Differential Flatness for Constrained Systems

Differential flatness is a characterization of specific nonlinear systems that allow a linear description in a suitable equivalent space. The equivalence does not necessarily preserve the dimension of the underlying manifold that describes the nonlinear systems. Among complicated systems that present challenging control issues, one can mention cranes, unmanned aerial vehicles, kinematically constrained (nonholonomic) chained systems. These systems are, on the one hand, differentially flat, but they can also be considered as trivial systems in a larger space of coordinates that is quadratically constrained. This point of view leads to the study of trivial ambient spaces that, once restricted on a submanifold, generate complicated dynamics. We characterize mathematically the type of reduction that occurs in the context of differential flatness.  

  Graf and P. MüllhauptApplication of Legendrian Foliations in Differential Flatness ProblemsIEEE CDC 2012, Hawaii, 2012.

B. Graf and P. Müllhaupt. Nonlinear Analysis of a Coaxial Micro-Helicopter with Bell Stabilizer Barsubmitted to Journal of the American Helicopter Society, 2011.

B. Graf and P. MüllhauptFeedback Linearizability and Flatness in Restricted Control Systems18th IFAC World Congress, Milano, Italy, 2011.

P. Mullhaupt and B. GrafModeling and Flatness of Rigid and Flexible Cable Suspended Underactuated Robots2010 IEEE International Conference on Control Applications Part of 2010 IEEE Multi-Conference on Systems and Control, Yokohama, Japan,IEEE International Conference on Control Applications, 2010.

P. Mullhaupt and B. GrafModeling and Flatness of Rigid and Flexible Cable Suspended Underactuated RobotsIEEE Multi-Conference on Systems and Control, Yokohama, Japan.