Here, you have an access to the videos only. If you want to have the real IAMOOC, with the diploma, the Quiz, the forum, etc. see http://iamooc.ensta-bretagne.fr

Certified Final Exam: it will be possible to take a certified exam at the end of the school. In case of positive result, the certification can be used by students to obtain the corresponding ECTS from their PhD courses, or to comply with any other requests by their home university.

- Pdf with all exercises iamooc_exos.pdf
- Python programs corresponding to the correction (when available): iamooc_py.zip.
- Slides of the lesson
- A small doc on PyIbex and Vibes
- Chapter 0. Install all you need
- Chapter 1. Interval Computation
- Chapter 2. Set inversion
- Chapter 3. Contractors
- Chapter 4. Application to robot localization
- References
- List of students who got the diploma

In the last version of PyIbex (2017), few things have changed in the Python
code and the code written in the videos is not always exactly consistent with the latest version of
PyIbex. Below are listed the changes.

from pyIbex import * should be replaced by from pyibex import *

SepQInterProjF should be replaced by SepQInter

Moreover, to start Vibes from your terminal, write
Vibes-viewer instead of vibes.

Some other modifications are described in the PyIbex documentation. (in magenta)

The goal of Chapter 0 is to help you to install all what you need to follow IAMOOC.
You need Vibes [Dre14] for graphics.

**Method**

1) Install Conda as described at http://conda.pydata.org/docs/install/.

2) Install pyibex

conda install -c benensta pyibex3) Install Vibes

conda install -c benensta vibes vibes-bin4) Install Spyder

conda install spyderA video to help you for the install is available for Windows and also for Linux (Ubuntu).

The goal of Chapter 1 is to
introduce all the mathematics related to interval analysis [Moo66]. After
this chapter, you should be able to compute with uncertain numbers
represented by intervals and also to approximate a set by subpavings [Jau01],
i.e., union of boxes. During the practice we will implement the
interval calculus under a Python environment.

What is an interval ?

Operators

Examples

Elementary functions extended to intervals

Examples

Boxes

Width

Subpavings

Inclusion functions

Monotonicity

Convergence

Natural inclusion function

Minimal inclusion function

Many problems of engineering such as
parameter estimation, tuning of a controller, etc., can be cast into
a set inversion problem. In this chapter, we will define the notions
of set inversion and illustrate these notions on some examples. An
algorithm for solving any set inversion problems will be given. This
algorithm, named SIVIA (Set Inverter Via Interval Analysis), will be
proposed. This algorithm will be implemented in
Python and some test-cases will be solved.

What is set inversion?

Example

Inclusion tests

SIVIA

Parameter estimation

A contractor [Cha09] is an operator which takes as an input a box X and contracts it into a subbox Y without
removing a single solution of the problem. Contractors are necessary to solve efficiently problems containing
a large number of unknowns. This chapter introduces the notion of contractor and
explains how they can be implemented in Python.

Motivations

What is a contractor?

Properties

Example

Contractor for z=x+y

Contractor for primitive equations

Decomposition of complex equations

Forward-backward contractor

This chapter considers a problem of localization inside an environment with landmarks. No lessons is given in this chapter, only exercises. The main problem to be treated here is SLAM (Simulataneous Localization And Mapping). It will be decomposed into a list of 4 exercises with an increasing complexity.

Illustration of Interval SLAM for real applications..

[Moo66] RE Moore (1966), *Interval analysis, * Prentice-Hall.

[Jau01] L. Jaulin, M. Kieffer, O. Didrit and E. Walter (2001), *Applied Interval Analysis
with Examples in Parameter and State Estimation, Robust Control and Robotics,* Springer-Verlag.

[Jau02] L. Jaulin and E. Walter (2002). Guaranteed robust nonlinear minimax estimation.
*IEEE Transaction on Automatic Control*.
Volume 47, number 11, pages 1857, 1864. pdf.

[Cha09] G. Chabert and L. Jaulin (2009), Contractor programming. *Artificial Intelligence*.
Vol. 173, pp 1079-1100. pdf.

[Kea96] B. Kearfott, Rigorous Global Search: Continuous Problems (Nonconvex Optimization and Its Applications), Kluwer, 1996.

