The negative impact of noises is inevitable in the learning and control processes of redundant manipulators, which may degrade the performance. To mitigate challenges posed by noises, this paper proposes an integral-enhanced hierarchical control and kinematics learning (IHCKL) algorithm. This algorithm comprises two components: an integral-enhanced kinematics learning (IKL) model that incorporates an integral feedback term to reduce the influence of noises during kinematics learning, and an integral-enhanced hierarchical control (IHC) model that combines neural dynamics with hierarchical control to improve the control accuracy and noise resistance in noisy environments. The proposed algorithm accurately learns the kinematics in noisy environments, while achieving multi-task execution with priorities. Different from existing state-of-the-art algorithms that are difficult to achieve multi-task executions under unknown kinematics and noisy conditions, the IHCKL algorithm integrates both kinematics learning and hierarchical control with noise resistance, exhibiting enhanced robustness and accuracy. Theoretical analyses demonstrate that the IHCKL algorithm guarantees the error convergence and noise resistance under varying noise conditions. Simulations and experiments confirm that the IHCKL algorithm offers improvements in the multi-task execution, kinematics learning, and noise resistance in noisy environments.

The image-based visual servoing (IBVS) describes a vision-based robot control. It controls the motion of the robot through the feedback from the vision sensors assembled at the end-effector of the robot, so that the feature points of the object are imaged at specific pixel points. Considering camera assembly error, end-effector assembly error, and vibration-induced noise during robot operation may affect vision servo control. We propose a model-free IBVS control scheme, which introduces a data-driven learning strategy to achieve the learning of the robot and camera Jacobian matrices and precise control of robots with unknown structures. Meanwhile, a neural dynamics-based noise-tolerant solver is proposed to solve the problems caused by noises during the robot's operation on visual servocontrol, and related theoretical analyses are carried out. Finally, the effectiveness of the proposed scheme is verified by simulations and experiments. Its superiority is demonstrated by comparison with other IBVS schemes.

Precise position and posture control of an omnidirectional mobile redundant manipulator (OMRM) with unknown structural information is challenging. This article develops a data-driven orthogonal repetitive motion-posture control (DDORMPC) scheme that leverages online learning to regulate repetitive motions in both position and end-effector quaternion orientation. Then, a dynamic neural network with nonconvex mappings (NCMDNN) is introduced by integrating structure learning with OMRM control to solve the DDORMPC problem. It employs a velocity-compensated gradient-descent update for accurate online estimation of the system Jacobian, theoretically driving the tracking error to zero. Theoretical analysis demonstrates that both the learning and control modules exhibit favorable convergence properties under necessary noise conditions. Numerical simulations, comparative experiments, and platform validation collectively verify the innovation, effectiveness, and practical value of both the proposed DDORMPC scheme and the NCMDNN model.

With the expansion of applications for robots, merely considering position control is no longer sufficient to meet practical requirements. Hence, it becomes crucial to develop a control method that synchronizes position and orientation for redundant manipulators. Over time, motion control schemes based on the quadratic programming (QP) have inevitably led to excessive joint movements. In this article, position and orientation control is modeled as a sparse optimization problem from a sparsity perspective. Meanwhile, a collective fuzzy gradient descent (CFGD) solver is designed to address the challenge of sparse position and orientation control for redundant manipulators. Theoretical analyses, simulations, and experiments demonstrate the effectiveness and superiority of the proposed method. The method is expected to provide a precise and efficient control strategy for redundant manipulators in complex tasks by reducing unnecessary joint movements and enhancing the overall performance.

This paper proposes discrete-time learning algorithms that utilize a data-driven technology to address the uncertain issues of optimization and structure. The main challenge lies in acquiring accurate optimization indices and Jacobian matrix, which can be addressed through iterative estimations enabled by these algorithms. On this basis, we propose a new model-adaptive kinematic control (MAKC) scheme for redundant manipulators without prior structure knowledge, incorporating the estimated optimization index and Jacobian matrix. To solve this scheme, a discretized data-driven neural dynamics (D3ND) controller is proposed based on the 94LVI algorithm, Kalman filter, and discrete-time learning algorithms. Theoretical analysis is provided to demonstrate its convergence. Subsequently, simulations and experiments are carried out on redundant manipulators using manipulability and joint drift as performance criteria. The results substantiate the robustness, practicability, and superiority of the proposed controller when encountering uncertain issues.

