and a continuous zeroing neural network (CZNN) model is obtained for solving the scheme. Meanwhile, the development of a discrete zeroing neural network (DZNN) model is desired for convenient computational processing. Based on this, this article proposes a 6-step discretization formula, which has high precision. By using the 6-step discretization formula and the 4-step backward difference formula, a 6-step DZNN (6SDZNN) model is further proposed to handle the repetitive motion control scheme. Theoretical analyses verify the efficacy of the 6SDZNN model. Additionally, some discrete forms of conventional models are developed for comparison. Computer simulations on the basis of the 4-link redundant manipulator are carried out, verifying the theoretical analyses and showing the efficacy of the 6SDZNN model. Finally, physical experiments on the basis of the Kinova Jaco2manipulator substantiate the practicability of the 6SDZNN model.

To realize the robust control of multirotor unmanned aerial vehicle (UAV) systems, adaptive multilayer neural dynamics (AMND) controllers are proposed and analyzed. The proposed AMND controllers with the strong anti-perturbation property can drive multirotor UAVs to track time-varying tasks and deal with parameter uncertainty problems. First, the design method of the general multilayer neural dynamics (MLND) controllers is introduced and analyzed. Second, based on the design method, the attitude angles, height, and position controllers of a UAV system are designed. Third, according to the adaptive control theory, a novel AMND controller is designed, which can self-tune the parameters of the UAV. Finally, the proposed AMND method applies to a real-world hexrotor UAV system to illustrate its reliability. Mathematical analysis, computer simulations, and experiments verify the reliability, stability, and effectiveness of the proposed controllers which are used to track time-varying tasks.

In recent years, the robotics industry has been a hotspot and provided much convenience in people's daily life. For further research on robots, we introduce the problem of velocity-level minimum joint motion planning and control in this paper. Firstly, by using the Zhang neural network (ZNN) method and the Lagrange multiplier method, a continuous-time ZNN model is presented to solve the problem. Besides, an advanced ten-instant time-discretization formula with higher precision is presented, and five discrete-time ZNN (DTZNN) models are listed because of the digital hardware's requirements. At last, computer and robot experiments verify the effectiveness and feasibility of the presented DTZNN models.

To solve a general time-varying Sylvester equation, a novel integral recurrent neural network (IRNN) is designed and analyzed. This kind of recurrent neural networks is based on an error-integral design equation and does not need training in advance. The IRNN can achieve global convergence performance and strong robustness if odd-monotonically increasing activation functions [i.e., the linear, bipolar-sigmoid, power, or sigmoid-power activation functions (SP-AFs)] are applied. Specifically, if linear or bipolar-sigmoid activation functions are applied, the IRNN possess exponential convergence performance. The IRNN has finite-time convergence property by using power activation function. To obtain faster convergence performance and finite-time convergence property, an SP-AF is designed. Furthermore, by using the discretization method, the discrete IRNN model and its convergence analysis are also presented. Practical application to robot manipulator and computer simulation results with using different activation functions and design parameters have verified the effectiveness, stability, and reliability of the proposed IRNN.

Because of the simple structure and strong flexibility, multirotor unmanned aerial vehicles (UAVs) have attracted considerable attention among scientific researches and engineering fields during the past decades. In this paper, a novel adaptive multilayer neural dynamic (AMND)-based controllers design method is proposed for designing the attitude angle (the roll angle ϕ , the pitch angle θ , and the yaw angle ψ ), height ( z ), and position ( x and y ) controllers of a general multirotor UAV model. Global convergence and strong robustness of the proposed AMND-based method and controllers are analyzed and proved theoretically. By incorporating the adaptive control method into the general multilayer neural dynamic-based controllers design method, multirotor UAVs with unknown disturbances can complete time-varying trajectory tracking tasks. AMND-based controllers with the self-tuning rates can estimate the unknown disturbances and solve the model uncertainty problems. Both the theoretical theorems and simulation results illustrate that the proposed design method and its controllers with strong anti-interference property can achieve the time-varying trajectory tracking control stably, reliably, and effectively. Moreover, a practical experiment by using a mini multirotor UAV illustrates the practicability of the AMND-based method.

