On the exact kinematic inversion of manipulators at singularity configurations

Proposes exact inverse velocity and acceleration solutions for nearly all types of singularity configurations of general six-degree-of-freedom serial manipulators. The solution is based on a two-step approach whereby timing is first ignored and whole families of joint rate solutions that provide spatially correct end-effector motion are determined. Afterwards, timing is considered to identify which solutions provide correct timing as well. Singularities are classified into three types: ordinary singularities, bifurcations, and isolated singularities. Techniques are developed to identify and analyze each type of singularity and a displacement-level interpretation is given as well. The developed method requires, for the most part, only standard linear algebra, but, depending on the type of singularity, singular value decomposition and the solution of a polynomial equation can also be involved