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A dynamics formulation of general constrained robots

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An Erratum to this article was published on 18 July 2006

Abstract

The complexity of a standard compact-in-form Lagrangian dynamical expression is proportional to the fourth power of the number of degrees of freedom (DOF) of a robotic system. This fact challenges both simulation and control of robots with hyper degrees of freedom. In this paper, a systematic approach for deriving the dynamical expression of so-called general constrained robots is proposed. This proposed approach has two main features. First, it uses the subsystem dynamics such as the dynamics of joints and rigid links to construct the dynamical expression of the entire robotic system in a closed form. The complexity of the resulted dynamic expression is linearly proportional to the number of DOF of a robotic system. Second, it extends the standard dynamical form and properties of the conventional single-arm constrained robots to a class of more general robotic systems including the coordinated multiple-arm robotic systems. Three spaces, namely the general joint space, the general task space, and the extended subsystems space, are connected through corresponding velocity/force mapping matrices.

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References

  1. Raibert, M.H., Craig, J.J.: Hybrid position/force control of manipulators. ASME J. Dynamic Systems, Measurement, and Control 102(2), 126–133 (1981)

    Article  Google Scholar 

  2. De Schutter, J., Van Brussel, H.: Compliant robot motion. Int. J. Robotics Research 7(4), 3–33 (1988)

    Article  Google Scholar 

  3. Seraji, H., Colbaugh, R.: Force tracking in impedance control. Int. J. Robotics Research 16(1), 97–117 (1997)

    Article  Google Scholar 

  4. McClamroch, N.H., Wang, D.: Feedback stabilization and tracking of constrained robots. IEEE. Trans. Automatic Control 33(5), 419–426 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chiaverini, S., Sciavicco, L.: The parallel approach to force/position control of robotic manipulators. IEEE Trans. Robotics and Automation 9(4), 361–373 (1993)

    Article  Google Scholar 

  6. Jean, J.H., Fu, L.C.: Adaptive hybrid control strategies for constrained robots. IEEE. Trans. Automatic Control 38(4), 598–603 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Yuan, J.: Composite adaptive control of constrained robots. IEEE Trans. Robotics and Automation 12(4), 640–645 (1996)

    Article  Google Scholar 

  8. Liu, Y.H., Arimoto, S., Kitagaki, K.: Adaptive control for holonomically constrained robots: time-invariant and time-variant cases. Proc. of 1995 IEEE Int. Conf. Robotics and Automation, pp. 905–912 (1995)

  9. Zhen, R.R.Y., Goldenberg, A.A.: An adaptive approach to constrained robot motion control. Proc. of 1995 IEEE Int. Conf. Robotics Automation pp. 1833–1838 (1995)

  10. Canudas de Wit, C., Brogliato, B.: Direct adaptive impedance control including transition phases. Automatica 33(4), 643–649 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Khatib, O.: A Unified approach for motion and force control of robot manipulators: the operational space formulation. IEEE J. of Robotics and Automation 3(1), 43–53 (1987)

    Article  Google Scholar 

  12. Kreutz, K., Lokshin, A.: Load balancing and closed chain multiple arm control. Proc. of 1988 ACC, 2148–2155 (1988)

  13. Hayati, S.: Hybrid position/force control of multi-arm cooperating robots. Proc. of 1986 IEEE Int. Conf. Robot. Automat., pp. 82–89 (1986)

  14. Luh, J.Y.S., Zheng, Y.F.: Constrained relations between two coordinated industrial robots for motion control. Int. J. Robotics Research 6(3), 60–70 (1987)

    Article  Google Scholar 

  15. Tarn, T.J., Bejczy, A.K., Yun, X.: Design of dynamic control of two cooperating robot arms: closed chain formulation. Proc. of 1987 IEEE Int. Conf. Robot. Automat., pp. 7–13 (1987)

  16. Dauchez, P., Fournier, A., Jourdan, R.: Hybrid control of a two-arm robot for complex tasks. Robot. Autonomous Syst. 5, 323–332 (1989)

    Article  Google Scholar 

  17. Nakamura, Y., Nagai, K., Yoshikawa, T.: Dynamics and stability in coordination of multiple robotic mechanisms. Int. J. Robotics Research 8(2), 44–61 (1989)

    Article  Google Scholar 

  18. Yun, X.P., Kumar, V.R.: An approach to simultaneous control of trajectory and interaction forces in dual-arm configurations. IEEE Trans. Robotics and Automation 7(5), 618–625 (1991)

    Article  Google Scholar 

  19. Walker, I.D., Freeman, R.A., Marcus, S.I., Analysis of motion and internal loading of objects grasped by multiple cooperating manipulators. Int J Robotics Research 10(4), 396–409 (1991)

