Configuration Flatness of Lagrangian Systems Underactuated by One Control

Rathinam, Muruhan and Murray, Richard M. (1996) Configuration Flatness of Lagrangian Systems Underactuated by One Control. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechCDSTR:1996.018]

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Abstract

Lagrangian control systems that are differentially flat with flat outputs that only depend on configuration variables are said to be configuration flat. We provide a complete characterisation of configuration flatness for systems with n degrees of freedom and n - 1 controls whose range of control forces only depends on configuration and whose Lagrangian has the form of kinetic energy minus potential. The method presented allows us to determine if such a system is configuration flat and, if so provides a constructive method for finding all possible configuration flat outputs. Our characterisation relates configuration flatness to Riemannian geometry. We illustrate the method by two examples.

EPrint Type:	Monograph (Technical Report)
Additional Information:	This is a revised version of CDS 96-006. http://resolver.caltech.edu/CaltechCDSTR:1996.CIT-CDS-96-006 Research supported in part by NSF grant CMS-9502224 and AFOSR grant F49620-95-1-0419. It is a pleasure to thank Jerrold Marsden for valuable comments and Naomi Leonard for important corrections on the underwater vehicle example. The authors would also like to thank the reviewers for the useful comments and corrections.
Uncontrolled Keywords:	Differential Flatness, Nonlinear Control, Lagrangian Mechanics.
Subjects:	All Records
ID Code:	151
Deposited By:	Arun Sannuti
Deposited On:	14 December 2007
Unique Identifier:	CaltechCDSTR:1996.018
Official Persistent URL:	http://resolver.caltech.edu/CaltechCDSTR:1996.018
Official Citation:	Rathinam, Muruhan and Murray Richard M. (1996) Configuration Flatness of Lagrangian Systems Underactuated by One Control Technical Report. California Institute of Technology, Pasadena, CA. http://resolver.caltech.edu/CaltechCDSTR:1996.018
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