Lessons and seminars of Luc Jaulin
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2024
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[286] 2024, 26,27 november, Meeting FARO. Palaiseau
Title: A time multiplexing technique to control the heading of an underwater robot using an inertia wheel
Contributors: Gabriel Betton, Mathis Riera, Loïck Degorre, Lionel Lapierre, Luc Jaulin
Abstract. In this presentation, we give a new control approach to stabilize the heading of an underwater robot with a single inertia wheel.
To our knowledge, the controllability of this nonlinear system cannot proved using existing controllability criteria.
Moreover, in our problem, we have several variables to control with a unique scalar input.
The principle of our approach is to ask the system to perform a cycle.
The shape of the cycle which is tuned using a multiplexing technique that will allow us to stabilize independently all outputs.
An illustration on a real underwater robot illustrates the feasibility of the approach.
[285] 2024 November 14 , Nantes, journée du pôle Robotique, Procédés et Calcul (RPC) du LS2N
Title: Explore and return for an underwater robot in a minimalist environment and with few computation
Abstract. The current advancements of robotics demand increasing amounts of computation, communication, sensors, energy, and complexity each year.
The objective of this work is to motivate the development of robotic systems which reduce the cost of the infrastructure, with less embedded
intelligence. Such systems are likely to be more predictable, robust against unforeseen events, and aligned with sustainable development principles.
As an illustration, we consider an underwater robot that has to explore a huge unknown environment and be able to come back home.
We assume that no localization system exists, the robot is not allowed to surface to collect the GPS,
and the environment is minimalist (i.e., with few landmarks).
Moreover, the embedded intelligence is poor with a simple micro-controller available for the mission.
We want to show that in this context, it can be possible to perform a safe exploration without being lost.
More precisely, it will be shown that considering the concept of 'stable cycle',
used by many migratory animals for navigation, an underwater robot can move autonomously
from zones to zones without getting lost, with an echo-sounder as a unique exteroceptive sensor.
I will show how the stability of these cycles can be proven using the concept of Poincaré map and interval analysis.
Some real experiments will show the feasibility of the approach for an underwater navigation where the GPS cannot be used.
[284] 2024 October 30 , Salle M109, ENSTA-Bretagne, Brest
Titre : The Luenberger contractor
Abstract.
In this presentation, I show how the classical Luenberger observer can be used to build an efficient interval tube
contractor for constraints described by linear differential equations.
I will also explain how the approach can be used to propagate forward in time an ellipsoid in the state space.
[283] 2024 October 16,17,18 , ICOSSOD24, Jerez, Cádiz, Spain
Title: Explore and return with robots in a minimalist environment and with few computation
Abstract. The current advancements of robotics demand increasing amounts of computation, communication, sensors, energy, and complexity each year.
The objective of this work is to motivate the development of robotic systems which reduce the cost of the infrastructure, with less embedded
intelligence. Such systems are likely to be more predictable, robust against unforeseen events, and aligned with sustainable development principles.
As an illustration, we consider an underwater robot that has to explore a huge unknown environment and be able to come back home.
We assume that no localization system exists, the robot is not allowed to surface to collect the GPS,
and the environment is minimalist (i.e., with few landmarks).
Moreover, the embedded intelligence is poor with a simple micro-controller available for the mission.
We want to show that in this context, it can be possible to perform a safe exploration without being lost.
For this purpose we will emulate the marine turtles which are able to travel long cycles in the ocean and
come back to their birth beaches or imitate the Polynesians that were able traverse great distances between islands.
[282] 2024, 2 October 2024, Contredo meeting, Paris
Title: The role of preconditioning for contractors
Abstract. Centered form is traditionally used to enclose the range of a function over narrow intervals.
The quadratic approximation property guarantees an asymptotically small overestimation for sufficiently narrow boxes.
In this presentation, I will show how the centered form can be included efficiently inside a propagation process to get more precise contractions.
I will also show the fundamental role of the preconditioning.
[281] 2024, 28 aout, Brest, a small Robex seminar.
Title: The swim disk
Abstract. The swim disk is 2D an underwater disk-shaped robot that can rotate on itself thank to an inertial wheel.
The robot has only one input which is the torque between the robot and the wheel. In the presentation, I will show that the
robot can be controlled using periodic sequences of inputs.
[280] 2024, 4 juillet, virtuel, Toulon.
Titre: RobMOOC pour l'enseignement à distance de la commande non linéaire des robots mobiles
Résumé. RobMOOC ( https://www.ensta-bretagne.fr/robmooc/ ) est un cours en français, gratuit et ouvert à tous.
Il s'agit d'un cours diplômant sur la commande non-linéaire des robots mobiles. Ce cours s'adresse à des débutants,
bien que certaines notions en mathématiques soient nécessaires (typiquement le niveau demandé à l'entrée des écoles d'ingénieur).
Dans cet exposé je présenterai les principes et le déroulement de ce cours. Je traiterai également un morceau d'exercice à l'aide de Python.
[280] 2024, 3 juillet, salle D002, 9h->15h, ENSTA, Brest.
Titre: EXOS 2024, Prévention des collisions en mer, avancement
Résumé. Présentation de différents scénarios pour la détection et l'évitement d'obstacles
pour des voiliers de type Imoca. Afin de pouvoir reproduire des situations complexes, nous envisageons
une solution où les obstacles sont des USV autonomes.
[279] 2024, June 10,11, Palaiseau. AID
Title: Validated control using interval and flatness; application to the car-trailer
Abstract.
This presentation proposes to combine methods coming from nonlinear control theory such as flatness,
or feedback linearization with interval analysis, in order to guarantee that a mobile robot
will not enter inside a forbidden zone.
The principle is to use flatness to transform differential constraints into analytical inequalities using Lie derivatives.
The resolution is performed numerically and rigorously using interval analysis tools without using any interval integration.
The methodology will be illustrated on the car-trailer vehicle.
[278] 2024, 16 Février, salle F201 à 14h Brest.
Titre: EXOS 2024, Prévention des collisions en mer, avancement
Résumé. Présentation de différents scénarios pour la détection et l'évitement d'obstacles
pour des voiliers de type Imoca. Afin de pouvoir reproduire des situations complexes, nous envisageons
une solution où les obstacles sont des USV autonomes de type BlueBoat.
[277] 2024, February 13-16 Winter School Set4MOST (Set-Based methods for Modeling, Estimation and Control), Lille
Title: Interval analysis with application to robust control of linear systems
Abstract. In this lesson, I will present the basic notions on Interval analysis.
Unlike classical numerical approaches (Monte-Carlo or local methods, for instance), the results provided by interval tools
are safe, even when strong non-linearities are involved in the problem.
In this lesson, I will show how interval methods can be used to solve robust control problems of uncertain parametric linear systems.
The uncertainty is represented by intervals which contain the unknown parameters.
[276] 2024, January 18, 11h. Apple seminars, Munich
Title: Interval analysis for the validation of autonomous vehicles properties
Abstract. In this lesson, I will present the basic notions on Interval analysis and constraint networks.
These tools can be used to solve a large class of nonlinear problems such as
(i) computing all global minimisers of a non-convex criterion,
(ii) computing all solutions of a set of nonlinear equations,
(iii) characterizing sets defined by nonlinear inequalities.
Unlike classical numerical approaches (Monte-Carlo or local methods, for instance), the results provided by interval tools
are obtained in a guaranteed way, even when strong non-linearities are involved in the problem.
This property makes interval analysis very attractive to address the safe navigation of autonomous mobile robots.
The purpose of this lesson is to introduce in a pedagogical way the principles of interval methods and
contractor programming techniques. To illustrate the efficiency and the reliability of the approach we will
consider nonlinear state estimation, dynamic localization and nonlinear control of autonomous vehicles.
Illustrations involving real robots will also be provided.
[275] 2023. December 5 Third Robexday
Brest, France
Title: Control of a enemy swarm by broadcasting false messages
Abstract.
In this talk, I will consider several enemy robots moving in a flat environment made with landmarks.
These robots have a controller which is known, i.e., we know the algorithm inside each robot.
