Velocity‐layer Zhang equivalency for time‐varying joint limits avoidance of redundant robot manipulator

Abstract

In the engineering field, a complex system or problem can be transformed into a relatively simple system or problem through equivalency. In this paper, the repetitive motion planning scheme of redundant robot manipulators with time-varying physical limits are to be optimized via Zhang equivalency (ZE) approach, which includes Zhang equality equivalency (ZEE) approach and Zhang inequality equivalency (ZIE) approach. The ZE approach is presented, theoretically proved, and applied to optimize the control scheme of redundant robot manipulators at the velocity layer. After that, an enhanced repetitive motion planning scheme via ZE (ERMPS-ZE) on the basis of quadratic programming is finally built up, which is subject to a ZEE constraint and a time-varying unified ZIE constraint for the solution of RMP in redundant robot manipulator systems. The simulation results on UR10 robot manipulator substantiate superiorities of the proposed scheme with regard to practicality, validity, and completeness over the traditional scheme. In addition, the results of simulation experiments under different limit situations show the adjusting manners and characteristics of the redundant robot manipulator adopting ERMPS-ZE when the manipulator encounters physical limits, which validate the correctness and efficacy of the ERMPS-ZE. Finally, the physical experiment also substantiates the practicability of the ERMPS-ZE.