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

Inverse kinematics (or say, redundancy resolution) is a fundamental issue in operating redundant manipulators, which has been widely investigated in the past three decades. Many redundancy-resolution schemes have been proposed for such a problem solving, which mainly work at a single level (e.g., the joint-velocity level or the joint-acceleration level). In this paper, for robotic redundancy resolution, two general scheme-formulations at two different levels are presented and investigated, one of which corresponds to the velocity-level schemes and the other corresponds to the acceleration-level schemes. The equivalent relationship between such two robotic schemes at two different levels is established via Zhang et al's neural-dynamics method, i.e., the so-called Zhang equivalence. Theoretical analysis on the case of minimum velocity norm (MVN) scheme, together with computer simulations based on the PA10 robot manipulator, substantiates well the reasonableness of Zhang equivalence. That is, the robotic redundancy-resolution schemes at different levels (e.g., at the joint-velocity level and at the joint-acceleration level) could be practically equivalent by using suitable performance indices and constraints.