The controllers use the information on the position of some landmarks that are broadcast
by the landmarks themselves (for instance, using AIS).
We assume that we have the control of the messages sent by the landmarks.
The problem to be considered is to control the trajectories of the robots by broadcasting false information.
[274] 2023. November 10, 15h30 Séminaire Lix
Polytechnique, Palaiseau, France
Title: Guaranteed numerical methods to secure a zone with autonomous robots
Abstract.
In this talk, we provide an interval-based method to prove that there are no submarine intruders inside a zone of the ocean (here the Bay of Biscay).
For this purpose, a group of underwater robots will be used. We assume that
- Our robots are able to localize themselves with a given accuracy.
- They are able to communicate at a low rate at low distances.
- Each robot is able to detect any intruder inside a disk of a known radius.
- The speed of the intruders is assumed to be bounded and is small with respect to that of our robots.
Our goal is twofold:
- to characterize a set for which we can guarantee that there is no intruder (this corresponds to the secure zone)
- to find a control strategy for the group of robots in order to extend the secure zone as much as possible.
[273] 2023. November 9, 10 Réunion AID
Université Paris-Saclay, Orsay, France
Title: Inertial control of a flat spinning disk
Abstract.
We propose a Lyapunov approach to control the rotation of a flat disk spinning in a three-dimensional space
without gravity nor any other external forces.
The motion of the disk is governed by the Euler's rotation equation for spinning objects.
The control is made through the inertia matrix of the disk.
Only a partial control of the rotation can be done since the angular momentum should remain constant.
The assumption that the disk is flat creates a difficulty since masses used to change the inertia matrix
are not allowed to move along the axis normal to the disk plane.
[272] 2023, November 6-9 Journées Drones du réseau DRONES and CAP,
Base de plein air du lac de Guerledan, Bretagne
Title: Validation a priori d'une mission sous-marine
Abstract. On considère un robot évoluant dans un environnement connu et on fait
hypothèses que les bruits de mesures et d'état sont inconnus, mais bornés.
Dans cette présentation, je vais chercher à montrer comment il est possible
de montrer que le robot atteindra la zone visée et ceci même dans le pire des scénarios.
[271] 2023, October 23-27 Summer School SAUTOS: Safe AUTOnomous Systems, Université Paris-Saclay, Orsay, France
Title: Interval analysis with application to the safe navigation of autonomous vehicles
Abstract. In this lesson, I will present the basic notions on Interval analysis and constraint networks.
These tools can be used to solve a large class of nonlinear problems such as
(i) computing all global minimisers of a non-convex criterion,
(ii) computing all solutions of a set of nonlinear equations,
(iii) characterizing sets defined by nonlinear inequalities.
Unlike classical numerical approaches (Monte-Carlo or local methods, for instance), the results provided by interval tools
are obtained in a guaranteed way, even when strong non-linearities are involved in the problem.
This property makes interval analysis very attractive to address the safe navigation of autonomous mobile robots.
The purpose of this lesson is to introduce in a pedagogical way the principles of interval methods and
contractor programming techniques. To illustrate the efficiency and the reliability of the approach we will
consider nonlinear state estimation, dynamic localization and nonlinear control of autonomous vehicles.
Illustrations involving real robots will also be provided.
[270] 2023, October 5, ENSTA, Brest
Title: Exploration based on the electric sense
Abstract. We present an approach to explore an environment
using the electric sense as a unique exteroceptive sensor.
[269] 2023, September 27, ENSTA, Brest
Title: Ocean exploration with robots
Abstract. Il s'agit d'une rencontre avec Syrehna.
Some novelties related to robotics exploration are presented. We mainly consider the underwater environment.
[268] 2023, August 23, Hannover. 9am, Room V411, Schneiderberg 50
Title: Interval methods for the detection and the capture of intruders using autonomous robots
Abstract. The talk is motivated by the detection of submarine intruders inside the Bay of Biscay (golfe de Gascogne).
In this project, we consider a group of underwater robots that are able to localize with a given accuracy using a state observer.
We assume that each robot is able to detect any intruder inside a disk of a known radius. Moreover, the speed of the intruders
is assumed to be bounded and is small with respect to that of our robots. The goal of this project is twofold:
(1) to characterize a set for which we can guarantee that there is no intruder (this corresponds to the secure zone)
(2) to find a control strategy for the group of robots in order to extend the secure zone as much as possible.
We will see how interval analysis can be used to compute efficiently the sets of interest.
[267] 2023, May, 4,5, Imagin : journée imprécision et incertitude en analyse et traitement d'images, à Jussieu, Paris.
Title: Detection and capture of intruders using robots
Abstract.
The talk is motivated by the detection of submarine intruders inside the Bay of Biscay (golfe de Gascogne).
In this project, we consider a group of underwater robots inside a zone with a known map (represented by an image).
We assume that each robot is able to detect any intruder nearby. Moreover, the speed of the intruders is assumed to be bounded and is small
with respect to that of our robots. The goal of this presentation is twofold:
(1) to characterize an image representing the secure zone, i.e., the area for which we can guarantee that there is no intruder
(2) to find a strategy for the group of robots in order to extend the secure zone as much as possible.
[266] 2023, May 2,3, Moulin mer.
Title: Helios Challenge : Build an ocean current map from navigation data of an autonomous boat
Abstract.
The challenge that is proposed is to collect data from an autonomous boat (Helios) that will navigate for hours
in the sea with strong currents. From these data, we will have to estimate the currents in navigation zone.
[265] 2023, April 26, Guerlédan.
Title: Méthode linéaire pour la calibration des magnétomètres et accéléromètres
Abstract.
Présentation d'une méthode simple pour la calibration des magnetomètres et des accéléromètres d'un petit drone
[264] 2023, April, 18,19, Palaiseau, AID meeting.
Title: A contractor which is minimal for narrow boxes
Abstract.
Centered form is one of the most fundamental brick in interval analysis. It is traditionally used to enclose the range of a function over narrow intervals.
The quadratic approximation property, guarantees an asymptotically small overestimation for sufficiently narrow boxes.
In this presentation, I will propose to use the centered form to build efficient contractors that are optimal when the intervals are narrow.
The method is based on the centered form combined with a Gauss Jordan band diagonalization preconditioning.
[263] 2023, March, 2, Moulin mer
Title: Robex: robotics for exploration
Abstract. Séminaire Lab-STICC à Moulin mer
Présentation de l'équipe Robex avec son rôle dans le pôle IA et Océan.
[263] 2023, Fébruary, 7, ENSTA, Brest
Title: Ocean exploration with robots
Abstract. Il s'agit d'une rencontre avec le conseiller technique innovation Minarm.
Some novelties related to robotics exploration are presented. We mainly consider the underwater environment
[262] 2023, January 09, Virtual,
Title: Toward dynamic epistemic robotics
Abstract.
We present how Dynamic Epistemic Logic can be extended to robotics systems where the
evolution can be represented by differential equations. The memory of the robot can be estimated from
its actions.
[261] 2022, November, 22,23, Télécom Paris, Palaiseau
Title: Inner and outer characterisation of the projection of polynomial equations using symmetries, quotients and intervals
Abstract. A new method for computing an inner and outer approximation for a set defined as a projection of polynomial equations will be presented.
To develop the algorithm, different concepts that are not common in the domain of interval analysis will be used : symmetries, the quotient by an equivalence relation and the choice function.
The approach will be illustrated by two important applications. The first one is the characterisation of the workspace of one object with one degree of freedom.
The second application is the estimation of the speed of one object seen by several observers with uncertain headings.
[260] 2022, 27 septembre, Navigation and control of Underwater vehicles, SeaTechWeek, Brest
Title: Underwater exploration by an autonomous robot with the method of stable cycles
Résumé. In an environment where almost no landmarks exist for localization, as it is the case
for many underwater applications, we show that considering the concept of 'stable cycle',
used by many migratory animals for navigation, an underwater robot can move autonomously
from zones to zones without getting lost. In the first part of the talk, I will show
how the stability of these cycles can be proven using the concept of Poincaré map and interval analysis.
