Vision-language models (VLMs) pre-trained on natural image and language data, such as CLIP, have exhibited significant potential in few-shot image recognition tasks, leading to development of various efficient transfer learning methods. These methods exploit inherent pre-learned knowledge in VLMs and have achieved strong performance on standard image datasets. However, their effectiveness is often limited when confronted with cross-domain tasks where imaging domains differ from natural images. To address this limitation, we propose Consistency-guided Multi-view Collaborative Optimization (CoMuCo), a novel fine-tuning strategy for VLMs. This strategy employs two functionally complementary expert modules to extract multi-view features, while incorporating prior knowledge-based consistency constraints and information geometry-based consensus mechanisms to enhance the robustness of feature learning. Additionally, a new cross-domain few-shot benchmark is established to help comprehensively evaluate methods on imaging domains distinct from natural images. Extensive empirical evaluations on both existing and newly proposed benchmarks suggest CoMuCo consistently outperforms current methods.

Diffusion policies excel at robotic manipulation by naturally modeling multimodal action distributions in high-dimensional spaces. Nevertheless, diffusion policies suffer from diffusion representation collapse: semantically similar observations are mapped to indistinguishable features, ultimately impairing their ability to handle subtle but critical variations required for complex robotic manipulation. To address this problem, we propose D²PPO (Diffusion Policy Policy Optimization with Dispersive Loss). D²PPO introduces dispersive loss regularization that combats representation collapse by treating all hidden representations within each batch as negative pairs. D²PPO compels the network to learn discriminative representations of similar observations, thereby enabling the policy to identify subtle yet crucial differences necessary for precise manipulation. In evaluation, we find that early-layer regularization benefits simple tasks, while late-layer regularization sharply enhances performance on complex manipulation tasks. On RoboMimic benchmarks, D²PPO achieves an average improvement of 22.7% in pre-training and 26.1% after fine-tuning, setting new SOTA results. In comparison with SOTA, the results of real-world experiments on a Franka Emika Panda robot show the excitingly high success rate of our method. The superiority of our method is especially evident in complex tasks.

Avoiding the usage of joint accelerations during robot online identification and control is significant in improving modeling and tracking accuracy. Regressor filtering is feasible to achieve acceleration-free online identification, where the robot dynamics is linearly parameterized and filtered to obtain an acceleration-free filtered regressor. Nevertheless, existing calculation methods of the filtered regressor are either applicable only to robots with low degrees of freedom (DoFs) or restricted by robot modeling techniques. We propose an acceleration-free analytical regressor filtering (AF-ARF) method to obtain the filtered regressor without restrictions on the number of DoFs or robot modeling techniques, where joint accelerations are eliminated by integration by parts, and the filtered regressor is derived by using the skew-symmetric property of the inertia matrix and some matrix operations. An acceleration-free composite learning robot control strategy based on AF-ARF is developed for exact online identification and control, where closed-loop exponential stability with parameter convergence is established under a weakened condition of interval excitation. Simulative and experimental comparisons based on a seven-DoF industrial robot have validated the superiority of our method over state-of-the-art methods in online identification, model prediction, and tracking control under reduced computing burden.

As China's infrastructure construction experiences rapid expansion, the telecommunications industry confronts significant challenges in energy consumption and carbon emissions. This article investigates how Chinese telecom operators can harness global expertise and competencies to participate in green finance initiatives, despite the intricacies of diverse standards and policy limitations. Specifically, this article evaluates the viability of implementing green financial instruments within China's telecommunication industry by examining relevant international case studies. Our research suggests that China's burgeoning green finance market offers growing prospects for telecom operators to engage in these initiatives. This article offers two primary recommendations for Chinese telecom operators: first, develop an internal system for green and sustainable finance, such as creating a green project repository and establishing green and sustainable finance frameworks; second, initiate green loans and sustainability-linked debt, signaling sustainable aspirations to the capital markets and reaping immediate reduction of capital costs.

Controlling articulated soft robots (ASRs) driven by variable stiffness actuators (VSAs) is challenging because they are highly nonlinear and difficult to model accurately. This paper proposes an efficient neural network (NN) learning control solution for ASRs driven by agonistic-antagonistic (AA)-VSAs to guarantee tracking performance without exact robot models. Composite learning resorts to memory regressor extension to enhance adaptive parameter estimation such that parameter convergence can be guaranteed without the stringent condition of persistent excitation. In the proposed method, an NN-based controller is constructed for the position tracking of AA-VSA-driven ASRs, and an NN weight update law based on composite learning is developed to enhance online modeling and control capabilities. Experiments are carried out on an ASR with three degrees of freedom and qbmove Advance actuators (a kind of AA-VSAs), which have validated the effectiveness and superiority of the proposed method in terms of modeling and tracking accuracy compared with existing control methods.

