Skip to main content
SpringerLink
Log in
Book cover

Springer Handbook of Robotics pp 243–282Cite as

Robots with Flexible Elements

  • Chapter
  • First Online:

Part of the book series: Springer Handbooks ((SHB))

Abstract

Design issues, dynamic modeling, trajectory planning, and feedback control problems are presented for robot manipulators having components with mechanical flexibility, either concentrated at the joints or distributed along the links. The chapter is divided accordingly into two main parts. Similarities or differences between the two types of flexibility are pointed out wherever appropriate.

For robots with flexible joints, the dynamic model is derived in detail by following a Lagrangian approach and possible simplified versions are discussed. The problem of computing the nominal torques that produce a desired robot motion is then solved. Regulation and trajectory tracking tasks are addressed by means of linear and nonlinear feedback control designs.

For robots with flexible links, relevant factors that lead to the consideration of distributed flexibility are analyzed. Dynamic models are presented, based on the treatment of flexibility through lumped elements, transfer matrices, or assumed modes. Several specific issues are then highlighted, including the selection of sensors, the model order used for control design, and the generation of effective commands that reduce or eliminate residual vibrations in rest-to-rest maneuvers. Feedback control alternatives are finally discussed.

In each of the two parts of this chapter, a section is devoted to the illustration of the original references and to further readings on the subject.

figure a

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   269.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   349.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Abbreviations

COM:

center of mass

DC:

direct current

DLR:

German Aerospace Center

EOA:

end of arm

FFT:

fast Fourier transform

LQR:

linear quadratic regulator

LWR:

light-weight robot

MEMS:

microelectromechanical system

MIMO:

multiple-input–multiple-output

MMSAE:

multiple model switching adaptive estimator

OAT:

optimal arbitrary time-delay

PDE:

partial differential equation

PD:

proportional–derivative

PID:

proportional–integral–derivative

RALF:

robotic arm large and flexible

robotic arm long and flexible

SEA:

series elastic actuator

TMM:

transfer matrix method

VSA:

variable stiffness actuator

References

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

    Article  Google Scholar 

  2. M.C. Good, L.M. Sweet, K.L. Strobel: Dynamic models for control system design of integrated robot and drive systems, ASME J. Dyn. Syst. Meas. Control 107, 53–59 (1985)

    Article  Google Scholar 

  3. E. Rivin: Mechanical Design of Robots (McGraw-Hill, New York 1988)

    Google Scholar 

  4. S. Nicosia, F. Nicolò, D. Lentini: Dynamical control of industrial robots with elastic and dissipative joints, 8th IFAC World Congr., Kyoto (1981) pp. 1933–1939

    Google Scholar 

  5. P. Tomei: An observer for flexible joint robots, IEEE Trans. Autom. Control 35(6), 739–743 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Höpler, M. Thümmel: Symbolic computation of the inverse dynamics of elastic joint robots, IEEE Int. Conf. Robotics Autom. (ICRA), New Orleans (2004) pp. 4314–4319

    Google Scholar 

  7. M.W. Spong: Modeling and control of elastic joint robots, ASME J. Dyn. Syst. Meas. Control 109, 310–319 (1987)

    Article  MATH  Google Scholar 

  8. S.H. Murphy, J.T. Wen, G.N. Saridis: Simulation and analysis of flexibly jointed manipulators, 29th IEEE Conf. Decis. Control, Honolulu (1990) pp. 545–550

    Google Scholar 

  9. R. Marino, S. Nicosia: On the Feedback Control of Industrial Robots with Elastic Joints: A Singular Perturbation Approach (Dipartimento di Ingegneria Elettronica, Univ. Rome Tor Vergata, Rome 1984), Rep. R-84.01

    Google Scholar 

  10. G. Cesareo, F. Nicolò, S. Nicosia: DYMIR: A code for generating dynamic model of robots, IEEE Int. Conf. Robotics Autom. (ICRA), Atlanta (1984) pp. 115–120

