Relevant bibliographies by topics / Systeme holonome

Academic literature on the topic 'Systeme holonome'

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Published: 6 July 2023

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Journal articles on the topic "Systeme holonome"

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LEVI, MARK. "GEOMETRY OF VIBRATIONAL STABILIZATION AND SOME APPLICATIONS." International Journal of Bifurcation and Chaos 15, no. 09 (September 2005): 2747–56. http://dx.doi.org/10.1142/s0218127405013745.

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This paper gives a short overview of various applications of stabilization by vibration, along with the exposition of the geometrical mechanism of this phenomenon. More specifically, the following observation is described: a rapidly vibrated holonomic system can be approximated by a certain associated nonholonomic system. It turns out that effective forces in some rapidly vibrated (holonomic) systems are the constraint forces of an associated auxiliary nonholonomic constraint. In particular, we review a simple but remarkable connection between the curvature of the pursuit curve (the tractrix) on the one hand and the effective force on the pendulum with vibrating support. The latter observation is a part of a recently discovered close relationship between two standard classical problems in mechanics: (1) the pendulum whose suspension point executes fast periodic motion along a given curve, and (2) the Chaplygin skate (known also as the Prytz planimeter, or the "bicycle"). The former is holonomic, the latter is nonholonomic. The holonomy of the skate shows up in the effective motion of the pendulum. This relationship between the pendulum with a twirled pivot and the Chaplygin skate has somewhat unexpected physical manifestations, such as the drift of suspended particles in acoustic waves. Finally, a higher-dimensional example of "geodesic motion" on a vibrating surface is described.
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Ito, Masahide. "Motion Planning of a Second-Order Nonholonomic Chained Form System Based on Holonomy Extraction." Electronics 8, no. 11 (November 12, 2019): 1337. http://dx.doi.org/10.3390/electronics8111337.

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This paper proposes a motion planning algorithm for dynamic nonholonomic systems represented in a second-order chained form. The proposed approach focuses on the so-called holonomy resulting from a kind of motion that traverses a closed path in a reduced configuration space of the system. According to the author’s literature survey, control approaches that make explicit use of holonomy exist for kinematic nonholonomic systems but does not exist for dynamic nonholonomic systems. However, the second-order chained form system is controllable. Also, the structure of the second-order chained form system analogizes with the one of the first-order chained form for kinematic nonholonomic systems. These survey and perspectives brought a hypothesis that there exists a specific control strategy for extracting holonomy of the second-order chained form system to the author. To verify this hypothesis, this paper shows that the holonomy of the second-order chained form system can be extracted by combining two appropriate pairs of sinusoidal inputs. Then, based on such holonomy extraction, a motion planning algorithm is constructed. Furthermore, the effectiveness is demonstrated through some simulations including an application to an underactuated manipulator.
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Cheon, Taksu, Atushi Tanaka, and Sang Wook Kim. "Exotic quantum holonomy in Hamiltonian systems." Physics Letters A 374, no. 2 (December 2009): 144–49. http://dx.doi.org/10.1016/j.physleta.2009.10.064.

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Stanchenko, S. V. "Non-holonomic Chaplygin systems." Journal of Applied Mathematics and Mechanics 53, no. 1 (January 1989): 11–17. http://dx.doi.org/10.1016/0021-8928(89)90126-3.

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Agrawal, S. K. "Multibody Dynamics: A Formulation Using Kane’s Method and Dual Vectors." Journal of Mechanical Design 115, no. 4 (December 1, 1993): 833–38. http://dx.doi.org/10.1115/1.2919276.

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This paper proposes a formulation based on Kane’s method to form the dynamic equations of motion of multibody systems using dual vectors. Both holonomic and nonholonomic systems are considered in this formulation. An example of a holonomic and a nonholonomic system is worked out in detail using this formulation. This algorithm is shown to be advantageous for a class of holonomic systems which has cylindrical joints.
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WU, SIYE. "GEOMETRIC PHASES IN THE QUANTISATION OF BOSONS AND FERMIONS." Journal of the Australian Mathematical Society 90, no. 2 (April 2011): 221–35. http://dx.doi.org/10.1017/s1446788711001236.

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AbstractAfter reviewing geometric quantisation of linear bosonic and fermionic systems, we study the holonomy of the projectively flat connection on the bundle of Hilbert spaces over the space of compatible complex structures and relate it to the Maslov index and its various generalisations. We also consider bosonic and fermionic harmonic oscillators parametrised by compatible complex structures and compare Berry’s phase with the above holonomy.
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Asadov, Hikmat, Sevindj Abdullayeva, and Ulviya Tarverdiyeva. "Questions on Optimization of Izomorphic-Holonomic Information-Measuring Systems." Известия высших учебных заведений. Электромеханика 63, no. 6 (2020): 51–56. http://dx.doi.org/10.17213/0136-3360-2020-6-51-56.

