Extending Flat Motion Planning to Non-flat Systems. Experiments on Aircraft Models Using Maple

Abstract: Aircraft models may be considered as flat if one neglects some terms associated to aerodynamics. Computational experiments in Maple show that in some cases a suitably designed feed-back allows to follow such trajectories, when applied to the non-flat model. However some maneuvers may be hard or even impossible to achieve with this flat approximation. In this paper, we propose an iterated process to compute a more achievable trajectory, starting from the flat reference trajectory. More precisely, the unknown neglected terms in the flat model are iteratively re-evaluated using the values obtained at the previous step. This process may be interpreted as a new trajectory parametrization, using an infinite number of derivatives, a property that may be called \emph{generalized flatness}. We illustrate the pertinence of this approach in flight conditions of increasing difficulties, from single engine flight, to aileron roll.