Michel COSTE

LISTE DES PUBLICATIONS /
LIST OF PUBLICATIONS

Prépublications

Articles de revues

[11c]

A Simple Proof that Generic 3-RPR Manipulators Have Two Aspects, Journal of Mechanisms and Robotics 4 (2012), 011008.1-

Avoiding singularities in the workspace of aparallel robot is an important issue. The case of 3-RPR planar robots is an important subject of theoretical studies. We study the singularities of planar 3-RPR robots by using a new parameterization of the singular locus in a modified workspace. This approach enables us to give a simple proof of a recent result of M. Husty: the complement of the singular locus in the workspace of a generic 3-RPR manipulator has two connected components (called aspects). The parameterization introduced in this paper, due to its simple geometric properties, proves to be useful for the study of the singularities of 3-RPR robots.

Keywords: parallel robots, singularities
Mathematical Subject Classification: 68T40, 70E60
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[11a]

Geodesic diameter of sets defined by few quadratic equations and inequalities (avec Seydou Moussa), Math. Z. 272 (2012), 239-251
We prove a bound for the geodesic diameter of a subset of the unit ball in Rⁿ described by a fixed number of quadratic equations and
inequalities, which is polynomial in n, whereas the known bound for general degree is exponential in n. Our proof uses methods borrowed from D'Acunto and Kurdyka (to deal with the geodesic diameter) and from Barvinok (to take advantage of the quadratic nature).
Fichier pdf

[05]

Generalized Budan-Fourier theorem and virtual roots (avec T. Lajous, H. Lombardi et M-F. Roy), J. Complexity 21 (2005), no. 4, 478--486.
In this Note we give a proof of a generalized version of the classical Budan-Fourier  theorem, interpreting sign variations in the derivatives in terms of virtual roots.
Mathematical Subject Classification: 12D10
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[04]

Global problems on Nash functions (avec J. Ruiz et M. Shiota), Rev. Mat. Complut. 17 (2004), no. 1, 83--115.
This is a survey on the history of and the solutions to the basic global problems on Nash functions,which have been only recently solved, namely: separation, extension, global equations, Artin-Mazur description and idempotency, also noetherianness. We discuss all of them in the various possible contexts,from manifolds over the reals to real spectra of arbitrary commutative rings.
Mathematical Subject Classification: 14P20
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[01c]

Dynamical method in algebra: Effective Nullstellensätze (avec H. Lombardi et M-F. Roy), Annals Pure Appl. Logic 111 (2001) 203-256
We give a general method for producing various effective Null and Positivstellensätze, getting new Positivstellensätze in algebraically closed valued fields and ordered groups. These various effective Nullstellensätze produce algebraic identities certifying that some geometric conditions cannot be simultaneously satisfied. We produce also constructive versions of abstract classical results of algebra based on Zorn's lemma in several cases where such constructive version did not exist. For example, the fact that a real field can be totally ordered, or the fact that a field can be embedded in an algebraically closed field. Our results are based on the concepts we develop of dynamical proofs and simultaneous collapse.
Mathematical Subject Classification: 03F65 (12Jxx 18B25)
Revised October 2000
Tiré à part disponible / Offprint available
 

[01b]

Uniform Bounds on Complexity and Transfer of Global Properties of Nash Functions (with Jesus M. RUIZ and Masahiro SHIOTA), J. reine angew. Math. 536 (2001) 209-235.

We show that the complexity of semialgebraic sets and mappings can be used to parametrize Nash sets and mappings by Nash families. From this we deduce uniform bounds on the complexity of Nash functions that lead to first-order descriptions of many properties of Nash functions and a good behaviour under real closed field extension (e.g. primary decomposition). As a distinguished application, we derive the solution of the extension and global equations problems over arbitrary real closed fields, in particular over the field of real algebraic numbers. This last fact and a technique of change of base are used to prove that the Artin-Mazur description holds for abstract Nash functions on the real spectrum of any commutative ring, and solve extension and global equations in that abstract setting. To complete the view, we prove the idempotency of the real spectrum and an abstract version of the separation problem. We also discuss the conditions for the rings of abstract Nash functions to be noetherian.
Keywords: Nash functions, real spectrum.
Mathematical Subject Classification: 14P20, 32C07, 12J15.
March 20th, 2000
Tiré à part disponible / Offprint available
 

[01a]

