Rathinam, Muruhan and Murray, Richard M. (1996) Configuration Flatness of Lagrangian Systems Underactuated by One Control. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1996.018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.
| Item Type: | Report or Paper (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. |
| Group: | Control and Dynamical Systems Technical Reports |
| Subject Keywords: | Differential Flatness, Nonlinear Control, Lagrangian Mechanics. |
| Record Number: | CaltechCDSTR:1996.018 |
| 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 |
| Usage Policy: | You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format. |
| ID Code: | 28122 |
| Collection: | CaltechCDSTR |
| Deposited By: | Imported from CaltechCDSTR |
| Deposited On: | 14 Dec 2007 |
| Last Modified: | 26 Dec 2012 14:31 |
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