Singularity-Robust Inverse Kinematics for Serial Manipulators

This paper is a practical~guideline how to analyze and evaluate literature algorithms of singularity-robust inverse kinematics or to construct new ones. Additive, multiplicative and based on the Singularity ValueDecomposition (SVD) methods are examined to retrieve well conditioning of a matrix to be inverted in the Newton algorithm of inverse kinematics. It is shown that singularity avoidance can be performedin two different, but equivalent, ways: either via properly modified manipulability matrix or not allowing to decreese the minimal singular value below a given threshold. It is discussed which method can always be used and which only when some pre-conditions are met. Selected methods are compared to with respect to the efficiency of coping with singularities based on a theoretical analysis as well as simulation results. Also some questions important for mathematically and/or practically oriented roboticians are stated and answered.