Position Control via Force Feedback in the Port-Hamiltonian Framework

Authors

Mauricio Muñoz-Arias, Jacquelien M. A. Scherpen, Daniel A. Dirksz

Abstract

In this chapter, position control strategies via force feedback are presented for standard mechanical systems in the port-Hamiltonian framework. The presented control strategies require a set of coordinate transformations, since force feedback in the port-Hamiltonian framework is not straightforward. With the coordinate transformations force feedback can be realized while preserving the port-Hamiltonian structure. The port-Hamiltonian formalism offers a modeling framework with a clear physical structure and other properties that can often be exploited for control design purposes, which is why we believe it is important to preserve the structure. The proposed control strategies offer an alternative solution to position control with more tuning freedom and exploit knowledge of the system dynamics.

Citation

• ISBN: 9783319303567
• Publisher: Springer International Publishing
• DOI: 10.1007/978-3-319-30357-4_9

BibTeX

@inbook{Mu_oz_Arias_2016,
  title={{Position Control via Force Feedback in the Port-Hamiltonian Framework}},
  ISBN={9783319303574},
  ISSN={1610-7411},
  DOI={10.1007/978-3-319-30357-4_9},
  booktitle={{Nonlinear Systems}},
  publisher={Springer International Publishing},
  author={Muñoz-Arias, Mauricio and Scherpen, Jacquelien M. A. and Dirksz, Daniel A.},
  year={2016},
  pages={181--207}
}

Download the bib file

References

• Andersson S, Söderberg A, Björklund S (2007) Friction models for sliding dry, boundary and mixed lubricated contacts. Tribology International 40(4):580–587. https://doi.org/10.1016/j.triboint.2005.11.014 – 10.1016/j.triboint.2005.11.014
• Bol, M.: Force And Position Control of the Philips Experimental Robot Arm in a Energy-Based Setting. University of Groningen, Groningen (2012)
• de Wit CC, Siciliano B, Bastin G (eds) (1996) Theory of Robot Control. Springer London, London – 10.1007/978-1-4471-1501-4
• Dirksz, D.A., Scherpen, J.M.A.: Power-based control: canonical coordinate transformations. Integr. Adapt. Control Autom. 48(6), 1046–1056 (2012)
• Donaire A, Junco S (2009) On the addition of integral action to port-controlled Hamiltonian systems. Automatica 45(8):1910–1916. https://doi.org/10.1016/j.automatica.2009.04.006 – 10.1016/j.automatica.2009.04.006
• Duindam, V., Macchelli, A., Stramigioli, S., Bruyninckx, H. (eds.): Modeling and Control of Complex Physical Systems: The Port-Hamiltonian Approach. Springer, Berlin (2009)
• Fujimoto K, Sugie T (2001) Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters 42(3):217–227. https://doi.org/10.1016/s0167-6911(00)00091-8 – 10.1016/s0167-6911(00)00091-8
• Fujimoto K, Sakurama K, Sugie T (2003) Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica 39(12):2059–2069. https://doi.org/10.1016/j.automatica.2003.07.005 – 10.1016/j.automatica.2003.07.005
• Gómez-Estern F, Van der Schaft AJ (2004) Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems. European Journal of Control 10(5):451–468. https://doi.org/10.3166/ejc.10.451-468 – 10.3166/ejc.10.451-468
• Gorinevsky, D., Formalsky, A., Scheiner, A.: Force Control of Robotics Systems. CRC Press LLC, Moscow (1997)
• Khalil, H.: Nonlinear Systems, 2nd edn. Prentice-Hall, New York (2001)
• Koop, F.: Trajectory Tracking Control of the Philips Experimental Robot Arm in the Port-Hamiltonian Framework. University of Groningen, Groningen (2014)
• Maschke, B.M., van der Schaft, A.J.: Port-controlled hamiltonian systems: modeling origins and system-theoretic properties. IN: Procedings of the IFAC Symposium on Nonlinear Control Systems, pp. 282–288. Bordeaux, France (1992)
• Maschke B, Ortega R, Van Der Schaft AJ (2000) Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Trans Automat Contr 45(8):1498–1502. https://doi.org/10.1109/9.871758 – 10.1109/9.871758
• Muñoz-Arias M, Scherpen JMA, Dirksz DA (2012) A Class of Standard Mechanical System with Force Feedback in the port-Hamiltonian Framework. IFAC Proceedings Volumes 45(19):90–95. https://doi.org/10.3182/20120829-3-it-4022.00038 – 10.3182/20120829-3-it-4022.00038
• Muñoz-Arias M, Scherpen JMA, Dirksz DA (2012) A Class of Standard Mechanical System with Force Feedback in the port-Hamiltonian Framework. IFAC Proceedings Volumes 45(19):90–95. https://doi.org/10.3182/20120829-3-it-4022.00038 – 10.3182/20120829-3-it-4022.00038
• Munoz-Arias M, Scherpen JMA, Dirksz DA (2013) Position control via force feedback for a class of standard mechanical systems in the port-Hamiltonian framework. In: 52nd IEEE Conference on Decision and Control. IEEE, pp 1622–1627 – 10.1109/cdc.2013.6760114
• Murray, R., Li, Z., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)
• Ortega R, Loría A, Nicklasson PJ, Sira-Ramírez H (1998) Passivity-based Control of Euler-Lagrange Systems. Springer London, London – 10.1007/978-1-4471-3603-3
• Ortega R, van der Schaft A, Maschke B, Escobar G (2002) Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38(4):585–596. https://doi.org/10.1016/s0005-1098(01)00278-3 – 10.1016/s0005-1098(01)00278-3
• Ortega R, Spong MW, Gomez-Estern F, Blankenstein G (2002) Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans Automat Contr 47(8):1218–1233. https://doi.org/10.1109/tac.2002.800770 – 10.1109/tac.2002.800770
• Ortega R, Romero JG (2012) Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances. Systems & Control Letters 61(1):11–17. https://doi.org/10.1016/j.sysconle.2011.09.015 – 10.1016/j.sysconle.2011.09.015
• Rijs, R., Beekmans, R., Izmit, S., Bemelmans, D.: Philips Experimental Robot Arm: User Instructor Manual, Version 1.1. Koninklijke Philips Electronics N.V., Eindhoven (2010)
• Siciliano B, Khatib O (eds) (2008) Springer Handbook of Robotics. Springer Berlin Heidelberg, Berlin, Heidelberg – 10.1007/978-3-540-30301-5
• Spong, M., Hutchinson, S., Vidjasagar, M.: Robot Modeling and Control. Wiley, Hoboken (2006)
• van der Schaft, A.J.: \(L_{2}\) L 2 -Gain and Passivity Techniques in Nonlinear Control: Lecture Notes in Control and Information Sciences 218. Springer, London (1999)
• Viola G, Ortega R, Banavar R, Acosta JA, Astolfi A (2007) Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes. IEEE Trans Automat Contr 52(6):1093–1099. https://doi.org/10.1109/tac.2007.899064 – 10.1109/tac.2007.899064