Titre du document / Document title

Symmetry and reduction for coordinated rigid bodies

Auteur(s) / Author(s)

HANSSMANN Heinz ⁽¹⁾ ; LEONARD Naomi Ehrich ⁽²⁾ ; SMITH Troy R. ⁽²⁾ ;

Affiliation(s) du ou des auteurs / Author(s) Affiliation(s)

⁽¹⁾ Institut für Reine und Angewandte Mathematik, RWTH Aachen, 52056 Aachen, ALLEMAGNE
⁽²⁾ Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, ETATS-UNIS

Résumé / Abstract

Motivated by interest in the collective behavior of autonomous agents, we lay foundations for a study of networks of rigid bodies and, specifically, the problem of aligning orientation and controlling relative position across the group. Our main result is the reduction of the (networked) system for the case of two individuals coupled by control inputs that depend only on relative configuration. We use reduction theory based on semi-direct products, yielding Poisson spaces that enable efficient formulation of control laws. We apply these reduction results to satellite and underwater vehicle dynamics, proving stability of coordinated behaviors such as two underwater vehicles moving at constant speed with their orientations stably aligned.

Revue / Journal Title

European journal of control   ISSN 0947-3580 

Source / Source

2006, vol. 12, n^o2, pp. 176-194 [19 page(s) (article)] (20 ref.)

Langue / Language

Anglais

Editeur / Publisher

Lavoisier, Cachan, FRANCE  (1995) (Revue)

Mots-clés anglais / English Keywords

Hamiltonian mechanics ; Hamiltonian system ; Solid dynamic ; Moving load ; Vehicle stability ; Submarine vehicle ; Satellite ; Orientation ; Collective process ; Rigid bodies ; Coordination ; N body system ; Dynamic stability ; Vehicle dynamics ; Control program ;

Mots-clés français / French Keywords

Mécanique hamiltonienne ; Système hamiltonien ; Dynamique solide ; Charge mobile ; Stabilité véhicule ; Engin sous marin ; Satellite ; Orientation ; Phénomène collectif ; Corps rigide ; Coordination ; Système n corps ; Stabilité dynamique ; Dynamique véhicule ; Programme commande ;

Mots-clés espagnols / Spanish Keywords

Mecánica hamiltoniana ; Sistema hamiltoniano ; Dinàmico sólido ; Carga móvil ; Estabilidad vehículo ; Artefacto submarino ; Satélite ; Orientación ; Fenómeno colectivo ; Coordinación ; Sistema n cuerpos ; Estabilidad dinámica ; Dinámica vehículo ; Programa mando ;

Mots-clés d'auteur / Author Keywords

Coordinated control ; multi-body dynamics ; Hamiltonian systems ; rigid bodies ; stability ; reduction ;

Localisation / Location

INIST-CNRS, Cote INIST : 26357, 35400014235163.0040