Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse

• Autorzy: Ratajczak J.

Identyfikatory

DOI

10.1515/acsc-2015-0003

• Języki publikacji: EN

Abstrakty

EN

The paper presents the approximation problem of the inverse kinematics algorithms for the redundant manipulators. We introduce the approximation of the dynamically consistent Jacobian by the extended Jacobian. In order to do that, we formulate the approximation problem and suitably defined approximation error. By the minimization of this error over a certain region we can design an extended Jacobian inverse which will be close to the dynamically consistent Jacobian inverse. To solve the approximation problem we use the Cholesky decomposition and the Ritz method. The computational example illustrates the theory.

Słowa kluczowe

EN

redundant manipulator; inverse kinematics; Jacobian; approximation

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2015
• Tom: Vol. 25, no. 1
• Strony: 35--50
• Opis fizyczny: Bibliogr. 17 poz., rys., wykr., wzory

Twórcy

autor

Ratajczak J.

• Electronics Faculty, Wroclaw University of Technology, ul. Janiszewskiego 11/17, 50–372 Wroclaw, Poland

Bibliografia

• [1] B. Armstrong, O. Khatib and J. Budric: The explicit dynamic model and inertial parameters of the PUMA 560 arm. Proc. IEEE Int. Conf. on Robotics and Automatomation, San Francisco, USA, (1986), 510-518.
• [2] J. Baillieul: Kinematic programming alternatives for redundant manipulators. Proc. IEEE Int. Conf. on Robotics and Automatomation, St. Louis, USA, (1985), 818-823.
• [3] I. N. Bronstein, K. A. Semendjajew, G. Musiol and H. Mühlig: Taschenbuch der Mathematik. Verlag Harry Deutsch, 2001.
• [4] S. Chiaverini, G. Oriolo and I. D. Walker: Kinematically redundant manipulators. In: Springer Handbook of Robotics, 245-268, Springer–Verlag, Berlin, 2008.
• [5] Y. Chitour: A continuation method for motion-planning problems. ESAIM: Control, Optimisation and Calculus of Variations, 12(1), (2006), 139-168.
• [6] I. M. Gel’fand and S. V. Fomin: Calculus of Variations. Prentice-Hall, Englewood Cliffs, 1963.
• [7] J. Karpińska and K. Tchoń : Optimal extended Jacobian inverse kinematics algorithm with application to attitude control of robotic manipulators. In: Robot motion and control 2011; Lecture Notes in Control and Information Sciences, Ed. Krzysztof Koz¸sowski, 2012, 237-246.
• [8] J. Karpińska and K. Tchoń: Performance-oriented design of inverse kinematics algorithms: extended Jacobian approximation of the Jacobian pseudo inverse. J. of Mechanisms and Robotics, 4(2), (2012), 021008-1–021008-8.
• [9] J. Karpińska, K. Tchoń and M. Janiak: Approximation of Jacobian inverse kinematics algorithms : differential geometric vs. variational approach. J. of Intelligent and Robotic Systems, 68(3-4), (2012), 211-224.
• [10] O. Khatib: Motion/force redundancy of manipulators. Proc. of the Japan-USA Symp. on Flexible Automation, 1 (1990), 337-342.
• [11] O. Khatib: Inertial properties in robotic manipulation: An object-level framework. Int. J. of Robotics Research, 14 (1995), 19-36.
• [12] Ch. A. Klein, C. Chu-Jeng and S. Ahmed: A new formulation of the extended Jacobian method and its use in mapping algorithmic singulairties for kinematically redundant manipulators. IEEE Trans. on Robotics and Automation, 11 (1995), 50- 55.
• [13] R. G. Roberts and A. A. Maciejewski: Nearest optimal repeatable control s rategies for kinematically redundant manipulators. IEEE Trans. on Robotics and Automation, 8(3), (1992), 327-337.
• [14] R. G. Roberts and A. A. Maciejewski: Repeatable generalized inverse control strategies for kinematically redundant manipulators. IEEE Trans. on Automatic Control, 38(5), (1993), 689-699.
• [15] R. G. Roberts and A. A. Maciejewski: Calculation of repeatable control strategies for kinematically redundant manipulators. J. of Intelligent and Robotic Systems, 14 (1995), 105-130.
• [16] T. Shamir and Y. Yomdin: Repeatability of redundant manipulators: Mathematical solution of the problem. IEEE Trans. on Automatic Control, 33 (1988), 1004-1009.
• [17] K. Tchoń: Optimal extended Jacobian inverse kinematics algorithms for robotic manipulators. IEEE Trans. on Robotics, 24(6), (2008), 1440-1445.

Uwagi

EN

The work of the author was supported by a statutory grant No. S40142W4/K7 provided by the Wroclaw University of Technology