Some real experiments show the feasibility of the approach for underwater navigation where the GPS cannot be used.
We also propose the new concept of Poincaré scan for the exploration of an unstructured environment
where no landmarks exist.In the second part of the talk, I will consider the exploration of an unknown environment.
For this, it will be shown how stable cycles can be found with the guarantee that the robot is never lost.
[259] 2022, 21 septembre, La robotique marine au service de l'observation, Amphi A - IUEM
Title: Exploration sous-marine autonome par la méthode des cycles stables
Résumé. L’homme effectue dans l’océan de nombreuses missions longues et périlleuses comme le transport de marchandises,
la construction d’infra-structures offshore, la recherche d’épaves, etc.Du fait de la pénibilité, du coût,
et de la dangerosité de ces missions, les robots marins y sont de plus en plus utilisés.
De nos jours, ils le sont principalement pour la prise de mesures, la construction de cartes sous-marines,
la recherche de mines ou l’étude des courants marins. Afin d’éviter les collisions avec le trafic en surface,
on demande généralement aux robots de rester sous l’eau et de ne jamais refaire surface.
La localisation devient difficile et même souvent impossible du fait de l’absence d’amers
(points de repère à terre utilisés pour se repérer en mer) et du non fonctionnement du système de géolocalisation
et navigation par un système de satellites (GNSS). En mimant les techniques des anciens navigateurs, ou des animaux marins
(comme les tortues marines), nous allons montrer comment un groupe de robots sous-marins faiblement communicants
peut explorer un environnement très vaste, sans se perdre, et sans pour autant chercher à se géolocaliser.
[258] 2022, September 7-9, TAROS 2022, Oxford, Culham science center, September 07-08, 2022
Title: Underwater exploration by an autonomous robot with the method of stable cycles
Abstract. In an environment where almost no landmarks exist for localization, as it is the case
for many underwater applications, we show that considering the concept of 'stable cycle',
used by many migratory animals for navigation, an underwater robot can move autonomously
from zones to zones without getting lost. In the first part of the talk, I will show
how the stability of these cycles can be proven using the concept of Poincaré map and interval analysis.
Some real experiments show the feasibility of the approach for underwater navigation where the GPS cannot be used.
We also propose the new concept of Poincaré scan for the exploration of an unstructured environment
where no landmarks exist.In the second part of the talk, I will consider the exploration of an unknown environment.
For this, it will be shown how stable cycles can be found with the guarantee that the robot is never lost.
[257] 2022, Tuesday, July 12, London, ECC Workshop on Control, Estimation and Modelling Practice for Robotic Applications in Challenging Environments.
Title: Estimation and navigation of marine robots in underwater exploration applications
Abstract. In an environment where almost no landmarks exist for localization, as it is the case for many underwater applications,
we show that considering the concept of 'stable cycle', used by many migratory animals for navigation,
an underwater robot can move autonomously from zones to zones without getting lost.
In the first part of the talk, I will show how the stability of these cycles can be proven using
the concept of Poincaré map and interval analysis. Some real experiments show the feasibility of the approach
for underwater navigation where the GPS cannot be used. We also propose the new concept of Poincaré scan
for the exploration of an unstructured environment where no landmarks exists. In the second part of the talk,
I will consider the exploration of an unknown environment.
For this, it will be shown how stable cycles can be found with the guarantee that the robot is never lost.
[256] 2022, June 15,16, AID meeting.
Title: Fuzzy set estimation using interval tools; Application to localization
Abstract. We propose a new approach to characterize alpha-cuts of fuzzy sets using interval analysis and interval solvers.
The information representing the random vector is represented by a membership function, which is issued from the composition
of a score function and a characteristic function associated to some elementary epistemic sets,
considered as the elementary granules of knowledge. Each granule is attached to a given measurement
or any other elementary information we have on the vector to be estimated. The proposed approach will make it possible
to obtain an efficient interval-based algorithm able to find an inner and an outer approximation of the \alpha-cut to be characterized.
An application related to the localization of an underwater robot will be presented to illustrate the efficiency of the approach.
[255] 2022, 3 Juin, 15e édition des Journées Scientifiques de La Cité des congrès de Nantes sur le thème
des "Capteurs communicants pour le génie océanique"
Title: Autonomous submarine exploration by a group of robots
Résumé. L’homme effectue dans l’océan de nombreuses missions longues et périlleuses comme le transport de marchandises,
la construction d’infra-structures offshore, la recherche d’épaves, etc.Du fait de la pénibilité, du coût,
et de la dangerosité de ces missions, les robots marins y sont de plus en plus utilisés.
De nos jours, ils le sont principalement pour la prise de mesures, la construction de cartes sous-marines,
la recherche de mines ou l’étude des courants marins. Afin d’éviter les collisions avec le trafic en surface,
on demande généralement aux robots de rester sous l’eau et de ne jamais refaire surface.
La localisation devient difficile et même souvent impossible du fait de l’absence d’amers
(points de repère à terre utilisés pour se repérer en mer) et du non fonctionnement du système de Géolocalisation
et navigation par un système de satellites (GNSS). En mimant les techniques des anciens navigateurs, ou des animaux marins
(comme les tortues marines), nous allons montrer comment un groupe de robots sous-marins faiblement communicants
peut explorer un environnement très vaste, sans se perdre, et sans pour autant chercher à se géolocaliser.
[254] 2022, April 26, Virtual,
Title: Isowinding method
Abstract.
We propose a method to characterize the winding number of a contour using an
homology based method. The principle is to follow edges corresponding to a constant winding number.
[253] 2022, March, 18, Submeeting 2022, Saint Raphaël
Titre: L’exploration sous-marine en autonomie
Résumé.
L’homme effectue dans l’océan de nombreuses missions longues et périlleuses comme le transport de marchandises,
la construction d’infra-structures offshore, la recherche d’épaves, etc.
Du fait de la pénibilité, du coût, et de la dangerosité de ces missions, les robots marins y sont de plus en plus utilisés.
De nos jours, ils le sont principalement pour la prise de mesures, la construction de cartes sous-marines,
la recherche de mines ou l’étude des courants marins. Afin d’éviter les collisions avec le trafic en surface,
on demande généralement aux robots de rester sous l’eau et de ne jamais refaire surface. La localisation devient difficile et
même souvent impossible du fait de l’absence d’amers (points de repère à terre utilisés pour se repérer en mer)
et du non fonctionnement du système de Géolocalisation et navigation par un système de satellites (GNSS).
En mimant les techniques des anciens navigateurs, ou des animaux marins (comme les tortues marines), un robot sous-marin
peut explorer un environnement très vaste et revenir à sa position initiale, sans pour autant être capable de se géolocaliser.
[252] 2022, March, 18, Pôle numérique, Plouzané, réunion pôle IA & océan
Titre: Intervalles pour l'exploration autonome
Résumé. Le calcul par intervalles est ici comparé aux méthodes probabilistes plus classiques.
Quelques exemples en localisation et en exploration par des robots sont donnés.
[251] 2022, March, 11, Louisiana State University (virtual)
Title: Interval contractors to solve dynamical geometrical equations; application to underwater robotics
Abstract. In an Euclidian space, the separation between two points corresponds to their distance which is purely
spatial, and is always positive. In space-time, the separation between two events takes into account
not only the spatial separation between the events, but also their temporal separation.
In this talk, we will consider problems involving geometrical constraints in the
space-time in an underwater robotics context.
The motion of the robots will be described by differential equations and the clocks attached to each robot
are not synchronized.
An interval contractor based technique will be used to solve the distributed state estimation problem.
The method will be illustrated on the localization of a group of underwater robots with unsynchronized clocks.
In this problem, we consider that the travel time of the sound that gives us the distances between robots cannot be neglected.
[250] 2022, March, 8,9, Télécom Paris, Palaiseau
Title: Actions of the hyperoctahedral group to compute minimal contractors
Abstract. The hyperoctahedral group Bn is the group of symmetries of a hypercube of R^n. For instance permutations,
or symmetries along each of the n canonical planes of R^n all belong to Bn. Now, many sets of equations we meet in our applications
contain hyperoctahedral symmetries. This is the case of the addition constraint x+y=z or the multiplication x*y=z.