    Google Scholar 

  11. A. De Luca: Feedforward/feedback laws for the control of flexible robots, IEEE Int. Conf. Robotics Autom. (ICRA), San Francisco (2000) pp. 233–240

    Google Scholar 

  12. G. Buondonno, A. De Luca: A recursive Newton–Euler algorithm for robots with elastic joints and its application to control, IEEE/RSJ Int. Conf. Intell. Robots Syst., Hamburg (2015) pp. 5526–5532

    Google Scholar 

  13. H.B. Kuntze, A.H.K. Jacubasch: Control algorithms for stiffening an elastic industrial robot, IEEE J. Robotics Autom. 1(2), 71–78 (1985)

    Article  Google Scholar 

  14. S.H. Lin, S. Tosunoglu, D. Tesar: Control of a six-degree-of-freedom flexible industrial manipulator, IEEE Control Syst. Mag. 11(2), 24–30 (1991)

    Article  Google Scholar 

  15. P. Tomei: A simple PD controller for robots with elastic joints, IEEE Trans. Autom. Control 36(10), 1208–1213 (1991)

    Article  MathSciNet  Google Scholar 

  16. A. De Luca, B. Siciliano: Regulation of flexible arms under gravity, IEEE Trans. Robotics Autom. 9(4), 463–467 (1993)

    Article  Google Scholar 

  17. A. De Luca, B. Siciliano, L. Zollo: PD control with on-line gravity compensation for robots with elastic joints: Theory and experiments, Automatica 41(10), 1809–1819 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  18. C. Ott, A. Albu-Schäffer, A. Kugi, S. Stramigioli, G. Hirzinger: A passivity based Cartesian impedance controller for flexible joint robots – Part I: Torque feedback and gravity compensation, IEEE Int. Conf. Robotics Autom. (ICRA), New Orleans (2004) pp. 2659–2665

    Google Scholar 

  19. L. Zollo, B. Siciliano, A. De Luca, E. Guglielmelli, P. Dario: Compliance control for an anthropomorphic robot with elastic joints: Theory and experiments, ASME J. Dyn. Syst. Meas. Control 127(3), 321–328 (2005)

    Article  Google Scholar 

  20. A. Albu-Schäffer, C. Ott, G. Hirzinger: A passivity based Cartesian impedance controller for flexible joint robots – Part II: Full state feedback, impedance design and experiments, IEEE Int. Conf. Robotics Autom. (ICRA), New Orleans (2004) pp. 2666–2672

    Google Scholar 

  21. C. Ott, A. Albu-Schäffer, A. Kugi, G. Hirzinger: On the passivity-based impedance control of flexible joint robots, IEEE Trans. Robotics 24(2), 416–429 (2008)

    Article  Google Scholar 

  22. A. De Luca, F. Flacco: A PD-type regulator with exact gravity cancellation for robots with flexible joints, IEEE Int. Conf. Robotics Autom. (ICRA), Shanghai (2011) pp. 317–323

    Google Scholar 

  23. R. Kelly, V. Santibanez: Global regulation of elastic joint robots based on energy shaping, IEEE Trans. Autom. Control 43(10), 1451–1456 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  24. J. Alvarez-Ramirez, I. Cervantes: PID regulation of robot manipulators with elastic joints, Asian J. Control 5(1), 32–38 (2003)

    Article  Google Scholar 

  25. A. De Luca, S. Panzieri: Learning gravity compensation in robots: Rigid arms, elastic joints, flexible links, Int. J. Adapt. Control Signal Process. 7(5), 417–433 (1993)

    Article  MATH  Google Scholar 

  26. A. Albu-Schäffer, G. Hirzinger: A globally stable state feedback controller for flexible joint robots, Adv. Robotics 15(8), 799–814 (2001)

    Article  Google Scholar 

  27. L.E. Pfeffer, O. Khatib, J. Hake: Joint torque sensory feedback in the control of a PUMA manipulator, IEEE Trans. Robotics Autom. 5(4), 418–425 (1989)

