Abstract:We study the set of intrinsic singularities of flat affine systems with n − 1 controls and n states using the notion of Lie-Bäcklund atlas, previously introduced by the authors. For this purpose, we prove two easily computable sufficient conditions to construct flat outputs as a set of independent first integrals of distributions of vector fields, the first one in a generic case, namely in a neighborhood of a point where the n − 1 control vector fields are independent, and the second one at a degenerate point … Show more
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 generalized flatness. We illustrate the pertinence of this approach in flight conditions of increasing difficulties, from single engine flight, to aileron roll.
CCS CONCEPTS• Computing methodologies → Symbolic and algebraic algorithms;
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