A comparison of Jacobian-based methods of inverse kinematics for serial robot manipulators

Ignacy Dulęba; Michał Opałka

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 2, page 373-382
  • ISSN: 1641-876X

Abstract

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The objective of this paper is to present and make a comparative study of several inverse kinematics methods for serial manipulators, based on the Jacobian matrix. Besides the well-known Jacobian transpose and Jacobian pseudo-inverse methods, three others, borrowed from numerical analysis, are presented. Among them, two approximation methods avoid the explicit manipulability matrix inversion, while the third one is a slightly modified version of the Levenberg-Marquardt method (mLM). Their comparison is based on the evaluation of a short distance approaching the goal point and on their computational complexity. As the reference method, the Jacobian pseudo-inverse is utilized. Simulation results reveal that the modified Levenberg-Marquardt method is promising, while the first order approximation method is reliable and requires mild computational costs. Some hints are formulated concerning the application of Jacobian-based methods in practice.

How to cite

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Ignacy Dulęba, and Michał Opałka. "A comparison of Jacobian-based methods of inverse kinematics for serial robot manipulators." International Journal of Applied Mathematics and Computer Science 23.2 (2013): 373-382. <http://eudml.org/doc/257109>.

@article{IgnacyDulęba2013,
abstract = {The objective of this paper is to present and make a comparative study of several inverse kinematics methods for serial manipulators, based on the Jacobian matrix. Besides the well-known Jacobian transpose and Jacobian pseudo-inverse methods, three others, borrowed from numerical analysis, are presented. Among them, two approximation methods avoid the explicit manipulability matrix inversion, while the third one is a slightly modified version of the Levenberg-Marquardt method (mLM). Their comparison is based on the evaluation of a short distance approaching the goal point and on their computational complexity. As the reference method, the Jacobian pseudo-inverse is utilized. Simulation results reveal that the modified Levenberg-Marquardt method is promising, while the first order approximation method is reliable and requires mild computational costs. Some hints are formulated concerning the application of Jacobian-based methods in practice.},
author = {Ignacy Dulęba, Michał Opałka},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {serial manipulator; inverse kinematics; Jacobian methods; comparison; applications},
language = {eng},
number = {2},
pages = {373-382},
title = {A comparison of Jacobian-based methods of inverse kinematics for serial robot manipulators},
url = {http://eudml.org/doc/257109},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Ignacy Dulęba
AU - Michał Opałka
TI - A comparison of Jacobian-based methods of inverse kinematics for serial robot manipulators
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 2
SP - 373
EP - 382
AB - The objective of this paper is to present and make a comparative study of several inverse kinematics methods for serial manipulators, based on the Jacobian matrix. Besides the well-known Jacobian transpose and Jacobian pseudo-inverse methods, three others, borrowed from numerical analysis, are presented. Among them, two approximation methods avoid the explicit manipulability matrix inversion, while the third one is a slightly modified version of the Levenberg-Marquardt method (mLM). Their comparison is based on the evaluation of a short distance approaching the goal point and on their computational complexity. As the reference method, the Jacobian pseudo-inverse is utilized. Simulation results reveal that the modified Levenberg-Marquardt method is promising, while the first order approximation method is reliable and requires mild computational costs. Some hints are formulated concerning the application of Jacobian-based methods in practice.
LA - eng
KW - serial manipulator; inverse kinematics; Jacobian methods; comparison; applications
UR - http://eudml.org/doc/257109
ER -

References

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