    Article  Google Scholar 

  28. M. Hashimoto, Y. Kiyosawa, R.P. Paul: A torque sensing technique for robots with harmonic drives, IEEE Trans. Robotics Autom. 9(1), 108–116 (1993)

    Article  Google Scholar 

  29. T. Lin, A.A. Goldenberg: Robust adaptive control of flexible joint robots with joint torque feedback, IEEE Int. Conf. Robotics Autom. (ICRA), Nagoya (1995) pp. 1229–1234

    Google Scholar 

  30. M.G. Forrest-Barlach, S.M. Babcock: Inverse dynamics position control of a compliant manipulator, IEEE J. Robotics Autom. 3(1), 75–83 (1987)

    Article  Google Scholar 

  31. K.P. Jankowski, H. Van Brussel: An approach to discrete inverse dynamics control of flexible-joint robots, IEEE Trans. Robotics Autom. 8(5), 651–658 (1992)

    Article  MATH  Google Scholar 

  32. W.M. Grimm: Robustness analysis of nonlinear decoupling for elastic-joint robots, IEEE Trans. Robotics Autom. 6(3), 373–377 (1990)

    Article  Google Scholar 

  33. A. De Luca, R. Farina, P. Lucibello: On the control of robots with visco-elastic joints, IEEE Int. Conf. Robotics Autom. (ICRA), Barcelona (2005) pp. 4297–4302

    Google Scholar 

  34. A. De Luca: Decoupling and feedback linearization of robots with mixed rigid/elastic joints, Int. J. Robust Nonlin. Control 8(11), 965–977 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  35. A. De Luca, B. Siciliano: Inversion-based nonlinear control of robot arms with flexible links, AIAA J. Guid. Control Dyn. 16(6), 1169–1176 (1993)

    Article  MATH  Google Scholar 

  36. A. De Luca: Dynamic control of robots with joint elasticity, IEEE Int. Conf. Robotics Autom. (ICRA), Philadelphia (1988) pp. 152–158

    Google Scholar 

  37. S. Nicosia, P. Tomei: On the feedback linearization of robots with elastic joints, 27th IEEE Conf. Decis. Control, Austin (1988) pp. 180–185

    Google Scholar 

  38. A. De Luca, P. Lucibello: A general algorithm for dynamic feedback linearization of robots with elastic joints, IEEE Int. Conf. Robotics Autom. (ICRA), Leuven (1998) pp. 504–510

    Google Scholar 

  39. J. Swevers, D. Torfs, M. Adams, J. De Schutter, H. Van Brussel: Comparison of control algorithms for flexible joint robots implemented on a KUKA IR 161/60 industrial robot, 5th Int. Conf. Adv. Robotics, Pisa (1991) pp. 120–125

    Google Scholar 

  40. K. Khorasani, P.V. Kokotovic: Feedback linearization of a flexible manipulator near its rigid body manifold, Syst. Control Lett. 6, 187–192 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  41. M.W. Spong, K. Khorasani, P.V. Kokotovic: An integral manifold approach to the feedback control of flexible joint robots, IEEE J. Robotics Autom. 3(4), 291–300 (1987)

    Article  Google Scholar 

  42. S. Nicosia, P. Tomei: Design of global tracking controllers for flexible-joint robots, J. Robotic Syst. 10(6), 835–846 (1993)

    Article  MATH  Google Scholar 

  43. B. Brogliato, R. Ortega, R. Lozano: Global tracking controllers for flexible-joint manipulators: A comparative study, Automatica 31(7), 941–956 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  44. M.W. Spong: Adaptive control of flexible joint manipulators, Syst. Control Lett. 13(1), 15–21 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  45. F. Ghorbel, J.Y. Hung, M.W. Spong: Adaptive control of flexible-joint manipulators, IEEE Control Syst. Mag. 9(7), 9–13 (1989)

