Advertisement

Linearised Feedforward Control of a Four-Chain Crane Manipulator

  • Michael Stoltmann
  • Pascal Froitzheim
  • Normen Fuchs
  • Wilko Flügge
  • Christoph WoernleEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 74)

Abstract

For a crane manipulator suspending a flexible metal plate by four chains feedforward control is derived that moves the payload along desired spatial trajectories. Due to the statically indeterminate suspension, the stiffness of the payload has to be taken into account. The actuator coordinates can be algebraically calculated from the desired trajectory of the plate at the position, velocity and acceleration levels exploiting the flatness property of the system. As the system is kinematically redundant, a technically meaningful solution like minimal inclination angles of the chains are determined by optimisation. As the iterative calculation of the nonlinear constrained optimisation problem is computationally expensive and not suitable for implementation on the crane controller, a linearised inverse dynamics model is derived that describes small sway motions of the flexible payload around a static equilibrium state. Linearised and nonlinear feedforward control are compared in a numerical simulation of the crane system.

Keywords

crane manipulator elastic payload underactuated system linearisation inverse dynamics quadratic programming feedforward control 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgement

This research and development project was supported by the European Regional Development Fund (EFRE). Support was also provided by the lead partner Technologie-Beratungsinstitut (TBI) according to the directive for support, development and innovation of the Ministry of Economics, Construction and Tourism of Mecklenburg-Vorpommern.

References

  1. 1.
    Abbasnejad, G., Carricato, M.: Direct geometrico-static problem of underconstrained cabledriven parallel robots with n cables. IEEE Transactions on Robotics 31, 468–478 (2015)Google Scholar
  2. 2.
    Berti, A., Merlet, J.P., Carricato, M.: Solving the direct geometrico-static problem of underconstrained cable-driven parallel robots by interval analysis. The International Journal of Robotics Research 35, 723–739 (2016)CrossRefGoogle Scholar
  3. 3.
    Bhaskar, K., Varadan, T.: Plates. John Wiley Sons (2014)Google Scholar
  4. 4.
    Blajer, W., Kolodziejczyk, K.: Improved DAE formulation for inverse dynamics simulation of cranes. Multibody System Dynamics 25, 131–143 (2011)CrossRefGoogle Scholar
  5. 5.
    Carricato, M., Abbasnejad, G., Walter, D.: Inverse geometrico-static analysis of underconstrained cable-driven parallel robots with four cables. In: J. Lenarčič, M. Husty (eds.) Latest Advances in Robot Kinematics, pp. 365–372. Springer, Dordrecht (2012)CrossRefGoogle Scholar
  6. 6.
    Carricato,M., Merlet, J.P.: Geometrico-static analysis of under-constrained cable-driven parallel robots. In: J. Lenarčič, M. Stanišić (eds.) Advances in Robot Kinematics, pp. 309–319. Springer, Berlin (2010)CrossRefGoogle Scholar
  7. 7.
    Fliess, M., Lévine, J., Martin, P., Rouchon, P.: Flatness and defect of nonlinear systems: Introductory theory and examples. International Journal of Control 51, 1327–1361 (1995)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Heyden, T., Woernle, C.: Dynamics and flatness-based control of a kinematically undetermined cable suspension manipulator. Multibody System Dynamics 16, 155–177 (2006)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Husty, M., Schadlbauer, J., Zsombor-Murray, P.: A new approach to the direct geometricostatic problem of cable suspended robots using kinematic mapping. In: C. Gosselin, P. Cardou, T. Bruckmann, A. Pott (eds.) Cable-Driven Parallel Robots, pp. 97–105. Springer, Cham (2018)Google Scholar
  10. 10.
    Hwang, S.W., Bak, J.H., Yoon, J., Park, J.H., Park, J.O.: Trajectory generation to suppress oscillations in under-constrained cable-driven parallel robots. Journal of Mechanical Science and Technology 30, 5689–5697 (2016)CrossRefGoogle Scholar
  11. 11.
    Knierim, K.L., Krieger, K., Sawodny, O.: Flatness based control of a 3-dof overhead crane with velocity controlled drives. IFAC Proceedings Volumes 43, 363 – 368 (2010)CrossRefGoogle Scholar
  12. 12.
    Ming, A., Higuchi, T.: Study on multiple degree-of-freedom positioning mechanisms using wires (parts 1 and 2). Int. Journal of the Japanese Society for Precision Engineering 28, 131–138 and 235–242 (1994)Google Scholar
  13. 13.
    Pott, A.: Cable-Driven Parallel Robots - Theory and Application. Springer, Berlin (2018)Google Scholar
  14. 14.
    Sawodny, O., Aschemann, H., Lahres, S.: An automated gantry crane as a large workspace robot. Control Engineering Practice 10, 1323 – 1338 (2002)CrossRefGoogle Scholar
  15. 15.
    Stoltmann, M., Froitzheim, P., Fuchs, N., Woernle, C.: Flatness-based feedforward control of a crane manipulator with four load chains. In: B. Corves, P. Wenger, M. Hüsing (eds.) EuCoMes 2018, pp. 61–68. Springer, Berlin (2019)Google Scholar
  16. 16.
    Woernle, C.: Trajectory tracking for a three-cable suspension manipulator. In: T. Bruckmann, A. Pott (eds.) Cable-Driven Parallel Robots, pp. 371–386. Springer, Berlin (2013)Google Scholar
  17. 17.
    Woernle, C.: Mehrk¨orpersysteme. Springer, Berlin (2016)Google Scholar
  18. 18.
    Yang, Y., Betsch, P.: Computer simulation of the inverse dynamics of underactuated mechanical systems. In: Proc. ECCOMAS Thematic Conference on Multibody Dynamics, Prague (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Michael Stoltmann
    • 1
  • Pascal Froitzheim
    • 2
  • Normen Fuchs
    • 2
  • Wilko Flügge
    • 2
  • Christoph Woernle
    • 1
    Email author
  1. 1.University of RostockRostockGermany
  2. 2.Fraunhofer Research Institution for Large Structures in Production Engineering IGPRostockGermany

Personalised recommendations