The addition and multiplication constraints for matrices such as A+B=C or A*B=C contain many hyperoctahedral symmetries.
In robotics, many specific geometrical constraints such as for instance constraints involving distances or angles
have hyperoctahedral symmetries. In this talk, I will present an algorithm which will allow us to build minimal contractors
with a polynomial complexity associated with constraints with hyperoctahedral symmetries.
[249] 2021, November 24, Mercredi 24 novembre 15:30, ENSTA-Bretagne, Brest, First Robex day.
Title: Solving geometrical constraints in space-time
Abstract. In an Euclidian space, the separation between two points corresponds to their distance which is purely
spatial, and is always positive. In space-time, the separation between two events takes into account
not only the spatial separation between the events, but also their temporal separation.
In this talk, we will consider problems involving geometrical constraints in the
space-time. The motion of the objects will be described by differential equations and the clocks attached to each robot
are not synchronized.
An interval-based technique will be used to solve the problem.
The method will be illustrated on the localization of a group of underwater robots with unsynchronized clocks.
In this problem, we consider that the travel time of the sound that gives us the distances between robots cannot be neglected.
[248] 2021, October 22, Virtual meetings : Interval Methods in Control.
Title: A modified twin arithmetic to characterize uncertain sets
Abstract.
Given an interval [a,b]. When the bounds a and b are not known exactly, then the interval becomes uncertain.
When we this uncertainty is represented by an interval for the bounds (i.e., a in [a] and b in [b]),
then the corresponding set of intervals is called a 'twin'. More precisely, a twin [[x]] is the set of all intervals [x]=[a,b]
such that a in [a] and b in [b]. A 'thick set' [[X]] with bounds A and B is a set of all subsets X of R^n such
that A is a subset of X which is a subset of B.
Thick sets occur naturally in several applications such as in robotics when we want to characterize the zone that has been explored
by a robot when the trajectory of the robot is uncertain (for instance represented by a tube). Whereas a twin can be interpreted as
an uncertain set of R, a thick set can thus be understood as an uncertain set of R^n.
In this talk, I will show that a modified twin arithmetic will allow us to characterize efficiently thick sets.
Some applications related to robotics exploration will be given.
[247] 2021, October 14, Hannover (virtual)
Title: Underwater exploration by an autonomous robot with the method of stable cycles
Abstract. In an environment where almost no landmarks exist for localization, as it is the case
for many underwater applications, we show that considering the concept of 'stable cycle',
used by many migratory animals for navigation, an underwater robot can move autonomously
from zones to zones without getting lost. In the first part of the talk, I will show
how the stability of these cycles can be proven using the concept of Poincaré map and interval analysis.
Some real experiments show the feasibility of the approach for underwater navigation where the GPS cannot be used.
We also propose the new concept of Poincaré scan for the exploration of an unstructured environment
where no landmarks exist.In the second part of the talk, I will consider the exploration of an unknown environment.
For this, it will be shown how stable cycles can be found with the guarantee that the robot is never lost.
[246] 2021, October 11,12, Palaiseau
Contributors: A. Rauh and L. Jaulin
Title: Determining Ellipsoidal Outer and Inner Enclosures of Nonlinear Mappings of Ellipsoidal Domains
Abstract. A large variety of approaches for set-valued simulation, parameter identification, state estimation as well as reachability,
observability and stability analysis for nonlinear discrete-time systems involve the propagation of ellipsoids via nonlinear
functions. It is well known that the corresponding image sets usually possess a complex shape and may even be non-convex
despite the convexity of the input data. For that reason, domain splitting procedures are often employed which help to
reduce the phenomenon of overestimation that can be traced back to the well-known dependency and wrapping effects
of interval analysis. In this talk, we propose a simple, yet efficient scheme for simultaneously determining outer and
inner ellipsoidal range enclosures of the solution for the evaluation of multi-dimensional functions if the input domains
are themselves described by ellipsoids. The Hausdorff distance between the computed enclosure and the exact solution
set reduces at least linearly when reducing the size of the input domains.
[245] 2021, October 1, Tampere, Finland
Title: Guidance, Navigation and Control for Autonomous Offshore Robots
Abstract. As introduction to the thesis defense of Jose Villa Escusol, I present the main problems
that are met in the context of offshore robotics. The difficulty of localization underwater and the limited
communications orients us toward a cooperation between different types of robots : those at the surface and
those that explore the seafloor.
[244] 2021, Septembre, Oléron, journées drones et capteurs embarqués
[243] 2021, September 23, Montage projet Horizon
Title: Intervals and symmetries for inertial units
Abstract. We discuss on the integrity in the context of inertial units for a safe estimation of the position and orientation of a robot.
[242] 2021, September 02, Virtual,
Title: Winding contractor
Abstract.
The winding contractor considers the constraint which links a tube for a trajectory, a tube for its derivative
and the winding number. We show how the resulting contractor can be built
[241] 2021, July 21, Virtual,
Title: Partial borders and injective covering
Abstract.
A new way to compute the inverse-image problem based on an injective covering of the search box is presented.
[240] 2021, July 21, Virtual,
Title: Directional inflation
Abstract.
How to classify some fake boxes boxes in the waterfall side ?
Some hints using inflation are proposed.
[239] 2021, le 26 mai, à Rennes, Futurobot
Titre: Exploration sous-marine par des robots
Résumé. L'homme effectue dans l'océan de nombreuses missions longues et périlleuses
comme le transport de marchandises, la construction d'infra-structures offshore, la recherche d'épaves, etc.
Du fait de la pénibilité, le coût, et dangerosité de ces missions, les robots marins y sont
de plus en plus utilisés. De nos jours, ils le sont principalement pour la prise de mesures,
la construction de cartes sous marines, la recherche de mines ou l'étude des courants marins.
Afin d'éviter les collisions avec le trafic en surface,
on demande généralement aux robots de rester sous l'eau et de ne jamais refaire surface.
La localisation devient difficile et même souvent impossible du fait de l'absence d'amers
et du non fonctionnement du GNSS.
En mimant les techniques des anciens navigateurs, ou des animaux marins (comme les tortues marines),
nous allons montrer qu'un robot sous marin peut explorer un environnement très vaste et revenir à sa position
initiale sans pour autant être capable de se géolocaliser.
[238] 2021, May 5, Virtual,
Title: Sweep function
Abstract.
I define the notion of sweep function which makes the link between the waterfall box and the mosaic.
[237] 2021, April 15, Virtual,
Title: Counting for exploration
Abstract.
I consider different types of problems in robotics such as counting the number of landmarks that
have been seen by a robot, the area that has been explored and the mathing between landmark detections.
[236] 2020, December 18, Virtual meetings : Interval Methods in Control.
Title: A boundary approach for set inversion
Abstract.
A set defined as a set-inversion problem X=f^-1(Y) has an inside and an outside, which may be possibly empty.
When we characterize the solution set X using contractors, existing techniques generally
perform the same computation twice: once for the inside of X and once for the outside. The factorization
of the calculus is generally not proposed to keep the solver simple and generic.
A simple way to factorize the computation is to inverse the boundary of Y only. We thus get a characterization of
the boundary of X.
Unfortunately, for each box of the generated paving, we lose the information on which side of the boundary the box is.
In this talk, I will explain how this information can obtained during the propagation process at a negligible cost.
For this purpose, I will introduce the notions of directional contractors and contractible functions.
These tools will also be used to derive contractor techniques that can be more efficient than existing ones.
[235] 2020, December 11, Heudiasyc, Compiègne.
Title: Lie symmetries for an efficient propagation of uncertainties ; application to robot localization
Abstract.
I will present a common work with Julien Damers (phd student) and Simon Rohou (co-supervisor).
In robotics, localization and SLAM problems generally have symmetries (translation, rotation, scales, time invariance, etc).
Moreover, as for many state estimation problems, we generally need a reliable propagation of uncertainties
through nonlinear differential equations.
