Skip to main content
SpringerLink
Log in

An approach to automatic generation of dynamic equations of elastic joint manipulators in symbolic language

  • Published:
Journal of Intelligent and Robotic Systems Aims and scope Submit manuscript

Abstract

This paper describes an approach for automatic generation of the equations of motion of elastic joint manipulators in symbolic language. It is based on a vector-parametrization of the Lie groupSO(3) and uses the Lagrange's formalism to derive the dynamical equations, the final forms of which are like the equations generated by a recursive Newton-Eulerian algorithm. These characteristics together increase the computational efficiency of the algorithm and give a very good insight into the dynamical structure of the system. In addition to this, the inertia matrix is explicitly given in the final equations, which is very important for the applicability of a mathematical model in different fields of control and simulation. The suggested algorithm is therefore quite appropriate for the purposes of robot modeling, identification as well as for the applications in real time simulations and control.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arnold, V. I.:Mathematical Methods in Classical Mechanics, Springer-Verlag, New York, 1978.

    Google Scholar 

  2. Cesareo, G., Nicolo, F., and Nicosia, S.: DYMIR: A code for generating dynamic model of robots,Proc. 1st IEEE Int. Conf. Robotics and Automation, Atlanta, 1984.

  3. Chang-Jin, Li: A new Langrangian formulation of dynamics for robot manipulators,ASME J. Dyn. Syst., Meas. and Control 111 (1989), 559–567.

    Google Scholar 

  4. Craig, J. J.:Introduction to Robots, Mechanics and Control, Addison-Wesley, Reading, MA, 1989.

    Google Scholar 

  5. Pars, L. A.:A Treatise on Analytical Dynamics, Heineman Educational Books, London, 1968.

    Google Scholar 

  6. Haug, E. J.: Computer aided analysis and optimization of mechanical system dynamics,NATO ASI Serie, Ser. F:Computer and Systems Science, Vol. 9, Springer-Verlag, Berlin, 1984.

    Google Scholar 

  7. Hollerbach, J. M.: A recurvise Langrangian formulation of manipulator dynamics and a comparative study of dynamic formulation complexity,IEEE J. Syst., Man and Cybern. 10(11) (1980), 730–736.

    Google Scholar 

  8. Kahn, M. E.: The Near Minimum Time Control of Open Loop Articulated Kinematic Chains, PhD Thesis, Stanford University, 1969.

  9. Marino, R. and Nicosia, S.: On the Feedback Control of Industrial Robots with Elastic Joints: A Singular Perturbation Approach, A Scientific Report, Universita di Roma, 1984.

  10. Mladenova, C. and Toshev, Y.: Vector parameter approach to analysis and control of manipulator systems,Trans. ASME Design Eng. Techn. Conf. DET-195, Columbus, OH, Oct. 5–8, 1986.

  11. Mladenova, C.: A contribution to the modelling and control of manipulators,J. Intelligent Robotic Systems 3 (1990), 349–363.

    Google Scholar 

  12. Mladenova, C.: Mathematical modelling and control of manipulator systems,Robot. Comput. Integr. Mfg. 8(4) (1991), 233–242.

    Google Scholar 

  13. Luh, J. Y. S., Walker, M. W., and Paul, R. P. C.: On-line computation scheme for mechanical manipulators,ASME J. Dyn. Syst., Meas. and Control 102(2) (1980), 69–76.

    Google Scholar 

  14. Schielen, W. O.: Computer generation of equations of motion,NATO ASI Serie, Ser. F:Computer Ans Systems Sciences, Vol. 9, Springer-Verlag, Berlin, 1984.

    Google Scholar 

  15. Schwertassek, R. and Roberson, R. E.:Dynamics of Multibody Systems, Springer-Verlag, Berlin, 1988.

    Google Scholar 

  16. Spong, M.W.: Modeling and control of elastic joint robots,ASME J. Dyn. Syst., Meas. and Control 109 (1987), 105–114.

    Google Scholar 

  17. Uicker, J. J.: On the Dynamic Analysis of Spatial Linkages Using 4 × 4 Matrices, PhD Thesis, Northwestern University, Evastone, August 1965.

  18. Vukobratovic, M. and Kircanski, N.:Real-Time Dynamics of Manipulation Robots, Springer-Verlag, Berlin, 1985.

    Google Scholar 

  19. Walters, R. C.: Mechanical arm control,A.I. Memo 549, MIT Artificial Intelligence Laboratory, 1979.

  20. Adongo, J. O. and Müller, P. C.: Control of multi axis robots with elastic joints via cascade compensation using the method of exact linearization, submitted for publication.

  21. Paul, R. P.:Robot Manipulators:Mathematics, Programming and Control, MIT Press, Cambridge, MA, 1986.

    Google Scholar 

Download references

Author information

Author notes

  1. C. D. Mladenova (Alexander von Humboldt Research Fellow)

    Present address: Institute of Mechanics, Bulg. Acad. Sciences, Acad. G. Bonchev Str., Bl. 4, 1113, Sofia, Bulgaria

Authors and Affiliations

  1. Safety Control Engineering, University of Wuppertal, Gauβstr. 20, 42097, Wuppertal, Germany

    J. Adongo Ochier (Friedrich-Ebert Scholar), C. D. Mladenova (Alexander von Humboldt Research Fellow) & P. C. Müller (University Professor)

Authors
  1. J. Adongo Ochier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. D. Mladenova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. C. Müller
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Adongo Ochier, J., Mladenova, C.D. & Müller, P.C. An approach to automatic generation of dynamic equations of elastic joint manipulators in symbolic language. J Intell Robot Syst 14, 199–218 (1995). https://doi.org/10.1007/BF01559612

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01559612

Key words

Search

Navigation