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A new factorization of the Coriolis/centripetal matrix

Published online by Cambridge University Press:  30 September 2008

Juan Ignacio Mulero-Martínez
Juan Ignacio Mulero-Martínez*
Affiliation:
Departamento de Ingeniería de Sistemas y Automática, Universidad Politécnica de Cartagena, Campus Muralla del Mar, Cartagena 30203, España
*
*Corresponding author. E-mail: juan.mulero@upct.es
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Summary

This paper provides a comprehensive description of a new method of factorization for the Coriolis/centripetal matrix. In the past three decades, studies on dynamics have rapidly developed through the efforts of many researchers in the field of mechanics. While direct methods for deriving the Coriolis/centripetal matrix are well known and have been widely used in the last century, the entries of this matrix were always obtained by means of the Christoffel symbols of first kind. Startling techniques for deriving dynamic equations of robot manipulators first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This work presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating aspects of mechanics, namely the factorization of structures, and offers the reader another point of view concerning a possible way to approach the Coriolis/centripetal matrix. It aims to study a theory of representation for such a matrix based on an elegant method of fundamental matrices. The paper is intended to be self-contained by presenting complete properties emerging from these novel structures. This work is useful not only to researchers in mechanics, but also to control engineers who are interested in learning some of the mechanical modeling. Toward this end, the paper provides numerical examples, as well as practical adaptive applications for modern designers to use at the system level.

Keywords

Coriolis/centripetal matrixFactorizationRobot Dynamics
Type
Article
Information
Robotica , Volume 27 , Issue 5 , September 2009 , pp. 689 - 700
Copyright
Copyright © Cambridge University Press 2008

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References

1. Sciavicco, L. and Siciliano, B., Modelling and Control of Robot Manipulators (Springer-Verlag, London, 2002).Google Scholar
2. Tourassis, V. D. and Neuman, C. P., “The inertial characteristics of dynamic robot models,” Mech. Mach. Theory 20 (1), 41–52 (1985).CrossRefGoogle Scholar
3. Tourassis, V. D. and Neuman, C. P., “Properties and structure of dynamic robot models for control engineering applications,” Mech. Mach. Theory 20 (1), 27–40 (1985).CrossRefGoogle Scholar
4. Craig, J., Introduction to Robotics (Addison-Wesley, Reading, MA, 1989).Google Scholar
5. Spong, M. W. and Vidyasagar, M., Robot Dynamics and Control (John Wiley and Sons, New York, 1989).Google Scholar
6. Lewis, F. L., Abdallah, C. T. and Dawson, D. M., Control of Robot Manipulators (Macmillan Co., New York, 1993).Google Scholar
7. Schilling, R. J., Fundamentals of Robotics: Analisis and Control (Prentice Hall, Englewood Cliffs, NJ, 1990).Google Scholar
8. Fu, K. S., Gonzalez, R. C. and Lee, C. S. G., Robotics: Control, Sensing, Vision and Intelligence (McGraw-Hill Education (ISE Editions), International Ed edition, June 1, 1987).Google Scholar
9. Paul, R. P., Robot Manipulators: Mathematics, Programming, and Control (The MIT Press, Cambridge, MA, Nov. 1981).Google Scholar
10. Mulero-Martínez, J. I., “Uniform bounds of the coriolis/centripetal matrix of serial robot manipulators,” IEEE Trans. Rob. 23 (5), 1083–1089 (2007).CrossRefGoogle Scholar
11. Mulero-Martínez, J. I., “An improved dynamic neurocontroller based on christoffel symbols,” IEEE Trans. Neural Networks 18 (3), 865–879 (2007).CrossRefGoogle ScholarPubMed
12. Mulero-Martínez, J. I., “Bandwidth of mechanical systems and design of emulators with rbf,” Neurocomputing 70 (7–9), 1453–1465 (2007).CrossRefGoogle Scholar
13. Asada, H. and Slotine, J.-J., Robot Analysis and Control (John Wiley & Sons, New York, 1986).Google Scholar
14. Tsai, L.-W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (Interscience, New York, Feb. 1999).Google Scholar
15. Wen, J. T. and Bayard, D. S., “New class of control laws for robotic manipulators. Part 1. Non-adaptive case,” Int. J. Control 47 (5), 1361–1385 (1988).CrossRefGoogle Scholar
16. Mulero-Martínez, J. I., “Canonical transformations used to derive robot control laws from a port-controlled hamiltonian system perspective,” Automatica 44 (9), 2435–2440 (Sept. 2008).CrossRefGoogle Scholar
17. Kelly, R., Santibañez, V. and Loria, A., Control of Robot Manipulators in Joint Space (Springer-Verlag, London, 2005).Google Scholar
18. Horn, R. A. and Johnson, C. R., Topics in Matrix Analysis (Cambridge University Press, Cambridge, UK, 1999).Google Scholar
19. Lewis, F. L., Dawson, D. M. and Abdallah, C. T., Robot Manipulator Control. Theory and Practice, 2nd ed. (Control Engineering Series, Marcel Dekker, New York, 2004).Google Scholar
20. Slotine, J.-J. E. and Asada, H., Robot Analysis and Control (John Wiley and Sons, New York, 1986).Google Scholar
21. Sanner, R. M. and Slotine, J. E., “Gaussian networks for direct adaptive control,” IEEE Trans. Neural Networks 3, 837–863 (1992).CrossRefGoogle ScholarPubMed
22. Polycarpou, M. M. and Ioannou, P. A., Identification and Control Using Neural Network Models: Design and Stability Analysis, Technical Report 91-09-01, Department of Electrical Engineering Systems, University of Southern California (1991).Google Scholar
23. Albus, J. S., “Data storage in the cerebellar model articulation controller (CMAC),” Trans. ASME. J. Dyn. Sys. Meas. Control 63 (3), 228–233 (1975).CrossRefGoogle Scholar
24. Sadegh, N., “A perceptron network for functional identification and control of nonlinear systems,” IEEE Trans. Neural Networks 4, 982–988 (Nov. 1993).CrossRefGoogle Scholar