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Questions on optimization of isomorphic-holonomic information –measuring systems, characterized by in-ternal holomorphic relation are considered. It is shown that isomorphic-holonomic property of information measuring and mechatronic systems make it possible to carry out optimization of them transforming of this task to Lagrange task where the target functional (Lagrange functional) is sum of initial target functional and integral of function of holonomic relation function with limitation imposed on it multiplied by Lagrange multi-plier. It is proved that if searched for function of holonomic relation with imposed limitation condition pro-vides for minimum (maximum) of target functional and if inegrant of initial target functional can be linearized so the function is always exists and is featured as inversed to link function upon which maximum (minimum) can be achieved.
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Niu, Xiaoji, You Li, Quan Zhang, Yahao Cheng, and Chuang Shi. "Observability Analysis of Non-Holonomic Constraints for Land-Vehicle Navigation Systems." Journal of Global Positioning Systems 11, no. 1 (June 30, 2012): 80–88. http://dx.doi.org/10.5081/jgps.11.1.80.

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Ortiz-Bobadilla, L., E. Rosales-González, and S. M. Voronin. "Extended Holonomy and Topological Invariance of Vanishing Holonomy Group." Journal of Dynamical and Control Systems 14, no. 3 (July 2008): 299–358. http://dx.doi.org/10.1007/s10883-008-9041-0.

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Cai, J. L., and F. X. Mei. "Conformal Invariance and Conserved Quantity of the Higher-Order Holonomic Systems by Lie Point Transformation." Journal of Mechanics 28, no. 3 (August 9, 2012): 589–96. http://dx.doi.org/10.1017/jmech.2012.67.

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AbstractIn this paper, the conformal invariance and conserved quantities for higher-order holonomic systems are studied. Firstly, by establishing the differential equation of motion for the systems and introducing a one-parameter infinitesimal transformation group together with its infinitesimal generator vector, the determining equation of conformal invariance for the systems are provided, and the conformal factors expression are deduced. Secondly, the relation between conformal invariance and the Lie symmetry by the infinitesimal one-parameter point transformation group for the higher-order holonomic systems are deduced. Thirdly, the conserved quantities of the systems are derived using the structure equation satisfied by the gauge function. Lastly, an example of a higher-order holonomic mechanical system is discussed to illustrate these results.
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Dissertations / Theses on the topic "Systeme holonome"

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Rebahi, Yacine. "Irrégularité des D-modules algébriques holonomes." Université Joseph Fourier (Grenoble ; 1971-2015), 1996. http://www.theses.fr/1996GRE10205.

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Ce travail est consacre a l'etude de l'irregularite des systemes differentiels algebriques holonomes. Nous demontrons que les complexes de solutions de type exponentiel, associes a ces systemes, sont a cohomologie constructible et nous calculons leur caracteristique d'euler poincare. Pour cela, et dans le cas d'un fibre de rang un, nous utilisons un passage a l'infini qui nous permet de nous ramener a des resultats connus pour des solutions formelles de croissance appropriee pour des systemes analytiques holonomes. D'autre part, si nous microlocalisons nos constructions, nous obtenons des resultats analogues dans le cas d'un fibre de rang quelconque
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Abdel, Gadir Basil. "Analyse microlocale des systèmes différentiels holonomes." Grenoble 1, 1992. http://www.theses.fr/1992GRE10071.

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Nous nous placerons dans le contexte analytique-complexe. Les systemes differentiels holonomes traduisent algebriquement les systemes differentiels lineaires surdetermines maximaux, et ils generalisent les fibres vectoriels a connexion integrale. La question de leur classification (jusqu'ici limitee au cas des systemes a singularite reguliere et a celui d'une variable) a ete entreprise par un certain nombre d'auteurs, parmi lesquels il faut notamment citer m. Kashiwara et b. Malgrange. Dans cette direction nous contribuons aux resultats lies a la description microlocale (i. E. Locale sur l'espace cotangent) des systemes differentiels holonomes a singularite arbitraire. Nous generalisons un theoreme de finitude de b. Malgrange en utilisant un lemme de m. Kashiwara et t. Kawai affirmant que le germe du support d'un systeme microdifferentiel holonome possede (apres une transformation symplectique convenable) une position generique. Le theoreme de finitude assure qu'un tel systeme microdifferentiel admet un reseau microdifferentiel de type fini sur l'anneau commutatif des fonctions holomorphes. A l'aide de ce resultat, nous demontrons que ces systemes microdifferentiels holonomes sont en fait des systemes differentiels holonomes. En outre, nous formulons et nous etudions la transformation de fourier-deligne-katz-laumon-malgrange pour les systemes differentiels holonomes ainsi trouves. Ici, le resultat interessant est que l'etude de tels objets se ramene a celle des connexions meromorphes etudiee par p. Deligne et b. Malgrange
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Gloukhikh, Ioulia. "Systèmes mécaniques réversibles en dynamique holonome et non-holonome des corps solides rigides." Phd thesis, Ecole des Ponts ParisTech, 2003. http://tel.archives-ouvertes.fr/tel-00005724.