In this talk, I will show that symmetries make it possible to drastically improve the accuracy of these propagations.
As an illustration, the interval propagation will be considered, but a particle approach could be used as well.
[234] 2020, December 3, en virtuel, Rencontre SENI, avec Naval Group
Title: Navigation sous-marine autonome : Partenariat Polytechnique - ENSTA Bzh
Abstract. In this talk, I will present motivations, experiments and perspectives
we have with Ecole Polytechnique and related to autonomous underwater navigation.
[233] 2020, November 3, en virtuel, rencontre de l'AID
Title: Autonomous parachute
Abstract. In this talk, I will present the realization by Kevin Bedin at ENSTA-Bretagne of a small-size, small-capacity,
autonomous parachute. This project has been initiated by the AID, for the benefit of the 1st RPIM
(1er Régiment de Parachutistes d’Infanterie de Marine). I will present the control laws that have been implemented in the parachute,
how the wind can be estimated and how we can guarantee that the parachute will land within a given bounded area.
[232] 2020, October 21, en virtuel, exposés du comité de direction du GDR MACS
Title: Ocean exploration with underwater robots
Abstract. Presentation of the Robex team of Lab-STICC with a focus on
cycle-based navigation and validation.
[231] 2020, March 13, Palaiseau, MRIS meeting
Title: Underwater navigation with stable cycles
Abstract. In an environment where almost no landmarks exists for localization, as it it the case
for many underwater applications, we show that using the concept of 'stable cycle', we can move from zones to zones without getting lost.
Stable cycles are used by many animals for navigation.
We prove the stability of these cycles using the concept of Poincaré map and interval analysis.
Some real experiments show the feasibility of the approach for underwater navigation.
As a perspective, we define the new concept of Poincaré scan for the exploration of an unstructured environment with no landmarks.
[230] 2020, March 2, Nantes, Réunion Contredo
Titre: Stable cycles for exploration
Résumé. In an environment where almost no landmarks exists for localization, we show that using
the concept of stable cycle, we can move from a zone to another zone without getting lost. Some real experiments
show the feasibility of the approach.
[229] 2020, January 5, ISIR Paris
Titre: Cartographie magnétique sous-marine des fonds marins pour la recherche de la Cordelière
Résumé. Depuis plusieurs années, nous cherchons des méthodes entièrement robotisées pour
la recherche d'épaves et plus particulièrement la Cordelière, une épave ayant coulé à la sortie du goulet de Brest en 1512.
L'épave est probablement enfouie sous le sable et donc invisible par sonar.
La voie que nous retenons est la construction d'une carte des anomalies magnétiques des fonds marins à
l'aide d'un magnétomètre devant effectuer un balayage proche du fond (<5m).
Une lecture et une interprétation de cette carte devrait permettre de trouver des zones susceptibles
de contenir l'épave convoitée. En effet, la Cordelière, du fait de ses canons et de ses ancres, pourrait
être localisée à l'aide d'une telle carte.
Or, la zone à explorer est très vaste, les courants marins sont forts et le trafic en surface est dense.
La recherche pourrait prendre des mois voire des années.
Dans cet exposé, nous allons étudier une solution bas coût, entièrement sous-marine,
où les robots n'auraient pas à refaire surface pour faire des points GPS, et qui utiliseraient
les courants comme moyen de déplacement.
[228] 2019, December 3, Brest. LMBA (Laboratoire de Mathématiques de Bretagne Atlantique)
Title: Interval integration of an ODE
Abstract. Interval analysis is a numerical tool used to solve nonlinear problems, such
as global optimization or solving equations, with guarantee. Resulting algorithms
provide a set which is proved to contain all solutions of the problem.
Interval analysis is also used to prove conjectures. For instance,
Warwick Tucker used intervals to solve the 14th Smale problem which
claims that the Lorenz system has a strange attractor.
In this talk, I will briefly introduce Interval Arithmetic and show how it can be used
to perform interval integration, i.e., to compute a guaranteed enclosure of an initial value problem
or equivalently, to compute a tube which encloses all trajectories that are solution of the ODE.
This resolution will allow us to compute numerically guaranteed inner and outer approximations of
invariant sets, forward reach sets or viability kernels.
Moreover, I will show how Lie symmetries can improve significantly existing guaranteed integration methods
in the case of strong uncertainties.
Examples taken from underwater robotics will illustrate the applicability of interval methods.
[227] 2019, Novembre 27, Brest, Shom, projet MAGIDRO (Mesures MAGnétiques Innovantes par DROnes)
Titre: Des robots marins et sous-marins pour cartographier les fonds de l'océan
Résumé. En mer, les robots, qu'ils soient volants, flottants, coulants, peuvent être
utilisés pour la construction de cartes (bathymétrique, magnétique, visuelle, etc) des fonds de l'océan.
Un exemple type est le Boatbot qui a été utilisé pour construite des cartes magnétiques
dans le cadre de la recherche de la Cordelière en 2018 et 2019. Dans ce contexte, un GPS est souvent indispensable pour
effectuer la navigation.
Cependant, sous l'eau, une localisation reste très approximative du fait de l'absence d'amers
et du non fonctionnement du GPS. En mimant les techniques des anciens navigateurs, ou des animaux marins
(comme les tortues marines), nous allons montrer qu'un robot sous marin peut explorer et cartographier
un environnement très vaste, revenir à sa position, sans jamais refaire surface et sans utiliser de balises.
[226] 2019, November 25, Présentation devant les représentants de l'AID à Brest.
Titre: Les robots pour l'exploration sous-marine
Résumé. Je présente à nos financeurs de lAID comment utiliser les robots sous-marins pour faire
de l'exploration des fonds de l'océan sans avoir accès aux à un positionnement externe comme le GNSS.
[225] 2019, November 18, Présentation devant l'école St Anne de Plougastel à Brest.
Titre: Les robots sous-marins
Résumé. Je présente pendant environ une heure les principes de la robotique sous marine,
avec les applications qui en découlent.
[224] 2019, November 8, Réunion MRIS, Palaiseau.
Title: Lie symmetries applied to interval integration
Abstract. We propose a new approach for improving significantly existing guaranteed integration of a state equation in the case
where the initial box is large. We first find a tube which encloses
the solution in the case where the initial state is known.
Then using Lie symmetries we extend the tube to contain the uncertainty associated to the initial state.
The method is shown to be efficient on examples taken from robotics.
[223] 2019, October 15, 16, 17, Vittel, JNRR
Title: Cooperative Underwater Navigation
Abstract. When robots cooperate for navigation they can explore further without getting
lost, they have a better precision of localization, they have a more accurate prediction,
they have a higher probability of capturer an intruder, etc.
In this presentation, I will show how set membership methods can be used in this context.
The approach will be illustrated on the localization of a group of underwater robots with unsynchronized clocks.
[222] 2019, October 3, Rennes, Technoférence
Titre: Exploration de l'océan par des robots sous-marins
Résumé. Sous l'eau, la localisation est souvent impossible du fait de l'absence d'amers
et du non fonctionnement du GPS. En mimant les techniques des anciens navigateurs, ou des animaux marins
(comme les tortues marines), nous allons montrer qu'un robot sous marin peut explorer un environnement
très vaste et revenir à sa position, sans jamais se perdre.
[221] 2019, July 16, Paris, siège du CNRS, Atelier de la Task Force Océan.
Title: Underwater satellites
Abstract. Underwater satellites are robots which move with the ocean currents and build
some magnetic (or bathymetric) maps of the seafloor without surfacing.
For the localization, these robots cannot use the GPS. They copy ancestral navigation methods
and bio-mimetic techniques to avoid getting lost.
[220] 2019, July 8, Brest, pour la venue de Ian_Reid.
Title: Cooperative Exploration and Mapping
Abstract. We consider the exploration of a large zone with few islands,
where that a group robots have to explore and build the map without getting lost.
[219] 2019, July 8, Limoges.
Title: Cooperative Robotics and Intervals
Abstract. In the context underwater robotics, the environment in not well structured and the landmarks
are rare. The collaboration between robots is a paradigm that can be used in to perform complex missions in a reliable way.
