Characteristics of optimal solutions in resolving manipulator redundancy under inequality constraints

Presents our finding of a critical point that has not been reported thus far in the inverse kinematics of redundant manipulators under inequality constraints. The critical point, named algorithmic barrier was first encountered in the form of peculiar phenomena in our experiment with an 8-DOF robot, which we believe to have significance in the order of so-called algorithmic singularity. In addition, the paper deals with the characteristics of optimal solutions (COS) in resolving manipulator redundancy under inequality constraints. In order to analyze the COS, analytic functions of sufficient conditions and critical point conditions are derived. As a result, we find that COS is drastically affected by the introduction of inequality constraints. That is, COS under no inequality constraints is known to change only at algorithmic singularity while COS under inequality constraints turns out to change at semi-singularity and algorithmic barrier as well as algorithmic singularity. We prove the existence the critical points and present their analytical properties by using a planar 3-DOF manipulator.