An Initial-Rectifying-Constraint Optimization Scheme for Repetitive Motion Planning by Using Prescribed-Time Zeroing Neural Networks

To realize repetitive motion planning (RMP) for redundant robot manipulators in the presence of initial shifts, this paper introduces an initial-rectifying-constraint optimization scheme that reformulates the problem as a constrained time varying quadratic programming task. Using the initial-rectifying zeroing neural network (IRZNN) proposed in this article, the initial-rectifying-constraint optimization problem can be solved, and a repeatable solution with prescribed-time convergence can be obtained. The polynomial rectifying functions are developed to maintain smooth operation of manipulators during rectification. Convergence of the IRZNN model in solving the initial-rectifying-constraint optimization scheme is analyzed. The proposed scheme takes the initial shift problem into account, realizes RMP for redundant manipulators, and achieves prescribed-time convergence of the end-effector position error. The simulation and experiment results validate the effectiveness and practicality of the proposed approach. Note to Practitioners—The motivation of this article is the joint-angular-drift phenomenon found in closed trajectory tracking of redundant manipulators. This phenomenon, where a closed path of the end-effector may result in non-closed joint motion, is regarded as a potential menace in the operation of redundant manipulators. Existing solutions assume the initial state of joints aligns with the desired one, which is too idealistic and usually requires additional adjustment to meet the assumption. This article suggests a novel RMP scheme to alleviate the joint-angular-drift phenomenon in the presence of initial joint shifts. The proposed scheme enables the specification of the settling time for the end-effector position error in accordance with task requirements. To be more practical, polynomial rectifying functions are formed to facilitate smooth operation of robotic manipulators.