Following the idea of using first-order time derivatives, this paper presents a general recurrent neural network (RNN) model for online inversion of time-varying matrices. Different kinds of activation functions are investigated to guarantee the global exponential convergence of the neural model to the exact inverse of a given time-varying matrix. The robustness of the proposed neural model is also studied with respect to different activation functions and various implementation errors. Simulation results, including the application to kinematic control of redundant manipulators, substantiate the theoretical analysis and demonstrate the efficacy of the neural model on time-varying matrix inversion, especially when using a power-sigmoid activation function.

Tracking control of robot manipulators is a fundamental and significant problem in robotic industry. As a conventional solution, the Jacobian-matrix-pseudo-inverse (JMPI) method suffers from two major limitations: one is the requirement on known information of the robot model such as parameter and structure; the other is the position error accumulation phenomenon caused by the open-loop nature. To overcome such two limitations, this paper proposes a novel Jacobian-matrix-adaption (JMA) method for the tracking control of robot manipulators via the zeroing dynamics. Unlike existing works requiring the information of the known robot model, the proposed JMA method uses only the input-output information to control the robot with unknown model. The solution based on the JMA method transforms the internal, implicit, and unmeasurable model information to the external, explicit, and measurable input-output information. Moreover, simulation studies including comparisons and tests substantiate the efficacy and superiority of the proposed JMA method for the tracking control of robot manipulators subject to unknown models.

This paper proposes a novel robust zeroing neural-dynamics (RZND) approach as well as its associated model for solving the inverse kinematics problem of mobile robot manipulators. Unlike existing works based on the assumption that neural network models are free of external disturbances, four common forms of time-varying disturbances suppressed by the proposed RZND model are investigated in this paper. In addition, theoretical analyses on the antidisturbance performance are presented in detail to prove the effectiveness and robustness of the proposed RZND model with time-varying disturbances suppressed for solving the inverse kinematics problem of mobile robot manipulators. That is, the RZND model converges toward the exact solution of the inverse kinematics problem of mobile robot manipulators with bounded or zero-oriented steady-state position error. Moreover, simulation studies and comprehensive comparisons with existing neural network models, e.g., the conventional Zhang neural network model and the gradient-based recurrent neural network model, together with extensive tests with four common forms of time-varying disturbances substantiate the efficacy, robustness, and superiority of the proposed RZND approach as well as its time-varying disturbances suppression model for solving the inverse kinematics problem of mobile robot manipulators.