Comparing Methods Using Homogeneous Transformation Matrices for Kinematics Modeling of Robot Manipulators

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Multibody Mechatronic Systems (MuSMe 2021)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 94))

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Abstract

The forward pose kinematics (FPK) model of a robotic manipulator allows to obtain the position and orientation (i.e., the pose) of the manipulator’s end effector as a function of the joint coordinates. There are several methods for computing the FPK model, being the most common those that employ homogeneous transformation matrices (HTM). This paper reviews and compares two of those methods: the one which employs the Denavit–Hartenberg parameters, with all of its variants, and that which uses the theory of differential screws developed by Ball. The relation among these methods is established and, at the end, the procedure is validated by showing its application for computing the FPK of a simple serial manipulator.

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References

  1. Aspragathos, N.A., Dimitros, J.K.: A comparative study of three methods for robot kinematics. IEEE Trans. Syst. Man Cybern. 28(2), 135–145 (1998)

    Article  Google Scholar 

  2. Ball, R.S.: A Treatise on the Theory of Screws. Cambridge University Press, Cambridge (1900)

    Google Scholar 

  3. Brockett, R.: Robotic manipulators and the product of exponentials formula, In: Fuhrmann, P.A., (ed.) Mathematical Theory of Networks and Systems: Proceedings of the MTNS-83 International Symposium Beer Sheva, Israel, vol. 58, pp. 120-129 (1983)

    Google Scholar 

  4. Campa, R., Bernal, J.: Analysis of the different conventions of Denavit-Hartenberg parameters. Int. Rev. Modell. Simul. 12(1), 45–55 (2019)

    Google Scholar 

  5. Campa, R., de la Torre, H.: Pose control of robot manipulators using different orientation representations: a comparative review. In: Proceedings of the American Control Conference, St. Louis, MO, USA (2009)

    Google Scholar 

  6. Denavit, J., Hartenberg, R.S.: A kinematic notation for lower-pair mechanism based on matrices. J. Appl. Mech. 77, 215–221 (1955)

    MathSciNet  MATH  Google Scholar 

  7. Jia, Y.-B.: Plucker coordinates for lines in the space. In: Problem Solver Techniques for Applied Computer Science, Com-S-477/577 Course Handout. Iowa State University. http://web.cs.iastate.edu/~cs577/handouts/plucker-coordinates.pdf

  8. Murray, R., Li, Z., Sastry, S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)

    Google Scholar 

  9. Park, F.C.: Computational aspects of the product-of-exponentials formula for robot kinematics. IEEE Trans. Autom. Control 39(3), 643–647 (1994)

    Google Scholar 

  10. Sariyildis, E., Telmetas, H.: Solution of inverse kinematic problem for serial robot using dual quaternions and plücker coordinates. In: Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Singapore (2009)

    Google Scholar 

  11. Selig, J.M.: Geometric Fundamentals of Robotics. Springer (2005)

    Google Scholar 

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Acknowledgements

This work was partially supported by CONACyT and Tecnológico Nacional de México (TecNM).

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Correspondence to Ricardo Campa .

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Martínez, O., Campa, R. (2021). Comparing Methods Using Homogeneous Transformation Matrices for Kinematics Modeling of Robot Manipulators. In: Pucheta, M., Cardona, A., Preidikman, S., Hecker, R. (eds) Multibody Mechatronic Systems. MuSMe 2021. Mechanisms and Machine Science, vol 94. Springer, Cham. https://doi.org/10.1007/978-3-030-60372-4_13

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  • DOI: https://doi.org/10.1007/978-3-030-60372-4_13

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  • Print ISBN: 978-3-030-60371-7

  • Online ISBN: 978-3-030-60372-4

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