Redundant robots may undergo structural changes due to factors such as modifications, which pose challenges to their precise control and obstacle avoidance. To resolve this issue, this article proposes a data-driven obstacle avoidance (DDOA) scheme for redundant robots with unknown structures, which integrates obstacle avoidance control and structure learning. To ensure collision-free operations, an obstacle avoidance method for redundant robots is devised to maintain a safe distance from obstacles. Simultaneously, a data-driven learning equation is developed to estimate two Jacobian matrices of robots for obstacle avoidance and motion planning. A recurrent neural network (RNN) is then established to find the optimal solution to the DDOA scheme with theoretical analyses. Furthermore, we demonstrate the learning and control capabilities of the proposed RNN by providing illustrative simulations and experiments on a Franka Emika Panda robot. The results exhibit significant collision avoidance and learning performance of the proposed method with tiny errors.

Different from conventional motion/force control strategies based on robotic dynamics, this paper presents a kinematic perspective to convert the motion/force control problem into a bi-criteria optimization problem. Specifically, the motion and force errors are formulated as an equality constraint at the kinematics level. Through a weight coefficient, the minimum infinite norm of joint velocity and the alternative kinematic index are integrated as a bi-criteria objective function. On this basis, a bi-criteria hybrid motion/force control (BHMFC) strategy is proposed with kinematic analyses on robotic manipulators. This bi-criteria kinematic strategy fulfills the potentials of robotic manipulators involving the functions of hybrid index optimization, hybrid control of motion and force, end-effector posture maintaining, and physical constraints. Furthermore, the related dynamic neural network (DNN) with theoretical analyses is presented to explore the optimal solution to the BHMFC strategy. Finally, computer simulations, physical experiments, and strategy comparisons are conducted to demonstrate the feasibility, efficiency, and superiority of the proposed BHMFC strategy. This work presents an efficient kinematic approach to address robot motion/force control problems with promising research prospects.Note to Practitioners—This paper is motivated by potential improvements of motion/force hybrid control schemes of robotic manipulators in a kinematic manner. Existing motion/force control methods typically rely on robot dynamics, which are difficult to satisfy kinematic task requirements, such as physical constraints and task optimizations. To this end, a bi-criteria hybrid motion/force control (BHMFC) strategy is proposed to achieve kinematic performance improvements in a quadratic program framework. Specifically, the designed constraints exploit the functions of hybrid control of motion and force, physical constraints, and end-effector posture maintaining. Besides, the kinematic optimization and joint velocity reduction are implemented by a bi-criteria objective function. Besides, we propose a dynamic neural network (DNN) based on Karush-Kuhn-Tucker conditions to solve the BHMFC strategy and theoretically analyze its global convergence ability and convergence rate. Simulative and experimental results show that the proposed method outperforms the traditional pseudoinverse method in terms of accurate position/force control performance and end-effector posture maintenance. In addition, computational analysis of control signals and comparisons with existing technologies highlight the feasibility and superiority of the proposed method.

In real-world robotics applications, kinematic parameters of redundant manipulators may need to be changed, thus creating difficulties in achieving precise control. To address this issue, this article proposes a fuzzy neural controller to learn kinematic parameters online and synchronously achieve the model-free control of redundant manipulators. Specifically, this controller consists of a gradient-based fuzzy (GBF) subsystem and a neural dynamics (ND) subsystem. On the one hand, the GBF subsystem is designed to achieve online learning of kinematic parameters, considering additional noise and a fuzzy parameter. Notably, the fuzzy parameter can drive the GBF subsystem to automatically terminate the learning process and convert the acquired information into usable structural knowledge once the kinematic parameters are precisely learned. On the other hand, based on the learned kinematic parameters, the ND subsystem is employed to solve a quadratic programming scheme for the kinematic control of manipulators. Such a scheme implements functions of orientation maintenance, trajectory tracking, and joint constraints in a model-free manner. Theoretical analyses confirm the effectiveness of the proposed controller's learning and control abilities. Finally, simulations, experiments, and comparisons demonstrate the feasibility and superiority of the fuzzy neural controller in controlling manipulators with unknown kinematic parameters.

Motion-force control is one of the critical technologies for a manipulator to accomplish some tasks, such as polishing and burring. Some optimization-based and kinematics-related methods for motion-force control of redundant manipulators have good performance but exist some shortcomings. First, these methods utilize transformation techniques to deal with different levels of joint limits, such as joint angle, velocity, or acceleration limits, which reduces the feasible region of decision variables. Second, these methods require the direction for the end-effector of the manipulator to be perpendicular to the contact surface and thus are not applicable to some scenarios. In response to these shortcomings, this article proposes a noise-resilient neural-dynamics-based planning (NRNDP) scheme, which includes a model predictive motion-force control (MPMFC) strategy and a discrete-time noise-resilient neural dynamics solver. The proposed NRNDP scheme directly handles three levels of joint limits without reducing the feasible region. Meanwhile, it can achieve the desired force with the end-effector of the manipulator being at any suitable angle to the work surface. Moreover, it can reduce the impact of noise and thus improve the control accuracy and operational stability of redundant manipulators. Besides, the MPMFC strategy is improved to achieve motion-force control of pose-varying workpieces. Simulations, comparisons, and experiments demonstrate the effectiveness and superiority of the proposed scheme.

