Maya mendez, Mauro Eduardo (2007) Sensor-based control of nonholonomic robots. PhD thesis Informatique Temps Réel, Automatique et Robotique, ENSMP - CMA Centre de Mathématiques Appliquées, ENSMP.

Official URL: http://tel.archives-ouvertes.fr/tel-00142742/fr/

Alternative Locations: http://tel.archives-ouvertes.fr/tel-00142742/fr/, http://www-sop.inria.fr/dias/Theses/phd-227.pdf

Abstract

This thesis concerns the design of sensor-based control laws for nonholonomic robots, based on the transverse function control approach, and the robustness analysis of these control laws. The control of nonhlonomic robots has been a very active research field for the last fifteen years. Even so, when one wishes to stabilize the full robot pose, the robustness of control laws with respect to state estimation errors (which typically arise in practice due to sensor model errors) remains an open problem. The main obtacles to this work comme from this problem. The results obtained in this work can be classified into two main contributions. The first one concerns the obtention of methodologies for synthesizing control laws from sensor signals. Several methods are proposed and in particular we devise a control scheme directly in the signal space by analogy with manipulator control techniques. The second and more fundamental part of this work concerns the analysis of the robustness of the proposed control schemes with respect to sensor model errors. Theoretical stability results have been obtained and validated by simulations and experiments.

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Table of content

Table des matières

Introduction 1

1 État de l’art et modélisation

1.1 Modélisation des robots mobiles non holonomes

1.1.1 Rappels sur la notion de nonholonomie

1.1.2 La contrainte de roulement sans glissement

1.1.3 Modèle cinématique d’un véhicule de type unicycle

1.1.4 Modèle cinématique d’un robot de type voiture

1.1.5 Modèle cinématique de la pose et propriétés

1.2 Propriétés du modèle cinématique

1.2.1 Commandabilité

1.2.2 Stabilisabilité

1.2.3 Propriétés de symétrie et modèles d’erreur

1.3 Commande par retour d’état des robots non holonomes

1.3.1 Définitions

1.3.2 Stabilisation de configurations fixes

1.3.3 Stabilisation de trajectoires admissibles non stationnaires

1.3.4 Stabilisation pratique de trajectoires générales

1.4 Rappels sur la commande référencée capteur des robots manipulateurs

1.4.1 Rappel sur le formalisme de commande par fonction de tâche

1.4.2 Synthèse de commandes dans les différents espaces

1.5 Conclusion

2 Commande référencée capteur via une estimation de la pose

2.1 Robustesse vis-à-vis de dynamiques non modélisées

2.2 Conditions suffisantes de stabilité vis-à-vis de l’estimation de la pose

2.3 Quelques techniques pour l’estimation de la pose

2.4 Résultats de simulation pour un capteur visuel

2.4.1 Estimation linéaire de la pose

2.4.2 Estimations non linéaires

2.Fonctions Transverses Généralisées

3.2.5 Résultats expérimentaux

4.2.6 Conclusions

5.3 Synthèse de commande dans l’espace capteur

6.3.1 Synthèse de stabilisateurs pratiques dans les coordonnées signal

7.3.2 Estimations de termes intervenant dans l’expression de la commande

8.3.3 Résultats de simulation pour un capteur visuel

9.3.3.1 Estimations basées sur des approximations linéaires

10.3.3.2 Estimations basées sur des approximations non-linéaires

11.3.3.3 Fonction transverse généralisée

12.3.4 Conclusion

13.4 Conclusion et perspectives

14.4.1 Conclusion

15.4.2 Perspectives

16.A Preuves

17.A.1 Preuve du Lemme 1 (p. 48)

18.A.2 Preuve de la Proposition 6 (p. 49)

19.A.3 Preuve de la Proposition 7 (p. 51)

20.A.4 Preuve des Propositions 9 et 10 (pp. 52, 53)

21.A.5 Preuve du Lemme 2 (p. 79)

22.A.6 Preuve de la Proposition 12 (p. 81)

23.A.7 Preuve du lemme 3 (p. 83)

24.B Reconstruction géométrique de la pose d’une caméra (p. 71)

25.C Relations dans les groupes de Lie

26.C.1 Équivalences dans les groupes de Lie

27.C.2 Relations cinématiques sur les groupes de Lie

28.Bibliographie

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