Revisit and compare Ma equivalence and Zhang equivalence of minimum velocity norm (MVN) type

In this paper, by revisiting Ma et al.’s inspiring work (specifically, Ma equivalence, ME) and Zhang et al.’s inspiring work (specifically, Zhang equivalence, ZE), which both investigate the equivalence relationships of redundancy-resolution schemes at two different levels, but with different formulations, the general scheme formulations and equivalence analyses of ME and ZE are presented. Besides, being a case study, the ME and ZE of minimum velocity norm (MVN) type are investigated for the inverse-kinematics (IK) problem solving. Moreover, the link and difference between the MVN-type ME and ZE are analyzed, summarized and presented methodologically, systematically, and computationally in this paper. In order to numerically compare the ME and ZE of MVN type, a Rhodonea-path tracking task based on PUMA560 robot manipulator is tested and fulfilled by employing the original velocity-level MVN schemes and its equivalent acceleration-level MVN schemes of ME and ZE. The simulative and numerical results not only verify the effectiveness of the velocity-level and acceleration-level schemes of MVN-type ME and ZE, but also validate the reasonableness of such two proved equivalence relationships. More importantly, these results show quantitatively and comparatively the respective advantages and future applications of MVN-type ME and ZE for the IK problem solving.