To enhance robustness against noise resulting from velocity measurement and acceleration estimation in robot online identification and adaptive control, the robot dynamics should be filtered and parameterized to generate a filtered regression matrix regarding identifiable parameters. However, generating a filtered regression matrix is complicated for robots with high degrees of freedom (DoFs). The power balance model (PBM) of robots with spatial notations stands out as an effective option for online applications owing to its simplicity in generating an easily computed and acceleration-free filtered regression vector. This paper proposes a PBM-based recursive composite learning robot control (RCLRC) method to enhance parameter convergence so as to boost tracking control. Based on the PBM, a filtered regressor with a computational complexity of O(n) (instead of O(n2) to O(n4) for its dynamic model-based counterpart) is employed to calculate an excitation matrix, and a generalized regression equation for composite parameter update is normalized to provide more uniform convergence rates across all parameter components. Experiments on a 7-DoF robot manipulator have shown that the proposed PBM-RCLRC outperforms state-of-the-art methods on parameter estimation and tracking control.

Articulated soft robots (ASRs) driven by variable stiffness actuators (VSAs) are challenging to control well due to their highly nonlinear dynamics and difficulties in accurate modeling. The paper proposes a locally weighted learning (LWL)-based robust composite learning control (RCLC) solution for ASRs with agonistic-antagonistic (AA)-VSAs to enable the favorable tracking of both joint position and stiffness without exact robot models. In our solution, two LWL models are adopted online to estimate uncertainties in the link-side and stiffness dynamics, respectively, a nonlinear disturbance observer (DOB) is applied to improve tracking robustness at the link side, and a composite learning law is developed to achieve parameter convergence under a condition of interval excitation strictly weaker than persistent excitation so as to improve online modeling speed and accuracy. A distinctive feature of the proposed LWL-RCLC framework lies in the fact that the estimation of the DOB and the learning of LWL are independent yet work in a synergistic manner, which enables exact robot modeling online while improving tracking robustness. Experiments on a multi-DoF ASR with AA-VSAs have verified the superiority of the proposed method.

In minimally invasive surgery (MIS), the field of view (FOV) control is crucial. Autonomous endoscope robots have been developed to facilitate MIS procedures by enabling autonomous surgical target tracking, thus reducing the workload on surgeons. However, existing visual servoing-based target tracking methods for autonomous endoscopes often overlook the insecurity stemming from restricted workspace conditions. Instances, such as collisions between the endoscope robot’s tip and the patient’s chest or abdominal wall pose risks to patient tissue, while extensive motion of the endoscope shaft may damage incision port tissue. Addressing these security concerns, this article proposes a novel approach called virtual fixture-based restricted workspace constraint (RWSC) to reconstruct the endoscope robot’s movement range. A quadratic programming (QP) optimization framework is employed to govern the robot’s motion, ensuring autonomous target tracking while adhering to RWSCs. To solve the QP problem, we propose an adaptive zeroing neural network (ZNN) featuring a newly designed activation function (AF). This AF enhances the ZNN with predefined-time convergence and noise rejection capabilities, making it especially suitable for time-sensitive and noise-prone surgical applications. Theoretical analysis and experimental results demonstrate that our adaptive ZNN achieves shorter convergence times than existing neural dynamic-based QP solvers. Physical validations show the efficacy of the proposed RWSCs in limiting the workspace of the endoscope robot, while the FOV control strategy enables autonomous target tracking of flexible endoscopes under diverse constraints and objectives.

Parameter convergence in adaptive control is crucial for improving the stability and robustness of robotic systems. Nevertheless, a stringent condition named persistent excitation (PE) needs to be satisfied to ensure parameter convergence in the conventional adaptive robot control. Composite learning robot control (CLRC) is an innovative methodology that guarantees parameter convergence under a condition of interval excitation (IE) that is strictly weaker than PE. This paper puts forward a time-division multi-channel (TDMC) CLRC strategy such that parameter convergence is achieved even without the IE condition. In the TDMC mechanism, a filtered regressor is integrated with multiple time intervals to generate a generalized prediction error for parameter update, such that excitation information of regressor channels at different instants is exploited more effectively and efficiently to achieve fast and accurate parameter estimation. Global exponential stability with parameter convergence of the closed-loop system is achieved under a partial IE condition that is much weaker than IE. Experiments on a collaborative robot with 7 degrees of freedom have demonstrated the superiority of the proposed approach in both parameter estimation and trajectory tracking compared to start-of-the-art approaches.

Robot visual servoing gives the possibility of exact pose control in unstructured environments, and homography-based visual servoing (HBVS) enables 3-D control over robot end-effectors using 2-D data from cameras. However, existing methods of visual servoing usually depend on the exact information of camera and robot models. This work put forward a dynamics-based HBVS control method to achieve 3-D visual tracking under both unknown camera extrinsic and robot dynamic parameters, where exact parameter estimation is performed online by using a composite learning technique. The proposed method achieves exponential stability along with the convergence of both camera extrinsic and dynamic parameters when a weak condition known as interval excitation is satisfied. Experiments conducted with a 7-degree-of-freedom robot manipulator known as Franka Emika Panda have provided evidence that the proposed method is effective concerning parameter estimation as well as 3-D robot tracking.

