Matrix inversion-free quasi-differential approach in solving the inverse kinematic task

Bertalan Csanadi, J. Tar, Janos F. Bito

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

The traditionally viable way for the solution of the inverse kinematic task for general open kinematic structure is the differential approach in which the Jacobian of the robot arm usually is inverted by the use of some generalized matrix inverse. These approaches suffer from the kinematic singularities nearby which these 'inverses' are ill-conditioned and behave in a very inconvenient way. For dealing with the singularities complementary tricks used to be introduced that so deform the original task that the obtained 'solution' behaves conveniently though it cannot solve the original task that does not have exact solution. In this paper an alternative approach is suggested that requires only the computation of the Jacobian but does not need the calculation of its 'generalized inverse'. Instead of that it applies an iterative sequence that has nice convergence properties. The method automatically handles the problem of the singularities, ambiguity, redundancies, and non-existing exact solutions without the application of any complementary trick or artificial parameter. Its operation is demonstrated for a simple 2 Degree of Freedom (DoF) arm, and for an 8 DoF arm, that is an irregular extension of a 6 DoF PUMA-type robot.

Original languageEnglish
Title of host publicationCINTI 2016 - 17th IEEE International Symposium on Computational Intelligence and Informatics: Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages61-66
Number of pages6
ISBN (Electronic)9781509039098
DOIs
Publication statusPublished - Feb 7 2017
Event17th IEEE International Symposium on Computational Intelligence and Informatics, CINTI 2016 - Budapest, Hungary
Duration: Nov 17 2016Nov 19 2016

Other

Other17th IEEE International Symposium on Computational Intelligence and Informatics, CINTI 2016
CountryHungary
CityBudapest
Period11/17/1611/19/16

Fingerprint

Inverse Kinematics
Matrix Inversion
Inverse kinematics
Kinematics
Degree of freedom
Singularity
Robots
Exact Solution
Robot
Redundancy
Inverse matrix
Generalized Inverse
Convergence Properties
Irregular
Alternatives

Keywords

  • Fixed Point Transformations
  • Inverse Kinematic Task
  • Open Kinematic Chain
  • Redundant Robot Arms

ASJC Scopus subject areas

  • Control and Optimization
  • Artificial Intelligence
  • Information Systems

Cite this

Csanadi, B., Tar, J., & Bito, J. F. (2017). Matrix inversion-free quasi-differential approach in solving the inverse kinematic task. In CINTI 2016 - 17th IEEE International Symposium on Computational Intelligence and Informatics: Proceedings (pp. 61-66). [7846380] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CINTI.2016.7846380

Matrix inversion-free quasi-differential approach in solving the inverse kinematic task. / Csanadi, Bertalan; Tar, J.; Bito, Janos F.

CINTI 2016 - 17th IEEE International Symposium on Computational Intelligence and Informatics: Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. p. 61-66 7846380.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Csanadi, B, Tar, J & Bito, JF 2017, Matrix inversion-free quasi-differential approach in solving the inverse kinematic task. in CINTI 2016 - 17th IEEE International Symposium on Computational Intelligence and Informatics: Proceedings., 7846380, Institute of Electrical and Electronics Engineers Inc., pp. 61-66, 17th IEEE International Symposium on Computational Intelligence and Informatics, CINTI 2016, Budapest, Hungary, 11/17/16. https://doi.org/10.1109/CINTI.2016.7846380
Csanadi B, Tar J, Bito JF. Matrix inversion-free quasi-differential approach in solving the inverse kinematic task. In CINTI 2016 - 17th IEEE International Symposium on Computational Intelligence and Informatics: Proceedings. Institute of Electrical and Electronics Engineers Inc. 2017. p. 61-66. 7846380 https://doi.org/10.1109/CINTI.2016.7846380
Csanadi, Bertalan ; Tar, J. ; Bito, Janos F. / Matrix inversion-free quasi-differential approach in solving the inverse kinematic task. CINTI 2016 - 17th IEEE International Symposium on Computational Intelligence and Informatics: Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 61-66
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