Sensitivity Analysis of Multibody Systems

A New Approach Based on the Concept of Global Inertia
  • F. Pfister
  • M. Fayet
  • A. Jutard
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 361)


The paper presents a unified formalism for sensitivity model construction of open-loop mechanical systems. Using global-inertia tensors in conjunction with basic-kinetic tensors as an “unifying vehicle” it is shown that the sensitivity model with respect to any system-parameter (kinematic, geometric, inertia) can be formulated in one coherent and economical framework. The integral formulation of Christoffel-Symbols, not much used hitherto, now comes into its own. The procedure involves vector algebraic manipulations, but not numerical differentation. The evaluation of the obtained expressions is computational efficient and naturally follows a recursive procedure. Beyond the advantages of representation, the theory presented herein stresses the common, fundamental structure of the elements that make up motion equations and provides significant physical insight.


Order Partial Derivative Multibody System Sensitivity Model Inertia Parameter Mass Moment 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. ATKESON, C. and AN, C. and HOLLERBACH J.: Estimation of Inertial Parameters of Manipulator Loads and Links, Int. J. Rob. Res., Vol. 5, No. 3, 1986.Google Scholar
  2. BENNIS, F. and KHALIL, W. and GAITRIER, M.: Calculation of the base inertial Parameters of Closed-loops robots, IEEE Conference on Robotics and Automation, Nice, France, 1992.Google Scholar
  3. DOMBRE, M. and KHALIL, W.: Modélisation et commande des robots. Paris, Hermes, 1988.Google Scholar
  4. DUMAS, W.A.: Ober Schwingungen verbundener Pendel. Festschrift zur dritten Sdcularfeier des Berlinischen Gymnasiums run grauen Kloster. Berlin, 1874.Google Scholar
  5. FAYET, M. and PFISTER, F.: Analysis of multibody systems with indirect coordinates and global inertia tensors. Europ. J. of Mech, in press.Google Scholar
  6. FAYET, M. and RENAUD, M.: Quasi-Minimal Computation under an Explicit Form of the Inverse Dynamic Model of a Robot-Manipulator. Mech. Mach. Theory, 1989, Vol. 24, No. 3 pp. 165–174.CrossRefGoogle Scholar
  7. FISCHER, O.: Die Arbeit der Muskeln und die lebendige Kraft des menschlichen Körpers. Abh. der math.-phys. Klasse d. Kandrigl. Saechs. Gesellsch. d. Wissensch, 1893, Vol. 20, No. 1.Google Scholar
  8. FISCHER, O.: Ober die Bewegungsgl. rsuml. Gelmksystane. Abh. der path.-phys. Klasse d. Kdnigl. Sechs. Gesellsch. d. Wissensch, 1905, Vol. 29, No. 1.Google Scholar
  9. GAUTIER, M.: Contribution d la modélisation et d Pidentifcation des robots. These de Doctorat d’état, E.N.S.M., 1990, 265 p.Google Scholar
  10. GAUTIER, M. and KHALIL, W.: Exciting Trajectories for the Identification of Base Inertial Parameters of Robots, Int. J. Rob. Res., Vol. 11, No. 4, 1992.Google Scholar
  11. LI, C. J. et al.: A New Computational Method for Linearized Dynamic Models for Robot Manipulators. Inc J. of Rob. Res., Vol. 9, No. 1, 1990Google Scholar
  12. MAYEDA, H., YOSIIIDA, K. and OSUKA, K.: Base parameters of manipulator dynamics. Proc. IEEE Conf. on Rob. And Autom., Philadelphia, 1988.Google Scholar
  13. MILLS, J. and ANDREW, A. K.: Constrained motion task of robotic manipulators. Mech. Mach. Theory, Vol. 29, No. 1, pp. 95–114, 1994.CrossRefGoogle Scholar
  14. PFISTER, F.: Die Bewegungsgleichungen der Kreiselketten, Dem Erweiterten Körper zum hundertsten Geburtstag. GAMM-Jahrestagwsg. Braunschweig, 1994.Google Scholar
  15. SEEGER, G.: Selbsteinstellende, modellgenützte Regelung eines Industrieroboters. Braunschweig: Viehweg, 1992.CrossRefGoogle Scholar
  16. VUCOBRATOVIC, M. and KIRCANSKI, N.: Computer-oriented Method for Linearization of Dynamic Models of Active Spatial Mechanisms. Mech. and Mach. Theory, Vol. 17, No. 1, pp. 21–32, 1982.CrossRefGoogle Scholar
  17. VUCOBRATOVIC, M. and KIRCANSKI, N.: Computer assisted Sensitivity Model Generation in Manipulation Robots Dynamics. Mech. and Mach. Theory, Vol. 19, No. 2, pp. 223–233, 1984.CrossRefGoogle Scholar
  18. VUCOBRATOVIC, M. and STOKIC, D.: Control of Manipulation Robots. Berlin: Springer, 1982.CrossRefGoogle Scholar
  19. YOUCEF-TOUMI, K. and ASADA, H.: The Design of Open-Loop Manipulator Anus with Decoupled and Configuration-Invariant Inertia Tensors, Proc. of IEEE International Conference on Robotics and Automation, San Francisco, pp. 2018–2026, 1986.Google Scholar
  20. YANG, D.C.H. and TZENG, S.W.: Simplification and Linearization of Manipulator Dynamics by the Design of Inertia Distribution, Int. J. Rob. Res., Vol. 5, No. 3, pp. 261–268, 1989.Google Scholar

Copyright information

© Springer-Verlag Wien 1995

Authors and Affiliations

  • F. Pfister
    • 1
  • M. Fayet
    • 1
  • A. Jutard
    • 1
  1. 1.National Institute of Applied Sciences of LyonVilleurbanneFrance

Personalised recommendations