Cartesian impedance control plays a significant role in improving the safety and compliance of robot end-effectors when executing collaborative tasks with humans or environments. However, achieving target impedance is challenging under uncertain robot dynamics. In this study, we raise a composite learning-based Cartesian impedance control method to ensure exact Cartesian trajectory tracking in free motion and Cartesian target impedance in interaction under uncertain robot dynamics. Introducing a composite learning update to precise robot modeling online, so the exponential convergence and passivity of the closed-loop robot dynamics are guaranteed under a weak condition known as interval excitation. The efficacy and superiority of this method have been demonstrated through experiments on a collaborative robot with 7 degrees of freedom known as Franka Emika Panda.

The ability to handle contact makes robots qualified for many complicated tasks, such as welding, hammering, and wiping. Robot cameras facilitate position planning and control without the geometric knowledge of contact surfaces since they can project contact surfaces onto a 2-dimensional image plane. However, existing hybrid vision-force control (HVFC) methods still rely on this knowledge to project the force on the constraint subspace and do not adequately leverage the redundant degrees of freedom (DoFs) for redundant robots with contact tasks. This paper proposes an enhanced HVFC solution for redundant robots equipped with an eye-to-hand camera to unify HVFC in the Cartesian space and impedance control in the joint nullspace into one closed-loop dynamics with rigorous stability guarantees. Any geometric knowledge of contact surfaces is not required by projecting the force into the redundant space of the visual task rather than the surface’s normal space. Experiments on a seven- DoF collaborative robot have verified that the proposed method is qualified for simultaneous contact tasks in the Cartesian space and compliant interaction in the joint nullspace.

Due to the large deformation gradient caused by mining, it is easy to cause serious incoherence phenomenon in radar interferometry, and the traditional phase unwrapping (PU) method is limited in this case. To solve this problem, a novel PU method for mining area based on edge detection using the SegNet model is proposed for mining subsidence basins with large deformation. First, SegNet network was used to extract the edge information of the subsidence basin in the mining area. Then, the edges were refined and connected by the Zhang-Suen thinning method and regional growth method, respectively. Finally, PU was completed by the determined phase jump variables. Simulated interferograms with different signal-to-noise ratio (SNR) and two real interferograms with different interference qualities are selected for experiments. Compared with the three traditional PU methods and two deep learning PU methods, the proposed model has higher accuracy and better robustness. When the SNR is 1 and 4, the unwrapping error distribution area of the proposed method is the smallest, and the PU result is more close to the real situation in the interferogram of real mining area. The novel two-step PU method effectively solves the problem that the traditional PU method is seriously affected by noise and large deformation.

Time-variant quadratic programming (TVQP) has widespread applications and often involves equality, inequality, and bound constraints. An effective solver for TVQP problems is zeroing neural network (ZNN), and nonlinear complementary problem function-based ZNN (NCP-ZNN) is a state-of-the-art ZNN solver that can handle equality and inequality constraints. However, when dealing with bound constraints, NCP-ZNN expands the dimension of the matrix and then introduces twice the number of Lagrange multipliers. To overcome this deficiency, this article develops a modified NCP-ZNN solver by introducing the first-order optimality conditions. Numerical validation is performed to substantiate the superior solving efficiency of the modified NCP-ZNN solver, which can achieve the same or lower order of residual errors compared with the original NCP-ZNN. Then, the modified NCP-ZNN solver is applied to the pose control of a redundant manipulator, demonstrating its superiority in solving practical problems.

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.

Manual rigid endoscopes have defects such as a low efficiency, difficult operation, and safety risks, and the antinoise interference ability, convergence speed, and control accuracy of the neural network control technology for the existing autonomous endoscopes are often ignored. Solving these problems is important for the stable operation of endoscopes. Therefore, a new adaptive fast convergent antinoise dual neural network (AFA-DNN) controller for the visual servo control of ten-degree of freedom flexible endoscope robots (FERs) with physical constraints is proposed in this work. First, the control scheme of the FERs is formulated as a quadratic programming problem, and then, an AFA-DNN visual servo controller is designed for the FERs. The adaptive gains of the controller can accelerate the convergence, improve the antinoise ability, and increase the convergence accuracy of the controller. Then, according to the Lyapunov theory, the fast convergence of the AFA-DNN in finite time is proven for both noise-free and noisy conditions. The experimental results indicate that the FER controlled by the proposed AFA-DNN can accurately track various trajectories and that the AFA-DNN has a better antinoise interference ability, higher convergence accuracy, and faster convergence speed than conventional methods. The convergence speed of the AFA-DNN is increased by a factor of 4.22 by using the adaptive gains. Experiments also indicate that the AFA-DNN remains well functioning under various noise disturbances (such as constant, periodic, linear, and Gaussian noise).