[Nin11] J. Ninin et F. Messine. A metaheuristic methodology based on the limitation of the memory of interval branch and bound algorithms. Journal of Global Optimization (2011) 50:629-644.

[Jau15a] L. Jaulin, *Automation for robotics*, ISTE WILEY, 2015.

[Jau15b] L. Jaulin, *Mobile robotics*, ISTE WILEY, 2015.

[Dre14] V. Drevelle and J. Nicola. *VIBes: A Visualizer for Intervals and Boxes.
*Mathematics in Computer Science, 2014.

[Jau14] L. Jaulin and B. Desrochers (2014). Introduction to the Algebra of Separators with
Application to Path Planning. *Engineering Applications of Artificial Intelligence*
pdf.

[Mei02] D. Meizel, O. Lévêque, L. Jaulin and E. Walter (2002). Initial Localization by Set Inversion. *IEEE
Transactions on Robotics and Automation *. Volume 18, Number 6, pages 966-971.
pdf.

[Kie99] M. Kieffer, L. Jaulin, E. Walter and D. Meizel. Guaranteed mobile robot tracking using interval analysis, MISC'99 Workshop on Application of Interval Analysis to System and Control, Girona, 24-26 février 1999. pdf.

[Jau11] L. Jaulin (2011). Range-only SLAM with occupancy maps; A set-membership approach. *IEEE-TRO*.
Vol 27, Issue 5. pdf.

[Jau96] L. Jaulin, E. Walter and O. Didrit (1996). Guaranteed robust nonlinear parameter bounding, CESA'96 IMACS
Multiconference (*Symposium on Modelling, Analysis and Simulation*), Lille.
pdf.

[Kre97] V. Kreinovich, A.V. Lakeyev, J. Rohn, P.T. Kahl (1997). Computational complexity and feasibility of data processing and interval computations, Springer Science Business Media.

[Poi03] P Poignet, N Ramdani, O Vivas, Robust estimation of parallel robot dynamic parameters with interval analysis, CDC, 2003.

[Ben99] F. Benhamou, F. Goualard, L. Granvilliers, Revising hull and box consistency, Proceedings of the 1999 International Conference on Logic Programming.

AUBERTOT Quentin

BARONI Kévin

BARONNIER Romain

BASSET Pierre

BEAUDOIN Maxime

BERNARDES Evandro

BOENNING Hannah

BOURGOIS Auguste

CHANU Simon

COTTEN Guillaume

DALIN Eloïse

EL ABDALAOUI Zacharie

ENNOUHI M'hamed Fadil

FONTANA Werner

GALLAND Alexandre

GY Morgan

KARKOUB El Wali

LE ROCH Gwenn

LEGAY Kevin

LI Ang

LIU Wanxin

MARTIN Pierre

MEHDI Nima

MILHEM Rémi

NEAU Guillaume

PERTIERRE DO MONTE

PLANCHOT Antoine

RAYNEAU Vincent

SOLA Yoann

SOULIE Camille

SUN Tithnara

TANGUY Florian

TERTRAIS Donatien

THIBAULT Adrien

TOMEZACH Julien

VADAINE Hugo

WELTE Anthony

ZHU Lei

ZIANE Mohamed Mahrez

BEN SAID Hela

BHIRI Bessem

BOUKALYassine

El JAWAD Alaa

MANSOUR Fatma

MESLEM Nacim

ORJUELA Rodolfo

RENAUDEAU Brice

ROUSSEAU Gauthier

TANGUY Noel

VANDERMOTTE Sylvain

Alain Acevedo

Yacine Benhnini

Justine Bonnot

François Cébron

Jean-Marie CODOL

Julien Damers

Hani Dbouk

Lionel Génevé

Gabriel GODEAU

Jean-Philippe Gras

Yoann Guguen

Fabrice Lallement

Philippe Lambert

Julien Langlois

Francois Leborne

Nisha Mahato

Fatma Mansour

Mohamad Mezher

Yasmine Najar

Mohamed Outahar

Clément Rolinat

Joris Tillet

Sophie Tuton

Nicolas Veylon

Raphael Voges

Jean Walter

Mohamed Ouadrhiri

Maha Abouzai

Yves Le Palud

Emilien Fournier

Philipe Miranda de Moura

Julien Brisset