For the image-based visual servoing (IBVS) of a manipulator with an unknown structure, the unavailability of the robot Jacobian matrix impedes the accurate control of the manipulator. To solve this issue, this article proposes a data-driven IBVS (DDIBVS) scheme combining model-free learning, matrix inversion estimation, feature tracking, and joint limits. On the one hand, a data-driven learning algorithm is designed, which enables an estimated end-effector velocity to approach the real one and outputs an estimated robot Jacobian matrix. On the other hand, we consider the desired velocity information of the visual feature to improve the tracking accuracy and design an auxiliary parameter to estimate the inversion operation and address the singularity problem. On this basis, a neural dynamic controller (NDC) is developed, which possesses learning, estimation, and control capabilities. Subsequently, the effectiveness, practicability, and superiority of the proposed method are evaluated through simulations and experiments conducted on a 7-degree-of-freedom (DOF) manipulator for visual servoing tasks.

Motion-force control of redundant manipulators is universally regarded as a pivotal issue in industrial manufacturing, especially for the processing of precision instruments. This paper proposes a kinematics-based motion-force control (KBMFC) scheme for redundant manipulators, which is driven by joint velocity commands and different from the dynamics-based methods. Specifically, the force and motion are modeled and decoupled in the end-effector frame with the help of a stiffness coefficient. To control the orientation of the force, a quaternion control equation is designed by combining the rotation matrix and neural dynamics method. Different from traditional motion-force control methods, the proposed scheme is constructed as quadratic programming with the corresponding recurrent neural network (RNN) solver derived, which considers the kinematic optimization index and joint constraints. According to the generated control signals, a redundant manipulator is able to accurately fulfill the hybrid control of motion and force with the desired quaternion, which is intuitively confirmed by simulations and experiments.Note to Practitioners—This paper is motivated by the deficiencies that restrict the real-world applications of the motion-force control of redundant manipulators. On the one hand, most existing motion-force control schemes are implemented under the framework of dynamics, which inevitably leads to some kinematics-related defects. On the other hand, the latest kinematics-based techniques introduce an admittance control to achieve motion-force control. However, they model the force in the Z-axis of the base coordinate while the motion planning is limited in the X-Y plane, which dramatically reduces real-world applications. In this paper, the deformation force is designed in the end-effector frame, and a quaternion control technology of the end-effector is developed. Such a scheme can realize the real-time control of the orientation and magnitude of the force while ensuring trajectory tracking. In addition, the introduction of optimization indexes and joint constraints dramatically improves the functionality of the proposed scheme. Finally, the contributions of this paper are verified through simulations, experiments and comparisons. This work proposes a feasible framework for the motion-force control and orientation control of redundant manipulators.

Position and orientation of the end-effector of redundant manipulators perform a core role in various complex tasks. However, most quadratic programming (QP)-based robot control approaches merely take the position of the end-effector into account, which is relatively inadequate and impractical. Driven by this significant deficiency, this article develops a control method for end-effector orientation representations by analyzing a rotation matrix. Specifically, it is formulated as an equality constraint and applied to control issues of Euler angles and axis-angle representation. On this basis, a QP-based position and orientation control (POC) scheme is proposed for the kinematic control of redundant manipulators. To handle such a POC problem, a dynamic neural network (DNN) is designed with rigorous theoretical analyses. Simulation results show that the POC scheme can accurately control the orientation representations and position of the end-effector. Experimental results and comparisons with state-of-the-art approaches highlight the feasibility and superiority of the proposed method.

Redundant manipulators play a critical role in industry and academia, which can be controlled from the kinematic or dynamic perspective. The motion-force control of redundant manipulators is a core problem in robot control, especially for the task requiring keeping contact with objectives, such as cutting, polishing, deburring, etc. However, when a manipulator’s model structure is unknown, it is challenging to take motion-force control of redundant manipulators. This article proposes a data-driven-based motion-force control scheme, which solves the motion-force control problem from the kinematic perspective. The scheme can take effect and estimate the structure information, i.e., the model parameters involved in the forward kinematics when the structure of the manipulator is incomplete or unknown. A recurrent neural network is devised to find the solution to the scheme. Besides, the theoretical analysis is presented to prove the correctness of the scheme. Simulations and physical experiments running on seven degrees of freedom redundant manipulators illustrate the superb performance and practicability of the scheme intuitively. The key contribution of this article is that, for the first time, a motion-force control scheme aided with data-driven technology is proposed from a kinematic perspective for the redundant manipulators.