Zeroing neural network (ZNN), as an important class of recurrent neural network, has wide applications in various computation and optimization fields. In this article, based on the traditional-type zeroing neural network (TT-ZNN) model, an adaptive fuzzy-type zeroing neural network (AFT-ZNN) model is proposed to settle time-variant quadratic programming problem via integrating an adaptive fuzzy control strategy. The most prominent feature of the AFT-ZNN model is to use an adaptive fuzzy control value to adaptively adjust its convergence rate according to the value of the computational error. Four different activation functions are injected to analyze the convergence rate of the AFT-ZNN model. In addition, different membership functions and different ranges of the fuzzy control value are discussed to study the character of the AFT-ZNN model. Theoretical analysis and numerical comparison results further show that the AFT-ZNN model has better performance than the TT-ZNN model.

As an increasing number of unmanned aerial vehicles (UAVs) have been widely applied in many aspects, controllers with higher performance are preferred. In this paper, a new varying-parameter adaptive multi-layer neural dynamic based controller (termed as VP-AMND controller) design method is proposed and applied to controllers of multi-rotor UAVs. First, a varying-parameter convergent neural dynamic (VP-CND) based controller is proposed and its convergence and robustness are theoretically proven. Second, by incorporating the adaptive control method into the VP-CND controller, the VP-AMND controller design method is proposed, of which the global stability, fast convergence speed and strong robustness can be guaranteed. Different from traditional triple zeroing dynamic (TZD) and VP-CND controllers, the proposed VP-AMND controller with self-tuning rates can estimate the unknown disturbances and enhance the stability of the system in the face of uncertainty. Third, computer simulation results verify that the multi-rotor UAVs with VP-AMND controllers can track time-varying trajectories quickly and solve the parameter uncertainty and disturbances problems effectively.

Collision between dual robot manipulators during working process will lead to task failure and even robot damage. To avoid mutual collision of dual robot manipulators while doing collaboration tasks, a novel recurrent neural network (RNN)-based mutual-collision-avoidance (MCA) scheme for solving the motion planning problem of dual manipulators is proposed and exploited. Because of the high accuracy and low computation complexity, the linear variational inequality-based primal-dual neural network is used to solve the proposed scheme. The proposed scheme is applied to the collaboration trajectory tracking and cup-stacking tasks, and shows its effectiveness for avoiding collision between the dual robot manipulators. Through network iteration and online learning, the dual robot manipulators will learn the ability of MCA. Moreover, a line-segment-based distance measure algorithm is proposed to calculate the minimum distance between the dual manipulators. If the computed minimum distance is less than the first safe-related distance threshold, a speed brake operation is executed and guarantees that the robot cannot exceed the second safe-related distance threshold. Furthermore, the proposed MCA strategy is formulated as a standard quadratic programming problem, which is further solved by an RNN. Computer simulations and a real dual robot experiment further verify the effectiveness, accuracy, and physical realizability of the RNN-based MCA scheme when manipulators cooperatively execute the end-effector tasks.

Time-varying matrix pseudoinverse (TVMP) problem has been investigated by many researchers in recent years, but a new class of matrix termed Zhang matrix has been found and not been handled by some conventional models, e.g., Getz-Marsden dynamic model. On the other way, future matrix pseudoinverse (FMP), as a more challenging and intractable discrete-time problem, deserves more attention due to its significant role-playing on some engineering applications, such as redundant manipulator. Based on the zeroing neural network (ZNN), this article concentrates on designing new discrete ZNN models appropriately for computing the FMPs of all matrices of full rank, including the Zhang matrix. First, an inverse-free continuous ZNN model for computing TVMP is derived. Subsequently, Zhang et al. discretization (ZeaD) formulas and equidistant extrapolation formulas are used to discretize the continuous ZNN model to two discrete ZNN models for computing FMPs with different truncation errors. The numerical experiments are conducted for the five conventional discrete models and two new discrete ZNN models. Distinct numerical results substantiate the effectiveness and choiceness of newly proposed models. Finally, one of the newly proposed models is implemented on simulating and physical instances of robot manipulators, respectively, to show its practicability.

To obtain the optimal solution to the time-varying quadratic programming (TVQP) problem with equality and multitype inequality constraints, a penalty strategy combined varying-parameter recurrent neural network (PS-VP-RNN) for solving TVQP problems is proposed and analyzed. By using a novel penalty function designed in this article, the inequality constraint of the TVQP can be transformed into a penalty term that is added into the objective function of TVQP problems. Then, based on the design method of VP-RNN, a PS-VP-RNN is designed and analyzed for solving the TVQP with penalty term. One of the greatest advantages of PS-VP-RNN is that it cannot only solve the TVQP with equality constraints but can also solve the TVQP with inequality and bounded constraints. The global convergence theorem of PS-VP-RNN is presented and proved. Finally, three numerical simulation experiments with different forms of inequality and bounded constraints verify the effectiveness and accuracy of PS-VP-RNN in solving the TVQP problems.

