Skip to main content
SpringerLink
Log in

Real-time inverse dynamics control of parallel manipulators using general-purpose multibody software

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

This work deals with the problem of computing the inverse dynamics of complex constrained mechanical systems for real-time control applications. The main goal is the control of robotic systems using model-based schemes in which the inverse model itself is obtained using a general purpose multibody software, exploiting the redundant coordinate formalism. The resulting control scheme is essentially equivalent to a classical computed torque control, commonly used in robotics applications. This work proposes to use modern general-purpose multibody software to compute the inverse dynamics of complex rigid mechanisms in an efficient way, so that it suits the requirements of realistic real-time applications as well. This task can be very difficult, since it involves a higher number of equations than the relative coordinates approach. The latter is believed to be less general, and may suffer from topology limitations. The use of specialized linear algebra solvers makes this kind of control algorithms usable in real-time for mechanism models of realistic complexity. Numerical results from the simulation of practical applications are presented, consisting in a “delta” robot and a bio-mimetic 11 degrees of freedom manipulator controlled using the same software and the same algorithm.

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. Sciavicco, L., Siciliano, B.: Modeling and Control of Robot Manipulators. Springer, Berlin (2000)

    Google Scholar 

  2. Blajer, W., Kolodziejczyk, K.: A geometric approach to solving problems of control constraints: theory and a DAE framework. Multibody Syst. Dyn. 11(4), 343–364 (2004). doi:10.1023/B:MUBO.0000040800.40045.51

    Article  MATH  MathSciNet  Google Scholar 

  3. Blajer, W., Kolodziejczyk, K.: Control of underactuated mechanical systems with servo-constraints. Nonlinear Dyn. 50(4), 781–791 (2007). doi:10.1007/s11071-007-9231-4

    Article  MathSciNet  Google Scholar 

  4. Balafoutis, C.A.: A survey of efficient computational methods for manipulator inverse dynamics. J. Intell. Robot. Syst. 9(1–2), 45–71 (1994)

    Article  MATH  Google Scholar 

  5. Li, C.-J., Sankar, T.S., Hemami, A.: Real-Time Computational Schemes for Inverse Dynamics of Robot Manipulators, pp. 551–556. IEEE Press, New York (1990), WP-4-2

    Google Scholar 

  6. Haug, E.J.: Computer Aided Kinematics and Dynamics of Mechanical Systems, vol. 1: Basic Methods. Allyn and Bacon, Boston (1989)

    Google Scholar 

  7. Schiehlen, W.: Multibody system dynamics: Roots and perspectives. Multibody Syst. Dyn. 1(2), 149–188 (1997). doi:10.1023/A:1009745432698

    Article  MATH  MathSciNet  Google Scholar 

  8. Laulusa, A., Bauchau, O.A.: Review of classical approaches for constraint enforcement in multibody systems. J. Comput. Nonlinear Dyn. 1(1), (2008). doi:10.1115/1.2803257

  9. Morandini, M., Mantegazza, P.: Using dense storage to solve small sparse linear systems. ACM Trans. Math. Softw. 33(1) (2007)

  10. Attolico, M., Masarati, P.: A multibody user-space hard real-time environment for the simulation of space robots. In: Fifth Real-Time Linux Workshop, Valencia, Spain, 9–11 November 2003

  11. Masarati, P., Attolico, M., Nixon, M.W., Mantegazza, P.: Real-time multibody analysis of wind-tunnel rotorcraft models for virtual experiment purposes. In: AHS 4th Decennial Specialists’ Conference on Aeromechanics, Fisherman’s Wharf, San Francisco, CA, 21–23 January 2004

  12. Attolico, M., Masarati, P., Mantegazza, P.: Trajectory optimization and real-time simulation for robotics applications. In: Multibody Dynamics 2005, ECCOMAS Thematic Conference, Madrid, Spain, 21–24 June 2005

  13. Masarati, P., Morandini, M., Quaranta, G., Mantegazza, P.: Open-source multibody analysis software. In: Multibody Dynamics 2003, International Conference on Advances in Computational Multibody Dynamics, Lisboa, Portugal, 1–4 July 2003

  14. Masarati, P., Morandini, M., Quaranta, G., Mantegazza, P.: Computational aspects and recent improvements in the open-source multibody analysis software “MBDyn”. In: Multibody Dynamics 2005, ECCOMAS Thematic Conference, Madrid, Spain, 21–24 June 2005

  15. Clavel, R.: Delta, a fast robot with parallel geometry. In: Proceedings of the 18th International Symposium on Industrial Robot (ISIR), Lousanne, April 26–28 1988, pp. 91–100. Springer, Berlin (1988)

