The non-orthogonal Serret-Frenet parametrization applied to the path following problem of a manipulator with partially known dynamics

• Autorzy: Mazur Alicja , Dyba Filip

Identyfikatory

DOI

10.24425/acs.2023.146279

• Języki publikacji: EN

Abstrakty

EN

In this paper an application of the Serret-Frenet parametrization of a curve to the path following task is presented. This curvilinear parametrization method is used to obtain a control object description relative to the desired curve defined in the three-dimensional space. In order to derive proper equations, the innovative approach of the non-orthogonal projection of a control object on the given path is investigated. The non-orthogonal projection allows to design a global control algorithm. The proposed solution results in a cascade structure of the control system. Thus, the backstepping integrator algorithm was applied to create a control law. Due to the partial knowledge of control object dynamic parameters, an adaptive algorithm is taken into account. Theoretical considerations are confirmed with simulation study. Conducted simulations illustrated following paths at different levels of complexity by a holonomic non-redundant manipulator with a fixed base.

Słowa kluczowe

EN

backstepping integrator algorithm; holonomic manipulator; non-orthogonal projection; path following; Serret-Frenet parametrization

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2023
• Tom: Vol. 33, No. 2
• Strony: 339--370
• Opis fizyczny: Bibliogr. 25 poz., rys., tab., wzory

Twórcy

autor

Mazur Alicja

• Department of Cybernetics and Robotics, Faculty of Electronics, Photonics and Microsystems, Wrocław University of Science and Technology, Janiszewskiego Street 11/17, Wrocław 50-372, Poland

autor

Dyba Filip

• Department of Cybernetics and Robotics, Faculty of Electronics, Photonics and Microsystems, Wrocław University of Science and Technology, Janiszewskiego Street 11/17, Wrocław 50-372, Poland

Bibliografia

• [1] R.L. Bishop: There is more than one way to frame a curve. The American Mathematical Monthly, 82(3), (1975), 246-251. DOI: 10.2307/2319846.
• [2] C. Canudas de Wit, G. Bastin and B. Siciliano: Theory of Robot Control. Springer-Verlag, London, 1st edition, 1996.
• [3] M. Cholewiński and A. Mazur: Path tracking by the nonholonomic mobile manipulator. In 2019 12th International Workshop on Robot Motion and Control (RoMoCo), (2019), 203-208. DOI: 10.1109/RoMoCo.2019.8787375.
• [4] V. Cichella, I. Kaminer, E. Xargay, V. Dobrokhodov, N. Hovakimyan, A.P. Aguiar and A.M. Pascoal: A Lyapunov-based approach for time-coordinated 3D path-following of multiple quadrotors. In Proceedings of the 51st Annual IEEE Conference on Decision and Control, Maui, Hawaii, USA, IEEE, (2012), 1776-1781.
• [5] W. Domski and A. Mazur: Path tracking with orthogonal parametrization for a satellite with partial state information. In Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2018), 2 (2018), 252-257. DOI: 10.5220/0006835102520257.
• [6] P. Encarnação and A. Pascoal: 3D path following for autonomous under-water vehicle. In Proceedings of the 39th IEEE Conference on Decision and Control, 3 (2000), 2977-2982. DOI: 10.1109/CDC.2000.914272.
• [7] E. Erkan and S. Yüce: Serret-Frenet frame and curvatures of Bézier curves. Mathematics, 6(12), (2018). DOI: 10.3390/math6120321.
• [8] F. Frenet: Sur les courbes à double courbure. Journal de Mathématiques Pures et Appliquées, pages 437-447, 1852.
• [9] M. Galicki: Path tracking by the end-effector of a redundant manipulator. Archives of Control Sciences, 11(3-4), (2001), 245-261.
• [10] M. Galicki: Adaptive control of kinematically redundant manipulator along a prescribed geometric path. In K. Kozłowski, editor, Robot Motion and Control, 335 129-139, London, 2006. Springer London.
• [11] O. Karahan and Z. Bingul: Modelling and Identification of STAUBLI RX-60 Robot. In 2008 IEEE Conference on Robotics, Automation and Mechatronics, Chengdu, China, IEEE, (2008), 78-83. DOI: 10.1109/RAMECH.2008.4681356.
• [12] M. Krstić, I. Kanellakopoulos and P.V. Kokotović: Nonlinear and Adaptive Control Design. John Wiley & Sons, Inc., New York, USA, 1995.
• [13] Y.-L. Liao, M.-J. Zhang and L. Wan: Serret-Frenet frame based on path following control for underactuated unmanned surface vehicles with dynamic uncertainties. Journal of Central South University, 22(1), (2015), 214-223. DOI: 10.1007/s11771-015-2512-z.
• [14] I. Lugo-Cárdenas, S. Salazar and R. Lozano: Lyapunov based 3D path following kinematic controller for a fixed wing UAV. IFAC-Papers OnLine, 20th IFAC World Congress, 50(1), (2017), 15946-15951. DOI: 10.1016/j.ifacol.2017.08.1747.
• [15] A. Mazur: Hybrid adaptive control laws solving a path following problem for non-holonomic mobile manipulators. International Journal of Control, 77(15), (2004), 1297-1306. DOI: 10.1080/0020717042000297162.
• [16] A. Mazur, J. Płaskonka and M. Kaczmarek: Following 3D paths by a manipulator. Archives of Control Sciences, 25(1), (2015), 117-133.
• [17] A. Mazur and D. Szakiel: On path following control of nonholonomic mobile manipulators. International Journal of Applied Mathematics and Computer Science, 19(4), (2009), 561-574.
• [18] A. Micaelli and C. Samson: Trajectory Tracking for Unicycle-Type and Two-Steering-Wheels Mobile Robots. Technical Report No. 2097, Sophia-Antipolis, INRIA, 1993.
• [19] J. Oprea: Differential Geometry and its Applications. Upper Saddle River: Pearson Prentice Hall, 2nd edition, 2004.
• [20] J. Płaskonka: Path following algorithms for non-holonomic mobile manipulators. Doctoral dissertation, Wroclaw University of Science and Technology, Poland, 2014, (in Polish).
• [21] J.-A. Serret: Sur quelques formules relatives à la théorie des courbes à double courbure. Journal de Mathématiques Pures et Appliquées, (1851), 193-207, (in French).
• [22] J. Slotine and W. Li: Adaptive manipulator control: a case study. IEEE Transactions on Automatic Control, 33(11), (1988), 995-1003. DOI: 10.1109/9.14411.
• [23] D. Soetanto, L. Lapierre and A. Pascoal: Adaptive, non-singular path-following control of dynamic wheeled robots. In 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2 (2003), 1765-1770. DOI: 10.1109/CDC.2003.1272868.
• [24] B. Subudhi and D. Atta: Design of a path following controller for an underactuated AUV. Archives of Control Sciences, 19(4), (2009), 437-450.
• [25] K. Tchoń, A. Mazur, I. Dulęba, R. Hossa and R. Muszyński: Manipulators and Mobile Robots: Models, Motion Planning, Control. Academic Publishing House PLJ, Warsaw, 2000, (in Polish).

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).