The use and comparison of a special global optimal control algorithm with a local optimal control solution for redundant mechanisms

Abstract

Redundant robot manipulators are the challenge in the research of manipulator mechanisms because of their advantages. But there is a great major disadvantage-namely the control of them. There are a lot of different approaches to solve this problem. In this work, the authors show a special global optimal control algorithm based on the minimisation of the change of Yoshikawa's manipulability index with the use of calculus of variation and Lagrange multipliers. This approach leads them to a two-point boundary value problem which must be solved numerically. The numerical solution is complicated and depends on the correct choice of the boundary values. The global optimal solution is the best solution for the chosen cost criteria, but the use of complicated numerical methods makes this solution suitable just for simulations and offline programming. The local optimal control solution is derived from the global optimal solution. It assures easier numerical handling. This easier handling has its influence on the solution which is not always stable and it does not guarantees global optimum of the chosen cost criteria but it guarantees easier obtained control solutions.