    Article  Google Scholar 

  46. R. Lozano, B. Brogliato: Adaptive control of robot manipulators with flexible joints, IEEE Trans. Autom. Control 37(2), 174–181 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  47. H. Sira-Ramirez, M.W. Spong: Variable structure control of flexible joint manipulators, Int. Robotics Autom. 3(2), 57–64 (1988)

    Google Scholar 

  48. A. De Luca, G. Ulivi: Iterative learning control of robots with elastic joints, IEEE Int. Conf. Robotics Autom. (ICRA), Nice (1992) pp. 1920–1926

    Google Scholar 

  49. O. Dahl: Path constrained motion optimization for rigid and flexible joint robots, IEEE Int. Conf. Robotics Autom. (ICRA), Atlanta (1993) pp. 223–229

    Google Scholar 

  50. A. De Luca, L. Farina: Dynamic scaling of trajectories for robots with elastic joints, IEEE Int. Conf. Robotics Autom. (ICRA), Washington (2002) pp. 2436–2442

    Google Scholar 

  51. S. Haddadin, M. Özparpucu, A. Albu-Schäffer: Optimal control for maximizing potential energy in a variable stiffness joint, IEEE 51st Conf. Decis. Control, Maui (2012) pp. 1199–1206

    Google Scholar 

  52. M. Özparpucu, S. Haddadin: Optimal control of elastic joints with variable damping, 13th European Control Conf., Strasbourg (2014) pp. 2526–2533

    Google Scholar 

  53. S. Nicosia, P. Tomei, A. Tornambè: A nonlinear observer for elastic robots, IEEE J. Robotics Autom. 4(1), 45–52 (1988)

    Article  Google Scholar 

  54. S. Nicosia, P. Tomei: A method for the state estimation of elastic joint robots by global position measurements, Int. J. Adapt. Control Signal Process. 4(6), 475–486 (1990)

    Article  MATH  Google Scholar 

  55. A. De Luca, D. Schröder, M. Thümmel: An acceleration-based state observer for robot manipulators with elastic joints, IEEE Int. Conf. Robotics Autom. (ICRA), Rome (2007) pp. 3817–3823

    Google Scholar 

  56. M.W. Spong: On the force control problem for flexible joint manipulators, IEEE Trans. Autom. Control 34(1), 107–111 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  57. J.K. Mills: Stability and control of elastic-joint robotic manipulators during constrained-motion tasks, IEEE Trans. Robotics Autom. 8(1), 119–126 (1992)

    Article  Google Scholar 

  58. K.P. Jankowski, H.A. El Maraghy: Dynamic decoupling for hybrid control of rigid-/flexible-joint robots interacting with the environment, IEEE Trans. Robotics Autom. 8(5), 519–534 (1992)

    Article  Google Scholar 

  59. T. Lin, A.A. Goldenberg: A unified approach to motion and force control of flexible joint robots, IEEE Int. Conf. Robotics Autom. (ICRA), Minneapolis (1996) pp. 1115–1120

    Google Scholar 

  60. A. Albu-Schäffer, C. Ott, G. Hirzinger: A unified passivity-based control framework for position, torque and impedance control of flexible joint robots, Int. J. Robotics Res. 26(1), 23–39 (2007)

    Article  MATH  Google Scholar 

  61. W. Book, O. Maizza-Neto, D.E. Whitney: Feedback control of two beam, two joint systems with distributed flexibility, ASME J. Dyn. Syst. Meas. Control 97(4), 424–431 (1975)

    Article  Google Scholar 

  62. W. Book: Characterization of strength and stiffness constraints on manipulator control. In: Theory and Practice of Robots and Manipulators, ed. by W. Book (Elsevier, Amsterdam 1977) pp. 37–45

    Google Scholar 

  63. T.E. Alberts, W. Book, S. Dickerson: Experiments in augmenting active control of a flexible structure with passive damping, AIAA 24th Aerosp. Sci. Meet., Reno (1986)

