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Tytuł artykułu

Singularity-robust inverse kinematics for serial manipulators

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EN
Abstrakty
EN
This paper is a practical guideline on how to analyze and evaluate the literature algorithms of singularity- robust inverse kinematics or to construct new ones. Additive, multiplicative, and based on the Singularity Value Decomposition (SVD) methods are examined to retrieve well-conditioning of a matrix to be inverted in the Newton algorithm of inverse kinematics. It is shown that singularity avoidance can be performed in two different, but equivalent, ways: either via properly modified manipulability matrix or not allowing the decrease of the minimal singular value below a given threshold. It is discussed which method can always be used and which can only be used when some pre‐conditions are met. Selected methods are compared to with respect to the efficiency of coping with singularities based on a theoretical analysis as well as simulation results. Also, some questions important for mathematically and/or practically oriented roboticians are stated and answered.
Twórcy
  • Department of Cybernetics and Robotics, Wroclaw University of Science and Technology, Janiszewski St. 11/17, 50‐372 Wroclaw, Poland, www.kcir.pwr.edu.pl/~iwd.
Bibliografia
  • [1] W. Cheney, and D. Kincaid, Linear Algebra: Theory and Applications, Jones & Bartlett Publ., 2009.
  • [2] I. Dulęba. “Robust inverse kinematics at singular con gurations,” A. Mazur and C. Zieliński, eds., Advances in Robotics, vol. 197 of Electronics, pp. 5–10. Publ. House of the Warsaw Univ. Of Technology, 2022 (in Polish).
  • [3] I. Duleba. “A comparison of jacobian‐based methods of inverse kinematics for serial robot manipulators,” Int. Journal of Applied Mathematics and Computer Science, vol. 23, no. 2, 2013, pp. 373–382.
  • [4] I. Duleba. “Channel algorithm of transversal passing through singularities for non‐redundant obot manipulators,” IEEE Int. Conf. on Robotics and Automation, vol. 2, 2000, pp. 1302–1307; doi: 10.1109/ROBOT.2000.844778.
  • [5] G. Golub, and C. Reinsch. “Singular value decomposition and least squares solutions,” Numerische Mathematik, vol. 14, no. 5, 1970, pp. 403–420.
  • [6] B. Grossmann. “The product of two symmetric, positive semidefinite matrices has non‐negative eigenvalues”. Mathematics Stack Exchange; http s://math.stackexchange.com/q/982822 (version: 2014‐10‐21).
  • [7] R. Horn, and C. Johnson, Matrix analysis, Cambridge Univ. Press, 2012.
  • [8] C.‐G. Kang. “Online trajectory planning for a PUMA robot,” Int. Journal of Precision Enginnering and Manufacturing, vol. 8, no. 4, 2007, pp. 16–21.
  • [9] S. Lloyd, R. A. Irani, and M. Ahmadi. “Fast and robust inverse kinematics of serial robots using Halley’s method,” IEEE Transactions on Robotics, vol. 38, no. 5, 2022, pp. 2768–2780; doi: 10.1109/TRO.2022.3162954.
  • [10] A. A. Maciejewski, and C. Klein. “The singular value decomposition: Computation and appliations to robotics,” Int. Journal of Robotics Research, vol. 8, 1989, pp. 63–79.
  • [11] Y. Nakamura, Advanced Robotics: Redundancy and Optimization, Addison‐Wesley, 1991.
  • [12] A. Ratajczak, J. Ratajczak, and K. Tchoń. “Task‐priority motion planning of underactuated systems: an endogenous configuration space approach,” Robotica, vol. 28, no. 6, 2010, pp. 885–892.
  • [13] M. Spong, and M. Vidyasagar, Robot Dynamics and Control, MIT Press, 1989.
  • [14] J. Sun, Y. Liu, and C. Ji. “Improved singular robust inverse solutions of redundant serial manipulators,” Int. Journal of Advanced Robotic Systems, vol. 17, no. 3, 2020, pp. 1–12; doi: 10.1177/1729 881420932046.
  • [15] K. Tchoń, and J. Ratajczak. “Singularities of holonomic and non‐holonomic robotic systems: a normal form approach,” Journal of the Franklin Institute, vol. 358, no. 15, 2021, pp. 7698–7713.
  • [16] L. V. Vargas, A. C. Leite, and R. R. Costa. “Over‐coming kinematic singularities with the filtered inverse approach”,IFAC Proceedings Volumes, vol. 47, no. 3, 2014, pp. 8496–8502; doi: 10.3182/20140824‐6‐ZA‐1003.01841, 19th IFAC World Congress.
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).
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Bibliografia
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