Delay and Stiffness Dependent Polytopic LPV Modelling of Impedance Controlled Robot Interaction

  • József KutiEmail author
  • Péter Galambos
  • Péter  Baranyi
Part of the Studies in Computational Intelligence book series (SCI, volume 530)


Impedance/admittance control algorithms are considered as key technologies in human–robot interaction and other fields of advanced robotics where complex physical interaction plays role. In this chapter, we utilize a Tensor Product (TP) Model Transformation based method to derive the delay and stiffness dependent polytopic LPV representation of the impedance controlled physical interaction. The applied transformation method is feasible with bounded delay that is the non-linear function of the environmental stiffness. Thus, the ideal transformation space is non-rectangular that makes it improper for the TP model transformation. We propose a dimensionless parametrisation to define a rectangular grid upon witch the transformation is viable. The resulted model form is promptly appropriate for the modern multi-objective LMI based control design techniques.


Interaction robotics LPV/qLPV modelling Impedance control Admittance control Time delay systems Telemanipulation Haptics 



The research was supported by the Hungarian National Development Agency, (ERC-HU-09-1-2009-0004 MTASZTAK) (OMFB-01677/2009) and the “Talent care and cultivation in the scientific workshops of BME” under the grant TÁMOP-4.2.2.B-10/1—2010-0009.


  1. 1.
    Gil, J.J., Sanchez, E., Hulin, T., Preusche, C., Hirzinger, G.: Stability boundary for haptic rendering: Influence of damping and delay. J. Comput. Inf. Sci. Eng. 9(1), 1–8 (2009)Google Scholar
  2. 2.
    Galambos, P., Baranyi, P.: Representing the model of impedance controlled robot interaction with feedback delay in polytopic lpv form: Tp model transformation based approach. Acta Polytech. Hung. 10(1), 139–157 (2013)Google Scholar
  3. 3.
    Baranyi, P.: TP model transformation as a way to LMI based controller design. IEEE Trans. Industr. Electron. 51(2), 387–400 (2004)Google Scholar
  4. 4.
    Baranyi, P.: Convex hull generation methods for polytopic representations of LPV models, in Applied Machine Intelligence and Informatics, SAMI 2009. 7th International Symposium on IEEE 2009, pp. 69–74 (2009)Google Scholar
  5. 5.
    Baranyi, P.: Tensor-product model-based control of two-dimensional aeroelastic system. J. Guidance Control Dyn. 29(2), 391–400 (2005)Google Scholar
  6. 6.
    Baranyi, P.: Output feedback control of two-dimensional aeroelastic system. J. Guidance Control Dyn. 29(3), 762–767 (2005)Google Scholar
  7. 7.
    Lathauwer, L.D., Moor, B.D., Vandewalle, J.: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21(4), 1253–1278 (2000)Google Scholar
  8. 8.
    Gróf, P., Baranyi, P., Korondi, P.: Convex hull manipulation based control performance optimisation. WSEAS Trans. Syst. Control 5, 691–700 (2010)Google Scholar
  9. 9.
    Baranyi, P., Szeidl, L., Várlaki, P., Yam, Y.: Definition of the HOSVD-based canonical form of polytopic dynamic models. In: 3rd International Conference on Mechatronics (ICM 2006), pp. 660–665. Budapest, Hungary, 3–5 July 2006Google Scholar
  10. 10.
    Szeidl, L., Várlaki, P.: HOSVD based canonical form for polytopic models of dynamic systems. J. Adv. Comput. Intell. Intell. Inf. 13(1), 52–60 (2009)Google Scholar
  11. 11.
    Kolonic, F., Poljugan, A., Petrovic, I.: Tensor product model transformation-based controller design for gantry crane control system—an application approach. Acta Polytech. Hung. 3(4), 95–112 (2006)Google Scholar
  12. 12.
    Precup, R., Dioanca, L., Petriu, E.M., Radac, M., Preitl, S., Dragos, C.: Tensor product-based real-time control of the liquid levels in a three tank system. In: 2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Montreal, QC, Canada, Accessecd July 2010, pp. 768–773
  13. 13.
    Szabó, Z., Gáspár, P., Bokor, J.: A novel control-oriented multi-affine qLPV modeling framework. In: 18th Mediterranean Conference on Control Automation (MED), June 2010, pp. 1019–1024 (2010)Google Scholar
  14. 14.
    Ilea, S., Matusko, J., Kolonic, F.: Tensor product transformation based speed control of permanent magnet synchronous motor drives. In: 17th International Conference on Electrical Drives and Power Electronics, EDPE 2011 (5th Joint Slovak-Croatian Conference), 2011Google Scholar
  15. 15.
    Precup, R., Dragos, C., Preitl, S., Radac, M., Petriu, E.M.: Novel tensor product models for automatic transmission system control. IEEE Syst. J. 6(3), 488–498 (2012)Google Scholar
  16. 16.
    Galambos, P.: Stability boundary of impedance controlled robots: effect of stiffness, damping, friction and delay. In: Proceedings of the 15th WSEAS International Conference on Systems. World Scientific and Engineering Academy and Society (WSEAS), pp. 247–252. (2011)Google Scholar
  17. 17.
    TP Toolbox for matlab, (2011)

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • József Kuti
    • 1
    Email author
  • Péter Galambos
    • 1
  • Péter  Baranyi
    • 1
  1. 1.Institute for Computer Science and ControlHungarian Academy of SciencesBudapestHungary

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