Time-variant quadratic programming (QP) with multi-type constraints including equality, inequality, and bound constraints is ubiquitous in practice. In the literature, there exist a few zeroing neural networks (ZNNs) that are applicable to time-variant QPs with multi-type constraints. These ZNN solvers involve continuous and differentiable elements for handling inequality and/or bound constraints, and they possess their own drawbacks such as the failure in solving problems, the approximated optimal solutions, and the boring and sometimes difficult process of tuning parameters. Differing from the existing ZNN solvers, this article aims to propose a novel ZNN solver for time-variant QPs with multi-type constraints based on a continuous but not differentiable projection operator that is deemed unsuitable for designing ZNN solvers in the community, due to the lack of the required time derivative information. To achieve the aforementioned aim, the upper right-hand Dini derivative of the projection operator with respect to its input is introduced to serve as a mode switcher, leading to a novel ZNN solver, termed Dini-derivative-aided ZNN (Dini-ZNN). In theory, the convergent optimal solution of the Dini-ZNN solver is rigorously analyzed and proved. Comparative validations are performed, verifying the effectiveness of the Dini-ZNN solver that has merits such as guaranteed capability to solve problems, high solution accuracy, and no extra hyperparameter to be tuned. To illustrate potential applications, the Dini-ZNN solver is successfully applied to kinematic control of a joint-constrained robot with simulation and experimentation conducted.

Obstacle avoidance (OA) and joint-limit avoidance (JLA) are essential for redundant manipulators to ensure safe and reliable robotic operations. One solution to OA and JLA is to incorporate the involved constraints into a quadratic programming (QP), by solving which OA and JLA can be achieved. There exist a few non-iterative solvers such as zeroing neural networks (ZNNs), which can solve each sampled QP problem using only one iteration, yet no solution is suitable for OA and JLA due to the absence of some derivative information. To tackle these issues, this paper proposes a novel solution with a non-iterative neural controller termed NCP-ZNN for joint-constrained redundant manipulators. Unlike iterative methods, the neural controller involving derivative information proposed in this paper possesses some positive features including non-iterative computing and convergence with time. In this paper, the reestablished OA-JLA scheme is first introduced. Then, the design details of the neural controller are presented. After that, some comparative simulations based on a PA10 robot and an experiment based on a Franka Emika Panda robot are conducted, demonstrating that the proposed neural controller is more competent in OA and JLA.

Zeroing neural networks (ZNNs) are powerful alternatives to solving quadratic programming (QP) for constrained control of parallel and serial robots. A recent study showed that a ZNN solver designed based on a perturbed Fischer-Burmeister function (pFB-ZNN) achieves more satisfactory performance than other ZNN solvers. The pFB-ZNN solver suffers from manual tuning of an extra hyper-parameter and may encounter residual error peaks. To tackle the above issues, this paper proposes a new Mangasarian-Solodov function-based ZNN (MS-ZNN) solver. The MS-ZNN solver has no extra hyper-parameter to be tuned and it can eliminate residual error peaks appeared in the pFB-ZNN solver, ensuring a higher solution accuracy. Mathematically, this paper details the design and convergence analysis of the MS-ZNN solver, demonstrating its convergence in the sense of Lyapunov. Numerical studies are comparatively performed, verifying the effectiveness and superiority of the MS-ZNN solver. The MS-ZNN solver is then successfully applied to kinematic control of a parallel robot and a serial robot under joint constraints. Both simulative and experimental results demonstrate that the proposed MS-ZNN solver is applicable to constrained control of parallel and serial robots with joint-limit avoidance achieved.

Generally, the infinity-norm joint-velocity minimization (INVM) of physically constrained kinematically redundant robots can be formulated as time-variant linear programming (TVLP) with equality and inequality constraints. Zeroing neural network (ZNN) is an effective neural method for solving equality-constrained TVLP. For inequality-constrained TVLP, however, existing ZNNs become incompetent due to the lack of relevant derivative information and the inability to handle inequality constraints. Currently, there is no capable ZNN in the literature that has achieved the INVM of redundant robots under joint limits. To fill this gap, a classical INVM scheme is first introduced in this article. Then, a new joint-limit handling technique is proposed and employed to convert the INVM scheme into a unified TVLP with full derivative information. By using a perturbed Fisher-Burmeister function, the TVLP is further converted into a nonlinear equation. These conversion techniques lay a foundation for the success of designing a capable ZNN. To solve the nonlinear equation and the TVLP, a novel continuous-time ZNN (CTZNN) is designed and its corresponding discrete-time ZNN (DTZNN) is established using an extrapolated backward differentiation formula. Theoretical analysis is rigorously conducted to prove the convergence of the neural approach. Numerical studies are performed by comparing the DTZNN solver and the state-of-the-art (SOTA) linear programming (LP) solvers. Comparative results show that the DTZNN consumes the least computing time and can be a powerful alternative to the SOTA solvers. The DTZNN and the INVM scheme are finally applied to control two kinematically redundant robots. Both simulative and experimental results show that the robots successfully accomplish user-specified path-tracking tasks, verifying the effectiveness and practicability of the proposed neural approach and the INVM scheme equipped with the new joint-limit handling technique.

