Repeatable pseudoinverse control for planar kinematically redundant manipulators

The necessary and sufficient conditions for repeatable pseudoinverse control are now well known. A very simple example of a configuration for planar manipulators that is conservative is also known. It is also known there is no conservative configuration for the most common definition of joint angles. The question remains whether there exists any other conservative case using other definitions of joint angles, or equivalently, for pseudoinverse control using different, but constant, joint norms. This paper addresses this question using a combination of analytical and numerical methods. Such cases have been found, however, the resulting configurations are the same as previously known.