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Cette thèse a pour objet détudier des problèmes réversibles dans la dynamique holonome et non-holonome du corps solide. Dans la thèse sont analysés les rotations permanentes, les oscillations et les mouvements rotatifs dun ellipsoïde homogène pesant sur un plan absolument rugueux et dun satellite sur une orbite elliptique ; le problème de la stabilité de ces mouvements est également étudié.
Les recherches présentées dans cette thèse démontrent lefficacité des méthodes fondées sur les propriétés de réversibilité des systèmes mécaniques, propriété dont lusage est essentiel dans tous les résultats obtenus :
Létude de la stabilité des rotations autour de laxe vertical de lellipsoïde pesant homogène sur le plan horizontal.
Létude de la stabilité des mouvements de roulement sans glissement dun ellipsoïde creux pesant le long de la ligne droite sur le plan horizontal : conclusion sur linstabilité causée par la résonance paramétrique et conditions nécessaires de stabilité, obtenues par calcul numérique.
Lexpression détaillée du coefficient de résonance en cas de résonance paramétrique pour les systèmes réversibles du troisième ordre (et la réalisation du code de calcul correspondant).
La conservation des oscillations 2pik périodiques du satellite sur lorbite circulaire sous leffet des moments gravitationnel et aérodynamique dans le cas de lorbite faiblement elliptique.
Lexistence des rotations 2pi périodiques du satellite sur lorbite elliptique arbitraire sous leffet des moments gravitationnel et aérodynamique (détermination des vitesses initiales pour les rotations, étude de leur stabilité).
La détermination des rotations rapides dans le problème de V.V. Beletsky (le satellite étant soumis aux seules forces gravitationnelles sans prendre en considération la résistance de latmosphère) et létude de leur stabilité.
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Li, Shunjie. "Géométrie et classification des systèmes de contact : applications du contrôle des systèmes mécaniques non holonomes." Phd thesis, INSA de Rouen, 2010. http://tel.archives-ouvertes.fr/tel-00665223.

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Dans la première partie de cette thèse, nous caractérisons complètement toutes les x-sorties plates et leurs lieux singuliers pour un système avec deux contrôles qui est équivalent au système chaîné. Nous appliquons aussi ce résultat au système de robot mobile avec des remorques pour calculer toutes ses x-sorties plates. Dans la deuxième partie, nous présentons un nouveau modèle pour le système à n-barres dans l'espace de dimension m+1. Nous montrons que ce système est localement équivalent au système m-chaîné et caractérisons aussi ses lieux singuliers. Ensuite, nous analysons sa propriété de platitude et donnons ses sorties plates minimales. Dans la troisième partie, nous donnons des conditions nécessaires et suffisantes pour qu'une distribution soit équivalente à la distribution de Cartan pour des surfaces. Finalement, dans la quatrième partie, nous donnons des conditions nécessaires et suffisantes vérifiables pour qu'un système multi-entrées soit linéarisable par bouclage orbital.
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JEAN, FREDERIC. "Complexites pour les systemes non-holonomes." Paris 6, 1998. http://www.theses.fr/1998PA066170.

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Cette these de geometrie sous-riemannienne s'articule en deux parties. Une premiere partie est consacree a l'etude de deux quantites dont on montrera qu'elles sont equivalentes, la complexite de la planification de trajectoires non-holonomes d'une part, et d'autre part la mesure d'entropie des sous-varietes unidimensionnelles. On estime ces quantites en fonction des coordonnees de la tangente a une sous-variete dans une base de l'algebre de lie de controle et du vecteur de croissance. Il apparait en particulier que la dimension de hausdorff peut etre non seulement superieure a la dimension topologique, mais egalement non entiere. On presente de plus une methode de planification de mouvements non-holonomes basee sur un resultat dans les algebres de lie libres : pour tout element p d'une algebre de lie libre l(x 1,, x m), exp(p) peut etre approxime a tout ordre par un produit de facteurs elementaires exp(a ix i). Dans la deuxieme partie de ce memoire, on s'interesse aux proprietes de l'algebre de lie de controle pour des classes de systemes particuliers. On traite d'abord un exemple significatif, le systeme de controle de la voiture a n remorques, pour lequel on determine completement la structure de l'algebre de lie en calculant en chaque point le vecteur de croissance. Enfin on considere les systemes de controle algebriques en dimension 3. On donne pour ces systemes une borne optimale pour le degre de non-holonomie. Ce calcul repose sur une estimation de la multiplicite d'un polynome sur la trajectoire d'un champ de vecteur polynomial que l'on obtient en utilisant une technique d'estimation de multiplicites d'intersections pfaffiennes.
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Yuan, Hongliang. "Control of NonH=holonomic Systems." Doctoral diss., University of Central Florida, 2009. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2751.

