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Trajectory control of flexible manipulators

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Book cover Control Problems in Robotics and Automation

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 230))

Abstract

We present some feedback control techniques recently developed for the exact solution of trajectory tracking problems for manipulators with flexible elements. Two classes are considered: i) robots with rigid links but with elastic transmissions, in which flexibility is concentrated at the joints, and ii) robots with lightweight and/or long arms, where flexibility is distributed along the links. For robots with elastic joints, we introduce a generalized inversion algorithm for the synthesis of a dynamic feedback control law that gives input-output decoupling and full state linearization. For robots with flexible links, the end-effector trajectory tracking problem is solved based on the iterative computation of the link deformations associated with the desired output motion, combined with a state trajectory regulator. For both robot models, the control design is performed directly on the second-order dynamic equations.

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References

  1. Arimoto S, Kawamura S, Miyazaki F 1984 Bettering operation of robots by learning. J Robot Syst. 1:123–140

    Google Scholar 

  2. Barbieri E, Özgüner Ü 1988 Unconstrained and constrained mode expansions for a flexible slewing link. ASME J Dyn Syst Meas Contr. 110:416–421

    Google Scholar 

  3. Bayo E 1987 A finite-element approach to control the end-point motion of a single-link flexible robot. J Robot Syst. 4:63–75

    Google Scholar 

  4. Bayo E, Serna M A, Papadopoulus P, Stubbe J 1989 Inverse dynamics and kinematics of multi-link elastic robots: An iterative frequency domain approach. Int J Robot Res. 8(6):49–62

    Google Scholar 

  5. Book W J 1984 Recursive Lagrangian dynamics of flexible manipulator arms. Int J Robot Res. 3(3):87–101

    Google Scholar 

  6. Book W J 1990 Modeling, design, and control of flexible manipulator arms: A tutorial review. In: Proc 29th IEEE Conf Decision Contr. Honolulu, HI, pp 500–506

    Google Scholar 

  7. De Luca A 1988 Dynamic control of robots with joint elasticity. In: Proc 1988 IEEE Int Conf Robot Automat. Philadelphia, PA, pp 152–158

    Google Scholar 

  8. De Luca A 1988 Control properties of robot arms with joint elasticity. In: Byrnes C I, Martin C F, Saeks R E (eds) Analysis and Control of Nonlinear Systems. North-Holland, Amsterdam, The Netherlands, pp 61–70

    Google Scholar 

  9. De Luca A, Lanari L 1995 Robots with elastic joints are linearizable via dynamic feedback. In: Proc 34th IEEE Conf Decision Contr. New Orleans, LA, pp 3895–3897

    Google Scholar 

  10. De Luca A, Lanari L, Lucibello P, Panzieri S, Ulivi G 1990 Control experiments on a two-link robot with a flexible forearm. In: Proc 29th IEEE Conf Decision Contr. Honolulu, HI, pp 520–527

    Google Scholar 

  11. De Luca A, Lanari L, Ulivi G 1991 End-effector trajectory tracking in flexible arms: Comparison of approaches based on regulation theory. In: Canudas de Wit C (ed) Advanced Robot Control. Springer-Verlag, Berlin, Germany, pp 190–206

    Google Scholar 

  12. De Luca A, Lucibello P, Ulivi G 1989 Inversion techniques for trajectory control of flexible robot arms. J Robot Syst. 6:325–344

    Google Scholar 

  13. De Luca A, Siciliano B 1993 Inversion-based nonlinear control of robot arms with flexible links. AIAA J Guid Contr Dyn. 16:1169–1176

    Google Scholar 

  14. De Luca A, Siciliano B 1996 Flexible Links. In: Canudas de Wit C, Siciliano B, Bastin G (eds) Theory of Robot Control. Springer-Verlag, London, UK, pp 219–261

    Google Scholar 

  15. De Luca A, Tomei P 1996 Elastic Joints. In: Canudas de Wit C, Siciliano B, Bastin G (eds) Theory of Robot Control. Springer-Verlag, London, UK, pp 179–217

    Google Scholar 

  16. Devasia S, Chen D, Paden B 1996 Nonlinear inversion-based output tracking. IEEE Trans Automat Contr. 41:930–942

    Google Scholar 

  17. Fraser A R, Daniel R W 1991 Perturbation Techniques for Flexible Manipulators. Kluwer, Boston, MA

    Google Scholar 

  18. Huang J, Rugh W J 1992 An approximation method for the nonlinear servomechanism problem. IEEE Trans Automat Contr. 37:1395–1398

    Google Scholar 

  19. Isidori A 1995 Nonlinear Control Systems. 3nd Edition, Springer-Verlag, London, UK

    Google Scholar 

  20. Isidori A, Moog C H, De Luca A 1986 A sufficient condition for full linearization via dynamic state feedback. In: Proc 25th IEEE Conf Decision Contr. Athens, Greece, pp 203–208

    Google Scholar 

  21. Lucibello P, Di Benedetto M D 1993 Output tracking for a nonlinear flexible arm. ASME J Dyn Syst Meas Contr. 115:78–85

    Google Scholar 

  22. Lucibello P, Panzieri S 1996 End point trajectory control with internal stability of a flexible link by learning. In: Proc 1996 IEEE Int Conf Robot Automat. Minneapolis, MN, pp 2117–2123

    Google Scholar 

  23. Meirovitch L 1967 Analytical Methods in Vibrations. Macmillan, New York

    Google Scholar 

  24. Panzieri S, Ulivi G 1995 Disturbance rejection of iterative learning control applied to trajectory tracking for a flexible manipulator. In: Proc 3rd Euro Contr Conf. Roma, Italy, pp 2374–2379

    Google Scholar 

  25. Spong M W 1987 Modeling and control of elastic joint robots. ASME J Dyn Syst Meas Contr. 109:310–319

    Google Scholar 

  26. Sweet L M, Good M C 1985 Redefinition of the robot motion control problem. IEEE Contr Syst Mag. 5(3):18–24

    Google Scholar 

  27. Tomei P 1991 A simple PD controller for robots with elastic joints. IEEE Trans Automat Contr. 36:1208–1213

    Google Scholar 

  28. Zhao H, Chen D 1993 Exact and stable tip trajectory tracking for multi-link flexible manipulator. In: Proc 32nd IEEE Conf Decision Contr. San Antonio, TX, pp 1371–1376

    Google Scholar 

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Bruno Siciliano Kimon P. Valavanis

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© 1998 Springer-Verlag London Limited

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De Luca, A. (1998). Trajectory control of flexible manipulators. In: Siciliano, B., Valavanis, K.P. (eds) Control Problems in Robotics and Automation. Lecture Notes in Control and Information Sciences, vol 230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015078

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  • DOI: https://doi.org/10.1007/BFb0015078

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76220-1

  • Online ISBN: 978-3-540-40913-7

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