Joint-drift problems could result in failures in executing task or even damage robots in actual applications and different schemes have been presented to deal with such a knotty problem. However, in these existing schemes, there exists the coupling in coefficients for eliminating the drift in the joint space and the equality constraint for completing the given task in the Cartesian space, thereby, theoretically, leading to a paradox in achieving zero joint drift in the joint space and zero position error in the Cartesian space simultaneously. A novel joint-drift-free (JDF) scheme synthesized by a projected zeroing neural network (PZNN) model for the motion generation and control of redundant robot manipulators perturbed by disturbances is proposed and analyzed in this article. Besides, the PZNN model could adopt saturated or even nonconvex projection functions. The proposed scheme completely decouples the interferences of joint errors in the joint space and position errors in the Cartesian space for the first time. Beyond that, theoretical analysis is conducted in order to validate that the PZNN model is of global convergence to the theoretical kinematics solution to the motion generation of robots, and that the joint-drift problems are thus remedied. Moreover, several simulations and physical experiments on the strength of different robot manipulators are carried out to confirm the superiority, efficiency, and accuracy of the proposed JDF scheme synthesized by the PZNN model for remedying joint-drift problems of redundant robot manipulators in noisy environments.

To make manipulators fulfill end-effector maintaining tasks, such as writing or drawing tasks in a complex environment, two hybrid multiobjective motion planing schemes, i.e., end-effector posture-maintaining and obstacle avoidance (hybrid PM-OA) schemes are proposed and investigated for wheeled mobile redundant robot manipulators. Specifically, the end-effector posture maintaining, obstacle avoidance, and joint physical limits are considered in a quadratic programming (QP) problem. With these two hybrid PM-OA schemes, the wheeled mobile robot manipulators can maintain its end-effector posture, avoid the obstacle and joint physical limits during executing end-effector tasks. The hybrid PM-OA schemes are finally formulated into a piecewise-linear projection equations (PLPEs) and solved by a recurrent neural network (RNN). Computer simulations are given to substantiate the effectiveness, accuracy, safety, and practicability of the proposed hybrid PM-OA schemes. Comparisons with other schemes and simulations further show that the proposed hybrid PM-OA schemes are more suitable for applications.

In order to effectively decrease the joint-angular drifts and end-effector position accumulation errors, a novel adaptive fuzzy recurrent neural network (AFRNN) is proposed and exploited to solve the nonrepetitive motion problem of redundant robot manipulators in this paper. First, a quadratic programming (QP)-based repetitive motion scheme is designed according to the kinematics constraint of redundant robot manipulators. Second, the QP-based repetitive motion scheme is converted to a matrix equation according to the Lagrangian multiplier method. Third, inspired by the neural-dynamic and fuzzy control theory, the AFRNN model is designed, which can effectively solve the matrix equation as well as the original nonrepetitive motion problem of redundant robot manipulators. Computer simulation results verify the effectiveness, high accuracy, and robustness to resist external disturbance of the proposed AFRNN scheme.

Spatial regularization has been proved as an effective method for alleviating the boundary effect and boosting the performance of a discriminative correlation filter (DCF) in aerial visual object tracking. However, existing spatial regularization methods usually treat the regularizer as a supplementary term apart from the main regression and neglect to regularize the filter involved in the correlation operation. To address the aforementioned issue, this article introduces a novel object saliency-aware dual regularized correlation filter, i.e., DRCF. Specifically, the proposed DRCF tracker suggests a dual regularization strategy to directly regularize the filter involved with the correlation operation inside the core of the filter generating ridge regression. This allows the DRCF tracker to suppress the boundary effect and consequently enhance the performance of the tracker. Furthermore, an efficient method based on a saliency detection algorithm is employed to generate the dual regularizers dynamically and provide the regularizers with online adjusting ability. This enables the generated dynamic regularizers to automatically discern the object from the background and actively regularize the filter to accentuate the object during its unpredictable appearance changes. By the merits of the dual regularization strategy and the saliency-aware dynamical regularizers, the proposed DRCF tracker performs favorably in terms of suppressing the boundary effect, penalizing the irrelevant background noise coefficients and boosting the overall performance of the tracker. Exhaustive evaluations on 193 challenging video sequences from multiple well-known challenging aerial object tracking benchmarks validate the accuracy and robustness of the proposed DRCF tracker against 27 other state-of-the-art methods. Meanwhile, the proposed tracker can perform real-time aerial tracking applications on a single CPU with sufficient speed of 38.4 frames/s.