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Many real-world electrical and mechanical systems have velocity-dependent constraints in their dynamic models. For example, car-like robots, unmanned aerial vehicles, autonomous underwater vehicles and hopping robots, etc. Most of these systems can be transformed into a chained form, which is considered as a canonical form of these nonholonomic systems. Hence, study of chained systems ensure their wide applicability. This thesis studied the problem of continuous feed-back control of the chained systems while pursuing inverse optimality and exponential convergence rates, as well as the feed-back stabilization problem under input saturation constraints. These studies are based on global singularity-free state transformations and controls are synthesized from resulting linear systems. Then, the application of optimal motion planning and dynamic tracking control of nonholonomic autonomous underwater vehicles is considered. The obtained trajectories satisfy the boundary conditions and the vehicles' kinematic model, hence it is smooth and feasible. A collision avoidance criteria is set up to handle the dynamic environments. The resulting controls are in closed forms and suitable for real-time implementations. Further, dynamic tracking controls are developed through the Lyapunov second method and back-stepping technique based on a NPS AUV II model. In what follows, the application of cooperative surveillance and formation control of a group of nonholonomic robots is investigated. A designing scheme is proposed to achieves a rigid formation along a circular trajectory or any arbitrary trajectories. The controllers are decentralized and are able to avoid internal and external collisions. Computer simulations are provided to verify the effectiveness of these designs.
Ph.D.
School of Electrical Engineering and Computer Science
Engineering and Computer Science
Electrical Engineering PhD
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Brevet, Guillaume. "Sur l'irrégularité d'un système différentiel holonome le long d'une courbe plane." Angers, 1999. http://www.theses.fr/1999ANGE0025.

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Z. Mebkhout a défini le faisceau d'irrégularité d'un système différentiel holonome le long d'un sous-espace analytique. Cet objet était apparu dans le cas particulier du module constitue des fonctions holomorphes sur une variété analytique complexe, comme l'obstruction au théorème de comparaison de Grothendieck, qui traduit en définitive la régularité du faisceau structural. Le faisceau d'irrégularité généralisé aussi en dimensions supérieures l'espace d'irrégularité de B. Malgrange dans le cas d'une variable. Les faisceaux d'irrégularité ont la propriété de perversité mais certains faisceaux pervers ne sont pas l'irrégularité de systèmes différentiels. Ceci pose le problème de la détermination de l'image essentielle du foncteur irrégularité. Dans ce travail nous étudions ce problème lorsque l'hypersurface est une courbe plongée dans une surface. Dans un premier temps, nous donnons un contre-exemple a l'essentielle subjectivité : nous considérons l'irrégularité sur la surface d'éclatement de l'origine du plan le long de la transformée totale d'une courbe et nous exhibons un faisceau pervers d'image directe non-perverse. Nous prouvons ensuite, en utilisant la désingularisation d'une courbe plane, que l'irrégularité restreinte au germe d'une courbe épointée irréductible fournit un foncteur essentiellement surjectif vers les systèmes locaux sur la courbe épointée. Nous calculons également de manière précise les faisceaux de cohomologie de l'irrégularité de certains d-modules du type exponentielle le long d'un croisement normal. Ces calculs permettent de trouver des systèmes différentiels tels que la monodromie du système local associe ait pour valeurs propres les racines de l'unité. Enfin, nous montrons le résultat suivant : l'irrégularité le long d'un germe de courbe lisse est un foncteur essentiellement surjectif a valeurs dans les germes de faisceaux pervers monodromiques. La preuve de ce théorème repose sur l'équivalence de catégories entre les faisceaux pervers monodromiques et une catégorie de diagrammes d'espaces vectoriels de dimension finie. Dans cette dernière catégorie, les objets indécomposables sont connus. Tout le travail consiste donc à les atteindre, ce qui est fait par des arguments de dévissage en exploitant le caractère exact du foncteur irrégularité
Z. Mebkhout defined the irregularity bundle of a holonomic differential system along an analytic subspace. This object had appeared in the special case of the constitutive module of holomorphic functions on a complex analytic variety, as the obstruction to Grothendieck's comparison theorem, which ultimately translates the regularity of the structural bundle. The irregularity bundle also generalises in higher dimensions the irregularity space of B. Malgrange in the case of one variable. Irregularity bundles have the property of perversity but some perverse bundles are not the irregularity of differential systems. This raises the problem of determining the essential image of the irregularity functor. In this work we study this problem when the hypersurface is a curve embedded in a surface. First, we give a counterexample to the essential subjectivity: we consider the irregularity on the splitting surface of the origin of the plane along the total transform of a curve and we exhibit a perverse beam of direct non-perverse image. We then prove, using the desingularisation of a plane curve, that the irregularity restricted to the seed of an irreducible blunt curve provides an essentially surjective functor to local systems on the blunt curve. We also compute precisely the cohomology bundles of the irregularity of certain d-modules of the exponential type along a normal crossing. These calculations allow us to find differential systems such that the monodromy of the associated local system has as eigenvalues the roots of unity. Finally, we show the following result: the irregularity along a smooth curve seed is an essentially surjective functor with values in the seeds of monodromic perverse bundles. The proof of this theorem relies on the category equivalence between monodromic perverse bundles and a category of diagrams of finite dimensional vector spaces. In the latter category, the indecomposable objects are known. All the work consists therefore in reaching them, which is done by unscrewing arguments by exploiting the exactness of the irregularity functor
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MOURA, CLAIRE. "Non-holonomie des systemes de champs de vecteurs analytiques." Toulouse 3, 1998. http://www.theses.fr/1998TOU30161.

