A new kind of singularity in redundant manipulation: semi algorithmic singularity

Abstract

Reports the discovery of a new type of singularity that is as significant as other singularities like kinematic singularity, algorithmic singularity, and semi-singularity. This singularity, named semi algorithmic singularity (SAS), occurs when a redundant manipulator, faced with inequality constraints arising from kinematic limits such as joint angle limits and obstacles, proceeds to conduct optimization of a performance measure. Through mathematical analysis, we have proved its existence and proposed an analytic matrix function to identify its presence. In conjunction, we have exposed its relationship with the other singularities above. More specifically, SAS is similar to the algorithmic singularity in that it is an artificial singularity coming from an endeavor for performance optimization. They are different in that the former occurs in one direction in the C-space, whereas the latter occurs bidirectionally. Besides, we have also found an analogy in the real singularities that while the semi-singularity is unidirectional in the workspace, the kinematic singularity is bi-directional. Through a simulation for a three DOF planar manipulator we have visualized the existence of SAS and its relationship with the other singularities.