In recent years, many models with high precision for redundant manipulator tracking control have been proposed based on precise kinematics equations. Nevertheless, without precise kinematic equations, developing a model with high precision for tracking control is meaningful. With the help of zeroing neural dynamics (ZND), a continuous ZND model with adaptive Jacobian matrix is obtained. For better computer operation and easier understanding, developing corresponding discrete ZND (DZND) model is also significant. Therefore, two DZND models (termed DZND-I model and DZND-II model) are proposed in this article on the basis of two discretization formulas, respectively. Meanwhile, theoretical analyses are conducted to ensure the efficacy of DZND-I model and DZND-II model. Finally, the efficacy of the two DZND models with adaptive Jacobian matrix is substantiated by experimental results on the basis of the four-link manipulator, UR5 manipulator, and Jaco2 manipulator, respectively.

To fulfill path tracking tasks with the end-effector posture controlled in a complex environment, maintaining the robot manipulator end-effector posture and avoiding obstacles are two important issues needed to be considered. In this paper, two hybrid end-effector posture-maintaining and obstacle-limits avoidance (hybrid PM-OLA) schemes are proposed and investigated for motion planning of redundant robot manipulators, which are based on the quadratic programming (QP) framework. The end-effector posture-maintaining, obstacle-avoidance, and the joint-angular-limits are formulated as an equality constraint, inequality constraint, and bound constraint into the QP problem. With these hybrid PM-OLA schemes, the robot manipulator can avoid the obstacle and joint physical limits when executing end-effector tasks. The hybrid PM-OLA schemes are finally transformed into linear variational inequalities and solved by a recurrent neural network. Computer simulations and physical experiments substantiate the effectiveness, accuracy, safety, and the practicability of the proposed hybrid PM-OLA schemes. Comparisons with other schemes show that the proposed hybrid PM-OLA schemes are more suitable for applications.

To solve the disturbed time-varying inversion problem, an exponential-type anti-noise varying-gain network (EAVGN) is proposed and analyzed. To do so, a vector-based error function is first defined. By using the varying-gain neural dynamic design method, an EAVGN model is then formulated. Furthermore, the differentiation error and the model-implementation error are considered into the model, and the perturbed EAVGN model is obtained. For better illustrations, comparisons between the EAVGN and the conventional fixed-parameter recurrent neural network (FP-RNN) are conducted to illustrate the advantages of the proposed EAVGN. Mathematical proof demonstrates that the proposed EAVGN has much better anti-noise properties than FP-RNN. On one hand, the residual error of EAVGN can be reduced to zero in any case, but that of FP-RNN is large and cannot be convergent, in particular when the bound of Frobenius norm of the exact solution is large or the noise is large. On the other hand, the bound of the residual error of EAVGN is always smaller than that of FP-RNN. Simulation results verify that when different types of noises exist, the proposed EAVGN owns better anti-noise property compared with the state-of-the-art methods. In addition, a practical application is presented to illustrate the implementation process and the practical benefits of the EAVGN.

Varying-parameter recurrent neural network, being a special kind of neural-dynamic methodology, has revealed powerful abilities to handle various time-varying problems, such as quadratic minimization (QM) and quadratic programming (QP) problems. In this paper, a novel power-type varying-parameter recurrent neural network (PT-VP-RNN) is proposed to solve the perturbed time-varying QM and QP problems. First, based on the generalization of time-varying QM and QP problems, the design process of the PT-VP-RNN is presented in detail. Second, the robustness performance of the proposed PT-VP-RNN is theoretically analyzed and proved. What is more, two numerical examples are simulated to illustrate the robustness convergence performance of PT-VP-RNN even in a large disturbance condition. Finally, two practical application examples (i.e., a robot tracking example and a venture investment example) further verify the effectiveness, accuracy, and widespread applicability of the proposed PT-VP-RNN.