To solve the problems of discomfort and potential colon perforations of patients that arise when standard colonoscopes are used for colonoscopy, an electromagnetically actuated soft-tethered colonoscope robot (EASCR) is here introduced. Owing to EASCRs’ highly nonlinear and complex application environments, the hybrid vision/magnetic-force tracking control for these types of robots remains a challenging research issue, and the lack of current constraints may also give rise to safety concerns. Therefore, a hybrid vision/magnetic-force fast convergent dual neural network (DNN) tracking controller for an EASCR with current constraints is developed to alleviate patient discomfort and ensure the safe and smooth progression of colonoscopy. First, EASCR motion/vision and electromagnetically actuated force nonlinear coupling models are established, and a quadratic programming visual servo-tracking control scheme with current constraints is designed. Second, a novel DNN solver for the nonlinear control scheme is developed, and its convergence in finite time is strictly proved. The results of simulations and experiments indicate that the designed control method can well control EASCRs with current constraints to achieve tracking tasks, and it has a stronger anti-disturbance ability, faster convergence, and higher convergence accuracy than existing methods.

Zeroing neural network (ZNN) is an effective neural solution to time-varying problems, including time-varying complex Sylvester equations. Generally, a ZNN model involves a convergence design parameter (CDP) that influences its convergence rate. In traditional fixed-parameter ZNNs (FP-ZNNs), the CDPs are set to be constant, which is not realistic since the CDPs are actually time-varying in practical hardware environments. By considering this fact, varying-parameter ZNNs (VP-ZNNs) with time-varying CDPs have been researched in the literature. Although these VP-ZNNs have been demonstrated to deliver superior convergence as compared with FP-ZNNs, they have one drawback, that is, their CDPs usually keep increasing with time, meaning that the CDPs tend to be infinity large with time progresses. Evidently, infinity large CDPs are unacceptable in practice. Moreover, computing resources will be wasted by growing the CDPs with time after the VP-ZNNs become convergent. To tackle the above issues, this article, for the first time, proposes an arctan-type VP-ZNN (ATVP-ZNN) with finite-time convergence for solving time-varying complex Sylvester equations. The ATVP-ZNN is able to adjust its CDPs that finally converge to be constant when the ATVP-ZNN becomes convergent in finite time. In theory, the finite-time convergence of the ATVP-ZNN and the upper bound of the CDPs are mathematically analyzed. Numerical studies are comparatively performed with the superior convergence of the ATVP-ZNN substantiated.

Colorectal cancer incidence has been steadily rising worldwide. Magnetic colonoscopes provide new approaches to conduct colon inspection and treatment. This paper presents a novel electromagnetically actuated soft-tethered colonoscope to achieve precise and stable orientation control. An inflated balloon is designed to eliminate the unpredictable disturbance of the floating tether. A 2OR Pseudo-Rigid-Body (PRB) model of the soft tether is developed to analyze the relationship between the tether deflection and applied force and torque. A closed-loop control framework is constructed with visual position feedback. Experiments are first conducted to validate the assumption of the PRB model and the efficacy of the magnetic field model. Then, trajectory tracking tasks and disturbance rejection tests are performed to validate the feasibility of the proposed solution and closed-loop control. Results show that the colonoscope can stably and accurately orient to the desired orientation with an absolute mean position error of less than 0.5 mm and an average velocity of 3.5 mm/s. The distal tip can quickly re-stabilize to the desired orientation even when a large disturbance exists.

In this paper, we proposed an autonomous robotic flexible endoscope system for the laparoscopic bariatric surgery (LBS). This system comprises a UR5 robot and a flexible endoscope equipped with a novel continuum joint, named reinforced double helix continuum mechanism. Compared with the simple helix structure, the compressional and torsional stiffness of the proposed joint are improved significantly. To automate the robotic flexible endoscope, image-based visual servoing technique is employed. A deep learning algorithm named TernausNet-16 is improved and incorporated into the control framework to detect surgical instruments inside the camera view. The experimental studies verified the effectiveness and feasibility of the robotic flexible endoscope system for the visual serviong control scheme assisted by deep learning methods.

