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2013 | 23 | 2 | 373-382
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
23
Numer
2
Strony
373-382
Opis fizyczny
Daty
wydano
2013
otrzymano
2012-03-14
poprawiono
2012-09-05
Twórcy
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, ul. Janiszewskiego 11/17, 50-372 Wrocław, Poland
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, ul. Janiszewskiego 11/17, 50-372 Wrocław, Poland
Bibliografia
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  • Chiacchio, P. and Siciliano, B. (1989). A closed-loop Jacobian transpose scheme for solving the inverse kinematics of nonredundant and redundant wrists, Journal of Robotic Systems 6(5): 601-630.
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  • Dulęba, I. and Jagodziński, J. (2011). Motion representations for the Lafferriere-Sussmann algorithm for nilpotent control systems, International Journal of Applied Mathematics and Computer Science 21(3): 525-534, DOI: 10.2478/v10006-011-0041-y.
  • Dulęba, I. and Sasiadek, J. (2002). Modified Jacobian method of transversal passing through the smallest deficiency singularities for robot manipulators, Robotica 20(4): 405-415.
  • Golub, G. and Van Loan, C. (1996). Matrix Computations, 3rd Edn., Johns Hopkins, Baltimore, MD.
  • Horn, R. and Johnson, C. (1986). Matrix Analysis, Cambridge University Press, New York, NY.
  • Hunek, W. and Latawiec, K.J. (2011). A study on new right/left inverses of nonsquare polynomial matrices, International Journal of Applied Mathematics and Computer Science 21(2): 331-348, DOI: 10.2478/v10006-011-0025-y.
  • Lee, C. (1982). Robot arm kinematics, dynamics, and control, Computer 15(12): 62-80.
  • Levenberg, K. (1944). A method for the solution of certain problems in least squares, Quarterly of Applied Mathematics 2: 164-168.
  • Maciejewski, A. and Klein, C. (1989). The singular value decomposition: Computation and applications to robotics, International Journal of Robotics Research 8(6): 63-79.
  • Marquardt, D. (1963). An algorithm for least-squares estimation of nonlinear parameters, SIAM Journal on Applied Mathematics 11(2): 431-441.
  • Nakamura, Y. (1991). Advanced Robotics: Redundancy and Optimization, Addison Wesley, New York, NY.
  • Nearchou, A. (1998). Solving the inverse kinematics problem of redundant robots operating in complex environments via a modified genetic algorithm, Mechanism and Machine Theory 33(3): 273-292.
  • Tchoń, K. and Dulęba, I. (1993). On inverting singular kinematics and geodesic trajectory generation for robot manipulators, Journal of Intelligent and Robotic Systems 8(3): 325-359.
  • Tchoń, K., Dulęba, I., Muszyński, R., Mazur, A. and Hossa, R. (2000). Manipulators and Mobile Robots: Models, Motion Planning, Control, PLJ, Warsaw, (in Polish).
  • Tchoń, K., Karpińska, J. and Janiak, M. (2009). Approximation of Jacobian inverse kinematics algorithms, International Journal of Applied Mathematics and Computer Science 19(4): 519-531, DOI: 10.2478/v10006-009-0041-3.
  • Tejomurtula, S. and Kak, S. (1999). Inverse kinematics in robotics using neural networks, Information Sciences 116(2-4): 147-164.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv23z2p373bwm
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