Singularity-robust inverse kinematics for serial manipulators

This paper is a practical guideline on how to analyze and evaluate the literature algorithms of singularity- robust inverse kinematics or to construct new ones. Additive, multiplicative, and based on the Singularity Value Decomposition (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 performed in two different, but equivalent, ways: either via properly modified manipulability matrix or not allowing the decrease of the minimal singular value below a given threshold. It is discussed which method can always be used and which can only be used 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.

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Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).