Atypical values at infinity of a polynomial function on the real plane: an erratum, and an algorithmic criterion (with Maria Jesus DE LA PUENTE), J. Pure Appl. Algebra 162 (2001) 23-35.
We correct a previously published theorem by proving a criterion to decide whether the fibration given by a real polynomial function $f:\R^2\to \R$ is locally trivial at infinity. The algorithmical nature of this criterion provides a test that can be applied to any real polynomial $f$.
January 10, 2000
Tiré à part disponible / Offprint available
 

[00]

Nash functions on noncompact Nash manifolds (avec M. Shiota), Ann. Scient. Éc. Norm. Sup. 4e série, 33 (2000) 139-149
Several conjectures concerning Nash functions (including the conjecture that globally irreducible Nash sets are globally analytically irreducible) were proved in [95b] for compact affine Nash manifolds. We prove these conjectures for all affine Nash manifolds.
Tiré à part disponible / Offprint available
 

[98a]

Le discriminant d'un morphisme de variétés algébriques réelles (avec K. Kurdyka), Topology 37 (1998), 393-399. MR 99a:14083. Tiré à part disponible / Offprint available
Let f: W --> V be a regular morphism of real algebraic varieties, where V is irreducible. It is well known that the Euler characteristic of the fibers of f is generically constant modulo 2. We show that there is a rational function on V whose sign generically determines the Euler characteristic of the fibers of f modulo 4. This function is essentially obtained as the discriminant of a quadratic form whose signature generically gives the Euler characteristic of the fibers.
 

[96]

Separation, factorization and finite sheaves on Nash manifolds (avec J. Ruiz, M. Shiota), Compositio Mathematica 103 (1996) 31-62. Tiré à part disponible / Offprint available
 

[95b]

Approximation in compact Nash manifolds (avec J. Ruiz, M. Shiota), Amer. J. Math. 117 (1995) 905-927. Tiré à part disponible / Offprint available
 

[92e]

Epaississement d'hypersurfaces algébriques réelles, Proc. Japan Acad. Ser. A Math. Sci. 68 (1992) 175-180. Tiré à part disponible / Offprint available
 

[92c]

On the link of a stratum in a real algebraic set (avec K. Kurdyka), Topology 31 (1992) 323-336. Tiré à part disponible / Offprint available
 

[92b]

Real algebraic 1-cocycles are Nash coboundaries (avec M. Diop), Boll. U.M.I. (7) 6-A (1992), 249-254. Tiré à part disponible / Offprint available
 

[92a]

Nash triviality in families of Nash manifolds (avec M. Shiota), Invent. math. 108 (1992) 349-368. Tiré à part disponible / Offprint available
 

[91]

Unicité des triangulations semi-algébriques : validité sur un corps réel clos et effectivité forte, C-R. Acad. Sc. Paris 312 (1991) 395-398. Tiré à part disponible / Offprint available
 

[89b]

Encore une démonstration de l'existence de stratifications satisfaisant la condition w de Verdier (avec M-F. Roy), Bull. Polish Ac. Sc. Math. 37 (1989) 597-601. Tiré à part disponible / Offprint available
 

[85]

Sous-ensembles algébriques réels de codimension 1, C-R. Acad. Sc. Paris 300 (1985) 661-664. Tiré à part disponible / Offprint available
 

[83]

Normal spectral spaces and their dimensions (avec M. Carral), J. Pure Appl. Algebra 30 (1983) 227-235. Tiré à part disponible / Offprint available
 

[81b]

Le topos étale réel d'un anneau (avec M-F. Roy), Cahiers de Topologie et de Géométrie Différentielle 22 (1981), 19-24.
 

[81a]

Petits et gros topos en géométrie algébrique (avec G. Michon), Cahiers de Topologie et de Géométrie Différentielle 22 (1981), 25-30.
 

[80b]

Le spectre étale réel d'un anneau est spatial (avec M-F. Roy), C-R. Acad. Sc. Paris 290 (1980) 91-94. Tiré à part disponible / Offprint available
 

[80a]

Contribution to the study of the natural number object in elementary topoi (avec L. Mahé, M-F Roy), J. Pure Appl. Algebra 17 (1980), 35-68.
 

