Advertisement

A near Minimum Iterative Analytical Procedure for Obtaining a Robot-Manipulator Dynamic Model

  • Marc Renaud
Part of the IUTAM Symposium book series (IUTAM)

Summary

The dynamic control synthesis of robot manipulators requires a great number of arithmetic operations, and it cannot be effected in real time unless this number is reduced. This paper presents a systematic analytical procedure for obtaining the dynamic model necessary for the dynamic control synthesis. This procedure which uses a Lagrangian formulation is applicable to all manipulators having a simple kinematic chain structure with revolute and/or prismatic joints.

An example shows that the calculation of the dynamic model requires 368 multiplications and 271 additions for a particular 6 revolute joint manipulator using the systematic procedure. The examination of the results shows that only a few simpliciations are a fortiori possible and proves that the procedure is near-minimum.

Keywords

Generalize Link Robot Manipulator Multi Body System Prismatic Joint Homogeneous Transformation Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [l]
    A. K. Bejczy, 1974, “Technical memorandum 33–669”, Pasadena J.P.L. California Institute of Technology.Google Scholar
  2. [2]
    O. Fischer, 1906, “Einführung in die mechanik lebender Mechanismen”, Leipzig.Google Scholar
  3. [3]
    J.M. Hollerbach, 1980, “A.I. Memo n°533”, Boston, MITGoogle Scholar
  4. [4]
    J.M. Hollerbach and G. Sahar, 1983, “Partitioned inverse kinematic accelerations and manipulator dynamics”, The International Journal of Robotics Research, vol.2, n°4.Google Scholar
  5. [5]
    M.E. Kahn, The near minimum time control of open loop articulated kinematic chains“, Ph.D. thesis, Stanford University. 1970.Google Scholar
  6. [6]
    A.G. Leskov and V.S. Medvedev, 1974, “Analysis of dynamics and synthesis of movement control of robot manipulator functional organs”, Engineering Cybernetics, vol.12, n°6, pp. 56–65.Google Scholar
  7. [7]
    P.W. Likins, 1971, October, “Passive and semi-active attitude stabilizations-flexible space-craft”, AGARD.Google Scholar
  8. [8]
    J.Y.S. Luh, M.W. Walker and R.P.C. Paul, 1980, “Online computational scheme for mechanical manipulators”, ASME Journal of Dynamic Systems, Measurement and Control, vol. 102, pp. 69–76.MathSciNetCrossRefGoogle Scholar
  9. [9]
    S. Megahed and M. Renaud, 1982, “Minimization of the computation time necessary for the dynamic control of robot manipulators”, 12th ISIR, Paris.Google Scholar
  10. [10]
    M. Renaud, 1980, “Contribution à la modélisation et à la commande dynamique des robots manipulateurs”, Thèse d’Etat, Université Paul Sabatier, Toulouse, France.Google Scholar
  11. [11]
    M. Renaud, 1983, “An efficient iterative analytical procedure for obtaining a robot manipulator dynamic model”, 1st Int. Symposium of Robotics Research, B.Woods.Google Scholar
  12. [12]
    W.M. Silver, 1982, “On the equivalence of Lagrangian and Newton-Euler dynamics for manipulators”, The International Journal of Robotics Research, vol.1, n°2.Google Scholar
  13. [13]
    J.J. Uicker, 1968, “Dynamic behaviour of spatial linkages”, ASME, Mech. 5, n°68, pp. 1–15.Google Scholar
  14. [14]
    M. Vukobratovie and V. Potkonjak, 1982, “Dynamics of manipulation robots”, Berlin, Heidelberg, New-York, Springer-Verlag.Google Scholar
  15. [15]
    M.W. Walker and D.E. Orin, 1981, “Efficient dynamic’ computer simulation of robotic mechanisms”, JACC, Charlotteville.Google Scholar
  16. [16]
    J. Wittenburg, 1977, “Dynamics of systems of rigid bodies”, Stuttgart, B.G. Teubner.MATHGoogle Scholar

Copyright information

© Springer, Berlin Heidelberg 1986

Authors and Affiliations

  • Marc Renaud
    • 1
  1. 1.Laboratoire d’Automatique et d’Analyse des Systèmesdu Centre National de la Recherche Scientifique 7Toulouse CedexFrance

Personalised recommendations