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

Redundant robot manipulators are usually applied to various complex scenarios where harmful noise especially periodic calculating noise always exists. In order to avoid the task failure affected by the periodic noise, a circadian rhythms neural network (CRNN) is applied to solve motion planning problems of redundant robot manipulators suffering from the periodic noise. First, in this article, we formulate a tracking problem of redundant manipulators as a convex quadratic programming (QP) problem. Second, the QP problem is converted into a matrix equation. Third, based on the neural dynamic design method, a CRNN model is exploited and developed to solve the matrix equation of the tracking problem. Comparative simulations between the proposed CRNN and the traditional zeroing neural network show that the CRNN has better robustness and performance on solving the end-effector tracking task. Two physical experiments are conducted to further certify the effectiveness, robustness, and practicability of the proposed CRNN. [ABSTRACT FROM AUTHOR]

In order to solve a nonlinear time-varying system, a novel varying-gain recurrent neural network (termed as VG-RNN) is proposed and analyzed. To achieve a fast convergent performance, a vector-based unbounded error function is first defined. Second, a varying-gain neural dynamic approach is employed to design the recurrent neural network formula. Being different from the traditional constant-gain recurrent neural networks with fixed design parameters such as the gradient-based neural network (termed as GNN) and the zeroing neural network (termed as ZNN), the gain coefficient of the proposed VG-RNN is time-varying, which can change with time evolves. Otherwise, compared to the previous numerical methods on solving nonlinear time-varying systems, the solution obtained by VG-RNN is more precise. Third, rigorous mathematics analysis proves the super exponential convergence and accuracy of the proposed VG-RNN. Numerical experiments demonstrate the high accuracy, effectiveness and superiority of the VG-RNN compared with the conventional neural networks for solving nonlinear time-varying systems. Furthermore, we hope to apply the theory proposed in this paper to practical nonlinear time-varying automatic control systems, such as robots with nonlinear time-varying systems. [ABSTRACT FROM AUTHOR]