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A dynamical simulation facility for hybrid systems

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Hybrid Systems (HS 1992, HS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 736))

Abstract

This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the dynamical system are crucial since they provide the link between a natural mathematical formulation of a problem and the correct application of standard numerical algorithms. We describe a partial implementation of the design methodology and use this simulation tool for a specific control problem in robotics as an illustration of the utility of the approach for practical applications.

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References

  1. Back, A., Guckenheimer, G., Myers, M., Wicklin, F. and P. Worfolk, ‘dstool: Computer Assisted Exploration of Dynamical Systems,’ AMS Notices, April, 1992.

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  2. Guckenheimer, J., Myers, M.R., Wicklin, F.J. and P.A. Worfolk, ‘dstool: A Dynamical System Toolkit with an Interactive Graphical Interface', Center for Applied Mathematics, Cornell University, Ithaca, NY, 1991.

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  3. Koditschek, D.E. and M. Buhler, ‘Analysis of a Simplified Hopping Robot,’ to appear in the International Journal of Robotics Research, 1991.

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  4. Raibert, M.H., Legged Robots That Balance, MIT Press, Cambridge, Mass., 1986.

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  5. Raibert, M.H. and H.B. Brown, Jr. ‘Experiments in Balance with a 2D One-Legged Hopping Machine,’ ASME Journal for Dynamical Systems, Measurement and Control, Vol. 106, 1984, pps. 75–81.

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  6. Vakakis, A.F. and J.W. Burdick, ‘Chaotic Motions in the Dynamics of a Hopping Robot,’ Procedings of the IEEE International Conferance on Robotics and Automation, Cincinnati, OH, 1990, pps. 1464–469.

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Author information

Authors and Affiliations

  1. Center for Applied Mathematics, Cornell University, 14850, Ithaca, New York

    Allen Back, John Guckenheimer & Mark Myers

Authors
  1. Allen Back
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  2. John Guckenheimer
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  3. Mark Myers
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Editor information

Robert L. Grossman Anil Nerode Anders P. Ravn Hans Rischel

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© 1993 Springer-Verlag Berlin Heidelberg

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Back, A., Guckenheimer, J., Myers, M. (1993). A dynamical simulation facility for hybrid systems. In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds) Hybrid Systems. HS HS 1992 1991. Lecture Notes in Computer Science, vol 736. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57318-6_32

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  • DOI: https://doi.org/10.1007/3-540-57318-6_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57318-0

  • Online ISBN: 978-3-540-48060-0

  • eBook Packages: Springer Book Archive

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