    Google Scholar 

  64. T. Bailey, J.E. Hubbard Jr.: Distributed piezoelectric-polymer active vibration control of a cantilever beam, J. Guid. Control Dyn. 8(5), 605–611 (1985)

    Article  MATH  Google Scholar 

  65. W. Book, V. Sangveraphunsiri, S. Le: The Bracing Strategy for Robot Operation, Jt. IFToMM-CISM Symp. Theory Robots Manip. (RoManSy), Udine (1984)

    Google Scholar 

  66. W. Book: Analysis of massless elastic chains with servo controlled joints, ASME J. Dyn. Syst. Meas. Control 101(3), 187–192 (1979)

    Article  MATH  Google Scholar 

  67. E.C. Pestel, F.A. Leckie: Matrix Methods in Elastomechanics (McGraw-Hill, New York 1963)

    Google Scholar 

  68. R. Krauss: Transfer Matrix Modeling, Ph.D. Thesis (School of Mechanical Engineering, Georgia Institute of Technology, Atlanta 2006)

    Google Scholar 

  69. W.J. Book: Modeling, Design and Control of Flexible Manipulator Arms, Ph.D. Thesis (Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge 1974)

    Google Scholar 

  70. W. Book: Recursive lagrangian dynamics of flexible manipulators, Int. J. Robotics Res. 3(3), 87–106 (1984)

    Article  Google Scholar 

  71. W.J. Book, S.H. Lee: Vibration control of a large flexible manipulator by a small robotic arm, Proc. Am. Control Conf., Pittsburgh (1989) pp. 1377–1380

    Google Scholar 

  72. J. Lew, S.-M. Moon: A simple active damping control for compliant base manipulators, IEEE/ASME Trans. Mechatron. 2, 707–714 (1995)

    Google Scholar 

  73. W.J. Book, J.C. Loper: Inverse dynamics for commanding micromanipulator inertial forces to damp macromanipulator vibration, IEEE, Robot Soc. Int. Conf. Intell. Robots Syst., Kyongju (1999)

    Google Scholar 

  74. I. Sharf: Active damping of a large flexible manipulator with a short-reach robot, Proc. Am. Control Conf., Seattle (1995) pp. 3329–3333

    Google Scholar 

  75. L. George, W.J. Book: Inertial vibration damping control of a flexible base manipulator, IEEE/ASME Trans. Mechatron. 8(2), 268–271 (2003)

    Article  Google Scholar 

  76. J.F. Calvert, D.J. Gimpel: Method and apparatus for control of system output in response to system input, U.S. Patent 2801351 (1957)

    Google Scholar 

  77. O.J.M. Smith: Feedback Control Systems (McGraw-Hill, New York 1958)

    Google Scholar 

  78. N. Singer, W.P. Seering: Preshaping command inputs to reduce system vibration, ASME J. Dyn. Syst. Meas. Control 112(1), 76–82 (1990)

    Article  Google Scholar 

  79. W. Singhose, W. Seering, N. Singer: Residual vibration reduction using vector diagrams to generate shaped inputs, J. Mech. Des. 2, 654–659 (1994)

    Article  Google Scholar 

  80. D.P. Magee, W.J. Book: The Application of Input Shaping to a System with Varying Parameters, Proc. 1992 Japan-USA Symp. Flex. Autom., San Francisco (1992) pp. 519–526

    Google Scholar 

  81. D.P. Magee, W.J. Book: Optimal arbitrary time-delay (OAT) filter and method to minimize unwanted system dynamics, U.S. Patent 6078844 (2000)

    Google Scholar 

  82. S. Rhim, W.J. Book: Noise effect on time-domain adaptive command shaping methods for flexible manipulator control, IEEE Trans. Control Syst. Technol. 9(1), 84–92 (2001)

    Article  Google Scholar 

  83. D.-S. Kwon, W.J. Book: A time-domain inverse dynamic tracking control of a single-link flexible manipulator, J. Dyn. Syst. Meas. Control 116, 193–200 (1994)

