Nicolas Delanoue

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In this paper, we give a numerical algorithm able to prove whether a set S described by nonlinear inequalities is path-connected or not. To our knowledge, no other algorithm (numerical or symbolic) is able to deal with this type of problem. The proposed approach uses interval arithmetic to build a graph which has exactly the same number of connected(More)
This paper provides an effective method to create an abstract simplicial complex homotopy equivalent to a given set S described by non-linear inequalities (polynomial or not). To our knowledge, no other numerical algorithm is able to deal with this type of problem. The proposed approach divides S into subsets that have been proven to be contractible using(More)
This paper presents a new numerical algorithm based on interval analysis able to prove that a differentiable function f : A ⊂ R → R is injective. This algorithm also performs a partition of the domain A in subsets Ai where, for all x ∈ Ai, the cardinality of f−1(f(x)) is constant. In the context of parameter estimation, we show how this algorithm provides(More)
This paper gives a numerical algorithm able to compute the number of path-connected components of a set S defined by nonlinear inequalities. This algorithm uses interval analysis to create a graph which has the same number of connected components as S. An example coming from robotics is presented to illustrate the interest of this algorithm for(More)
This paper proposes a new approach to solve the problem of computing the capture basin C of a target T. The capture basin corresponds to the set of initial states such that the target is reached in finite time before possibly leaving of constrained set. We present an algorithm, based on interval analysis, able to characterize an inner and an outer(More)
The problem of optimal transportation was formalized by the French mathematician Gaspard Monge in 1781. Since Kantorovitch, this (generalized) problem is formulated with measure theory. Based on Interval Arithmetic, we propose a guaranteed discretization of the Kantorovitch’s mass transportation problem. Our discretization is spatial: supports of the two(More)
Generalized Voronoı̈ Diagrams has been demonstrated to be a relevant tool for planification in a mobile robotics context. Therefore, the generated trajectories may suffer of discontinuities and non-optimality. This paper introduces a reflexion on the use of Bézier curves to solve both of these drawbacks. The key idea of this paper is to be able to smoothen(More)
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