In the report, a novel recurrent neural network based on integral enhancement to solve time-varying systems of equations and inequations was proposed. Firstly, a set of non-negative relaxation variables was introduced, the time-varying inequality system was transformed into the form of a matrix equation, and a matrix differential equation about the error function was constructed; secondly, the inverse transformation of the matrix was used to derive the explicit solution of the matrix differential equation, and on which an integral enhancement term was added to improve the anti-interference ability of the solving model; lastly, the final computational simulation results validated the effectiveness and superiority of the proposed integral enhanced recurrent neural network.

Aimed at the problem that the accuracy of Euler's difference formula is low, in the report, a new numerical difference formula for estimating the first-order derivative of the objective function was proposed. Based on Taylor Series Expansions, the expanded forms of the objective function at difference data points were presented. Aided with the transposition and conversion, the higher order terms in the expanded forms were eliminated, and the new numerical difference formula with high computational precision was thus derived. The theoretical analysis was performed to obtain the optimal step size of the difference formula. The effectiveness of the proposed new numerical difference formula was verified by the numerical experimental results. The simulation experiment of UR5 manipulator proved that when the sampling time was 0.01 s, the motion accuracy of the manipulator was increased by 10 000 times, which further verified the superiority of the new numerical difference formula.

The research on repetitive motion planning (RMP) of redundant robot manipulators has realized great success. However, noise is generally ignored in the design of RMP schemes at velocity or acceleration level. Noise can lead to significant deviations in key parameters such as position, velocity and acceleration, causing these schemes to be ineffective as they may result in unstable or inaccurate motion. In this paper, with the consideration of additive noise, an improved formulation of the acceleration-level RMP (ALRMP) scheme is proposed and studied for redundant robot manipulators. Specifically, by utilizing the integral of the end-effector tracking error and velocity error, a new acceleration-level equality criterion is established. Based on the equality criterion, the improved ALRMP scheme with noise rejection capability is developed for redundant robot manipulators. Such an improved scheme is then rewritten as a quadratic program and is solved via a neural network. Comparative simulation results on the UR5 robot manipulator in the different cases of noise further validate the effectiveness and superiority of the improved ALRMP scheme over the previous scheme.