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

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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
Strony
373--382
Opis fizyczny
Bibliogr. 19 poz., tab., wykr.
Twórcy
autor
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, ul. Janiszewskiego 11/17, 50-372 Wrocław, Poland
autor
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, ul. Janiszewskiego 11/17, 50-372 Wrocław, Poland
Bibliografia
  • [1] Ben-Isreal, A. and Cohen, D. (1966). On iterative computation of generalized inverses and associated projections, SIAM Journal on Numerical Analysis 3(3): 410–419.
  • [2] Ben-Isreal, A. and Greville, T. (2003). Generalized Inverses: Theory and Applications, CMS Books in Mathematics, 2nd Edn., Springer, New York, NY.
  • [3] 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.
  • [4] D’Souza, A., Vijaykumar, S. and Schaal, S. (2001). Learning inverse kinematics, International Conference on Intelligent Robots and Systems, Maui, HI, USA, pp. 298–303.
  • [5] 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.
  • [6] 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.
  • [7] Golub, G. and Van Loan, C. (1996). Matrix Computations, 3rd Edn., Johns Hopkins, Baltimore, MD.
  • [8] Horn, R. and Johnson, C. (1986). Matrix Analysis, Cambridge University Press, New York, NY.
  • [9] 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.
  • [10] Lee, C. (1982). Robot arm kinematics, dynamics, and control, Computer 15(12): 62–80.
  • [11] Levenberg, K. (1944). A method for the solution of certain problems in least squares, Quarterly of Applied Mathematics 2: 164–168.
  • [12] Maciejewski, A. and Klein, C. (1989). The singular value decomposition: Computation and applications to robotics, International Journal of Robotics Research 8(6): 63–79.
  • [13] Marquardt, D. (1963). An algorithm for least-squares estimation of nonlinear parameters, SIAM Journal on Applied Mathematics 11(2): 431–441.
  • [14] Nakamura, Y. (1991). Advanced Robotics: Redundancy and Optimization, Addison Wesley, New York, NY.
  • [15] 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.
  • [16] 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.
  • [17] Tchoń, K., Dulęba, I., Muszyński, R., Mazur, A. and Hossa, R. (2000). Manipulators and Mobile Robots: Models, Motion Planning, Control, PLJ, Warsaw, (in Polish).
  • [18] 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.
  • [19] Tejomurtula, S. and Kak, S. (1999). Inverse kinematics in robotics using neural networks, Information Sciences 116(2–4): 147–164.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3166ab28-a8a4-48e2-b25d-ddba69f7a572
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