Comptes Rendus
Optimal control theory and Newton–Euler formalism for Cosserat beam theory
[Commande optimale et formalisme de Newton–Euler pour les poutres de Cosserat]
Comptes Rendus. Mécanique, Volume 334 (2006) no. 3, pp. 170-175.

Un formalisme de Newton–Euler pour les théories de poutres de Cosserat est obtenu de manière purement déductive, grâce à une analogie avec la théorie de la commande optimale. La méthode repose sur l'utilisation conjointe du principe de la moindre contrainte de Gauss, des équations d'Appell et de la théorie de la commande optimale, de façon analogue à un travail précédent sur le formalisme de Newton–Euler bien connu pour les systèmes multicorps.

A Newton–Euler formalism is derived for Cosserat beam theory in a purely deductive manner, thanks to an analogy with optimal control theory. The method relies upon joint use of Gauss least constraint principle, Appell's equations and optimal control theory, that was used successfully in a previous work for the classical case of discrete Newton–Euler backward and forward recursions of multibody systems.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2006.01.006
Keywords: Dynamics of rigid or flexible systems, Newton–Euler, Gauss principle, Appell's equations, Optimal control
Mot clés : Dynamique des systèmes rigides ou flexibles, Newton–Euler, principe de Gauss, équations d'Appell, Commande optimale

Georges Le Vey 1

1 IRCCyN-UMR CNRS 6597, École des mines de Nantes, 4, rue A. Kastler, 44307 Nantes cedex 1, France
@article{CRMECA_2006__334_3_170_0,
     author = {Georges Le Vey},
     title = {Optimal control theory and {Newton{\textendash}Euler} formalism for {Cosserat} beam theory},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {170--175},
     publisher = {Elsevier},
     volume = {334},
     number = {3},
     year = {2006},
     doi = {10.1016/j.crme.2006.01.006},
     language = {en},
}
TY  - JOUR
AU  - Georges Le Vey
TI  - Optimal control theory and Newton–Euler formalism for Cosserat beam theory
JO  - Comptes Rendus. Mécanique
PY  - 2006
SP  - 170
EP  - 175
VL  - 334
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crme.2006.01.006
LA  - en
ID  - CRMECA_2006__334_3_170_0
ER  - 
%0 Journal Article
%A Georges Le Vey
%T Optimal control theory and Newton–Euler formalism for Cosserat beam theory
%J Comptes Rendus. Mécanique
%D 2006
%P 170-175
%V 334
%N 3
%I Elsevier
%R 10.1016/j.crme.2006.01.006
%G en
%F CRMECA_2006__334_3_170_0
Georges Le Vey. Optimal control theory and Newton–Euler formalism for Cosserat beam theory. Comptes Rendus. Mécanique, Volume 334 (2006) no. 3, pp. 170-175. doi : 10.1016/j.crme.2006.01.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.01.006/

[1] G. Rodriguez Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics, IEEE Trans. Robotics and Automation, Volume 3 (1987) no. 6, pp. 624-639

[2] G.M.T. d'Eleuterio; C.J. Damaren The relationship between recursive multibody dynamics and discrete-time optimal control, IEEE Trans. Robotics and Automation, Volume 7 (1991) no. 6, pp. 743-749

[3] G. Le Vey, The Newton–Euler formalism for general multibody systems as the solution of an optimal control problem, Technical Report 05/4/AUTO, IRCCyN/Ecole des Mines de Nantes, 2005

[4] F. Boyer, M. Porez, W. Khalil, Macro-continuous computed torque algorithm for a 3d eel-like robot, IEEE Trans. Robotics, 2006, in press

[5] P. Appell Traité de Mécanique Rationnelle, Gauthier–Villars, 1921

[6] C.F. Gauss, Journal de Crelle, t. IV, 1829

[7] G. Le Vey, Hyperredundant manipulators, continuous Newton–Euler algorithms and optimal control theory, Technical Report 05/3/AUTO, IRCCyN/Ecole des Mines de Nantes, 2005

[8] A.E. Bryson; Y.C. Ho Applied Optimal Control, Hemisphere Pub. Corp., 1975 (revised printing)

[9] K.E. Brenan; S.L. Campbell; L.R. Petzold Numerical Solution of Initial-Value Problems in Differential/Algebraic Equations, North-Holland, Amsterdam, 1989

Cité par Sources :

This work was supported by the French CNRS ROBEA program.

Commentaires - Politique