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

Abstract

A new acceleration-level performance index is proposed and studied for robotic redundancy resolution, which achieves purpose of the minimum kinetic energy (MKE) redundancy resolution originally designed at the joint-velocity level in this paper. Theoretical analysis is then given to show the relationship about the original MKE scheme at velocity level and its equivalent redundancy-resolution scheme at acceleration level, i.e., the so-called Zhang equivalence (ZE) relationship. Note that the ZE is in the iZ1eD1 manner, where i stands for the performance index and Z1 stands for using Zhang dynamics (ZD) once, while e stands for the equality constraint and D1 stands for using direct derivative dynamics (DDD or D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) once. Moreover, such two schemes are described/reformulated and unified as a dynamic quadratic program (DQP). Simulative results conducted on a robot manipulator (i.e., PUMA560 in this paper) further substantiate the effectiveness of the acceleration-level MKE scheme, and more importantly, the presented the ZE of such a MKE resolution at two different levels.