The acceleration of urbanization in China makes people more concerned about the livability of urban environment. The concept of 15-minute living circle is gradually applied to land space planning to provide guidance for the construction of high-quality community to serve citizens. This paper used multi-source data of remote sensing imagery and POI to build Qingdao's urban convenience index from the perspectives of travel, shopping, health care, catering, entertainment, education and so on, so as to evaluate the livability of urban life. The results show that areas with higher convenience of living circle are located in the regions with flat terrain. The highest convenience degree distributes along the East and West Coast of Jiaozhou Bay, almost all of which were located in traditional old urban districts. The urban livability assessment from the perspective of convenience of 15-minute living circle can provide guidance for city and landscape planning.

Aiming at time-variant problems solving, a special type of recurrent neural networks, termed zeroing neural network (ZNN), has been proposed, developed, and validated since 2001. Although equality-constrained time-variant quadratic programming (TVQP) has been well solved using the ZNN approach, TVQP problems with inequality constraints involved have not been satisfactorily handled by the existing ZNN models. To overcome this issue, this paper designs a ZNN model with exponential convergence for solving equality- and inequality-constrained TVQP problems. Considering a fast convergence is preferred in some time-critical applications in practice, a predefined-time stabilizer is for the first time utilized to endow the ZNN model with predefined-time convergence, leading to a predefined-time convergent ZNN (PTCZNN) model that exhibits an antecedently- and explicitly-defined convergence time. Theoretical analysis is performed with the convergence of the two ZNN models including the predefined-time convergence of the PTCZNN model rigorously proved. Validations are comparatively conducted to verify the effectiveness and superiority of the PTCZNN model in terms of convergence performance. To demonstrate the potential applications, the PTCZNN model is applied to image fusion and kinematic control of two robotic arms with joint limits considered. The efficacy and applicability of the PTCZNN model are validated by the illustrative examples. This is the first time to develop a ZNN model working as a quadratic programming solver that is applicable to kinematic control of robotic arms with joint constraints handled since the emergence of ZNNs.

Nonlinear optimization problems with dynamical parameters are widely arising in many practical scientific and engineering applications, and various computational models are presented for solving them under the hypothesis of short-time invariance. To eliminate the large lagging error in the solution of the inherently dynamic nonlinear optimization problem, the only way is to estimate the future unknown information by using the present and previous data during the solving process, which is termed the future dynamic nonlinear optimization (FDNO) problem. In this paper, to suppress noises and improve the accuracy in solving FDNO problems, a novel noise-tolerant neural (NTN) algorithm based on zeroing neural dynamics is proposed and investigated. In addition, for reducing algorithm complexity, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is employed to eliminate the intensively computational burden for matrix inversion, termed NTN-BFGS algorithm. Moreover, theoretical analyses are conducted, which show that the proposed algorithms are able to globally converge to a tiny error bound with or without the pollution of noises. Finally, numerical experiments are conducted to validate the superiority of the proposed NTN and NTN-BFGS algorithms for the online solution of FDNO problems.

This article focuses on the research of a general time-varying nonlinear optimization (TVNO) problem solving especially in a noise-disturbance environment. For addressing this problem more efficiently, a new noise-enduring and finite-time convergent design formula is suggested to establish a novel zeroing neural network (NZNN). In contrast to the initial zeroing neural network or the noising-enduring zeroing neural network, which either only achieves finite-time convergence or only suppresses external disturbances, the merit of the proposed NZNN model is able to find an error-free optimal solution in a finite time under various different types of external noises. In addition, the detailed mathematical analyses about finite-time convergence and noise endurance are given to prove the excellent characteristics of the NZNN model. Numerical comparative results are provided to demonstrate the accuracy, efficiency, and advantages of the NZNN model for TVNO under various types of external disturbances. Robotic tracking example further validates the applicability of the NZNN model especially in a noise-disturbance environment.

Sylvester equation is often applied to various fields, such as mathematics and control systems due to its importance. Zeroing neural network (ZNN), as a systematic design method for time-variant problems, has been proved to be effective on solving Sylvester equation in the ideal conditions. In this paper, in order to realize the predefined-time convergence of the ZNN model and modify its robustness, two new noise-tolerant ZNNs (NNTZNNs) are established by devising two novelly constructed nonlinear activation functions (AFs) to find the accurate solution of the time-variant Sylvester equation in the presence of various noises. Unlike the original ZNN models activated by known AFs, the proposed two NNTZNN models are activated by two novel AFs, therefore, possessing the excellent predefined-time convergence and strong robustness even in the presence of various noises. Besides, the detailed theoretical analyses of the predefined-time convergence and robustness ability for the NNTZNN models are given by considering different kinds of noises. Simulation comparative results further verify the excellent performance of the proposed NNTZNN models, when applied to online solution of the time-variant Sylvester equation.