For the existing repetitive motion generation (RMG) schemes for kinematic control of redundant manipulators, the position error always exists and fluctuates. This article gives an answer to this phenomenon and presents the theoretical analyses to reveal that the existing RMG schemes exist a theoretical position error related to the joint angle error. To remedy this weakness of existing solutions, an orthogonal projection RMG (OPRMG) scheme is proposed in this article by introducing an orthogonal projection method with the position error eliminated theoretically, which decouples the joint space error and Cartesian space error with joint constraints considered. The corresponding new recurrent neural networks (NRNNs) are structured by exploiting the gradient descent method with the assistance of velocity compensation with theoretical analyses provided to embody the stability and feasibility. In addition, simulation results on a fixed-based redundant manipulator, a mobile manipulator, and a multirobot system synthesized by the existing RMG schemes and the proposed one are presented to verify the superiority and precise performance of the OPRMG scheme for kinematic control of redundant manipulators. Moreover, via adjusting the coefficient, simulations on the position error and joint drift of the redundant manipulator are conducted for comparison to prove the high performance of the OPRMG scheme. To bring out the crucial point, different controllers for the redundancy resolution of redundant manipulators are compared to highlight the superiority and advantage of the proposed NRNN. This work greatly improves the existing RMG solutions in theoretically eliminating the position error and joint drift, which is of significant contributions to increasing the accuracy and efficiency of high-precision instruments in manufacturing production.

Currently, the Newton–Raphson iterative algorithm has been extensively employed in the fields of basic research and engineering. However, when noise components exist in a system, its performance is largely affected. To remedy shortcomings that the conventional computing methods have encountered in a noisy workspace, a novel modified Newton integration (MNI) algorithm is proposed in this article. In addition, the steady-state error of the proposed MNI algorithm is smaller than that of the Newton–Raphson algorithm under a noise-free or noisy workspace. To lay the foundations for the corresponding theoretical analyses, the proposed MNI algorithm is first converted into a homogeneous linear equation with a residual term. Then, the related theoretical analyses are carried out, which indicate that the MNI algorithm possesses noise-tolerance ability under various noisy environments. Finally, multiple computer simulations and physical experiments on robot control applications are performed to verify the feasibility and advantage of the proposed MNI algorithm.

It is generally considered that controlling a robot precisely becomes tough on the condition of unknown structure information. Applying a data-driven approach to the robot control with the unknown structure implies a novel feasible research direction. Therefore, in this article, as a combination of the structural learning and robot control, an acceleration-level data-driven repetitive motion planning (DDRMP) scheme is proposed with the corresponding recurrent neural network (RNN) constructed. Then, theoretical analyses on the learning and control abilities are provided. Moreover, simulative experiments on employing the acceleration-level DDRMP scheme as well as the corresponding RNN to control a Sawyer robot and a Baxter robot with unknown structure information are performed. Accordingly, simulation results validate the feasibility of the proposed method and comparisons among the existing repetitive motion planning (RMP) schemes indicate the superiority of the proposed method. This work offers sufficient theoretical and simulative solutions for the acceleration-level redundancy problem of redundant robots with unknown structure and joint limits considered.

In this paper, in order to analyze the existing repetitive motion planning (RMP) schemes for kinematic control of redundant robot manipulators, a generalized RMP scheme, which systematizes the existing RMP schemes, is presented. Then, the corresponding dynamic neural networks are derived, which leverage the gradient descent method with the velocity compensation with the feasibility proven theoretically. Given that the position errors of the end-effector should be tiny enough in the applications of redundant robot manipulators when executing a given task, especially for a precision instrument, the performance analyses on the control schemes are urgently desirable. In this paper, the upper bound of the position error on the existing RMP schemes is deduced theoretically and verified by computer simulations, with the relationship between the position error and the manipulability derived. In addition, dynamic neural networks are constructed to solve the generalized RMP schemes, with the joint velocity limits in RMP schemes extended to the nonconvex constraint. Finally, computer simulations based on different redundant robot manipulators and comparisons based on different controllers are conducted to verify the feasibility of the generalized RMP scheme and the proposed dynamic neural networks.