 

Chapitres de livres ou d'actes / chapters of books or proceedings

[12b]

Perturbation of symmetric 3-RPR manipulators and asymptotic singularities (avec D. Chablat et P. Wenger). New Trends in Mechanism and Machine Science (Ed : F. Viadero, M. Ceccarelli), pp. 23--31, Springer (2012)
Small perturbations can affect the kinematic properties of manipulators with non-generic architecture. We study in this paper the perturbations of symmetric planar 3-RPR manipulators. We show in particular that one can obtain any of the three possible stable types of behaviour of 3-RPR manipulators for large values of the lengths of the legs.
hal

[12a]

Asymptotic singularities of planar parallel 3-RPR manipulators, Latest Advances in Robot Kinematics, (Ed. : J. Lenarcic, M. Husty)  pp. 35-42, Springer (2012)

We study the limits of singularities of planar parallel 3-RPR manipulators as the lengths of their legs tend to infinity, paying special attention to the presence of cusps. These asymptotic singularities govern the kinematic behavior of the manipulator in a rather large portion of its workspace.

Keywords: parallel robots, singularities
Mathematical Subject Classification: 68T40, 70E60
Fichier pdf

[11b]

Singular surfaces and cusps in symmetric planar 3-RPR manipulators (avec D. Chablat et P. Wenger), 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems. San Francisco, CA, USA, pp. 1453-1458.

We study in this paper a class of 3-RPR manipulators for which the direct kinematic problem (DKP) is split into a cubic problem followed by a quadratic one. These manipulators are geometrically characterized by the fact that the moving triangle is the image of the base triangle by an indirect isometry. We introduce a specific coordinate system adapted to this geometric feature and which is also well adapted to the splitting of the DKP. This allows us to obtain easily precise descriptions of the singularities and of the the cusp edges. These latter second order singularities are important for nonsingular assembly mode changing. We show how to sort assembly modes and use this sorting for motion planning in the joint space.
Mathematical Subject Classification: 68T40, 70E60
Fichier pdf 

[07]

Real Algebraic Sets, dans Arc spaces and additive invariants in real algebraic and analytic geometry, 1--32, Panor. Synthèses 24, Soc. Math. France, Paris, 2007.
Ces notes ont pour ambition d'expliquer les outils nécessaires à l'étude de la topologie des ensembles algébriques réels singuliers au moyen des fonctions algébriquement constructibles. La première section passe en revue les faits de base de la géométrie semialgébrique, notamment le théorème de triangulation et les résultats de trivialisation, cruciaux pour la notion d'entrelacs qui joue un rôle important dans ces notes. La deuxième section présente quelques résultats sur les ensembles algébriques réels, dont le théorème de Sullivan qui dit que la caractéristique d'Euler de l'entrelacs est paire, et l'existence d'une classe fondamentale. La troisième section est consacrée aux fonctions constructibles et algébriquement constructibles; l'outil principal qui rend ces fonctions utiles est l'intégration par rapport à la caractéristique d'Euler. On donne une idée de la façon dont les fonctions algébriquement constructibles donnent des invariants topologiques combinatoires qui permettent de caractériser les ensembles algébriques réels de petite dimension.
Mots clefs : ensembles algébriques réels, ensembles semialgébriques, intégrale d'Euler, fonctions algébriquement constructibles, invariants topologiques
The aim of these notes is to present the material needed for the study of the topology of singular real algebraic sets via algebraically constructible functions. The first chapter reviews basic results of semialgebraic geometry, notably the triangulation theorem and triviality results which are crucial for the notion of link, which plays an important role in these notes. The second chapter presents some results on real algebraic sets, including Sullivan's theorem stating that the Euler characteristic of a link is even, and the existence of a fundamental class. The third chapter is devoted to constructible and algebraically constructible functions; the main tool which makes these functions useful is integration against Euler characteristic. We give an idea of how algebraically constructible functions give rise to combinatorial topological invariants which can be used to characterize real algebraic sets in low dimensions.
Key words: Real algebraic sets, semi-algebraic sets, Euler integral, algebraically constructible functions, topological invariants

[98b]

Topological types of fewnomials, dans Singularities symposium - Lojasiewicz 70, Banach Center Publications, vol. 44 (1998), 81-92. Tiré à part disponible / Offprint available
We prove that the number of topological types of "fewnomials" f : Rⁿ --> R is bounded in terms of the number of monomials appearing in f. This is obtained as a consequence of a result of triangulation  of definable functions (with values in R) in o-minimal structures. 

[95a]

Thom's first isotopy lemma: a semialgebraic version, with uniform bound (avec M. Shiota), Real algebraic and analytic geometry, de Gruyter (1995), 83-101.
 

[92d]

Trivialités en famille (avec M. Reguiat), dans Real Algebraic Geometry, Lecture Notes in Math. 1524, Springer-Verlag (1992), 193-204.
 

