CONFIGURATION FLATNESS OF LAGRANGIAN SYSTEMS UNDERACTUATED BY ONE CONTROL

Lagrangian control systems that are differentially flat with flat outp uts that depend only on configuration variables are said to be configu ration flat. We provide a complete characterization of configuration f latness for systems with n degrees of freedom and n-1 controls whose r ange of control forces only depends on configuration and whose Lagrang ian has the form of kinetic energy minus potential. The method present ed allows us to determine if such a system is configuration flat and, if so, provides a constructive method for finding all possible configu ration flat outputs. Our characterization relates configuration flatne ss to Riemannian geometry. We illustrate the method with two examples.