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

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


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.


Torque Sine 


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  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

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