Model Inversion of a Two Degrees of Freedom Linearized PUMA from Bicausal Bond Graphs
A bond graph model of a two degrees of freedom
PUMA is described. System inversion gives the system input
required to generate a given system output. In order to get the system
inversion of the PUMA manipulator, a linearization of the nonlinear
bond graph is obtained. Hence, the bicausality of the linearized bond
graph of the PUMA manipulator is applied. Thus, the bicausal bond
graph provides a systematic way of generating the equations of the
system inversion. Simulation results to verify the calculated input for
a given output are shown.
[1] Mark W. Spong and M. Vidyasagar, "Robot Dynamics and Control",
John Wiley & Sons, 1989.
[2] V. Damic and J. Montgomery, "Mechatronics by Bond Graphs",
Springer, 2003.
[3] Dean C. Karnopp, Donald L. Margolis and Ronald C. Rosenberg,
"System Dynamics Modeling and Simulation of Mechatronic Systems",
John Wiley & Sons, 2000.
[4] P. E. Wellstead, "Physical System Modelling", Academic Press,
London, 1979.
[5] C. Sueur and G. Dauphin-Tanguy, "Bond graph approach for structural
analysis of MIMO linear systems", Journal of the Franklin Institute, Vol.
328, No. 1, pp. 55-70, 1991.
[6] Peter Gawthrop and L. Smith, "Metamodelling", Prentice-Hall, 1996.
[7] M. J. L. Tiernego, J. J. Dixhoorn, "Three Axis Platform Simulation:
Bond Graph and Lagrangian Approach", Journal of the Franklin
Institute, Vol. 308, No. 1/2, pp. 157-171, 1985.
[8] A. Zeid, Ch. H. Chung, "Bond Graph Modelling of Multibody System: a
Library of Three dimensional Joints", Journal of the Franklin .Institute,
Vol. 329, No. 4, pp. 605-636, 1992.
[9] D. Karnopp, "Understanding Multibody Dynamics using Bond Graph
Representations", Journal of the Franklin Institute, Vol. 334B, No. 4,
pp. 631-642, 1997.
[10] L. M. Silverman, "Inversion of multivariable linear systems", IEEE
Trans. Automat. Contr., Vol. AC-14, No. 3, pp. 270-276, June, 1969.
[11] P. J. Gawthrop, "Bicausal bond graphs", in Proceedings of the 1995
International Conference on Bond Graph Modelling and Simulation:
ICBGM'95, pp. 83-88, 1995.
[12] R. Fotsu Ngwompo, S. Scavarda and D. Thomasset, "Inversion of
Linear Time-invariant SISO Systems Modelled by Bond Graph", Journal
of the Franklin Institute, Vol. 333(B), No. 2, pp. 157-174, 1996.
[13] Gilberto Gonzalez-A and R. Galindo, "A Linearization Procedure for a
Class of Nonlinear Systems Based on Bond Graph", Proceedings of the
International Mediterranean Modeling Multiconference, pp. 77-82,
2005.
[1] Mark W. Spong and M. Vidyasagar, "Robot Dynamics and Control",
John Wiley & Sons, 1989.
[2] V. Damic and J. Montgomery, "Mechatronics by Bond Graphs",
Springer, 2003.
[3] Dean C. Karnopp, Donald L. Margolis and Ronald C. Rosenberg,
"System Dynamics Modeling and Simulation of Mechatronic Systems",
John Wiley & Sons, 2000.
[4] P. E. Wellstead, "Physical System Modelling", Academic Press,
London, 1979.
[5] C. Sueur and G. Dauphin-Tanguy, "Bond graph approach for structural
analysis of MIMO linear systems", Journal of the Franklin Institute, Vol.
328, No. 1, pp. 55-70, 1991.
[6] Peter Gawthrop and L. Smith, "Metamodelling", Prentice-Hall, 1996.
[7] M. J. L. Tiernego, J. J. Dixhoorn, "Three Axis Platform Simulation:
Bond Graph and Lagrangian Approach", Journal of the Franklin
Institute, Vol. 308, No. 1/2, pp. 157-171, 1985.
[8] A. Zeid, Ch. H. Chung, "Bond Graph Modelling of Multibody System: a
Library of Three dimensional Joints", Journal of the Franklin .Institute,
Vol. 329, No. 4, pp. 605-636, 1992.
[9] D. Karnopp, "Understanding Multibody Dynamics using Bond Graph
Representations", Journal of the Franklin Institute, Vol. 334B, No. 4,
pp. 631-642, 1997.
[10] L. M. Silverman, "Inversion of multivariable linear systems", IEEE
Trans. Automat. Contr., Vol. AC-14, No. 3, pp. 270-276, June, 1969.
[11] P. J. Gawthrop, "Bicausal bond graphs", in Proceedings of the 1995
International Conference on Bond Graph Modelling and Simulation:
ICBGM'95, pp. 83-88, 1995.
[12] R. Fotsu Ngwompo, S. Scavarda and D. Thomasset, "Inversion of
Linear Time-invariant SISO Systems Modelled by Bond Graph", Journal
of the Franklin Institute, Vol. 333(B), No. 2, pp. 157-174, 1996.
[13] Gilberto Gonzalez-A and R. Galindo, "A Linearization Procedure for a
Class of Nonlinear Systems Based on Bond Graph", Proceedings of the
International Mediterranean Modeling Multiconference, pp. 77-82,
2005.
@article{"International Journal of Electrical, Electronic and Communication Sciences:64118", author = "Gilberto Gonzalez-A and Ignacio Rodríguez- A. and Dunia Nuñez-P", title = "Model Inversion of a Two Degrees of Freedom Linearized PUMA from Bicausal Bond Graphs", abstract = "A bond graph model of a two degrees of freedom
PUMA is described. System inversion gives the system input
required to generate a given system output. In order to get the system
inversion of the PUMA manipulator, a linearization of the nonlinear
bond graph is obtained. Hence, the bicausality of the linearized bond
graph of the PUMA manipulator is applied. Thus, the bicausal bond
graph provides a systematic way of generating the equations of the
system inversion. Simulation results to verify the calculated input for
a given output are shown.", keywords = "Bond graph, system inversion, bicausality, PUMA
manipulator", volume = "6", number = "9", pages = "1062-6", }