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How humans fly

Published online by Cambridge University Press:  03 June 2013

Alain Ajami ,
Jean-Paul Gauthier ,
Thibault Maillot  and
Ulysse Serres
Alain Ajami
Affiliation:
Université du Sud-Toulon-Var, LSIS, UMR CNRS 7296, B.P 20132, 83957 La Garde Cedex, France. alain.ajami@univ-tln.fr; jean-paul.gauthier@univ-tln.fr; thibault.maillot@univ-tln.fr
Jean-Paul Gauthier
Affiliation:
Université du Sud-Toulon-Var, LSIS, UMR CNRS 7296, B.P 20132, 83957 La Garde Cedex, France. alain.ajami@univ-tln.fr; jean-paul.gauthier@univ-tln.fr; thibault.maillot@univ-tln.fr INRIA GECO Project 
Thibault Maillot
Affiliation:
Université du Sud-Toulon-Var, LSIS, UMR CNRS 7296, B.P 20132, 83957 La Garde Cedex, France. alain.ajami@univ-tln.fr; jean-paul.gauthier@univ-tln.fr; thibault.maillot@univ-tln.fr
Ulysse Serres
Affiliation:
Université de Lyon, 69 622 Lyon, France Université Lyon 1, Villeurbanne; LAGEP, UMR CNRS 5007, 43 bd du 11 novembre 1918, 69100 Villeurbanne, France; ulysse.serres@univ-lyon1.fr
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Abstract

This paper is devoted to the general problem of reconstructing the cost from the observation of trajectories, in a problem of optimal control. It is motivated by the following applied problem, concerning HALE drones: one would like them to decide by themselves for their trajectories, and to behave at least as a good human pilot. This applied question is very similar to the problem of determining what is minimized in human locomotion. These starting points are the reasons for the particular classes of control systems and of costs under consideration. To summarize, our conclusion is that in general, inside these classes, three experiments visiting the same values of the control are needed to reconstruct the cost, and two experiments are in general not enough. The method is constructive.

The proof of these results is mostly based upon the Thom’s transversality theory.

This study is partly supported by FUI AAP9 project SHARE, and by ANR Project GCM, program “blanche”, project number NT09-504490.

Keywords

Inverse optimal controlanthropomorphic controltransversality
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 4 , October 2013 , pp. 1030 - 1054
Copyright
© EDP Sciences, SMAI, 2013

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