<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

Singularity-Robust Inverse Kinematics for Serial Manipulators

Wroclaw University of Science and Technology

Journal of Automation, Mobile Robotics and Intelligent Systems

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"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....

Singularity-Robust Inverse Kinematics for Serial Manipulators

Published Online: Mar 04, 2024

Page range: 38 - 45

Received: Dec 04, 2022

Accepted: Apr 21, 2023

DOI: https://doi.org/10.14313/jamris/3-2023/21

Keywords
Serial manipulator, Forward kinematics, Jacobi matrix, Inverse kinematics, Singularities, Robustness, Evaluation

© 2023 Ignacy Dulęba, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Singularity-Robust Inverse Kinematics for Serial Manipulators

Published Online: Mar 04, 2024

Page range: 38 - 45

Received: Dec 04, 2022

Accepted: Apr 21, 2023

DOI: https://doi.org/10.14313/jamris/3-2023/21

KeywordsSerial manipulator, Forward kinematics, Jacobi matrix, Inverse kinematics, Singularities, Robustness, Evaluation

© 2023 Ignacy Dulęba, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Serial manipulator, Forward kinematics, Jacobi matrix, Inverse kinematics, Singularities, Robustness, Evaluation