Cours de Robotique

IAMOOC : Interval analysis with applications to parameter estimation and robot localization [MOOC]
Publié le 31/01/2019 - Luc Jaulin
Description :
IAMOOC is a free MOOC on Interval Analysis with application to parameter estimation and robot localization.
Interval analysis concerns the methods which computes with intervals in place of real numbers.
There is a large number of applications in Control, Optimization, Robotics, Chemistry.
Interval Computation is a numerical tool which allows us to solve nonlinear problems in a guaranteed way. One of the pioneers of interval computations is Ramon E. Moore. He contributed largely to its development and dissemination. Nowadays, Interval Computations can be found in many fields: global optimization, set inversion, parameter estimation, localization of robots, etc. Interval Computation offers a general numerical framework to easily get reliable results.
Interval Computation can deal with a huge class of problems involving equations or inequalities which can be non-smooth, non-convex, or with different kind of variables.
Interval tools are easy to understand. They only require basic knowledge on mathematics and computer sciences.
The results provided by interval methods are guaranteed, which means that from correct assumptions.
Interval Computations will provide correct conclusions. The results are guaranteed in any case. As a consequence, Interval Computations can be used to prove mathematical theorems. For instance, W. Tucker has proven the conjecture of Lorenz and Thomas Hales the conjecture of Kepler, both using Interval Computations.

Mots clés :
Interval analysis, Analyse par Intervalles, Estimation, Localisation, Mooc.