Moreover, collaborative robotics combined with interval based methods may allow us to prove that a mission will succeed,
provided that some realistic assumptions are fulfilled.
After briefly presenting some notions on interval analysis and contractor based methods, I will consider three different applications:
- The collaborative Polynesian exploration where new islands have to be discovered without getting lost.
- The capture of an intruder using a group of communicating robots.
- The global and distributed localization of a robot swarm.
[218] 2019, 28 juin 2019 , Paris, Jussieu
Titre: Résultats du workshop expérimental 'Submeeting 2019'
Abstract. Le workshop qui s'est tenu en juin 2019 avait pour objectif la recherche de la Cordelière qui a
coulé en 1512 au large de Brest lors d'un affrontement naval avec les Anglais.
Je présenterai les robots qui ont navigué (marins et sous-marins), les stratégies d'exploration, les capteurs utilisés et les cartes
qui ont été construites lors de ce workshop.
[217] 2019, mardi 18 juin 2019, Toulouse, réunion MRIS
Title: Explore and return problem in a minimalist environment
Abstract. We consider an underwater robot that has to explore a huge unknown environment and be able to come back home.
We assume that no localization system exists, the robot is not allowed to surface to collect the GPS,
and the environment is minimalist (i.e., with few landmarks).
We want to show that in this context, it can be possible to perform a safe exploration without being lost.
For this purpose we will copy the marine turtles which are able to travel long cycles in the ocean and
come back to their birth beach or imitate the polynesians that were able to travel across islands far from each other.
To guarantee that all along the mission, the robot will never be
lost, we combine interval analysis, constraint-based methods and graph theory.
[216] 2019, 3 au 5 juin 2019, Ecole d'été sur la vérification et la synthèse des systèmes cyber-physiques
Ecole MACS à Bordeaux
[215] 2019, Jeudi 27 mai, Présentation des futures équipes Lab-STICC
IMTA, Brest.
Titre: Equipe ROBEX : ROBotique d'EXploration
[214] 2019, Jeudi 23 mai, GT VS-CPS Vérification et Synthèse des Systèmes Cyber Physiques, CNAM, 292 rue Saint-Martin, 75003 Paris
Title: Computing sliding surfaces of cyber-physical systems
Abstract. The evolution function of a cyber-physical system is generally non-continuous
due to 'if' statements inside the control algorithm.
The control signal may not even be piecewise continuous along the trajectory since an unwanted chattering
effect may occur along sliding surfaces.
We propose here a set-membership method based on
interval analysis to detect different types of discontinuities of the system and compute the sliding surfaces.
As an application, we consider the validation of a sailboat controller.
We show that our approach is able to detect and explain some unwanted effects that may sometimes be observed
in rare specific situations on our actual sailboat robots.
[213] 2019, May 21 2019 , Montpellier, Workshop "Recent Advances in Marine Robotics"
Title: Explore and return problem in a minimalist environment
Abstract. We consider an underwater robot that has to explore a huge unknown environment and be able to come back home.
We assume that no localization system exists, the robot is not allowed to surface to collect the GPS,
and the environment is minimalist (i.e., with few landmarks).
We want to show that in this context, it can be possible to perform a safe exploration without being lost.
For this purpose we will copy the marine turtles which are able to travel long cycles in the ocean and
come back to their birth beach or imitate the polynesians that were able to travel across islands far from each other.
To guarantee that all along the mission, the robot will never be
lost, we combine interval analysis, constraint-based methods and graph theory.
[212] 2019, May 17, Thales, Brest,
Title: Distributed localization with intervals
Abstract. This presentation deals with the problem of distributed localization for
robots in the case where (1) the evolutions are nonlinear, (2) delays exist in the equations and (3) we have a limited
rate of communication between robots.
Interval analysis and tube programming are shown to solve efficiently and in a reliable way the localization problem.
[211] 2019, Mars 15, Rennes,
Title: Des robots sous-marins à la recherche de Cordelière
Abstract. Nous présentons les travaux qui se sont déroulés, dans le cadre du projet NEPTUNE,
autour de la recherche de la Cordelière par des moyens robotisés.
[210] 2019, 5 Février, Palaiseau. Réunion MRIS.
Title: Characterizing discontinuities of an hybrid system
Abstract. When implementing a non-continuous controller in a cyber-physical system, it may happen that
the evolution function of the closed-loop system is not anymore piecewise continuous along the trajectory.
As a consequence, an unwanted chattering effect may occur. We propose here a set-membership method based on
interval analysis to detect different types of discontinuities. As an application, we consider
the validation of a sailboat controller.
We show that our approach is able to detect and explain some unwanted effects that may sometimes be observed
in rare specific situations on our actual sailboat robots.
[209] 2019, Février 23, Montpellier. Journée Contredo à Montpellier
Title: Characterizing discontinuities of a dynamical system
Abstract. When implementing a non-continuous controller in a cyber-physical system, it may happen that
the evolution function of the closed-loop system is not anymore piecewise continuous along the trajectory.
As a consequence, an unwanted chattering effect may occur, due to the fact that the controller
hesitates between two control strategies. We propose here a set-membership method based on
interval analysis to detect different types of discontinuities. As an application, we consider
the validation of a sailboat controller.
We show that our approach is able to detect and explain some unwanted effects that may sometimes be observed
in rare specific situations on our actual sailboat robots.
[192] 2018, Janvier 18, Journée d'échange avec la MRIS.
Titre : Sûreté de fonctionnement des systèmes robotiques
Résumé. Je présenterai les avancées scientifiques obtenues avec l'aide de l'ENSTA Paris et Polytechnique
dans le domaine de la sûreté des groupes de robots. Plus particulièrement sera soulignée l'importance du concept
d'ensemble positivement invariant et comment le calcul ensembliste peut être utilisé pour leur caractérisation.
[193] 2018, janvier 24, siège de la Région Bretagne, Rennes.
Titre : Retrouver la Cordelière par des robots autonomes équipés de magnétomètres
Résumé. Dans cette présentation, je donnerai l'architecture robotique que
possible pour retrouver la cordelière par un groupe de robots chacun équipé d'un magnétomètre.
Pour éviter une localisation en temps réel, un suivi bathymétrique sera proposé.
[194] Hannover, 2018, February 20
Title: Intervals analysis for guaranteed localization.
Abstract. Interval analysis makes it possible to solve a large class on
nonlinear problems such as (i) computing all global minimisers of a nonconvex criterion, (ii) computing all solutions of a set of
nonlinear equations, (iii) characterizing sets defined by nonlinear inequalities, ... Unlike classical numerical approaches (Monte
Carlo or local methods, for instance), the results provided by interval analysis are obtained in a guaranteed way and in a finite
time, even when strong nonlinearities and discontinuities are involved in the problem.
The purpose of this presentation is to introduce in a pedagogical way the principles of interval methods and
contractor programming techniques. We will then show how these tools can be used to deal with nonlinear state estimation problems. To
illustrate the efficiency and the robustness of the approach, the dynamic localization of underwater
robots will be presented.
[195] 2018, march 15, Ecole polytechnique, Palaiseau.
Title: Kleene algebra to compute with invariant sets of dynamical systems
Abstract.
Consider sets X1,...,Xm of invariant sets associated to a continuous-time dynamical system.
We want to compute an approximation of a set X defined as an expression of the Xi's and linked by
the operators union, intersection, complementation. It will be shown that the problem can be formalized
in a Kleene algebra the elements of which are set-valued functions.
This formalization could help us to build efficient and simple algorithms to compute with invariant sets.
[196] 2018, April 10, ENSTA, Brest.
Title: Kleene algebra to compute with invariant sets of dynamical systems
Abstract.
Consider sets X1,...,Xm of invariant sets associated to a continuous-time dynamical system.
We want to compute an approximation of a set X defined as an expression of the Xi's and linked by
the operators union, intersection. It will be shown that the problem can be formalized
in a Kleene algebra the elements of which are set-valued functions.
This formalization could help us to build efficient and simple algorithms to compute with invariant sets.
[197] 2018, April 16, Nantes.
