DYNAMIC MODEL WITH A NEW FORMULATION OF CORIOLIS/CENTRIFUGAL MATRIX FOR ROBOT MANIPULATORS

Le Ngoc Truc, Nguyen Van Quyen, Nguyen Phung Quang
Author affiliations

Authors

  • Le Ngoc Truc Hanoi University of Science and Technology; Hung Yen University of Technology and Education
  • Nguyen Van Quyen Hanoi University of Science and Technology
  • Nguyen Phung Quang Hanoi University of Science and Technology

DOI:

https://doi.org/10.15625/1813-9663/36/1/14557

Keywords:

robot manipulator, Euler-Lagrange equations, dynamic model, Coriolis/centrifugal matrix, Kronecker product

Abstract

The paper presents a complete generalized procedure based on the Euler-Lagrange equations to build the matrix form of dynamic equations, called dynamic model, for robot manipulators. In addition, a new formulation of the Coriolis/centrifugal matrix is proposed. The link linear and angular velocities are formulated explicitly. Therefore, the translational and rotational Jacobian matrices can be derived straightforward from definition, which makes the calculation of the generalized inertia matrix more convenient. By using Kronecker product, a new Coriolis/centrifugal matrix formulation is set up directly in matrix-based manner and guarantees the skew symmetry property of robot dynamic equations. This important property is usually exploited for developing many control methodologies. The validation of the proposal formulation is confirmed through the symbolic solution and simulation of a typical robot manipulator.

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References

J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods and Algorithms, 3rd ed. New York, NY, USA: Springer Science+Business Media LLC, 2007.

R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation. Boca Raton, FL, USA: CRC Press, 1994.

M. W. Spong, S. Hutchinson, and V. M., Robot Modeling and Control, 1st ed. Hoboken, NJ, USA: John Wiley & Sons, 2006.

E. Dombre and W. Khalil, Eds., Modeling, Performance Analysis and Control of Robot Manipulators. London, UK: ISTE Ltd, 2007.

L. Sciavicco and B. Siciliano, Modelling and Control of Robot Manipulators, 2nd ed. London, UK: Springer London, 2000.

B. Siciliano, L. Sciavicco, L. Villani, and G. Oriolo, Robotics: Modelling, Planning and Control. London, UK: Springer London, 2009.

N. Q. Hoang and V. D. Vuong, “Sliding mode control for a planar parallel robot driven by electric motors in a task space,” J. Comput. Sci. Cybern., vol. 33, no. 4, pp. 325–337, 2017.

N. Van Khang, N. Q. Hoang, N. D. Sang, and N. D. Dung, “A comparison study of some control methods for delta spatial parallel robot,” J. Comput. Sci. Cybern., vol. 31, no. 1, pp. 71–81, 2015.

N. Trần Hiệp and P. Thượng Cát, “Điều khiển rôbôt theo nguyên lý trượt sử dụng mạng nơron,” Tạp chí Tin học và điều khiển học, vol. 24, no. 3, pp. 236–246, 2008.

P. Thượng Cát, “Điều khiển rôbốt N bậc tự do có nhiều tham số bất định trong không gian Đề Các,” Tạp chí Tin học và điều khiển học, vol. 24, no. 4, pp. 333–341, 2008.

N. Văn Khang and T. Quốc Trung, “Điều khiển chuyển động robot hai chân trong pha một chân trụ theo phương pháp trượt sử dụng mạng nơron,” Tạp chí Tin học và điều khiển học, vol. 30, no. 1, pp. 70–80, 2014.

S. R. Ploen, “A skew-symmetric form of the recursive Newton-Euler algorithm for the control of multibody systems,” in Proceedings of the 1999 American Control Conference, 1999, vol. 6, pp. 3770–3773.

Hong-Chin Lin, Tsung-Chieh Lin, and K. H. Yae, “On the skew-symmetric property of the Newton-Euler formulation for open-chain robot manipulators,” in Proceedings of 1995 American Control Conference - ACC’95, 1995, vol. 3, pp. 2322–2326.

M. Bjerkeng and K. Y. Pettersen, “A new Coriolis matrix factorization,” in 2012 IEEE International Conference on Robotics and Automation, 2012, pp. 4974–4979.

M. Becke and T. Schlegl, “Extended Newton-Euler based centrifugal/coriolis matrix factorization for geared serial robot manipulators with ideal joints,” in Proceedings of 15th International Conference Mechatronika, 2012, pp. 1–7.

P. Sánchez-Sánchez and M. A. Arteaga-Pérez, “Simplied Methodology for Obtaining the Dynamic Model of Robot Manipulators,” Int. J. Adv. Robot. Syst., vol. 9, no. 5, pp. 1–12, 2012.

F. L. Lewis, D. M. Dawson, and C. T. Abdallah, Robot Manipulator Control: Theory and Practice, 2nd ed. New York, NY, USA: Marcel Dekker, 2004.

N. Van Khang, “Consistent definition of partial derivatives of matrix functions in dynamics of mechanical systems,” Mech. Mach. Theory, vol. 45, no. 7, pp. 981–988, 2010.

N. Van Khang, “Kronecker product and a new matrix form of Lagrangian equations with multipliers for constrained multibody systems,” Mech. Res. Commun., vol. 38, no. 4, pp. 294–299, 2011.

J. Brewer, “Kronecker products and matrix calculus in system theory,” IEEE Trans. Circuits Syst., vol. 25, no. 9, pp. 772–781, 1978.

A. J. Laub, Matrix Analysis for Scientists and Engineers. Philadelphia, PA, USA: SIAM, 2005.

F. Zhang, Matrix Theory, 2nd ed. NY: Springer New York, 2011.

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Published

27-02-2020

How to Cite

[1]
L. N. Truc, N. V. Quyen, and N. P. Quang, “DYNAMIC MODEL WITH A NEW FORMULATION OF CORIOLIS/CENTRIFUGAL MATRIX FOR ROBOT MANIPULATORS”, JCC, vol. 36, no. 1, p. 89–104, Feb. 2020.

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