    Article  Google Scholar 

  20. Koga, M., Kosuge, K., Furuta, K., Nosaki, K.: Coordinated motion control of robot arms based on the virtual internal model. IEEE Trans Robotics and Automation 8(1), 77–85 (1992)

    Article  Google Scholar 

  21. Schneider, S.A. Cannon, Jr., R.H.: Object impedance control for cooperative manipulation: theory and experimental results. IEEE Trans Robotics and Automation 8(3), 383–394 (1992)

    Article  Google Scholar 

  22. Wen, J.T., Delgado, K.K.: Motion and force control of multiple robotic manipulators. Automatica 28(4), 729–743 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  23. Unseren, M.A.: A rigid body model and decoupled control architecture for two manipulators holding a complex object. Robot Autonomous Syst 10, 115–131 (1992)

    Article  Google Scholar 

  24. Hu, Y.R., Goldenberg, A.A.: An adaptive approach to motion and force control of multiple coordinated robots. ASME J Dynamic Systems, Measurement, and control 115(1), 60–69 (1993)

    Article  MATH  Google Scholar 

  25. Yoshikawa, T., Zheng, X.Z.: Coordinated dynamic hybrid position/force control for multiple robot manipulators handling one constrained object. Int J Robotics Research 12(3), 219–230 (1993)

    Article  Google Scholar 

  26. Hsu, P.: Coordinated control of multiple manipulator systems. IEEE Trans Robotics and Automation 9(4), 400–410 (1993)

    Article  Google Scholar 

  27. Xi, N., Tarn, T.J., Bejczy, A.K.: Intelligent planning and control for multirobot coordination: an event-based approach. IEEE Trans Robotics and Automation 12(3), 439–452 (1996)

    Article  Google Scholar 

  28. Bonitz, R.G., Hsia, T.C.: Internal force-based impedance control for cooperating manipulators. IEEE Trans Robotics and Automation 12(1), 78–89 (1996)

    Article  Google Scholar 

  29. Liu, Y.H., Xu, Y., Bergerman, M.: Cooperation control of multiple manipulators with passive joints. IEEE Trans Robotics and Automation 15(2), 258–267 (1999)

    Article  Google Scholar 

  30. De Luca, A., Manes, C.: Modeling of robots in contact with a dynamic environment. IEEE Trans Robotics and Automation 10(3), 542–548 (1994)

    Article  Google Scholar 

  31. Zhu, W.H., Xi, Y.G., Zhang, Z.J., Bien, Z., De Schutter, J.: Virtual decomposition based control for generalized high dimensional robotic systems with complicated structure. IEEE Trans Robotics and Automation 13(3), 411–436 (1997)

    Article  Google Scholar 

  32. Piedboeuf, J.-C.: Recursive modeling of serial flexible manipulators. Journal of the Astronautical Science 46(1), 1–24 (1998)

    MathSciNet  Google Scholar 

  33. Jain, A.: Unified formulation of dynamics for serial rigid multibody systems. AIAA J Guidance, Control, and Dynamics 14(3), 531–542 (1991)

    Article  MATH  Google Scholar 

  34. Murphy, S.H., Wen, J.T., Saridis, G.N., Simulation of cooperating robot manipulators on a mobile platform. IEEE Trans Robotics and Automation 8(4), 468–477 (1992)

    Google Scholar 

  35. Luh, J.Y.S., Walker, M.W., Paul, R.P.C.: Computational scheme for mechanical manipulators. ASME J Dynamic Systems, Measurement, and Control 102(2), 69–76 (1980)

    MathSciNet  Google Scholar 

  36. Hollerbach, J.M.: A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity. IEEE Trans Systems, Man, and Cybernetics 10(11), 730–736 (1980)

    Article  MathSciNet  Google Scholar 

  37. Silver, W.M.: On the equivalence of Lagrangian and Newton-Euler dynamics for manipulators. Int J Robotics Research 1(2), 60–70 (1982)

    Article  Google Scholar 

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Authors and Affiliations

  1. Spacecraft Engineering, Space Technologies, Canadian Space Agency 6767 route de l'Aeroport, Saint-Hubert, QC J3Y 8Y9, Canada

    Wen-Hong Zhu, Jean-Claude Piedboeuf & Yves Gonthier

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  1. Wen-Hong Zhu
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  2. Jean-Claude Piedboeuf
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  3. Yves Gonthier
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Correspondence to Wen-Hong Zhu.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s11044-006-9022-6

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Zhu, WH., Piedboeuf, JC. & Gonthier, Y. A dynamics formulation of general constrained robots. Multibody Syst Dyn 16, 37–54 (2006). https://doi.org/10.1007/s11044-006-9011-9

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  • DOI: https://doi.org/10.1007/s11044-006-9011-9

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