    Google Scholar 

  16. Stewart, D.: A platform with six degrees-of-freedom. In: Proceedings of the Institute of Mechanical Engineers, Part I, vol. 180, pp. 371–386, 1965–1966

  17. Dafaoui, El.-M., Amirat, Y., Pontnau, J., Francois, C.: Analysis and design of a six-dof parallel manipulator, modeling, singular configurations, and workspace. IEEE Trans. Robot. Autom. 14(4), 78–92 (1998)

    Article  Google Scholar 

  18. Pierrot, F., Fournier, A., Dauchez, P.: Towards a fully-parallel 6 dof robot for high-speed applications. In: Int. Conf. Robotics and Automation, Sacramento, CA, USA, pp. 1288–1293 (1991)

  19. Liu, M.-J., Li, C.-X., Li, C.-N.: Dynamics analysis of the Gough–Stewart platform manipulator. IEEE Trans. Robot. Autom. 16(1), 94–98 (2000)

    Article  Google Scholar 

  20. Codourey, A., Burdet, E.: A body-oriented method for finding a linear form of the dynamic equation of fully parallel robots. In: Int. Conf. Robotics and Automation, Albuquerque, NM, USA, April 1997, pp. 1612–1618 (1997)

  21. Codourey, A.: Dynamic modeling of parallel robots for computed-torque control implementation. Int. J. Robot. Res. 17(12), 1325–1326 (1998)

    Article  Google Scholar 

  22. Dasgupta, B., Mruthyunjaya, T.S.: A Newton–Euler formulation for the inverse dynamics of the Stewart platform manipulator. Mech. Mach. Theory 33(8), 1135–1152 (1998)

    MATH  MathSciNet  Google Scholar 

  23. Tsai, L.-W.: Solving the inverse dynamics of a Stewart–Gough manipulator by the principle of virtual work. J. Mech. Des. 122, 3–9 (2000)

    Article  Google Scholar 

  24. Khalil, W., Ibrahim, O.: General solution for the dynamic modeling of parallel robots. In: IEEE International Conference on Robotic and Automation, New Orleans, LA, USA, April 2004, pp. 3665–3670 (2004)

  25. Khalil, W., Ibrahim, O.: General solution for the dynamic modeling of parallel robots. J. Intell. Robot Syst. 49, 19–37 (2007)

    Article  Google Scholar 

  26. Fumagalli, A., Gaias, G., Masarati, P.: A simple approach to kinematic inversion of redundant mechanisms. In: IDETC/CIE 2007 ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Las Vegas, NE, USA, 4–7 September 2007

  27. Lambert, J.D.: Numerical Methods for Ordinary Differential Systems. Wiley, Chichester (1991)

    MATH  Google Scholar 

  28. Brenan, K.E., Campbell, S.L.V., Petzold, L.R.: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. North-Holland, New York (1989)

    MATH  Google Scholar 

  29. Hairer, E., Lubich, C., Roche, M.: The Numerical Solution of Differential-Algebraic Systems by Runge–Kutta Methods. Lecture Notes in Mathematics. Springer, Berlin (1989)

    MATH  Google Scholar 

  30. Strang, G.: Introduction to Applied Mathematics. Wellesley-Cambridge Press, Cambridge (1986)

    MATH  Google Scholar 

  31. Levi-Civita, T., Amaldi, U.: Lezioni di Meccanica Razionale, vol. II: Dinamica dei Sistemi con un Numero Finito di Gradi di Libertà, parte II. Zanichelli, Bologna (1974) (in Italian)

    Google Scholar 

  32. de Jalón, J.G., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems: the Real Time Challenge. Springer, New York (1994)

    Google Scholar 

  33. Brüls, O., Duysinx, P., Golinval, J.C.: A model reduction method for the control of rigid mechanisms. Multibody Syst. Dyn. 15(3), 213–227 (2006). doi:10.1007/s11044-006-1354-8

    Article  MATH  MathSciNet  Google Scholar 

  34. Quarteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, Berlin (2007)

    MATH  Google Scholar 

  35. Santibanez, V., Kelly, R.: PD control with feedforward compensation for robot manipulators: analysis and experimentation. Robotica 19, 11–19 (2001)

    Article  Google Scholar 

  36. Davis, T.A.: A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30(2), 165–195 (2004)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, 20156, Milano, Italy

    Alessandro Fumagalli & Pierangelo Masarati

Authors
  1. Alessandro Fumagalli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pierangelo Masarati
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pierangelo Masarati.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fumagalli, A., Masarati, P. Real-time inverse dynamics control of parallel manipulators using general-purpose multibody software. Multibody Syst Dyn 22, 47–68 (2009). https://doi.org/10.1007/s11044-009-9153-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-009-9153-7

Keywords

Search

Navigation