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Le contenu de cette these releve a la fois de la geometrie analytique et de la theorie du controle optimal. Il s'agit en effet d'etudier le degre de non holonomie associe a un systeme de champs de vecteurs analytiques, c'est-a-dire le nombre minimal de crochets de lie necessaires pour engendrer point a point l'algebre de lie du systeme. Etant donne un tel systeme t, la demarche pour majorer son degre de non holonomie s'appuie sur la geometrie des ensembles g, reunions de trajectoires de champs appartenant a l'algebre de lie de t. Le but est de produire un champ dont la trajectoire par 0 quitte une hypersurface fixee au prealable. Ces ensembles de courbes sont mis en relation avec les ensembles d'accessibilite associes a des sous-systemes de t. L'interpretation en termes de feuilletage qui decoule du theoreme de nagano nous permet d'affiner la description des espaces tangents. C'est le rang de l'algebre de lie en 0 de ces sous-systemes qui donne la strategie. Nous montrons ainsi comment controler d'une part la dimension des ensembles g, d'autre part le nombre de crochets de lie qui apparaissent dans leur fabrication. Nous ameliorons de ce fait un resultat de a. Gabrielov. La construction d'un ensemble g qui contient un ouvert nous permet de mettre en oeuvre la methode de j. -j. Risler pour tirer une majoration du degre de non holonomie. Dans le cas de systemes polynomiaux, nous donnons une majoration uniforme, ne dependant que du degre des champs de vecteurs et de la dimension de l'espace ambiant, via une analyse detaillee des multiplicites d'intersection entre une hypersurface algebrique et la trajectoire d'un champ de vecteurs polynomial.
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Borzone, Tommaso. "Decentralized control of multi-agent systems : a hybrid formalism." Thesis, Université de Lorraine, 2019. http://www.theses.fr/2019LORR0078/document.

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Au cours des dernières années, les problèmes multi-agents ont été étudiés de manière intensive par la communauté de la théorie du contrôle. L'un des sujets les plus populaires est le problème de consensus où un groupe d'agents parvient à un accord sur la valeur d'un certain paramètre ou d’une variable. Dans ce travail, nous nous concentrons sur le consensus des réseaux d'agents avec une dynamique non linéaire de poursuite de référence. Nous utilisons des interactions sporadiques modélisées par la détection relative, pour traiter le consensus décentralisé des références. La référence est donc utilisée pour alimenter la dynamique de poursuite de chaque agent. L'analyse de stabilité du système globale a nécessitée l'utilisation d'outils théoriques propre de la théorie des systèmes hybrides, en raison de la double nature de l'approche en deux étapes. L'analyse est effectuée en tenant compte de différents scénarios de topologie et interactions. Pour chaque cas, une condition suffisante de stabilité est fournie, en termes de temps minimum autorisé entre deux mises à jour de référence consécutives. Le cadre proposé est appliqué aux missions de rendez-vous et de réalisation de formation pour les robots mobiles non-holonomes. Le même problème est abordé dans le contexte d'une application réelle sur le terrain, à savoir un système de gestion de flotte pour un groupe de véhicules robotisés déployés dans un environnement industriel à des fins de surveillance et de collecte de données. Le développement d'une telle application a été motivé par le fait que cette thèse s'inscrit dans le cadre du projet FFLOR, développé par le département de recherche technologique du CEA tech
Over the last years, multi-agents problems have been extensively studied from the control theory community. One of the most popular multi-agents control topics is the consensus problem where a group of agents reaches an agreement over the value of a certain parameter or variable. In this work we focus our attention on the consensus problem of networks of non-linear reference tracking agents. In first place, we use sporadic interactions modeled by relative sensing to deal with the decentralized consensus of the references. The reference is therefore feeded the tracking dynamics of each agent. Differently from existent works, the stability analysis of the overall system required the usage of hybrid systems theory tools, due to dual nature of the two stages approach. The analysis is carried out considering different scenarios of network topology and interactions. For each case a stability sufficient condition in terms of the minimum allowed time between two consecutive reference updates is provided. The proposed framework is applied to the rendez-vous and formation realisation tasks for non-holonomic mobile robots, which appear among the richest research topics in recent years. The same problem is addressed in the context of a real field application, namely a fleet management system for a group of robotic vehicles deployable in an industrial environment for monitoring and data collection purpose. The development of such application was motivated by the fact that this thesis is part of the Future of Factory Lorraine (FFLOR) project, developed by the technological research department of the Commissariat à l'énergie atomique et aux énergies alternatives (CEA tech)
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Fruchard, Matthieu. "Méthodologies pour la commande de manipulateurs mobiles non-holonomes." Paris, ENMP, 2005. http://www.theses.fr/2005ENMPA001.

