Inspired by soft creatures and structures in nature, continuum robots exhibit remarkable flexibility, safe interaction, and ease of miniaturization, showcasing vast application potential. However, their flexible structure renders analytical methods inadequate for precise modeling and control, while existing data-driven approaches suffer from low data efficiency and unproven theoretical control performance. This paper aims to achieve data-efficient modeling and reliable control of continuum robots through innovative algorithms, exploring the performance of the new method from both theoretical and experimental perspectives. Specifically, we utilize neural ordinary differential equations (NODE) to achieve data-efficient modeling of continuum robots and investigate the performance of the modeling method. Then, we propose a novel predefined-time-synchronized stable zeroing neurodynamics (PTSS-ZND) model. By combining the NODE method and the PTSS-ZND method, we propose a reliable data-driven control system. Through rigorous theoretical analysis, we prove the stability and predefined-time convergence of the data-driven control system. Finally, through simulations and physical experiments, we validate the feasibility and convergence of the novel method and its advantages over existing data-driven methods. Experiments on one- and three-segment continuum robots indicate that the proposed method achieves a root mean square position error (e.g., 2.5 mm for the three-segment robot) of less than 1% of the robot length using fewer than 100 data samples. Our method also demonstrates robust performance under various external and internal disturbances. In addition, it can potentially be extended for end-effector pose control.

Traditional data-driven control methods often require large amounts of training data, posing significant challenges for continuum robots. Recently, neural ordinary differential equation (NODE) methods have demonstrated impressive capabilities for data-efficient modeling of continuum robots. However, existing NODE-based control methods still face limitations in terms of convergence and robustness. In this paper, we propose a data-driven iterative learning control system for continuum robots, leveraging NODE for modeling. Within this framework, by incorporating online parameter learning, the proposed control system continuously adapts to various uncertainties associated with continuum robots, resulting in improved convergence and robustness in repetitive tasks. The effectiveness of the proposed method is validated through simulations and physical experiments, and comparative analysis highlights its superior accuracy over existing approaches.

The reconfigurability and structural complexity of robotic manipulators introduce significant challenges to their kinematic modeling, making traditional model-based methods less feasible. This article studies the synchronized tracking control problem of a dual-arm system with completely unknown kinematic model for the first time. A gradient neurodynamic method is presented to learn the unknown Jacobian matrices of dual manipulators. Then, we innovatively employ the coupled error in dual quaternion form as the state function of the zeroing neurodynamic model to control position and orientation simultaneously, leading to a more streamlined and compact inverse kinematics solution. Furthermore, by transforming task-space coupled errors into joint-space errors, we improve the cerebellar neural network to a mode compatible with kinematic control and, for the first time, utilize it to optimize synchronized kinematic control. Finally, the effectiveness of the proposed method is validated by simulations and experiments on various robotic manipulators.

Neural networks have been widely investigated for the control of robot manipulators and recurrent neural network (RNN) is accepted as a powerful tool for visual servoing. Different from existing control schemes for robot-camera systems, this article proposes a novel image-based visual servoing (IBVS) control scheme for both the regulation and tracking control of robot manipulators in the framework of a special class of RNN, termed zeroing neural network (ZNN), which does not require prior knowledge about camera configuration and kinematic model parameters. The proposed control scheme is composed of a data-driven mapping estimator and a controller, both of which are designed based on ZNN. To facilitate the deployment of the proposed IBVS control scheme, a discrete-time version of the proposed control scheme is developed. Theoretical analysis for the proposed method is presented in terms of convergence, stability, and robustness. In addition, simulations and experiments are carried out based on different types of robot-camera systems to verify the efficacy and portability of the proposed control scheme for solving regulation and trajectory IBVS problems. Moreover, comparative studies are performed to reveal the merits of the proposed control scheme.

Heterogeneous continuum robots (HCRs) with different structures have been designed for different purposes, whereas the coordination of multiple HCRs has received little attention. On one hand, multiple HCRs coordination brings the possibility of performing complicated tasks. On the other hand, the structural diversity of HCRs poses great difficulties to their modeling and control. This article proposes a model-free scheme for the synchronous motion control of multiple HCRs. The control problem is formulated as two convex optimization problems in a model-free closed-loop framework, including control quantity estimation and Jacobian matrix estimation. The proposed approach aims at addressing the synchronous motion problem of multiple HCRs in a decentralized way. The design of model-free feedback control guarantees the high adaptability of the proposed method for a wide range of HCRs. Simulation studies are performed to verify the effectiveness and adaptability of the proposed scheme for multiple HCRs. Comparative studies verify that the tracking error synthesized by the proposed method is about two-thirds lower than that of the existing method while the computational cost is similar, which reveals the merit of the proposed method in terms of accuracy. Finally, the feasibility and effectiveness of the proposed method are also verified by hardware-in-loop simulations and physical experiments on the synchronous motion control of a cable-driven continuum robot and a concentric-tube robot.

This article proposes a model-free kinematic control method with predefined-time convergence for robotic manipulators with unknown models. The predefined-time convergence property guarantees that the regulation task can be finished by robotic manipulators in a preset time, in spite of the initial state of manipulators. This feature will facilitate the scheduling of a series of tasks in industrial applications. To this end, a varying-parameter predefined-time convergent zeroing neural dynamics (ZND) model is first proposed and employed to solve the regulation problem. As well as the primary task, a conventional ZND model is utilized to achieve the avoidance of obstacle. The stability of the proposed controller is analyzed based on the Lyapunov stability theory. For the sake of dealing with the unknown kinematic model of robotic manipulators, gradient neural dynamics (GND) models are exploited to adapt the Jacobian matrices just relying on the control signal and sensory output, which enables us to control robotic manipulators in a model-free manner. Finally, the efficacy and merits of the proposed control method are verified by simulations and experiments, including a comparison with the existing method.

