A Novel Neural Approach to Infinity-Norm Joint-Velocity Minimization of Kinematically Redundant Robots Under Joint Limits

Collective Neural Dynamics for Sparse Motion Planning of Redundant Manipulators Without Hessian Matrix Inversion

Redundant manipulators have been widely used in various industries whose applications not only improve production efficiency and reduce manual labor but also promote innovation in robotics and artificial intelligence. Kinematic control plays a fundamental and crucial role in robot control. Over the past few decades, numerous motion control schemes have been proposed and applied to trajectory tracking tasks. However, most of these schemes do not consider the introduction of sparsity into the motion control of redundant manipulators, resulting in excessive joint movements, which not only consume extra energy but also increase the risk of unexpected collisions in complex environments. To solve this problem, we transform the issue of increasing the sparsity into a nonconvex optimization problem. Furthermore, a collective neural dynamics for sparse motion planning (CNDSMP) scheme for motion planning of redundant manipulators is proposed. By incorporating sparsity into the control scheme, the excessive joint movements are minimized, leading to improved efficiency and reduced collision risks. Through simulations, comparisons, and physical experiments, the effectiveness and superiority of the proposed scheme are demonstrated.

Novel Snap-Layer MMPC Scheme via Neural Dynamics Equivalency and Solver for Redundant Robot Arms With Five-Layer Physical Limits

To obtain smoother kinematic control of minimum motion, a novel snap-layer minimum motion scheme, otherwise known as the minimum motion planning and control (MMPC) scheme for redundant robot arms, is proposed for the first time in this study. With the primary task of tracking planned paths and the consideration of satisfying five-layer physical limits, the snap-layer MMPC problem is transformed into a quadratic programming (QP) problem. Five-layer physical limits include angle-layer, velocity-layer, acceleration-layer, jerk-layer, and snap-layer limits, which are all considered and then transformed into a unified-layer bounded constraint through Zhang neural dynamics (ZND) equivalency. Furthermore, the snap-layer performance index and equation constraint are derived by utilizing the ZND formula. Therefore, the proposed snap-layer MMPC scheme is formulated as a standard QP that can avoid the potential physical damage of redundant robot arms. The snap-layer projection neural dynamics (PND) solver is presented and used to acquire the neural solution of the QP. Simulation results on a 6-degrees-of-freedom (DOF) planar redundant robot arm are presented to substantiate the effectiveness and superiority of the proposed snap-layer MMPC scheme by comparing it with the jerk-layer MMPC scheme and the minimum snap norm (MSN) scheme.

Predefined-Time Convergent Kinematic Control of Robotic Manipulators With Unknown Models Based on Hybrid Neural Dynamics and Human Behaviors

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.

A Dini-Derivative-Aided Zeroing Neural Network for Time-Variant Quadratic Programming Involving Multi-Type Constraints With Robotic Applications

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.

A Dynamic Parameter Noise-Tolerant Zeroing Neural Network for Time-Varying Quaternion Matrix Equation With Applications

As a common and significant problem in the field of industrial information, the time-varying quaternion matrix equation (TV-QME) is considered in this article and addressed by an improved zeroing neural network (ZNN) method based on the real representation of the quaternion. In the light of an improved dynamic parameter (IDP) and an innovative activation function (IAF), a dynamic parameter noise-tolerant ZNN (DPNTZNN) model is put forward for solving the TV-QME. The presented IDP with the character of changing with the residual error and the proposed IAF with the remarkable performance can strongly enhance the convergence and robustness of the DPNTZNN model. Therefore, the DPNTZNN model possesses fast predefined-time convergence and superior robustness under different noise environments, which are theoretically analyzed in detail. Besides, the provided simulative experiments verify the advantages of the DPNTZNN model for solving the TV-QME, especially compared with other ZNN models. Finally, the DPNTZNN model is applied to image restoration, which further illustrates the practicality of the DPNTZNN model.

An adaptive discretized RNN algorithm for posture collaboration motion control of constrained dual-arm robots

Although there are many studies on repetitive motion control of robots, few schemes and algorithms involve posture collaboration motion control of constrained dual-arm robots in three-dimensional scenes, which can meet more complex work requirements. Therefore, this study establishes the minimum displacement repetitive motion control scheme for the left and right robotic arms separately. On the basis of this, the design mentality of the proposed dual-arm posture collaboration motion control (DAPCMC) scheme, which is combined with a new joint-limit conversion strategy, is described, and the scheme is transformed into a time-variant equation system (TVES) problem form subsequently. To address the TVES problem, a novel adaptive Taylor-type discretized recurrent neural network (ATT-DRNN) algorithm is devised, which fundamentally solves the problem of calculation accuracy which cannot be balanced well with the fast convergence speed. Then, stringent theoretical analysis confirms the dependability of the ATT-DRNN algorithm in terms of calculation precision and convergence rate. Finally, the effectiveness of the DAPCMC scheme and the excellent convergence competence of the ATT-DRNN algorithm is verified by a numerical simulation analysis and two control cases of dual-arm robots.