In this paper, a multi-level simultaneous minimization (MLSM) scheme is proposed and investigated to remedy the joint-angle drift (JAD) and non-zero final joint-velocity (NZFJV) phenomena as well as to prevent the occurrence of high joint variables of redundant robot manipulators. The proposed scheme is novelly designed within multiple levels and finally resolved at the jerk level for a jerk-bounded robot motion, which is desirable for engineering applications. More importantly, the correctness of the proposed MLSM scheme is guaranteed by the corresponding theorems. Then, the MLSM scheme is formulated as a dynamical quadratic program (DQP) that is solved by a piecewise linear projection equation neural network (PLPENN). Furthermore, the path-tracking simulations based on a 6-degrees-of-freedom (DOF) robot manipulator substantiate the effectiveness and advantage of the MLSM scheme. Comparisons between the MLSM scheme and the minimum jerk norm (MJN) scheme illustrate that the proposed scheme is superior and more applicable. Finally, the additional validation on the KUKA robot in the virtual robot experimentation platform (V-REP) is provided for reproducible engineering applications by researchers and practitioners.Note to Practitioners—This paper is motivated by the inverse kinematics problem of jerk-bounded redundant robot manipulators in practical applications. Note that the joint-angle drift (JAD) and non-zero final joint-velocity (NZFJV) phenomena as well as the occurrence of high joint variables always encountered in the traditional norm-based scheme for robot manipulators, which is not suitable for the real-time control of robots. Besides, it would be appealing and desirable to resolve the robot redundancy at the jerk level for industrial robots in engineering. Therefore, an effective, flexible, and stable solution for such robot manipulators is significant for practitioners. This paper proposes a multi-level simultaneous minimization (MLSM) scheme for practitioners interested in robot kinematics to remedy the JAD and NZFJV phenomena as well as to prevent the occurrence of high joint variables of redundant robot manipulators. Unlike traditional single-level schemes, such as the minimum jerk norm (MJN) scheme, the proposed scheme is designed within multiple levels with distinct physical nature and finally resolved at the jerk level to achieve a desirable performance for the jerk-bounded redundant robot manipulators. Besides, for better understanding of practitioners, the corresponding block diagram and principle interpretation of the MLSM scheme are presented. Simulation studies and comparisons are designed and conducted on a 6-degrees-of-freedom (DOF) robot manipulator to substantiate the effectiveness and superiority of the proposed scheme. Extensive tests with different weighting factors fully verify the flexibility and stable performance of the proposed MLSM scheme. For reproducible engineering applications by researchers and practitioners, the additional validation on the KUKA robot in the virtual robot experimentation platform (V-REP) is further presented.

The so-called zeroing neural network (ZNN) is an effective recurrent neural network for solving dynamic problems including the dynamic nonlinear equations. There exist numerous unperturbed ZNN models that can converge to the theoretical solution of solvable nonlinear equations in infinity long or finite time. However, when these ZNN models are perturbed by external disturbances, the convergence performance would be dramatically deteriorated. To overcome this issue, this paper for the first time proposes a finite-time convergent ZNN with the noise-rejection capability to endure disturbances and solve dynamic nonlinear equations in finite time. In theory, the finite-time convergence and noise-rejection properties of the finite-time convergent and noise-rejection ZNN (FTNRZNN) are rigorously proved. For potential digital hardware realization, the discrete form of the FTNRZNN model is established based on a recently developed five-step finite difference rule to guarantee a high computational accuracy. The numerical results demonstrate that the discrete-time FTNRZNN can reject constant external noises. When perturbed by dynamic bounded or unbounded linear noises, the discrete-time FTNRZNN achieves the smallest steady-state errors in comparison with those generated by other discrete-time ZNN models that have no or limited ability to handle these noises. Discrete models of the FTNRZNN and the other ZNNs are comparatively applied to redundancy resolution of a robotic arm with superior positioning accuracy of the FTNRZNN verified.

This article designs and analyzes a recurrent neural network (RNN) for the visual servoing of a flexible surgical endoscope. The flexible surgical endoscope is based on a commercially available UR5 robot with a flexible endoscope attached as an end-effector. Most of the existing visual servo control frameworks of the robotic endoscopes or robot arms have not considered either the physical limits of the robot or the remote center of motion (RCM) constraints (i.e., the fulcrum effect). To tackle this issue, this article first conducts the kinematic modeling of the flexible robotic endoscope to achieve automation by visual servo control. The kinematic modeling results in a quadratic programming (QP) framework with physical limits and RCM constraints involved, making the UR5 robot applicable to surgical field. To solve the QP problem and accomplish the visual task, an RNN activated by a sign-bi-power activation function (AF) is proposed. The motivation of using the sign-bi-power AF is to enable the RNN to exhibit an accelerated finite-time convergence, which is more preferred in time-critical applications. Theoretically, the finite-time convergence of the RNN is rigorously proved using the Lyapunov theory. Compared with the previous AFs applied to the RNN, theoretical analysis shows that the RNN activated by the sign-bi-power AF delivers an accelerated convergence speed. Comparative validations are performed, showing that the proposed finite-time convergent neural network is effective to achieve visual servoing of the flexible endoscope with physical limits and RCM constraints handled simultaneously.

