Control of the Toycopter Using a Flat Approximation

Philippe Mullhaupt (1) , Balasubrahmanyan Srinivasan (2) , Jean Lévine (3) , Dominique Bonvin (4)

1 Laboratoire d'Automatique
2 Department of Chemical Engineering
3 CAS - Centre Automatique et Systèmes
4 Laboratoire d'Automatique

This paper considers a helicopter-like setup called the Toycopter. Its particularities reside first in the fact that the toycopter motion is constrained to remain on a sphere and second in the use of a variable rotational speed of the propellers to vary the propeller thrust. A complete model using Lagrangian mechanics is derived. The Toycopter is shown to be nondifferentially flat. Nevertheless, by neglecting specific cross-couplings, a differentially flat approximation can be generated and used for controller design, provided the controller gains do not exceed certain bounds that are given explicitly. The achieved performance is better than with standard linear controllers, especially during large displacements that induce strong nonlinear gyroscopical forces. The results are illustrated both in simulation and experimentally on the setup.

Mots clés: Flat systems; Lagrange mechanics; nonlinear control; underactuated mechanical system

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

Philippe Mullhaupt, Balasubrahmanyan Srinivasan, Jean Lévine, Dominique Bonvin. Control of the Toycopter Using a Flat Approximation. IEEE Transactions on Control Systems Technology, 2008, 16 (5), pp.882-896. ⟨10.1109/TCST.2007.916333⟩. ⟨hal-00492743⟩