A novel recurrent neural network, which is named as complex varying-parameter convergent-differential neural network (CVP-CDNN), is proposed in this paper for solving the time-varying complex Sylvester equation. Two kinds of CVP-CDNNs (i.e., CVP-CDNN Type I and Type II) are illustrated and proved to be effective. The proposed CVP-CDNNs can achieve super-exponential performance if the linear activation function is used. Some activation functions are considered for searching the better performance of the CVP-CDNN and the finite time convergence property of the CVP-CDNN with sign-bi-power activation function is testified. The convergence time of the CVP-CDNN with sign-bi-power activation function is shorter than complex fixed-parameter convergent-differential neural network (CFP-CDNN). Moreover, compared with traditional CFP-CDNN, better convergence performances of novel CVP-CDNN are verified by computer simulation comparisons.

Many practical problems can be solved by being formulated as time-varying quadratic programing (TVQP) problems. In this paper, a novel power-type varying-parameter recurrent neural network (VPNN) is proposed and analyzed to effectively solve the resulting TVQP problems, as well as the original practical problems. For a clear understanding, we introduce this model from three aspects: design, analysis, and applications. Specifically, the reason why and the method we use to design this neural network model for solving online TVQP problems subject to time-varying linear equality/inequality are described in detail. The theoretical analysis confirms that when activated by six commonly used activation functions, VPNN achieves a superexponential convergence rate. In contrast to the traditional zeroing neural network with fixed design parameters, the proposed VPNN has better convergence performance. Comparative simulations with state-of-the-art methods confirm the advantages of VPNN. Furthermore, the application of VPNN to a robot motion planning problem verifies the feasibility, applicability, and efficiency of the proposed method.

Two novel nonlinearly activated recurrent neural networks (RNNs) with finite-time convergence [called finite-time RNNs (FTRNNs)] are proposed and analyzed to solve efficiently time-varying systems of nonlinear equations (SoNEs). Compared with previously presented neural networks for solving such a SoNE, the FTRNNs are activated by new nonlinear activation functions and thus possess a better finite-time convergence property. In addition, theoretical analyses about FTRNNs are presented to determine the upper bounds of convergence time under the context of using such two novel nonlinear activation functions. Computer simulations based on a numerical example validate the preponderance of the proposed FTRNNs for time-varying SoNE, as compared to the recently proposed Zhang neural network and its improved version. Finally, an engineering practical example to motion tracking of a robot manipulator demonstrates the feasibility and applicability of the FTRNNs.

Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed in this paper for obtaining the online solution to the time-varying Sylvester equation. With time passing by, this kind of new varying-parameter neural network can achieve super-exponential performance. Computer simulation comparisons between the fixed-parameter neural networks and the proposed VP-CDNN via using different kinds of activation functions demonstrate that the proposed VP-CDNN has better convergence and robustness properties.

The Lyapunov equation is widely employed in the engineering field to analyze stability of dynamic systems. In this paper, based on a new evolution formula, a novel finite-time recurrent neural network (termed finite-time Zhang neural network, FTZNN) is proposed and studied for solving a nonstationary Lyapunov equation. In comparison with the original Zhang neural network (ZNN) model for a nonstationary Lyapunov equation, the convergence performance has a remarkable improvement for the proposed FTZNN model and can be accelerated to finite time. Besides, by solving the differential inequality, the time upper bound of the FTZNN model is computed theoretically and analytically. Simulations are conducted and compared to validate the superiority of the FTZNN model to the original ZNN model for solving the nonstationary Lyapunov equation. At last, the FTZNN model is successfully applied to online tracking control of a wheeled mobile manipulator.

Joint-drift problem may lead to task execution failure or robot damage. To solve this problem, a finite-time varying-parameter recurrent neural network (FT-VP-RNN) is proposed and investigated in this paper. First, a quadratic programming (QP) based joint-drift-free (JDF) scheme is developed, which consists of an optimization criterion and a kinematic equation at velocity layer. A feedback control is then added into the kinematic equation as the equality constraint, and a feedback-considered joint-drift-free (FC-JDF) scheme is obtained. Second, a novel FT-VP-RNN is designed to solve the FC-JDF scheme and a corresponding finite-time convergence theorem is proposed. The outstanding advantages of the proposed FT-VP-RNN are the real-time computation, exponential convergence, and the ability to eliminate the initial errors. Finally, three path-tracking simulations and comparisons are conducted to verify the effectiveness, accuracy, practicability, and safety of the proposed FT-VP-RNN for solving the joint-drift problems of redundant robot manipulators.