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Cette thèse se place dans le cadre de la commande des manipulateurs mobiles hybrides holonomes/ non-holonomes, c'est-à-dire des robots constitués d'un bras manipulateur embarqué sur une plate-forme porteuse. L'objectif de ce travail est de fournir un cadre méthodologique pour la synthèse de lois de commande par retour d'état de tels systèmes, en partant du constat qu'une stratégie de coordination entre la plate-forme et le manipulateur requiert génériquement de commander la situation complète de la plate-forme. L'originalité des deux nouvelles approches proposées est de permettre un contrôle coordonné d'une tâche prioritaire de manipulation et d'une tâche secondaire de locomotion, obtenu via la stabilisation pratique de la situation complète de la plate-forme le long d'une trajectoire de référence quelconque. Ces deux méthodes génériques s'appuient sur la fusion de deux outils de commande : l'approche par fonctions de tâches, dédiée au contrôle des bras manipulateurs, et l'approche par fonctions transverses, consacrée à la commande des plate-formes non-holonomes. Différentes applications de suivi de cible valident la flexibilité et la polyvalence de ces approches de commande à travers le choix de plusieurs stratégies de coopération entre manipulation et locomotion
This PhD thesis concerns the control of hybrid holonomic/ nonholonomic mobile manipulators, i. E. Robots composed of a manipulator arm mounted on a mobile platform. This work is devoted to the determination of a general framework for the feedback control of such systems. These control methodologies are based on the fact that a general strategy of motion coordination between the manipulator and the mobile platform requires to monitor the situation (position and orientation) of the platform. An original feature of the two approaches we propose is to allow a coordinated control of a priority manipulation task with a secondary locomotion task, obtained via the practical stabilization of the complete platform's situation along any reference trajectory. These two general methodologies rely on the fusion of two control tools: the task function approach, devoted to the control of manipulator arms, and the transverse functions approach, devoted to the control of nonholonomic platforms. Various application cases dealing with target tracking validate the flexibility and the polyvalence of these control approaches, through the choice of several strategies of cooperation between manipulation and locomotion subsystems
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Books on the topic "Systeme holonome"

1

Saito, Mutsumi. Gröbner deformations of hypergeometric differential equations. Berlin: Springer, 2000.

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Soltakhanov, Shervani Kh, Mikhail P. Yushkov, and Sergei A. Zegzhda. Mechanics of non-holonomic systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-85847-8.

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Conference on Geometric Control and Non-holonomic Mechanics (1996 Mexico City, Mexico). Geometric control and non-holonomic mechanics: Conference on Geometric Control and Non-holonomic Mechanics, June 19-21, 1996, Mexico City. Edited by Jurdjevic Velimir and Sharpe R. W. Providence, R.I: American Mathematical Society, 1998.

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Geometric, control, and numerical aspects of nonholonomic systems. Berlin: Springer, 2002.

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Saito, Mutsumi, Nobuki Takayama, and Bernd Sturmfels. Groebner Deformations of Hypergeometric Differential Equations, Algorithms and Computation in Mathematics, Volume 6. Springer, 2000.

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6

Soltakhanov, Sh Kh, Mikhail Yushkov, and S. Zegzhda. Mechanics of Non-Holonomic Systems: A New Class of Control Systems. Springer London, Limited, 2009.

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Soltakhanov, Sh Kh, Mikhail Yushkov, and S. Zegzhda. Mechanics of Non-Holonomic Systems: A New Class of Control Systems. Springer Berlin / Heidelberg, 2010.

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8

Mann, Peter. Coordinates & Constraints. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0006.

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This short chapter introduces constraints, generalised coordinates and the various spaces of Lagrangian mechanics. Analytical mechanics concerns itself with scalar quantities of a dynamic system, namely the potential and kinetic energies of the particle; this approach is in opposition to Newton’s method of vectorial mechanics, which relies upon defining the position of the particle in three-dimensional space, and the forces acting upon it. The chapter serves as an informal, non-mathematical introduction to differential geometry concepts that describe the configuration space and velocity phase space as a manifold and a tangent, respectively. The distinction between holonomic and non-holonomic constraints is discussed, as are isoperimetric constraints, configuration manifolds, generalised velocity and tangent bundles. The chapter also introduces constraint submanifolds, in an intuitive, graphic format.
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Mann, Peter. Constrained Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0008.