Titre : Expérimentations en mer pour Contredo
Résumé.
Dans cette présentation, nous montrerons quelques expérimentations qui se feront le 22-23 mai 2018 à la sortie du goulet de Brest.
Elles devraient permettre d'illustrer les méthodes de propagation de contraintes sur les trajectoires développées dans Contredo.
Ces expérimentations consistent à envoyer des
robots sous-marins afin de retrouver des épaves enfuies à l'aide de magnétomètres tractés par ces mêmes robots.
[198] 2018, May 15, Grenoble, Verimag.
Title: Computing inner and outer approximations of forward reach sets of a nonlinear dynamical system
Abstract.
Given a nonlinear continuous-time system and an initial set X0,
the forward reach set corresponds to the set of all states that can be reached for some given time t>0,
assuming that the initial state belongs to X0.
In the presentation, I will show that guaranteed inner and outer approximations of the forward reach set
can be computed by using a fixed point interval algorithm inside a Kleene algebra.
The elements of this algebra are set-valued functions which are automorphism with respect to the intersection.
Some illustrations associated with examples from the literature can be found at:
www.ensta-bretagne.fr/lemezo/pyinvariant/pyinvariant.html
[199] 2018, July 3, GT VS-CPS - GT MEA, CNAM Paris.
Title: Intervals of a Kleene algebra used to compute inner and outer approximations of invariant sets of a dynamical system
Abstract.
Kleene algebra is a powerful formalism to deal with fixed point methods involving monotonic
operators. After defining what is an interval in such an algebra, an interval arithmetic will be presented.
Further, we will consider the specific case where the elements of this Kleene algebra
are set-valued functions which are automorphism with respect to the intersection.
It will be shown how this formalism could help us to build efficient and simple algorithms to compute inner and outer
approximations of invariant sets of non-linear continuous-time dynamical systems.
[200] 2018, July 4, Palaiseau Paris, Methods and Tools for Distributed Hybrid Systems (DHS 2018)
Title: Distributed localization and control of underwater robots
Abstract.
We consider the problem of localizing a group of underwater robots
and to control the group in order to accomplish a survey. We assume
here that
1. When a robot surfaces, it can use the GPS for its localization
2. The robots can communicate with a very low symbol rate
3. The robots can measure their distances with a given accuracy, but
not the direction of arrival
4. Some outliers on the distances could occur, but their numbers is
limited
I will propose a Lagrangian approach based on interval analysis and constraint propagation.
It is based on the notion of 'tubes' which are intervals of trajectories and can easily be distributed.
Some test-cases will be presented in order to illustrate the efficiency of the approach.
Moreover an actual experiment involving actual underwater robots will be shown.
[201] 2018, July 9, Brest, Groupe transverse drone.
Titre : Suivi d'isobaths
Abstract.
Dans cet exposé, je montrerai comment suivre des isobaths pour des robots marins et sous-marins,
de façon robuste et à bas coût, en utilisant un echo-sondeur comme unique capteur proprioceptif.
L'idée est d'utiliser un filtre de Kalman afin de construire
une carte locale planaire du fond marin et d'appliquer une commande de suivi de ligne non-linéaire classique.
Des applications liées à la recherche de la Cordelière, une épave ayant coulé à la sortie du goulet
de Brest en 1511, seront montrées.
[204] 2018, September 17, ENSTA-Paris, Palaiseau.
Title: A constraint approach for the data association problem with application to underwater localization
Abstract. We consider a state estimation problem in the case where the data association has
to be solved conjointly. This problem occurs in an underwater localization context
in the case where the landmarks (for instance rocks at the bottom of the ocean) are indistinguishable.
We show that a interval constraint programming approach can solve the problem efficiently and rigorously.
[205] 2018, 8 novembre, 27èmes rencontres francophones sur la logique floue et ses applications
Arras - 8-9 Novembre 2018,
LFA,
Titre : Caractérisation d'une zone explorée par un robot sous-marin
[206] 2018, 14 novembre, Réunion d'avancement sur la recherche de la Cordelière et du Regent,
Rennes.
Titre : Des robots à la recherche de Cordelière
[207] 2018, 15-16 Nov 2018 , Nantes,
JAMACS.
Title: Computing the no-lost zone for a mobile robot to find safe paths
Abstract. In an underwater context, we want to validate, that an autonomous robot will be able to achieve a mission such as
an area scanning or reaching a target. The main difficulty is to be able to guarantee that all along its mission, the robot will never be
lost. By being lost, we mean not being able to come back home.
We will assume a world made with point landmarks which are all distinguishable and geolocalized. The number of landmarks is small compare
to the size of the world. This means that for long periods, the robot does not see any landmarks.
It explores forward with a dead reckoning navigation and is totally lost in a geolocalization point of view. But for us, the robot
is not lost as soon as it knows that it will meet some landmarks in the future.
[208] 2018, 29 novembre, Brest
Instrumentation sismique, acoustique électrique, magnétisme et gravimétrique , IUEM, Brest.
Titre : Apport de la robotique dans un survey géophysique
[168] 2 février -> 16 mars 2017
RobMOOC, 2ième édition.
Author: Luc Jaulin
Title: RobMOOC : Un MOOC sur la commande non-linéaire des robots.
[169] Jeudi 2 février 2017. à l'Ecole Navale, Crozon.
Title: Systèmes multi-drones pour les applications maritimes (en collaboration avec B. Zerr).
Résumé. Depuis plusieurs décennies, la robotique marine est en constant développement.
Comparativement au domaine terrestre, le milieu marin est plus difficile à aborder et la mise en œuvre de
solutions robotiques doit elle aussi faire face à ces difficultés. Durant toutes ces années, les architectures mono-robot
n'ont cessé de démontrer le fort potentiel de l'approche robotique à la conduite de missions en mer,
tant dans les domaines militaires que civils. Bien que le succès des systèmes mono-robots ait donné
une place toujours plus importante à la robotique marine, il est intéressant de constater qu'à
l'instar des organisations humaines, il peut être plus simple et plus efficace de résoudre un
problème en coordonnant plusieurs robots.
L'objet de cette conférence est de montrer, au travers de résultats de travaux de recherche conduits
depuis une décennie, l'intérêt de l'approche multi-robots coordonnés pour faire face aux problématiques maritimes complexes.
[170] 7 février 2017, Séminaires de l'équipe TOMS, Brest.
Title: Reliable detection of outliers with intervals methods.
Abstract. The q-relaxed intersection of n sets is defined as the set of all points which belongs to all
n sets except q of them. This notion allows us to detect outliers in a guaranteed way, provided that the errors and
the number of outliers are bounded. This detection can be used to improve the knowlelge we have on a system and to get a more reliable
identification process.
In a nonlinear context, the resolution of the set-membership problem can be performed using interval methods.
Interval analysis makes it possible to solve a large class on
nonlinear problems such as (i) computing all global minimisers of a nonconvex criterion, or
(ii) characterizing sets defined by nonlinear inequalities.
Unlike classical numerical approaches (Monte Carlo or local methods, for instance), the results provided by interval analysis
are guaranteed.
Combined with contractor-based methods, they can efficiently prove that a given data in an outlier by proving the inconsistency of a set of
constraints. The purpose of this presentation is to introduce in a pedagogical way the principles of interval analysis and to show how it can
be used to build contractors. By using the algebra of contractors, we will provide a method to detect outliers efficiently and show how this
can be used to increase the knowledge we have on the system.
Some applications related to robotics will be given.
[171] March 16, 2017 -> April 20, 2017.
IAMOOC, 2d edition.
Authors: L. Jaulin, J. Ninin, B. Desrochers
Title: IAMOOC : A MOOC on interval analysis with applications to parameter estimation and robot localization.
[172] 2 mars 2017. Workshop Contredo, Montpellier,
Title: Characterization of trajectories: an Eulerian apporach
Abstract. In this presentation, we consider constraint satisfaction problem
(CSP) where the variables are trajectories (i.e. functions from R into Rn). The constraints of the CSP could be
differential equations, or continuity, or periodicity, etc. A domain of the CSP is called a maze
which is a composition of graphs, pavings of boxes and polygons. The set of mazes forms a lattice with respect to the inclusion and
contractors can be build from each constraint of the CSP. I will show that a propagation can then be used to solve CSPs in
an efficient and guaranteed way.
