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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. [email protected]; [email protected]; [email protected]
Jean-Paul Gauthier
Affiliation:
Université du Sud-Toulon-Var, LSIS, UMR CNRS 7296, B.P 20132, 83957 La Garde Cedex, France. [email protected]; [email protected]; [email protected] INRIA GECO Project 
Thibault Maillot
Affiliation:
Université du Sud-Toulon-Var, LSIS, UMR CNRS 7296, B.P 20132, 83957 La Garde Cedex, France. [email protected]; [email protected]; [email protected]
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; [email protected]
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Abstract

This paper is devoted to the general problem of reconstructing the cost from theobservation of trajectories, in a problem of optimal control. It is motivated by thefollowing applied problem, concerning HALE drones: one would like them to decide bythemselves for their trajectories, and to behave at least as a good human pilot. Thisapplied question is very similar to the problem of determining what is minimized in humanlocomotion. These starting points are the reasons for the particular classes of controlsystems 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 neededto reconstruct the cost, and two experiments are in general not enough. The method isconstructive.

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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