Zhang equivalence of different-level robotic schemes: An MVN case study based on PA10 robot manipulator

ZE in iZ1eD1 manner for MKE redundancy resolution at velocity and acceleration levels

“…Such a result, together with [13], makes us further believe that more different types and manners of ZE possibly exist between various schemes at different (and/or even mixed) levels. This may give us new research directions for the planning and control of redundant robot manipulators; i.e., different schemes at different levels but with the same purpose of optimization as well as their hybrid (or say, mixed) optimization schemes can be developed for robotic redundancy resolution.…”

“…More importantly, the notion of Zhang equivalence (being a summary of the authors' previous work) was proposed in [13], i.e., by using suitable performance indices and constraints, the redundancy-resolution schemes at different levels are practically equivalent. Such a Zhang equivalence makes us believe that more equivalent relationships do possibly exist between various schemes at two different levels, such as the MKE-type Zhang equivalence discovered and investigated in this paper.…”

“…In [13], being a study case, the MVN-type Zhang equivalence was studied. As we know, due to its mathematical tractability, the MVN solution is widely used as the optimization criterion in lots of robotic applications [3].…”

Analysis, Verification and Comparison on Feedback‐Aided MA Equivalence and Zhang Equivalency of Minimum‐Kinetic‐Energy Type for Kinematic Control of Redundant Robot Manipulators

“…Considering that the concept of such an equivalent relationship, with MVN redundancy resolution being a study case, has firstly and actually been revealed and investigated by Ma et al for dynamic redundancy resolution of redundant robot manipulators, we thus term it Ma equivalence (ME) (or more specifically, MVN-type ME) for comparison purposes. On the other hand, under the inspiration of ME, Zhang et al's previous work [38,39] has discovered, developed and investigated another new class of equivalent relationship, which also reveals a link between the velocity-level and acceleration-level schemes. Specifically, as shown in the pioneering work [38], the MVN-type equivalency with a QP-based formulation has preliminarily been discovered and established via classical gradient-descent and Zhang et al's neural-dynamics methods.…”

“…Specifically, as shown in the pioneering work [38], the MVN-type equivalency with a QP-based formulation has preliminarily been discovered and established via classical gradient-descent and Zhang et al's neural-dynamics methods. Besides, the concept of Zhang equivalency (ZE) has been formally introduced in [39], together with the MVN scheme and its equivalent acceleration-level scheme revisited as a study case of ZE. Furthermore, the comparisons between ME and ZE of MVN type have been conducted and presented in [35] for solving the inverse-kinematics problem.…”