Control of Elastic Robots

  • H. Bremer
  • F. Pfeiffer
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Summary

A robot system is considered which consists of two elastic links (bending and torsional deflection) and three fexible joints. This leads to six degrees of freedom (dof) for the rigid body motion of the system, three of which are assigned to the motor torque input. The remaining three dof. describe the gross motion of the system in space. They are superimposed by small elastic deflections which are calculated using a Ritz series approximation. The differential équations of the interconnected rigid body and elastic motion are highly nonlinear. The aim of the present investigation is to evaluate an optimal endpoint control (gripper movement) for a prescribed path in space.

Keywords

Torque 

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References

  1. [1]
    J. E. Bobrow, S. Dubowsky, J. S. Gibson: Time-optimal Control of Robotic Manipulators Along Specified Paths. Int. J. Robot. Res., Vol. 4, 3–17, 1985.CrossRefGoogle Scholar
  2. [2]
    H. Brandi, R. Johanni, M. Otter: An Algorithm for the Simulation of Multibody Systems with Kinematic Loops, Proc. IFToMM Symp, Sevilla,1987.Google Scholar
  3. [3]
    H. Bremer: On the Dynamics of Flexible Manipulators. Proc. 2nd IEEE Conf. Robotics and Automation, Rayleigh/USA, 1556-1560, 1987.Google Scholar
  4. [4]
    H. Bremer: Über eine Zentralgleichung in der Dynamik, ZAMM 68, 307–311, 1988.MATHADSCrossRefGoogle Scholar
  5. [5]
    H. Bremer: Dynamik und Regelung mechanischer Systeme, Teubner, Stuttgart, 1988.MATHGoogle Scholar
  6. [6]
    G. Demaria, B. Siciliano: A Multilayer Approach to Control of a Flexible Arm. Proc. 2nd IEEE Conf. Robotics and Automation, Rayleigh/USA, 774-778, 1987.Google Scholar
  7. [7]
    S. Dubowsky, J. Maatuk: The Dynamic Analysis of Elastic Spatial Mechanisms. J. Mech. Eng., 927-932, 1975.Google Scholar
  8. [8]
    S. Dubowsky, Z. Shiller: Optimal Trajectories for Robotic Manipulators. Proc. 5th CISM-IFToMM Symp. on Theory and Practice of Robots and Manipulators, 1985.Google Scholar
  9. [9]
    T. Fukuda: Flexibility Control of Elastic Robot Arms. J. Robotic Syst., 73-88, 1985.Google Scholar
  10. [10]
    E. Freund, H. Hoyer: Das Prinzip nichtlinearer Systementkopplung mit Anwendung auf Industrieroboter. Regelungstechnik 18, 80–87 und 116-126, 1980.Google Scholar
  11. [11]
    B. Gebier: Modeling and Control of a Leightweight Robot, Proc. 2nd Europ. Space Mech. & Tribology Symp., ESA-SP-231, 59-64, 1985.Google Scholar
  12. [12]
    B. Gebier: Steuerung und Regelung für elastische Industrieroboter, Fortschrittberichte VDI, Reihe 11, Nr. 98, VDI-Verlag, Düsseldorf 1987.Google Scholar
  13. [13]
    B. Gebier, F. Pfeiffer: A Multistage Approach to the Dynamics and Control of Elastic Robots, Proc. of 1988 IEEE Conf. on Robotics and Automation, Philadelphia, PA.Google Scholar
  14. [14]
    G. Hamel: Theoretische Mechanik, Springer (1967).Google Scholar
  15. [15]
    M. Hiller, A. Kecskemethy: A Computer-Oriented Approach for the Automatic Generation and Solution of the Equations of Motion for Complex Mechanisms, Proc. 7th World Congr. Th. Mach. & Mech., Sevilla, 425-430, 1987.Google Scholar
  16. [16]
    R. Johanni: Automatisches Aufstellen der Bewegungsgleichungen von baumstrukturierten Mehrkörpersystemen mit elastischen Bauteilen, Lst. B f. Mech TUM, Diplomarbeit, 1984.Google Scholar
