Theoretics, Proofs, and Physical Experiment of ZIE (Zhang Inequality Equivalency) from Order 0 to Order 2 for Redundant Robot Arms

Recently, a novel equality equivalency originating from Zhang neurodynamics (ZN) has been proposed and thoroughly investigated from order 0 to high order. Inspired by that concept, we conduct a careful investigation and present that an inequality can also be transformed into an equivalent form at a different level, known as inequality equivalency (i.e., Zhang inequality equivalency, ZIE). Theoretical proofs and investigations are provided for the newly presented ZIE. Moreover, we illustrate the practical application of this concept in the control of redundant robot arms. Specifically, we address configuration adjustments and cyclic motion generation for redundant robot arms using the ZIE. Through comparative physical experimental results, we validate the effectiveness and feasibility of the presented approach. It is noteworthy that the ZIE holds potential for application in various real-world projects, catering to diverse practical requirements.