Using neural networks to handle intractability problems and solve complex computation equations is becoming common practices in academia and industry. It has been shown that, although complicated, these problems can be formulated as a set of equations and the key is to find the zeros of them. Zeroing neural networks (ZNN), as a class of neural networks particularly dedicated to find zeros of equations, have played an indispensable role in the online solution of time-varying problem in the past years and many fruitful research outcomes have been reported in the literatures. The aim of this paper is to provide a comprehensive survey of the research on ZNNs, including continuous-time and discrete-time ZNN models for various problems solving as well as their applications in motion planning and control of redundant manipulators, tracking control of chaotic systems, or even populations control in mathematical biosciences. By considering the fact that real-time performance is highly demanded for time-varying problems in practice, stability and convergence analyses of different continuous-time ZNN models are reviewed in detail in a unified way. For the case of discrete-time problems solving, the procedures on how to discretize a continuous-time ZNN model and the techniques on how to obtain an accuracy solution are summarized. Concluding remarks and future directions of ZNN are pointed out and discussed.

Quadrotor unmanned aerial vehicles (UAVs) have been widely used or have great potential applications in military, entertainment, postal delivery, agriculture for working aloft, photographing, etc. The position and angular stabilization of quadrotor UAVs is very significant and it is a challenging work because of the nonlinear dynamic behavior. In this paper, a neural dynamic method based control system is designed and investigated by combination of Zhang dynamics and gradient dynamic (ZD-GD) methods. Quadrotor UAVs equipped with the ZD-GD controllers can realize position and angular stabilization autonomously. Computer simulation results substantiate the efficiency and accuracy of the proposed neural dynamic method based ZD-GD controllers. Besides, the performance of the controllers can be remarkably advanced.

Facing and pointing toward moving targets is a usual and natural behavior in daily life. Social robots should be able to display such coordinated behaviors in order to interact naturally with people. For instance, a robot should be able to point and look at specific objects. This is why, a scheme to generate coordinated head-arm motion for a humanoid robot with two degrees-of-freedom for the head and seven for each arm is proposed in this paper. Specifically, a virtual plane approach is employed to generate the analytical solution of the head motion. A quadratic program (QP)-based method is exploited to formulate the coordinated dual-arm motion. To obtain the optimal solution, a simplified recurrent neural network is used to solve the QP problem. The effectiveness of the proposed scheme is demonstrated using both computer simulation and physical experiments.

We propose a dual-arm cyclic-motion-generation (DACMG) scheme by a neural-dynamic method, which can remedy the joint-angle-drift phenomenon of a humanoid robot. In particular, according to a neural-dynamic design method, first, a cyclic-motion performance index is exploited and applied. This cyclic-motion performance index is then integrated into a quadratic programming (QP)-type scheme with time-varying constraints, called the time-varying-constrained DACMG (TVC-DACMG) scheme. The scheme includes the kinematic motion equations of two arms and the time-varying joint limits. The scheme can not only generate the cyclic motion of two arms for a humanoid robot but also control the arms to move to the desired position. In addition, the scheme considers the physical limit avoidance. To solve the QP problem, a recurrent neural network is presented and used to obtain the optimal solutions. Computer simulations and physical experiments demonstrate the effectiveness and the accuracy of such a TVC-DACMG scheme and the neural network solver.

In this paper, a cyclic-motion generation (CMG) scheme at the acceleration level is proposed to remedy the joint-angle drift phenomenon of redundant robot manipulators which are controlled at the joint-acceleration level or torque level. To achieve this, a cyclic-motion criterion at the joint-acceleration level is exploited. This criterion, together with the joint-angle limits, joint-velocity limits, and joint-acceleration limits, is considered into the scheme formulation. In addition, the neural-dynamic method of Zhang is employed to explain and analyze the effectiveness of the proposed criterion. Then, the scheme is reformulated as a quadratic program, which is solved by a primal-dual neural network. Furthermore, four tracking path simulations verify the effectiveness and accuracy of the proposed acceleration-level CMG scheme. Moreover, the comparisons between the proposed acceleration-level CMG scheme and the velocity-level scheme demonstrate that the former is safer and more applicable. The experiment on a physical robot system further verifies the physical realizability of the proposed acceleration-level CMG scheme.