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

TL;DR

This paper introduces a method to extend flat motion planning to non-flat aircraft models by iteratively refining trajectories, enabling more accurate and feasible maneuvers in complex flight conditions.

Contribution

It proposes a generalized flatness approach using iterative re-evaluation of neglected aerodynamic terms for improved trajectory planning.

Findings

Iterative process improves trajectory feasibility for complex maneuvers.

Method successfully applied to various aircraft flight conditions.

Enhanced trajectory accuracy demonstrated in simulations.

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.