[90]

Sous-ensembles algébriques réels de codimension 2, dans Real Analytic and Algebraic Geometry, Lecture Notes in Mathematics n°1420, Springer-Verlag (1990) 111-121.
 

[89a]

Effective semialgebraic geometry, dans Geometry and Robotics, Lecture Notes in Computer Science n°391, Springer-Verlag (1989) 1-27.
 

[88]

Thom's lemma, the coding of real algebraic numbers and the computation of the topology of semialgebraic sets (avec M-F. Roy), dans Algorithms in Real Algebraic Geometry, Academic Press (1988) 121-130.
 

[82b]

Ensembles semi-algébriques, dans Géométrie Algébrique Réelle et Formes Quadratiques, Lecture Notes in Math. 959, Springer-Verlag (1982), 109-138.
 

[82a]

La topologie du spectre réel (avec M-F. Roy), dans Ordered Fields and Real Algebraic Geometry, Contemp. Math. 8, A.M.S. (1982), 27-59. Tiré à part disponible / Offprint available
 

[81c]

Le spectre réel et la topologie des variétés sur un corps réel clos (avec M-F. Roy), Séminaire sur la Géométrie Algébrique Réelle, Pub. Math. Univ. Paris 7 n°9 (1981).

[79c]

Localisation, spectra, and sheaf representation, dans Applications of sheaves, Lecture Notes in Math. 753, Springer-Verlag (1979), 212-238.
 

[79b]

Topologies for real algebraic geometry (avec M-F. Roy), dans Topos theoretic methods in geometry, Aarhus Univ. var. pub. series 30 (1979), 37-100.
 

[79a]

The generic model of an e -stable geometric extension of the theory of rings is of line type (avec M-F. Roy), dans Topos theoretic methods in geometry, Aarhus Univ. var. pub. series 30 (1979), 29-36.

Livres / Books

 

[B00a]

An Introduction to Semialgebraic Geometry. Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Istituti Editoriali e Poligrafici Internazionali, Pisa (2000)
Table des matières (pdf) - Texte complet (pdf - 1,1 Mo)/
Table of contents (pdf) - Complete text (pdf - 1,1 Mo)
 

[B00b]

An Introductionto O-minimal Geometry. Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Istituti Editoriali e Poligrafici Internazionali, Pisa (2000)
Table des matières (pdf) - Texte complet (pdf - 1 Mo)/
Table of contents (pdf) - Complete text (pdf - 1 Mo)
 

[B98]

Real Algebraic Geometry (avec J. Bochnak et M-F. Roy), Ergebnisse der Math. 36, Springer-Verlag (1998). (Version anglaise revue et augmentée de [B87] / Revised and augmented english version of [B87])
List of errata
 

[B87]

Géométrie Algébrique Réelle (avec J. Bochnak et M-F. Roy), Ergebnisse der Math. 12, Springer-Verlag (1987). Critiques : Bull. London Math. Soc. 21 (1989) 502-505 ; Bull. Amer. Math. Soc. 22 (1990) 208-214 ; MR 90b 14030 ; Gazette des Mathématiciens 45 (1990) 48-53.

 

Séminaires / Seminars

[P99a]

Reconnaître effectivement les ensembles algébriques réels
Article de vulgarisation, paru dans le bulletin de l'IREM de Rennes. Le sujet est la discussion de conditions nécessaires (et suffisantes en petite dimension) pour qu'un polyèdre soit homéomorphe à un ensemble algébrique réel, formulées au moyen de la notion de fonction algébriquement constructibles et de l'opérateur d'entrelacs sur ces fonctions (d'après des travaux de C. McCrory et A. Parusinski).
Fichier pdf - Fichier postscript (1,4 Mo) - Fichier postscript comprimé (575 ko)

[76]

Une approche logique des théories définissables par limites projectives finies. Séminaire de théorie des catégories dirigé par Jean Bénabou, Mars 1976. Fichief pdf

[75]

Théories cohérentes et topos cohérents (avec M-F. Coste). Séminaire de théorie des catégories dirigé par Jean Bénabou, Mai 1975. Fichief pdf

[74]

Logique d'ordre supérieur dans les topos élémentaires. Séminaire de théorie des catégories dirigé par Jean Bénabou, Novembre 1974. Fichief pdf

[73]

Logique du premier ordre dans les topos élémentaires. Séminaire de théorie des catégories dirigé par Jean Bénabou, 1973-74. Fichief pdf

  

 

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