  17. [17]
    R. Johanni: On the Automatic Generation of the Equations of Motion for Robots with Elastically Deformable Arms. Proc. IFAC/IFIP/IMACS Int. Symp. on Theory of Robots, Wien, 1986.Google Scholar
  18. [18]
    R. Johanni: Optimale Bahnplanung bei Industrierobotern. Fortschr.-Ber. VDI-Z., Reihe 18, Nr. 51 (1988).Google Scholar
  19. [19]
    T.R. Kane, R.R. Ryan, A.K. Banerjee: Dynamics of a Cantilever Beam Attached to a Moving Base. J. Guidance, Vol. 10, No.2, 139–151, 1987.CrossRefGoogle Scholar
  20. [20]
    U. Kleemann: Dynamics and Control of a Robotic System with Elastic Arms, Proc. Int. Symp. Robotics and Manipulators, Albuquerque 1986.Google Scholar
  21. [21]
    U. Kleemann: Regelung elastischer Roboter, Fortschrittberichte VDI, Reihe 8, Nr. 191, VDI-Verlag, Düsseldorf 1989.Google Scholar
  22. [22]
    M. Mason: Compliance and Force Control for Computer Controlled Manipulators. IEEE Trans. Syst.,Man an Cybernetics, Vol. SMC-11, Nr. 6, 418–432, 1981.CrossRefGoogle Scholar
  23. [23]
    J.K. Mills, A.A. Goldenberg: Force and Position Control of Manipulators During Constrained Motion Tasks. IEEE Trans. Robotics and Automation, Vol. 5, Nr. 1, 1989.Google Scholar
  24. [24]
    S. Nicosia, P. Tomei, A. Tornambe: Dynamic Modelling of Flexible Manipulators. Proc. IEEE Conf. on Robotics and Automation, San Francisco/USA, 365-372, 1986.Google Scholar
  25. [25]
    F. Pfeiffer, E. Reithmeier: Roboterdynamik. Teubner (1987).Google Scholar
  26. [26]
    F. Pfeiffer, R. Johanni: A Concept for Manipulator Trajectory Planning. IEEE J. Robotics and Automation, Vol. RA-3, Nr. 2, 1987.Google Scholar
  27. [27]
    F. Pfeiffer, B. Gebier: A Multistage Approach to the Dynamics and Control of Elastic Robots. Proc. IEEE Int. Conf. on Robotics and Automation, Philadelphia/USA, 2-8, 1988.Google Scholar
  28. [28]
    F. Pfeiffer, K. Richter: Optimal Path Planning Including Forces at the Gripper. To appear in J. of Intelligent and Robotic Systems, Reidel, Holland.Google Scholar
  29. [29]
    F. Pfeiffer, K. Richter, H. Wapenhans: Elastic Robot Trajectory Planning with Force Control, to appear in Proc. of IFIP International Symp. on Theory of Robots, Rom, Italien (1990).Google Scholar
  30. [30]
    M. H. Raibert, J. J. Craig: Hybrid Position/Force Control of Manipulators. Trans, of the ASME, Dyn. Syst., Measurement and Control, Vol. 102, 126–133, 1981.CrossRefGoogle Scholar
  31. [31]
    K. G. Shi, N. D. McKay: Minimum-Time Control of Robotic Manipulators with Geometric Path Constraints. IEEE Trans. Automatic Control 30, 531–541, 1985.CrossRefGoogle Scholar
  32. [32]
    P. Tomei, S. Nicosia, A. Ficola: Approach to the Adaptive Control Robots. Proc. IEEE Conf. on Robotics and Automation, San Francisco/USA, 552-558, 1986.Google Scholar
  33. [33]
    A. Truckenbrodt: Bewegungs verhalt en und Regelung hybrider Mehrkörpersysteme mit Anwendung auf Industrieroboter. Fortschr.-Ber. VDI-Z., Reihe 8, Nr. 33, 1980.Google Scholar
  34. [34]
    A. F. Vereshagin: Computer Simulation of the Dynamics of Complicated Mechanisms of Robot Manipulators, Eng. Cybernetics, No. 6, 65–70, 1974.Google Scholar

Copyright information

© Springer-Verlag, Berlin Heidelberg 1991

Authors and Affiliations

  • H. Bremer
    • 1
  • F. Pfeiffer
    • 1
  1. 1.Institute B of MechanicsTechnical University of MunichGermany

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