Suboptimal approximations in repeatable inverse kinematics for robot manipulators

• Autorzy: Duleba I. , Karcz-Duleba I.

Identyfikatory

DOI

10.1515/bpasts-2017-0025

• Języki publikacji: EN

Abstrakty

EN

In this paper a repeatable inverse kinematic task was solved via an approximation of a pseudo-inverse Jacobian matrix of a robot manipulator. An entry configuration to the task was optimized and a task-dependent definition of an approximation region, in a configuration space, was utilized. As a side effect, a relationship between manipulability and optimally augmented forward kinematics was established and independence of approximation task solutions on rotations in augmented components of kinematics was proved. A simulation study was performed on planar pendula manipulators. It was demonstrated that selection of an initial configuration to the repeatable inverse kinematic task heavily impacts solvability of the task and its quality. Some remarks on a formulation of the approximation task and its numerical aspects were also provided.

Słowa kluczowe

EN

manipulator; inverse kinematics; repeatability; optimization

PL

manipulator; odwrotna kinematyka; powtarzalność; optymalizacja

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2017
• Tom: Vol. 65, nr 2
• Strony: 209--217
• Opis fizyczny: Bibliogr. 11 poz., rys., tab.

Twórcy

autor

Duleba I.

• Faculty of Electronics, Wroclaw University of Science and Technology, 11/17 Janiszewski St., 50-372 Wroclaw, Poland

autor

Karcz-Duleba I.

• Faculty of Electronics, Wroclaw University of Science and Technology, 11/17 Janiszewski St., 50-372 Wroclaw, Poland

Bibliografia

• [1] I. Duleba and M. Opalka. "On application of elastic band method to repeatable inverse kinematics in robot manipulators". Journal of Automation, Mobile Robotics and Intelligent Systems. 7(4), 5-12, (2013).
• [2] I. Duleba and I. Karcz-Duleba: "A suboptimal solution of repeatable inverse kinematics in robot manipulators with a free entry configuration". Mediterranean Conf. on Control and Automation, Athens, 563-568, (2016).
• [3] G.H. Golub and C. Reinsch, "Singular value decomposition and least squares solutions”, Numerische Mathematik 14 (5), 403-420, (1970).
• [4] J. Karpinska. "Approximation of algorithms for robot motion planning", Ph. D. dissertation. Wroclaw University of Technology. 2012, [in Polish],
• [5] C.A. Klein. C. Chu-Jeng and S. Ahmed. "Anewr formulation of the extended Jacobian method and its use in mapping algorithmic singularities for kinematically redundant manipulators", IEEE Trans. Robot. Autom., 11. 50-55, (1995).
• [6] Y. Nakamura. Ach’anced Robotics: Redimdancy- and Optimization. Addison Wesley. New York, 1991.
• [7] A. Ratajczak. "Trajectory reproduction and trajectory tracking problem for the nonholonomic systems" Bull. Pol. Ac.: Tech., 64(1), 63-70, (2016).
• [8] J.E. Ratajczak. K. Tchon and M. Janiak. "Approximation of Jacobian inverse kinematics algorithms: differential geometric vs. variational approach". Journal of Intelligent and Robotic Systems, 68 (3/4), 211-224, (2012).
• [9] S. Richter and R DeCarlo. "Continuation methods: theory and applications". IEEE Tran, on Automatic Control, 28(6). 660-665. (1983).
• [10] R. Roberts and A.A. Maciejewski, "Repeatable generalized inverse control strategies for kinematically redundant manipulators", IEEE Trans, on Automatic Control, 38. 689-699. (1993).
• [11] M. Spong and M. Vidyasagar. Introduction to Robotics. Robot Dynamics and Control. MIT Press. Cambridge, 1989.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).