    Article  MATH  Google Scholar 

  84. D.S. Kwon: An Inverse Dynamic Tracking Control for a Bracing Flexible Manipulator, Ph.D. Thesis (School of Mechanical Engineering, Georgia Institute of Technology, Atlanta 1991)

    Google Scholar 

  85. A. De Luca, G. Di Giovanni: Rest-to-rest motion of a one-link flexible arm, Proc. IEEE/ASME Int. Conf. Adv. Intell. Mechatron., Como (2001) pp. 923–928

    Google Scholar 

  86. A. De Luca, G. Di Giovanni: Rest-to-rest motion of a two-link robot with a flexible forearm, Proc. IEEE/ASME Int. Conf. Adv. Intell. Mechatron., Como (2001) pp. 929–935

    Google Scholar 

  87. A. De Luca, V. Caiano, D. Del Vescovo: Experiments on rest-to-rest motion of a flexible arm. In: Experimental Robotics VIII, Springer Tracts in Advanced Robotics, Vol. 5, ed. by B. Siciliano, P. Dario (Springer, Berlin, Heidelberg 2003) pp. 338–349

    Chapter  Google Scholar 

  88. R.M. Murray, M. Rathinam, W. Sluis: Differential flatness of mechanical control systems: A catalog of prototype systems, Proc. ASME Int. Mech. Engr. Congr., San Francisco (1995)

    Google Scholar 

  89. M. Fliess, P. Martin, P. Rouchon: Flatness and defect of nonlinear systems: Introductory theory and examples, Int. J. Control 61(6), 1327–1361 (1995)

    Article  MATH  Google Scholar 

  90. R.H. Cannon, E. Schmitz: Initial experiments on the end-point control of a flexible one-link robot, Int. J. Robotics Res. 3(3), 62–75 (1984)

    Article  Google Scholar 

  91. A. Truckenbrot: Modeling and control of flexible manipulator structures, Proc. 4th CISM-IFToMM Symp. Theory Robots Manip. (RoManSy), Zaborow (1981) pp. 90–101

    Google Scholar 

  92. G.G. Hastings, W.J. Book: Reconstruction and robust reduced-order observation of flexible variables, ASME Winter Ann. Meet., Anaheim (1986)

    Google Scholar 

  93. B.S. Yuan, J.D. Huggins, W.J. Book: Small motion experiments with a large flexible arm with strain feedback, Proceedings of the 1989 Am. Control Conf., Pittsburgh (1989) pp. 2091–2095

    Chapter  Google Scholar 

  94. D. Wang, M. Vidyasagar: Passive control of a stiff flexible link, Int. J. Robotics Res. 11, 572–578 (1992)

    Article  Google Scholar 

  95. K. Obergfell, W.J. Book: Control of flexible manipulators using vision and modal feedback, Proc. Int. Conf. Risk Assess. Manag. (ICRAM), Istanbul (1995)

    Google Scholar 

  96. B. Post: Robust State Estimation for the Control of Flexible Robotic Manipulators, Ph.D. Thesis (School of Mechanical Engineering, Georgia Institute of Technology, Atlanta 2013)

    Google Scholar 

  97. B. Walcott, S. Zak: State observation of nonlinear uncertain dynamical system, IEEE Trans. Autom. Control 32, 166–170 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  98. B. Walcott, S. Zak: Observation of dynamical systems in the presence of bounded nonlinearities/uncertainties, Proc. IEEE Conf. Dec. Control 25, 961–966 (1986)

    Google Scholar 

  99. N.G. Chalhoub, G.A. Kfoury: Development of a robust nonlinear observer for a single-link, flexible manipulator, Nonlin. Dyn. 39(3), 217–233 (2005)

