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le (30m1s)

## La vérité (algorithmique) et ses réductions / Vangelis Th. Paschos

La vérité (algorithmique) et ses réductions / Vangelis Th. Paschos. In "La vérité", Journées Scientifiques annuelles de l'Institut Universitaire de France, organisées par le Pôle de recherche et d'enseignement supérieur (PRES) de Toulouse, l'Université Toulouse II-Le Mirail et l'Institut Universitaire de France. Toulouse : Hôtel-Dieu, 2-4 avril 2013. Miracle au SertãoSite dédié au film APAEB ValenteAssociation des Petits Agriculteurs de l'Etat de Bahia
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le (8m8s)

## ﻿2.1. Localization process in a probabilistic framework: basic concepts

In this part, we will talk about localization which is a fundamental problem that a robot has to be able to solve in order to accomplish almost any tasks. In particular, we will start by discussing several motion sensor models and, starting from them, we will derive and we will discuss the most appropriate approaches to solve localization which are adopted by the mobile robotics community.
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le (8m5s)

## 2.2. Characterization of proprioceptive and exteroceptive sensors

Before deriving the equations of the Bayes filter, I want to remind you a few concepts in the theory of probability, and also some mathematical characterization for the statistical error of the robot's sensors. In particular, in this sequence, what I want to do, is to derive the link between the robot configuration, and the physical quantities that are measured by the robot's sensors.
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le (11m53s)

## 2.7. Grid Localization: an example in 1D

Now that we have the equations of the Bayes filter, we need a method in order to implement in real cases these equations.So, in the following, I want to discuss two methods, which are commonly adopted by the Mobile Robotics Community and, these, if you want, correspond to two extreme solutions because one is a fully numerical and it is based on a grid and, for the case of localization, is known as the grid-localization approach – and the other one is a fully analytical and it is known as a ...
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le (8m2s)

## 2.8. The Extended Kalman Filter (EKF)

We have seen the grid localization, and the advantage of this approach is that we can deal with any kind of probability distribution; in particular we don't need to do a Gaussian assumption. The drawback is that the solution becomes very expensive.There exists another solution that is the Kalman filter, this is a completely different solution because it is a totally analytical solution.
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