View source for Configuration Flatness of Lagrangian Systems Underactuated by One Control

{{HTDB paper
| authors = Muruhan Rathinam and Richard M. Murray
| title = Configuration Flatness of Lagrangian Systems Underactuated by One Control
| source = <em>SIAM J. Control and Optimization</em>, 36(1):164-179
| year = 1998
| type = Conference paper
| funding = NSF
| url = http://www.cds.caltech.edu/~murray/preprints/rm96-cdc.pdf
| 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 but not on
velocity 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. 
| flags = 
| tag = rm96-cdc
| id = 1996g
}}