    Article  MATH  Google Scholar 

  100. W.J. Book: Controlled motion in an elastic world, ASME J. Dyn. Syst. Meas. Control 2B, 252–261 (1993)

    Article  MATH  Google Scholar 

  101. C. Canudas-de-Wit, B. Siciliano, G. Bastin (Eds.): Theory of Robot Control (Springer, Berlin, Heidelberg 1996)

    MATH  Google Scholar 

  102. G. Hirzinger, N. Sporer, J. Butterfass, M. Grebenstein: Torque-controlled lightweight arms and articulated hands: Do we reach technological limits now?, Int. J. Robotics Res. 23(4/5), 331–340 (2004)

    Article  Google Scholar 

  103. Camotion Inc.: http://www.camotion.com (Camotion Inc., Atlanta 2007)

  104. B. Rooks: High speed delivery and low cost from new ABB packaging robot, Ind. Robotics Int. J. 26(4), 267–275 (1999)

    Article  Google Scholar 

  105. T. Trautt, E. Bayo: Inverse dynamics of non-minimum phase systems with non-zero initial conditions, Dyn. Control 7(1), 49–71 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  106. B. Siciliano, W. Book: A singular perturbation approach to control of lightweight flexible manipulators, Int. J. Robotics Res. 7(4), 79–90 (1988)

    Article  Google Scholar 

  107. F. Ghorbel, M.W. Spong: Singular perturbation model of robots with elastic joints and elastic links constrained by a rigid environment, J. Intell. Robotics Syst. 22(2), 143–152 (1998)

    Article  Google Scholar 

  108. J. Guldner, J. Shi, V. Utkin: Sliding Mode Control in Electromechanical Systems (Taylor, London 1999)

    Google Scholar 

  109. J.-H. Ryu, D.-S. Kwon, B. Hannaford: Control of a flexible manipulator with noncollocated feedback: Time-domain passivity approach, IEEE Trans. Robotics 20(4), 776–780 (2004)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer, Control, and Management Engineering, Sapienza University of Rome, Via Ariosto 25, 00185, Rome, Italy

    Alessandro De Luca

  2. G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 771 Ferst Drive, GA 30332-0405, Atlanta, USA

    Wayne J. Book

Authors
  1. Alessandro De Luca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wayne J. Book
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alessandro De Luca .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Naples Federico II, Via Claudio 21, 80125, Naples, Italy

    Bruno Siciliano

  2. Department of Computer Sciences, Artificial Intelligence Laboratory, Stanford University, 450 Serra Mall, CA 94305, Stanford, USA

    Oussama Khatib

Video-References

Video-References

:

Cartesian impedance control with damping off available from http://handbookofrobotics.org/view-chapter/11/videodetails/133

:

Cartesian impedance control with damping on available from http://handbookofrobotics.org/view-chapter/11/videodetails/134

:

Control laws for a single-link arm with an elastic joint available from http://handbookofrobotics.org/view-chapter/11/videodetails/135

:

Feedforward/feedback law for path tracking with a KUKA KR15/2 robot available from http://handbookofrobotics.org/view-chapter/11/videodetails/136

:

Trajectory generation and control for a KUKA IR 161/60 robot available from http://handbookofrobotics.org/view-chapter/11/videodetails/770

:

Input shaping on a lightweight gantry robot available from http://handbookofrobotics.org/view-chapter/11/videodetails/777

:

Inverse dynamics control for a flexible link available from http://handbookofrobotics.org/view-chapter/11/videodetails/778

:

Rest-to-rest motion for a flexible link available from http://handbookofrobotics.org/view-chapter/11/videodetails/779

:

PID response to impulse in presence of link flexibility available from http://handbookofrobotics.org/view-chapter/11/videodetails/780

:

State feedback response to impulse in presence of link flexibility available from http://handbookofrobotics.org/view-chapter/11/videodetails/781

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

De Luca, A., Book, W.J. (2016). Robots with Flexible Elements. In: Siciliano, B., Khatib, O. (eds) Springer Handbook of Robotics. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-32552-1_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-32552-1_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32550-7

  • Online ISBN: 978-3-319-32552-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation