The next meeting of the MAX team seminar will be on Tuesday, May 10. We will welcome François Ollivier for a talk on Generalized flatness and motion planning for aircraft models.

Abstract: If one neglects the forces created by controls, an aircraft is modeled by a flat system. First, one uses a feedback to compensate model errors and keep the trajectory of the full non flat system close to the trajectory computed for the flat approximation. In a second time, the values of the controls provided by the flat approximation are used in the full model for better precision and the process is iterated, which provides a very precise motion planning for the full model. Some examples are provided to illustrate the possibilities of a Maple package. This new approach is called generalized flatness. The provided parametrization depends on an infinite number of flat outputs, which comforts a conjecture claiming that all controllable systems are flat if one allows parametrization depending on an infinite number of derivatives. On should notice that the necessary flatness conditions of Sluis and Rouchon express the fact that the order of the parametrization is finite. In the linear case, one may provide some theoretical interpretation.