To effectively diminish the kinetic energy dissipation, joint-angle drift, and joint-velocity discontinuity problems, and simultaneously achieve the end-effector position and direction control as well as the avoidance of joint-physical limits, a novel velocity layer weighted multicriteria optimization scheme is proposed, which outperforms the traditional schemes for the robotic manipulators with multiple constraints. Besides, considering that the existing joint-limit conversion strategies are not differentiable everywhere or with relatively complex formulation, a new exponential joint-limit conversion strategy is introduced to facilitate the dynamic quadratic programming reformulation of the proposed scheme. For easier numerical realization and real-time control, aided with a high-precision six-step extrapolated-backward discretization rule, a novel discretized zeroing neural network model is proposed to resolve the proposed scheme, which has higher precision than the existing neural network models. Finally, numerical and physical experiments are conducted to substantiate the efficacy, superiority, and practicability of the proposed scheme and model.

The effectiveness of continuous-time zeroing neural network (ZNN) (CZNN) in continuum robot control has been preliminarily verified. However, CZNN is not friendly to digital devices and hardware implementation. Although discrete ZNN (DZNN) has been investigated in other tasks, all the existing DZNNs are designed with fixed time steps, which cannot meet the needs of different tasks. This motivates us to develop a generic DZNN model with variable number of time steps and apply it to continuum robot control. In this article, we present a data-driven scheme based on CZNNs to learn the unknown kinematics of continuum robots and solve the kinematic control problem. Furthermore, a unified$m$-step forward discretization formula is derived to discretize the CZNN-based scheme into DZNN-based control algorithms. Finally, we take the 1-step and the 3-step algorithms as examples to show the discretization process, and verify their efficacy by simulations and experiments.

Tracking control of redundant and hyperredundant manipulators is a fundamental and critical problem in practical applications. In order to effectively decrease the end-effector position errors, a novel dual fuzzy-enhanced neurodynamic (DFEN) scheme is put forward for solving the position error accumulation problem followed by achieving accurate tracking control results. The proposed scheme is established based on a zeroing neurodynamic approach in conjunction with two fuzzy adjustment units that are capable of tuning the control parameters by monitoring the tracking error. Moreover, the DFEN scheme can effectively solve the tracking problem without requiring knowinga prioriknowledge of the kinematic model of the robot. The convergence and the stability of the proposed approach are demonstrated by theoretical analysis. The effectiveness, accuracy, and robustness of the proposed DFEN scheme are verified on the simulative redundant manipulator, continuum robot, and hybrid robot (integrating the redundant manipulator and the continuum robot). A practical experiment is provided to validate the proposed scheme as well.

Fault tolerance is a critical requirement for robust motion control of redundant robotic manipulators. This article aims to endow the redundant manipulator with the capability to achieve the required path of end-effector in the condition that one or some of its joints’ motion fail. Although many fault-tolerant control algorithms of redundant manipulator have been proposed in recent years. However, few of them are on the basis of the condition that the robotic model is unknown. The complexity of the calculation model limits the efficiency and portability of these algorithms. For the first time, we proposed a discrete model-free fault-tolerant tracking control scheme of redundant manipulator, which takes into account the fault tolerance in the control system of redundant manipulator by formulating it into a quadratic programming (QP) framework. The core of the proposed scheme consists of a discrete kinematic estimator and a discrete QP solver, powered by which the fault-tolerant control problem is transformed into a unified computing problem relaxing the need of knowing the redundant manipulator’s kinematic model. A discrete joint space observer is proposed for the detection of the happening of faulty states. Extensive simulations and experiments based on a redundant manipulator are performed and analyzed to support the verification of the efficiency and effectiveness of the proposed scheme.

In this study, a continuous-time gradient-Zhang neural dynamics model is proposed for computing pseudoinverses (also termed as Moore-Penrose inverses) of time-varying matrices on the basis of gradient and Zhang neural dynamics. For hardware realization, the discrete-time gradient-Zhang neural dynamics (DTGZND) models, including DTGZND-1 and DTGZND-2 models, are proposed by using Zhang et al. discretization (ZeaD) and extrapolation formulas. Compared with five conventional Zhang neural dynamics models in numerical experiments, the proposed DTGZND-1 and DTGZND-2 models own high precision, avoid computing inverse explicitly, and also work out for challenging Z-type matrices. Besides, the DTGZND-1 model is applied to robot manipulator motion planning and control via simulative and physical experiments. The experimental results substantiate the correctness and effectiveness of the proposed models.

Bio-inspired robots, e.g., soft continuum robots, have broad application prospects due to their structural dexterity and interaction safety. But these features also bring great challenges to the precise control of soft continuum robots. In this work, we investigate how to achieve the kinematic control of soft continuum robots without knowing model parameters of the robots. To this end, a model-free scheme based on varying-parameter recurrent neural networks (VP-RNN) is proposed. The scheme involves two components, one of which solves the inverse kinematics problem based on a VP-RNN model, and the other employs another VP-RNN model to estimate the pseudo-inverse of Jacobian matrix of continuum robots. Finally, the feasibility and robustness of the proposed control strategy are validated by simulations, including comparisons with other methods and case study with jammed actuation.