This article is focused on calculating the trajectory of an industrial robot in the production of composites for the automotive industry. The production technology is based on the winding of carbon fibres on a polyurethane frame. The frame is fastened to the end-effector of the robot arm (i.e. robot-end-effector, REE). The passage of the frame through the fibre processing head is determined by the REE trajectory. The position of the fibre processing head is fixed and is composed of three fibre guide...

We show that in the class of compact sets K in ${ℝ}^n$ with an analytic parametrization of order m, the sets with Zariski dimension m are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for tangential derivatives of (the traces of) polynomials on K.

Applying general results on separation of semialgebraic sets and spaces of orderings, we produce a catalogue of all possible geometric obstructions for separation of 3-dimensional semialgebraic sets and give some hints on how separation can be made decidable.

Soit $\Gamma$ un groupe de type fini non élémentaire. On note $D^n\left(\Gamma \right)$ l’ensemble des structures hyperboliques de dimension $n$ sur $\Gamma$. $D^n\left(\Gamma \right)$ peut se réaliser comme fermé dans un espace semi-algébrique qui admet une compactification naturelle par le spectre réel. On note ${\overline{D^n\left(\Gamma \right)}}^{\mathrm{sp}}$ le compactifié via le $\underset{\_}{spectre}$ réel de $D^n\left(\Gamma \right)$. L’objet de cet article est de décrire les points ajoutés dans ${\overline{D^n\left(\Gamma \right)}}^{\mathrm{sp}}$. La compactification obtenue de cette manière permet d’interpréter “les points frontières” comme des représentations de $\Gamma$ dans ${\mathrm{SO}}_F^{+}(n,1)$ où $F(\supset ℝ)$ est un corps réel...

This paper is devoted to the computation of distance to set, called S, defined by polynomial equations. First we consider the case of quadratic systems. Then, application of results stated for quadratic systems to the quadratic equivalent of polynomial systems (see [5]), allows us to compute distance to semi-algebraic sets. Problem of computing distance can be viewed as non convex minimization problem: $d(u,S)={inf}_{x\in S}{\parallel x-u\parallel }^2$, where u is in ${ℛ}^n$. To have, at least, lower approximation of distance, we consider the dual...

Deux types de courbures sont associés à un sous-ensemble compact et définissable d'une variété riemannienne analytique réelle. Si la variété est de courbure constante, il y a des relations linéaires entre ces mesures. Comme application, nous démontrons une formule cinématique, définissons des densités locales, et nous étudions les volumes des simplexes réguliers.