This article aims to solve the Moore-Penrose inverse of time-varying full-rank matrices in the presence of various noises in real time. For this purpose, two varying-parameter zeroing neural networks (VPZNNs) are proposed. Specifically, VPZNN-R and VPZNN-L models, which are based on a new design formula, are designed to solve the right and left Moore-Penrose inversion problems of time-varying full-rank matrices, respectively. The two VPZNN models are activated by two novel varying-parameter nonlinear activation functions. Detailed theoretical derivations are presented to show the desired finite-time convergence and outstanding robustness of the proposed VPZNN models under various kinds of noises. In addition, existing neural models, such as the original ZNN (OZNN) and the integration-enhanced ZNN (IEZNN), are compared with the VPZNN models. Simulation observations verify the advantages of the VPZNN models over the OZNN and IEZNN models in terms of convergence and robustness. The potential of the VPZNN models for robotic applications is then illustrated by an example of robot path tracking.

Matrix inversion ubiquitously arises in engineering. The so-called zeroing neural network (ZNN) is an effective recurrent neural network for solving time-variant matrix inversion. Without considering noises, the ZNN approach requires finite time or infinitely long time to converge to the exact solution. When perturbed by additive noises, the existing ZNN models exhibit limited ability to reject disturbances and are susceptible to be divergent. For instance, under time-variant bounded noises, steady-state residual errors of the existing ZNNs would be bounded. To make the steady-state residual errors arbitrarily small, infinitely long time is required and related design parameters must be set large enough or infinitely large, which is not realistic in practice. To overcome this situation, this paper for the first time systematically designs and analyses a finite-time convergent and noise-tolerant ZNN (FTNTZNN) that is capable of completely converging to the theoretical solution in finite time even under various types of noises. Theoretically, the finite-time convergence and disturbance-rejection properties of the FTNTZNN are rigorously proved. Comparative numerical results substantiate that the FTNTZNN model delivers superior convergence and robustness performance in solving time-variant matrix inversion and kinematic control of a robotic arm as compared with the existing ZNN models. The FTNTZNN model expands the current knowledge for designing neural-dynamic systems to solve matrix inversion, which can provide inspiration for other problems solving under noises.

A variable-gain finite-time convergent and noise-enduring zeroing neural network (VGFTNE-ZNN) is for the first time proposed for time-variant convex quadratic programming (QP). Differing from the existing finite-time convergent ZNNs with constant or variable design gains (i.e., CGFT-ZNN and VGFT-ZNN) that have limited noise-handling capabilities, the proposed VGFTNE-ZNN can endure additive noises by dynamically adjusting its design gains in finite time. Design gains of the unpolluted VGFTNE-ZNN are allowed to be constant when the QP problem is solved, whereas the design gain of the existing unpolluted VGFT-ZNN unrealistically increases to infinity when time evolves to infinity. Unlike existing polluted ZNNs with known noises involved, more practical unknown noises are successfully handled by the VGFTNE-ZNN. The finite-time convergence and noise-endurance properties of the VGFTNE-ZNN are mathematically proved based on the Lyapunov theory. Numerical verifications are comparatively performed with the superiorities of the VGFTNE-ZNN substantiated as compared with the existing CGFT-ZNN and VGFT-ZNN.

Time-variant linear matrix equations (TVLMEs) are ubiquitous in engineering. To solve TVLMEs, various zeroing neural network (ZNN) models have been developed. These ZNNs globally converge to the solution of TVLMEs either in infinity long time or in finite time. However, even the convergence time of a finite-time convergent ZNN is implicit and closely dependent on the initial condition of a problem. This may reduce its applicability to time-critical applications in practice. To overcome this problem, this paper for the first time accelerates a ZNN to fixed-time convergence using a novel activation function. The convergence time of the proposed ZNN can be antecedently defined as an explicit parameter. Theoretically, its fixed-time convergence and robustness properties are rigorously proved. Comparative numerical results substantiate the superior convergence and robustness performance of the fixed-time convergent ZNN for TVLMEs solving. Additionally, the fixed-time convergent ZNN is applied to motion planning of a redundant robotic arm.

This paper proposes a novel way of constructing strut-type modular robotic structures to avoid some difficulties of designing and implementing ideal compliant nodes. Rigid nodes are employed to replace the ideal compliant nodes and to reduce the structural complexity while the feasibility of hardware implementation is dramatically improved. To release some kinematic constraints caused by the rigid nodes, we introduce robotic struts that consist of two prismatic actuators linked by a passive revolute joint. Physics-based robot models are constructed using a robot simulator. A scalable distributed control method is implemented using coupled central pattern generators. And, for comparison, the same control method is applied to conventional and the proposed strut-type modular robotic structures. Simulation results show that the proposed strut-type structures have several advantages over the conventional ones including less number of passive joints and shape-maintenance property.