Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T13:22:53.949Z Has data issue: false hasContentIssue false
  • English
  • Français

Closed form Newton–Euler dynamic model of flexible manipulators

Published online by Cambridge University Press:  17 November 2015

Luca Bascetta Open the ORCID record for Luca Bascetta [Opens in a new window] ,
Gianni Ferretti  and
Bruno Scaglioni
Luca Bascetta
Affiliation:
Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria Piazza Leonardo da Vinci 32, 20133, Milano, Italy. E-mail: luca.bascetta@polimi.it
Gianni Ferretti*
Affiliation:
Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria Piazza Leonardo da Vinci 32, 20133, Milano, Italy. E-mail: luca.bascetta@polimi.it
Bruno Scaglioni
Affiliation:
Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria Piazza Leonardo da Vinci 32, 20133, Milano, Italy. E-mail: luca.bascetta@polimi.it MUSP Lab, Via Tirotti 9, Le Mose, 29122 Piacenza, Italy. E-mail: bruno.scaglioni@polimi.it
*
*Corresponding author. E-mail: gianni.ferretti@polimi.it
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, a closed-form dynamic model of flexible manipulators is developed, based on the Newton–Euler formulation of motion equations of flexible links and on the adoption of the spatial vector notation. The proposed model accounts for two main innovations with respect to the state of the art: it is obtained in closed form with respect to the joints and modal coordinates (including the quadratic velocity terms) and motion equations of the whole manipulator can be computed for any arbitrary shape of the links and any possible link cardinality starting from the output of several commercial (finite element analysis) FEA codes. The Newton–Euler formulation of motion equations in terms of the joint and elastic variables greatly improves the simulation performances and makes the model suitable for real-time control and active vibration damping. The model has been compared with literature benchmarks obtained by the classical multibody approach and further validated by comparison with experiments collected on an experimental manipulator.