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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.
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Book chapters on the topic "Systeme holonome"

1

Haraoka, Yoshishige. "Holonomic Systems." In Trends in Mathematics, 59–87. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52842-7_2.

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Soltakhanov, Shervani Kh, Mikhail P. Yushkov, and Sergei A. Zegzhda. "Holonomic Systems." In Foundations of Engineering Mechanics, 1–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-85847-8_1.

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Umerez, Jon, and Matteo Mossio. "Constraint, Holonomic." In Encyclopedia of Systems Biology, 494. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_706.

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Saito, Mutsumi, Bernd Sturmfels, and Nobuki Takayama. "Solving Regular Holonomic Systems." In Gröbner Deformations of Hypergeometric Differential Equations, 51–102. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04112-3_2.

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Umerez, Jon, and Matteo Mossio. "Constraint, Non-holonomic." In Encyclopedia of Systems Biology, 494. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_707.

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Meigniez, Gaêl. "Holonomy Groups of Solvable Lie Foliations." In Integrable Systems and Foliations, 107–46. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-4134-8_7.

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Björk, Jan-Erik. "Distributions and regular holonomic systems." In Analytic D-Modules and Applications, 281–332. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-0717-6_8.

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Iyengar, Srikanth, Graham Leuschke, Anton Leykin, Claudia Miller, Ezra Miller, Anurag Singh, and Uli Walther. "Holonomic rank and hypergeometric systems." In Graduate Studies in Mathematics, 247–56. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/gsm/087/24.

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Leitner, Felipe. "A Remark On Unitary Conformal Holonomy." In Symmetries and Overdetermined Systems of Partial Differential Equations, 445–60. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-73831-4_23.

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Teodorescu, Petre P. "Dynamics of Non-holonomic Mechanical Systems." In Mechanical Systems, Classical Models, 411–504. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2764-1_5.

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Conference papers on the topic "Systeme holonome"

1

Oprea, Maria, and William Clark. "How do we walk? Using hybrid holonomy to approximate non-holonomic systems *." In 2022 IEEE 61st Conference on Decision and Control (CDC). IEEE, 2022. http://dx.doi.org/10.1109/cdc51059.2022.9993246.

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Terze, Zdravko, Dubravko Matijasˇevic´, Milan Vrdoljak, and Vladimir Koroman. "Differential-Geometric Characteristics of Optimized Generalized Coordinates Partitioned Vectors for Holonomic and Non-Holonomic Multibody Systems." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86849.

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Differential-geometric characteristics and structure of optimized generalized coordinates partitioned vectors for generally constrained multibody systems are discussed. Generalized coordinates partitioning is well-known procedure that can be applied in the framework of numerical integration of DAE systems. However, although the procedure proves to be a very useful tool, it is known that an optimization algorithm for coordinates partitioning is needed to obtain the best performance. After short presentation of differential-geometric background of optimized coordinates partitioning, the structure of optimally partitioned vectors is discussed on the basis of gradient analysis of separate constraint submanifolds at configuration and velocity level when holonomic and non-holonomic constraints are present in the system. While, in the case of holonomic systems, the vectors of optimally partitioned coordinates have the same structure for generalized positions and velocities, when non-holonomic constraints are present in the system, the optimally partitioned coordinates generally differ at configuration and velocity level and separate partitioned procedure has to be applied. The conclusions of the paper are illustrated within the framework of the presented numerical example.
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Müller, Andreas. "A Proposal for a Unified Concept of Kinematic Singularities for Holonomic and Non-Holonomic Mechanisms." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70649.

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The study of mechanism singularities has traditionally focused on holonomic systems. On the other hand many robotic systems are characterized by non-holonomic constraints, such as mobile platforms and manipulators driven by non-holonomic joints, and a general concept of singularities seems in order. In this paper a possible generalization of the singularity concept is proposed that equally accounts for holonomic and non-holonomic kinematic systems. The central object is the associated kinematic control problem. Singularities are identified as those configurations where the iteration depth of Lie brackets required to compute the accessibility Lie algebra changes. This notion of singularities is applied to serial manipulator and to non-holonomic mobile platforms. It is shown for holonomic manipulators that this is equivalent to the usual Jacobian rank condition. As example the condition is discussed for a Scara manipulator, a 6R manipulator, and for a kinematic car with one or two trailers.
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Temizer, Selim, and Leslie Pack Kaelbling. "Holonomic planar motion from non-holonomic driving mechanisms: the front-point method." In Intelligent Systems and Advanced Manufacturing, edited by Douglas W. Gage and Howie M. Choset. SPIE, 2002. http://dx.doi.org/10.1117/12.457456.

