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.
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 ?
Elementary functions extended to intervals
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?
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.
What is a contractor?
Contractor for z=x+y
Contractor for primitive equations
Decomposition of complex equations
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.
[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.