Keywords

Flexible manipulatorsFlexible multibody systemsRoboticsDynamicsSimulation
Type
Articles
Information
Robotica , Volume 35 , Issue 5 , May 2017 , pp. 1006 - 1030
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Albu-Schäffer, A., Haddadin, S., Ott, C., Stemmer, A., Wimböck, T. and Hirzinger, G., “The DLR lightweight robot: design and control concepts for robots in human environments,” Ind. Robot: Int. J. 34 (5), 376–385 (2007).CrossRefGoogle Scholar
2. Baumgartner, E., Bonitz, R., Melko, J., Shiraishi, L. and Leger, P., “The Mars Exploration Rover Instrument Positioning System,” Aerospace Conference, 2005 IEEE, Big Sky, MT, USA (2005) pp. 1–19.Google Scholar
3. Filipović, M., Potkonjak, V. and Vukobatović, M., “Elasticity in humanoid robotics,” Scientific Technical Review, Military Technical Institute, Belgrade, vol. 1 (2007) pp. 24–33.Google Scholar
4. Book, W. J., “Recursive Lagrangian dynamics of flexible manipulator arms,” The Int. J. Robot. Res. 3 (3), 87–101 (1984).CrossRefGoogle Scholar
5. De Luca, A. and Siciliano, B., “Closed-form dynamic model of planar multilink lightweight robots,” IEEE Trans. Syst. Man Cybern. 21 (4), 826–839 (1991).CrossRefGoogle Scholar
6. Li, C. and Sankar, T. S., “Systematic methods for efficient modeling and dynamics computation of flexible robot manipulators,” IEEE Trans. Syst. Man Cybern. 23 (1), 77–95 (1993).CrossRefGoogle Scholar
7. Chen, W., “Dynamic modeling of multi-link flexible robotic manipulators,” Comput. Struct. 79 (2), 183–195 (2001).CrossRefGoogle Scholar
8. Zhang, D. and Zhou, S., “Dynamic analysis of flexible-link and flexible-joint robots,” Appl. Math. Mech. 27 (5), 695–704 (2006).CrossRefGoogle Scholar
9. Qingxuan, J., Xiaodong, Z., Hanxu, S. and Ming, C., “Active Control of Space Flexible-Joint/Flexible-Link Manipulator,” IEEE Conference on Robotics, Automation and Mechatronics, Chengdu, China (2008) pp. 812–818.Google Scholar
10. Chen, W., “Dynamic modeling of multi-link flexible robotic manipulators,” Comput. Struct. 79 (2), 183–195 (2001).CrossRefGoogle Scholar
11. Sadler, J. and Yang, Z., “A comprehensive study of modal characteristics of a cylindrical manipulator with both link and joint flexibility,” Mech. Mach. Theory 32 (8), 941–956 (1997).CrossRefGoogle Scholar
12. Wang, X. and Mills, J. K., “Dynamic modeling of a flexible-link planar parallel platform using a substructuring approach,” Mech. Mach. Theory 41 (6), 671–687 (2006).CrossRefGoogle Scholar
13. Rognant, M., Courteille, E. and Maurine, P., “A systematic procedure for the elastodynamic modeling and identification of robot manipulators,” IEEE Trans. Robot. 26 (6), 1085–1093 (2010).CrossRefGoogle Scholar
14. Theodore, R. J. and Ghosal, A., “Comparison of the assumed modes and finite element models for flexible multilink manipulators,” Int. J. Robot. Res. 14 (2), 91–111 (1995).CrossRefGoogle Scholar
15. Heckmann, A., “On the choice of boundary conditions for mode shapes in flexible multibody systems,” Multibody Syst. Dyn. 23 (2), 141–163 (2009).CrossRefGoogle Scholar
16. MSC Software Corporation, ADAMS/Flex – Theory of Flexible Bodies (2003).Google Scholar
17. Shihabudheen, K. and Jacob, J., “Composite Control of Flexible Link Flexible Joint Manipulator,” Annual IEEE India Conference (INDICON), Kochi, Kerala, India (2012) pp. 827–831.Google Scholar
18. Kirćanski, M., Vukobratović, M., Kirćanski, N. and Timčenko, A., “A new program package for the generation of efficient manipulator kinematic and dynamic equations in symbolic form,” Robotica 6 (04), 311–318 (1988).CrossRefGoogle Scholar
19. Mohan, A. and Saha, S., “A recursive, numerically stable, and efficient simulation algorithm for serial robots with flexible links,” Multibody Syst. Dyn. 21 (1), 1–35 (2009).CrossRefGoogle Scholar
20. Hollerbach, J., “A recursive Lagrangian formulation of maniputator dynamics and a comparative study of dynamics formulation complexity,” IEEE Trans. Syst. Man Cybern. 10 (11), 730–736 (1980).CrossRefGoogle Scholar
21. Shabana, A. A. and Yakoub, R. Y., “Three dimensional absolute nodal coordinate formulation for beam elements: Theory,” J. Mech. Des. 123 (4), 606–613 (2000).CrossRefGoogle Scholar
22. Shabana, A. A. and Yakoub, R. Y., “Three dimensional absolute nodal coordinate formulation for beam elements: Implementation and applications,” Journal of Mechanical Design 123 (4), 614–621 (2000).Google Scholar
23. Shabana, A. and Schwertassek, R., “Equivalence of the floating frame of reference approach and finite element formulations,” Int. J. Non-Linear Mech. 33 (3), 417–432 (1998).CrossRefGoogle Scholar
24. Pfeiffer, F. and Gebler, B., “A Multistage-Approach to the Dynamics and Control of Elastic Robots,” Proceedings IEEE International Conference on Robotics and Automation, Philadelphia, PA, USA, vol. 1 (1988) pp. 2–8.Google Scholar
