CONSIDERATIONS ABOUT MATRIX EXPONENTIALS IN GEOMETRICAL MODELING OF THE ROBOTS

Claudiu SCHONSTEIN

Abstract


In specialized literature, there are many approaches to the mathematical modeling of robots. Thus, different algorithms for geometric modeling are consecrated. Most approaches require the use of reference systems, which can lead to errors in computing. The geometrical study of any mechanical robot structure can be realized by matrix exponential, having essential advantages besides the classical approaches. As a result, within this paper, there will be presented an example of mathematical modeling, concerning the matrix exponentials applied in the geometrical modeling of serial robots.


Key words: robotics, geometry, matrix exponentials, control functions.


Full Text:

PDF

References


I., Negrean, Mecanică Avansată în Robotică, Editura UT PRESS, ISBN 978-973-662-420-9. Cluj-Napoca, 2008.

Negrean, I. I., Negrean, I., D. C., The Locating Matrix Algorithm in Robot Kinematics, Cluj-Napoca, October 2001, Acta Technica Napocensis, Series: Applied Mathematics and Mechanics, 2001

Negrean, I., Schonstein, C., Kacso, K., Duca, A., Matrix Exponentials and Differential Principles in the Dynamics of Robots, The 13-th World Congress in Mechanism and Machine Science, Guanajuato, Mexico, 19-25 June, 2011.

Negrean, I., Schonstein, C., Advanced Studies on Matrix Exponentials in Robotics, Published in the Acta Technica Napocensis, Series: Applied Mathematics and Mechanics, Nr. 53, Vol. I, 2010, pp. 13-18, Cluj-Napoca, ISSN 1221-5857, Romania.

Park, F.C., Computational Aspects of the Product-of-Exponentials Formula for Robot Kinematics, IEEE Transaction on Automatic Control, Vol. 39, No. 3, 1994.

Bernstein, D.S., So, W.G., Some explicit Formulas for the Matrix Exponential, IEEE Transaction on Automatic Control, Vol. 38, No. 8, August, 1993.

Schonstein, C., Panc N., - Kinematical modeling for R2T structure used in transfer parts between two workstations, published in Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue III, 2017, ISSN 1221-5872, Cluj-Napoca, Romania.

Schonstein, C., Negrean, I., Panc N., - Geometrical modeling using matrix exponential functions for a serial robot structure, published in Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue III, 2017, ISSN 1221-5872, Cluj-Napoca, Romania.


Refbacks

  • There are currently no refbacks.


JOURNAL INDEXED IN :