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Mukherjee, Rudranarayan M. "Operational Space Algorithm for Flexible Multibody Systems With Generalized Topologies." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48657.

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Multibody system with flexible and / or rigid bodies are found in various applications of science and engineering. Many of these systems have topological constraints in the form of kinematically closed loop topologies. Similarly, many of these systems have non-holonomic constraints that are either linear or nonlinear in the system velocities. In this paper, an efficient algorithm is presented for simulating the dynamics of multi-body systems of rigid or flexible bodies in generalized topologies with particular emphasis on treatment of topological and non-holonomic constraints. The flexible bodies are modeled using the small deformation large displacement approach. This algorithm achieve linear and logarithmic complexities in serial and parallel implementation and provides robust performance.
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Kazansky, Alexander B., and Daniel M. Dubois. "Bootstrapping of Life through Holonomy and Self-modification." In COMPUTING ANTICIPATORY SYSTEMS: CASYS ‘09: Ninth International Conference on Computing Anticipatory Systems. AIP, 2010. http://dx.doi.org/10.1063/1.3527167.

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Terze, Zdravko, and Joris Naudet. "Discrete Mechanical Systems: Projective Constraint Violation Stabilization Method for Numerical Forward Dynamics on Manifolds." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35466.

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During numerical forward dynamics of discrete mechanical systems with constraints, a numerical violation of system kinematical constraints is the basic source of time-integration errors and frequent difficulty that analyst has to cope with. The stabilized time-integration procedure, whose stabilization step is based on projection of the integration results to the underlying constraint manifold via post-integration correction of the selected coordinates, is proposed in the paper. After discussing optimization of the partitioning algorithm, the geometric and stabilization issues of the method are addressed and it is shown that the projective stabilization algorithm can be applied for numerical stabilization of holonomic and non-holonomic constraints in Pfaffian and general form. As a continuation of the previous work, a further elaboration of the projective stabilization method applied on non-holonomic discrete mechanical systems is reported in the paper and numerical example is provided.
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Yoshimura, Hiroaki, and Kenji Soya. "On the Geometric Stabilization for Discrete Hamiltonian Systems With Holonomic Constraints." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86354.

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This paper develops a discrete Hamiltonian system with holonomic constraints with Geometric Constraint Stabilization. It is first shown that constrained mechanical systems with nonconservative external forces can be formulated by using canonical symplectic structures in the context of Hamiltonian systems. Second, it is shown that discrete holonomic Hamiltonian systems can be developed via the discretization based on the Backward Differentiation Formula and also that geometric constraint stabilization can be incorporated into the discrete Hamiltonian systems. It is demonstrated that the proposed method enables one to stabilize constraint violations effectively in comparison with conventional methods such as Baumgarte Stabilization and Gear–Gupta–Leimkuhler Stabilization, together with an illustrative example of linkage mechanisms.
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Murakami, Hidenori, and Takeyuki Ono. "A Variational Derivation of Equations of Motion With Contact Constraints Using SE(3)." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87126.

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For rigid-body systems subjected to non-holonomic constraints, a streamlined method is presented to derive a minimum number of analytical equations of motion. To illustrate the method, a rolling disk problem is considered. In kinematics, an orthonormal coordinate system is attached to the center of mass together with additional coordinate systems introduced to define the connection path. For each coordinate system, a moving frame is defined by explicitly writing the coordinate vector basis and the position vector of the origin, whereby the attitude of the coordinate vector basis and the coordinates of the origin are compactly stored in a 4 × 4 frame connection matrix of the special Euclidean group, SE(3). Contact velocity constraints are transformed to pfaffians to obtain the associated variational constraints. In kinetics, the principle of virtual work is employed. The desired equations of motion are obtained by expressing the translational and angular velocities at the center of mass as the linear functions of the generalized velocities with the coefficients stored in [B]-matrix, and reducing it to [B*]-matrix after incorporating the contact constraints. The method can be easily extended to multi-body systems with both holonomic and non-holonomic constraints.
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Yoshimura, Hiroaki. "A Geometric Approach to Constraint Stabilization for Holonomic Lagrangian Systems." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35429.

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In this paper, we develop a geometric approach to constraint stabilization for holonomic mechanical systems in the context of Lagrangian formulation. We first show that holonomic mechanical systems, for the case in which a given Lagrangian is hyperregular, can be formulated by using the Lagrangian two-form, namely, a symplectic structure on the tangent bundle of a configuration manifold that is induced from the cotangent bundle via the Legendre transformation. Then, we present an idea of geometric constraint stabilization and we show that a holonomic Lagrangian system with geometric constraint stabilization can be formulated by the Lagrange-d’Alembert principle, together with its local coordinate expression for the sake of numerical computations. Finally, we illustrate the numerical verification that the proposed method enables to stabilize constraint violations effectively in comparison with the Baumgarte and Gear–Gupta–Leimkuhler methods together with an example of a linkage mechanism.
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