25. Pedersen, N. and Pedersen, M., “A direct derivation of the equations of motion for 3d-flexible mechanical systems,” Int. J. Numer. Methods Eng. 41 (4), 697–719 (1998).3.0.CO;2-Y>CrossRefGoogle Scholar
26. Wasfy, T., “Modeling Contact/Impact of Flexible Manipulators with a Fixed Rigid Surface, Proceedings IEEE International Conference on Robotics and Automation, Nagoya, Japan, vol. 1 (1995) pp. 621–626.Google Scholar
27. Hermle, M. and Eberhard, P., “Control and parameter optimization of flexible robots,” Mech. Struct. Mach. 28 (2–3), 137–168, (2000).CrossRefGoogle Scholar
28. Dignath, F., Breuninger, C., Eberhard, P. and Kübler, L., “Optimization of mechatronic systems using the software package NEWOPT/AIMS,” Multibody Syst. Dyn. 13 (1), 85–100 (2005).CrossRefGoogle Scholar
29. Reiner, M., Otter, M. and Ulbrich, H., “Modeling and Feed-forward Control of Structural Elastic Robots,” In: ICNAAM: International Conference of Numerical Analysis and Applied Mathematics (Simos, T. E., Psihoyios, G. and Tsitouras, C., eds.) vol. 1281 (AIP, Rhodes (Greece), 2010) pp. 378–381.Google Scholar
30. Dassault Systemés, Dassault Systèmes Simulia Corp. Abaqus Analysis Users Manual, Version 6.9. (2009).Google Scholar
31. Ansys Corp., Ansys Release 11.0 Documentation (2009).Google Scholar
32. MSC Software, MSC/NASTRAN Reference Manual, Version 68 - Lahey, Miller, et al. (1994).Google Scholar
33. Craig, R. R. and Bampton, M. C. C., “Coupling of substructures for dynamic analyses,” AIAA J. 6 (7), 1313–1319 (1968).CrossRefGoogle Scholar
34. Koutsovasilis, P. and Beitelschmidt, M., “Comparison of model reduction techniques for large mechanical systems,” Multibody Syst. Dyn. 20 (2), 111–128 (2008).CrossRefGoogle Scholar
35. Lehner, M. and Eberhard, P., “A two-step approach for model reduction in flexible multibody dynamics,” Multibody Syst. Dyn. 17, 157–176 (2007).CrossRefGoogle Scholar
36. Fehr, J. and Eberhard, P., “Simulation process of flexible multibody systems with non–modal model order reduction techniques,” Multibody Syst. Dyn. 25, 313–334 (2011).CrossRefGoogle Scholar
37. Nowakowski, C., Fehr, J., Fischer, M. and Eberhard, P., “Model Order Reduction in Elastic Multibody Systems using the Floating Frame of Reference Formulation,” Proceedings of the 7th Vienna International Conference on Mathematical Modelling – MATHMOD, Vienna, Austria, vol. 7, part 1 (2012) pp. 40–48.Google Scholar
38. Featherstone, R., Rigid Body Dynamics Algorithms (Springer, New York, 2008).CrossRefGoogle Scholar
39. Featherstone, R. and Orin, D., Springer Handbook of Robotics (Springer, Berlin, 2008) Ch. Dynamics, pp. 35–65.Google Scholar
40. Fijany, A. and Featherstone, R., “A new factorization of the mass matrix for optimal serial and parallel calculation of multibody dynamics,” Multibody Syst. Dyn. 29, 169–187 (2013).CrossRefGoogle Scholar
41. Boyer, F. and Coiffet, P., “Generalization of Newton-Euler model for flexible manipulators,” J. Robot. Syst. 13 (1), 11–24 (1996).3.0.CO;2-Y>CrossRefGoogle Scholar
42. Shabana, A. A., “Dynamics of flexible bodies using generalized newton-euler equations,” J. Dyn. Syst. Meas. Control 112 (3), 496–50 (1990).CrossRefGoogle Scholar
43. Lee, K., Wang, Y. and Chirikjian, G. S., “O (n) mass matrix inversion for serial manipulators and polypeptide chains using lie derivatives,” Robotica 25 (06), 739–750 (2007).CrossRefGoogle Scholar
44. Schiavo, F., Viganò, L. and Ferretti, G., “Object-oriented modelling of flexible beams,” Multibody Syst. Dyn. 15 (3), 263–286 (2006).CrossRefGoogle Scholar
45. Malzahn, J. and Bertram, T., A Multi-Elastic-Link Robot Identification Dataset (Institute of Control Theory and Systems Engineering, (RST), TU Dortmund, Germany, 2014).Google Scholar
46. Denavit, J. and Hartenberg, R. S., “A kinematic notation for lower-pair mechanisms based on matrices,” Trans. ASME E J. Appl. Mech. 22, 215–221 (1955).CrossRefGoogle Scholar
47. Meirovitch, L., Analytical Methods in Vibration (Macmillan Publishing, New York, 1967).Google Scholar
48. Shabana, A. A., Dynamics of Multibody Systems (Cambridge University Press, New York, 1998).Google Scholar
49. Schwertassek, R. and Wallrapp, O., Dynamik flexibler Mehrkörpersysteme (Vieweg, Wiesbaden, 1999).CrossRefGoogle Scholar
50. Bascetta, L. and Rocco, P., “Modelling flexible manipulators with motors at the joints,” Math. Comput. Modelling Dyn. Syst. 8 (2), 157–183 (2002).CrossRefGoogle Scholar
51. Escalona, J., Hussien, H., and Shabana, A., “Application of the absolute nodal coordinate formulation to multibody system dynamics,” J. Sound Vib. 214 (5), 833–851 (1998).CrossRefGoogle Scholar
52. Malzahn, R. F. R. and Bertram, J. T., “Dynamics Identification of a Damped Multi Elastic Link Robot Arm under Gravity,” IEEE International Conference on Robotics and Automation, Honkong, China (2014), pp. 2170–2175.Google Scholar