Small time local controllability of driftless nonholonomic systems in a task-space

• Autorzy: Duleba Ignacy , Mielczarek Arkadiusz

Identyfikatory

DOI

10.24425/acs.2019.130199

• Języki publikacji: EN

Abstrakty

EN

In this paper a small time local controllability, naturally defined in a configuration space, is transferred into a task-space. It was given its analytical characterization and practical implcations. A special attention was put on singular configurations. Theoretical considerations were illustrated with two calculation examples. An extensive comparison of the proposed construction with the controllability defined in an endogenous configuration space approach was presented pointing out to their advantages and disadvantages.

Słowa kluczowe

EN

nonholonomic system; small time local controllability; configuration space; task-space

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2019
• Tom: Vol. 29, No. 3
• Strony: 423--436
• Opis fizyczny: Bibliogr. 15 poz., rys., tab., wzory

Twórcy

autor

Duleba Ignacy

• Department of Cybernetics and Robotics, Wroclaw University of Science and Technology, Janiszewski St. 11/17, 50–372 Wroclaw, Poland

autor

Mielczarek Arkadiusz

• Department of Cybernetics and Robotics, Wroclaw University of Science and Technology, Janiszewski St. 11/17, 50–372 Wroclaw, Poland

Bibliografia

• [1] J. Borenstein, H. R. Everett, and L. Feng: Navigating Mobile Robots: Systems and Techniques. A. K. Peters Ltd., Wellesley, MA, 1996
• [2] W. L. Chow: Uber Systeme von linearen partiellen Differentialgleichungen erster Ordnung. Mathematische Annalen, 117(1), (1939), 98–105.
• [3] S. Dubowsky and E. Papadopoulos: The Kinematics, Dynamics nd Control of Free-Flying and Free-Floating Robotic Systems. IEEE Trans. on Robotics and Automation, 3(5), (1993), 531–543.
• [4] I. Duleba: Kinematic Models of Doubly Generalized N-trailer Systems. Journal of Intelligent and Robotic Systems, on-line, DOI: 10.1007/s10846-018-0817-5, (2018), 1–8.
• [5] I. Duleba and A. Mielczarek: Controllability of driftless nonholonomic systems in a task space. In: Scientific Works, Vol. 196, Eds. K. Tchon, C. Zielinski, Electronics series, Warsaw University of Technology Publ. House, Warsaw, (2018), 311–318, in Polish.
• [6] I. Duleba: Methods and algorithms of motion planning for manipulators and mobile robots. EXIT, Academic Science Publisher, Warsaw, 2001, in Polish.
• [7] I. Dulęba and W. Khefifi: Pre-control form of the generalized Campbell-Baker-Hausdorff-Dynkin formula for affine nonholonomic systems. Systems and Control Letters, 55(2), (2006), 146–157.
• [8] F. R. Gantmacher: The Theory of Matrices. Chelsea Pub. Co., 1960.
• [9] R. A. Horn and C. R. Johnson: Matrix analysis. Cambridge University Press, 1990.
• [10] J. Klamka: Controllability of dynamical systems. PWN, IPPT-PAN, Monographs in theoretical electrotechnics, Warsaw-Wroclaw, 1990, in Polish.
• [11] Y. Nakamura: Advanced robotics: redundancy and optimization. Addison Wesley, New York, 1991.
• [12] O. J. Sordalen, Y. Nakamura, and W. Chung: Design of a nonholonomic manipulator. In: Proc. IEEE Conf. on Robotics and Automation, San Diego CA, (1994) 8–13.
• [13] R. S. Strichartz: The Campbell–Baker–Hausdorff–Dynkin formula and solutions of differential equations. Journal of Functional Analysis, 72, (1987), 320–345.
• [14] K. Tchoń and J. Jakubiak: Endogenous configuration space approach to mobile manipulators: a derivation and performance assessment of Jacobian inverse kinematics algorithms. International Journal of Control, 26(14), (2003), 1387–1419.
• [15] K. Tchoń, A. Mazur, I. Dulęba, R. Hossa, and R. Muszyński: Manipulators and mobile robots: models, motion planning, control. PLJ Accad. Publ. House, Warsaw, 2000, in Polish.

Uwagi

EN

1. This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (CC BY-NC-ND 3.0 https://creativecommons.org/licenses/by-nc- nd/3.0/), which permits use, distribution, and reproduction in any medium, provided that the article is properly cited, the use is non-commercial, and no modifications or adaptations are made

PL

2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).