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A geometric algorithm for the output functional controllability in general manipulation systems and mechanisms

Paolo Mercorelli (2012)


In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined...

A geometric procedure for robust decoupling control of contact forces in robotic manipulation

Paolo Mercorelli, Domenico Prattichizzo (2003)


This paper deals with the problem of controlling contact forces in robotic manipulators with general kinematics. The main focus is on control of grasping contact forces exerted on the manipulated object. A visco-elastic model for contacts is adopted. The robustness of the decoupling controller with respect to the uncertainties affecting system parameters is investigated. Sufficient conditions for the invariance of decoupling action under perturbations on the contact stiffness and damping parameters...

A Riemann-Roch-Hirzebruch formula for traces of differential operators

Markus Engeli, Giovanni Felder (2008)

Annales scientifiques de l'École Normale Supérieure

Let D be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an n -dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of D as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology H H 2 n ( 𝒟 n , 𝒟 n * ) of the algebra of differential operators on a formal neighbourhood of a...

Algebraic K -theory of the first Morava K -theory

Christian Ausoni, John Rognes (2012)

Journal of the European Mathematical Society

For a prime p 5 , we compute the algebraic K -theory modulo p and v 1 of the mod p Adams summand, using topological cyclic homology. On the way, we evaluate its modulo p and v 1 topological Hochschild homology. Using a localization sequence, we also compute the K -theory modulo p and v 1 of the first Morava K -theory.

Asymptotic behaviour of numerical invariants of algebraic varieties

F. L. Zak (2012)

Journal of the European Mathematical Society

We show that if the degree of a nonsingular projective variety is high enough, maximization of any of the most important numerical invariants, such as class, Betti number, and any of the Chern or middle Hodge numbers, leads to the same class of extremal varieties. Moreover, asymptotically (say, for varieties whose total Betti number is big enough) the ratio of any two of these invariants tends to a well-defined constant.

Augmented Γ-spaces, the stable rank filtration, and a bu analogue of the Whitehead conjecture

Gregory Z. Arone, Kathryn Lesh (2010)

Fundamenta Mathematicae

We explore connections between our previous paper [J. Reine Angew. Math. 604 (2007)], where we constructed spectra that interpolate between bu and Hℤ, and earlier work of Kuhn and Priddy on the Whitehead conjecture and of Rognes on the stable rank filtration in algebraic K-theory. We construct a "chain complex of spectra" that is a bu analogue of an auxiliary complex used by Kuhn-Priddy; we conjecture that this chain complex is "exact"; and we give some supporting evidence. We tie this to work of...

Cohomologie et K-théorie équivariantes des variétés de Bott-Samelson et des variétés de drapeaux

Matthieu Willems (2004)

Bulletin de la Société Mathématique de France

L’objet de cet article est de calculer la cohomologie et la K-théorie équivariantes des variétés de Bott-Samelson (théorèmes 3.3 et 4.3) et d’en déduire des résultats sur les variétés de drapeaux des groupes de Kac-Moody. Dans la section 3, on retrouve la formule de restriction aux points fixes de la base { ξ ^ w } w W de H T * ( G / B ) (théorème 3.9) prouvée par Sara Billey dans [4]. Dans la section 4, on donne l’expression explicite de la restriction aux points fixes de la base { ψ ^ w } w W de K T ( G / B ) définie par Kostant et Kumar dans...

Equivariant K-theory of flag varieties revisited and related results

V. Uma (2013)

Colloquium Mathematicae

We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring K T ( G / B ) of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in K T ( G / B ) to R(T) ⊗ R(T), where R(T) denotes the representation ring of the torus T. We further apply our results to describe the multiplicative structure constants of K ( X ) where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure constants of...

Formal geometric quantization

Paul-Émile Paradan (2009)

Annales de l’institut Fourier

Let K be a compact Lie group acting in a Hamiltonian way on a symplectic manifold ( M , Ω ) which is pre-quantized by a Kostant-Souriau line bundle. We suppose here that the moment map Φ is proper so that the reduced space M μ : = Φ - 1 ( K · μ ) / K is compact for all μ . Then, we can define the “formal geometric quantization” of M as 𝒬 K - ( M ) : = μ K ^ 𝒬 ( M μ ) V μ K . The aim of this article is to study the functorial properties of the assignment ( M , K ) 𝒬 K - ( M ) .

Generalized holomorphic analytic torsion

José Ignacio Burgos Gil, Gerard Freixas i Montplet, Răzvan Liţcanu (2014)

Journal of the European Mathematical Society

In this paper we extend the holomorphic analytic torsion classes of Bismut and Köhler to arbitrary projective morphisms between smooth algebraic complex varieties. To this end, we propose an axiomatic definition and give a classification of the theories of generalized holomorphic analytic torsion classes for projective morphisms. The extension of the holomorphic analytic torsion classes of Bismut and Köhler is obtained as the theory of generalized analytic torsion classes associated to R = 2 , R being...

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