[173] 3 mars 2017. Workshop Contredo, Montpellier,
Title: Computing positive invariant tubes with interval analysis.
Abstract. Consider an autonomous time dependant nonlinear system dx/dt=f(x,t),
where x belongs to R^n. A tube X(t) is a function which associates to each t a
subset of R^n. A tube X(t) is said to be a positive invariant tube if the fact that x(t) in
X(t) implies that x(t+t1) in X(t+t1) for all t1>0. If a candidate positive invariant
tube is available, we can check that it is indeed positive invariant by
performing a Lyapunov analysis in order to cast the problem into checking the inconsistency
of a set of nonlinear equations. This inconsistency can then easily be checked using interval analysis. Now, for many systems such as non
holonomous systems, we rarely have a candidate for a positive invariant tube and we need to find one. The main contribution of this
talk is to show that how a positive invariant tube can be computed. The main idea if to start from a non positive
invariant tube Z(t) and to try to find the smallest capture tube which encloses Z(t).
[174] 28 mars 2017. Workshop MRIS, ENSTA-Paris,
Title: Chain of set inversion problems; Application to reachability analysis
Abstract. In this presentation, we deal with the set inversion problem X=f^-1(Y) in the case where
f:R^n->R^m depends on a parameter vector p in R^q
which is known to be inside a box [p] . We show that for a large class of problems, we can obtain an accurate approximation of the solution set,
without bisecting in the p-space. To do this, symbolic methods are required to cast our initial problem into a chain of set-inversion problems,
the links of which have some nice properties with respect to p . As an application, we consider the problem of computing the set of all initial
states of an uncertain discrete-time state system that reach a target set Y in a given time.
[175] 22 juin 2017. Workshop MRIS, Palaiseau, école polytechnique.
Title: Eulerian filter and Eulerian smoother,
Abstract. Eulerian state estimation can be seen as a problem of
estimating trajectories in the case where
temporal logic constraints are combined with state equations.
Typical constraints are
- "the robot A has met the robot B before the collision with robot C".
- "After the robot crossed the river, its speed was always lower than 1m/s"
In the presentation, it will be shown that Eulerian state estimation can
be solved efficiently using, as a basic stone, the concept of largest positive invariant set associated to a nonlinear state equation.
As a result, a new filter and a new smoother will be introduced to estimate efficiently
a trajectory in an Eulerian context.
[176] 2017. IAMACS. Summer school on Interval Analysis,
IFAC, Toulouse.
Abstract. In this lessons, I will present the basic notions on Interval analysis and constraint networks.
These tools can be used to solve a large class of nonlinear problems such as
(i) computing all global minimisers of a nonconvex criterion, (ii) computing all solutions of a set of
nonlinear equations, (iii) characterizing sets defined by nonlinear inequalities, etc. Unlike classical numerical approaches (Monte
Carlo or local methods, for instance), the results provided by interval analysis are obtained in a guaranteed way and in a finite
time, even when strong nonlinearities, differential equations and discontinuities are involved in the problem. These properties
make these tools very attractive to deal with Cyber Physical Systems.
Now, classical interval methods have some
difficulties to deal with problems involving a large number of variables (greater than 10, for instance). This limitation is mainly
due to the bisections involved in the interval algorithms that make the complexity exponential with respect to the number of variables.
Contractor based techniques make it possible to push back this frontier and to deal with high dimensional problems (with more than
1000 variables for instance). The purpose of this presentation is to introduce in a pedagogical way the principles of interval methods and
contractor programming techniques. To illustrate the efficiency and the robustness of the approach we will
consider nonlinear state estimation, dynamic localization, nonlinear control, and reliable conception in the context of cyber physical systems.
Illustrations involving real robots will also be provided.
In parallel, I will introduce the basic concepts on PyIbex, which is a Python plateform, based on Ibex, to deal easily with interval analysis.
During the lab, some exercises on the application of interval analysis will have to be solved with PyIbex.
[177] 2017, july 17-21. Summer school on cyber physical systems , CPS_2017, Halmstad, Sueden.
Title: Interval Analysis for the Conception of Autonomous and Reliable Cyber-Physical Systems.
[178] 2017, august 9 Plymouth, England. MSUB compagny
Title: Ocean Robotics
[179] 2017, august 11 Plymouth, England. University of Plymouth
Title: Ocean Robotics
[180] 2017, September 13, INRIA, Rennes,
Title: Guaranteed simulation of nonlinear continuous-time dynamical systems using interval methods
Abstract. We consider dynamical systems that can be expressed by nonlinear differential equations.
The system may be uncertain and all uncertainties are assumed to be bounded. We are interested in simulating
the system and computing an envelop containing all feasible trajectories in order to guarantee that no forbidden events will occur.
In this presentation, I will propose two approaches, both based on interval analysis and constraint propagation.
The first approach is Lagrangian and is based on the notion of 'tubes' which are intervals of trajectories.
Interval Lagrangian methods discretize the time space and can be efficient in high dimensions, but are very conservative.
The second approach is Eulerian, and is based on the notion of 'mazes' which are intervals of paths.
Interval Eulerian methods discretize the state space. They are accurate and can deal with small dimensional systems.
They can for instance detect limit cycles and can deal efficiently with zeno behaviors.
Finally, I will show how these two approaches can be combined.
Some test-cases will be presented in order to illustrate the efficiency of the approaches.
[181] 2017, Brest, september 21 ENSTA-Bretagne
Title: Research Activities of the Robotic Department, Visit of Flinders University, Australia,
[182] 2017, Palaiseau, september 28
ENSTA-Paris
Rendez-vous du Monde Maritime, Table ronde technologies de l'IA.
Title: Constraint Logic Programming for marine robotic applications.
[183] 2017, Octobre 18, Point région de Brest
Titre : Trouver la Cordelière avec des robots
Résumé. Dans cette présentation, je donnerai quelques pistes possibles pouvant être suivies pour retrouver à l'aide de robots
sous-marins une épave enfouie.
[184] 2017, November 2, Southampton.
Title: Detection and capture of intruders using robots
Abstract. The talk is motivated by the detection of submarine intruders inside the Bay of Biscay (golfe de Gascogne).
In this project, we consider a group of underwater robots that are able to localize with a given accuracy using a state observer.
We assume that each robot is able to detect any intruder inside a disk of a known radius. Moreover, the speed of the intruders
is assumed to be bounded and is small with respect to that of our robots. The goal of this project is twofold:
(1) to characterize a set for which we can guarantee that there is no intruder (this corresponds to the secure zone) and
(2) to find a control strategy for the group of robots in order to extend the secure zone as much as possible.
[185] 2017, November 7, Palaiseau, polytechnique
Title: Modelisation, control and guidance of a quadrotor
Abstract. In the first part of the presentation, a simple but realistic model for a quadrotor robot is proposed.
The quadrotor is composed with four propellers that can be tuned independently.
This will allow us to control the attitude and position of the robot by changing the speeds of the motors.
In the second part, I will show that the quadrotor can be seen as a chain of causal loops.
A controller will be built by inverting one by one each block of the causal chain.
In the last part, we will use a vector field approach, so that the quadrotor follows a path that obeys the Van der Pol equation.
[186] 2017, September 13, Journée MEA-STP, Nancy.
Title: Eulerian and Lagrangian approaches for filtering and Smoothing
Abstract. We consider dynamical systems that can be expressed by nonlinear differential equations.
The system may be uncertain and all uncertainties are assumed to be bounded.
Eulerian state estimation can be seen as a problem of
estimating trajectories in the case where temporal logic constraints are combined with state equations.
Typical constraints are
- "the robot A has met the robot B before the collision with robot C".
- "After the robot crossed the river, its speed was always lower than 1m/s"
In the presentation, it will be shown that Eulerian state estimation can
be solved efficiently using, as a basic stone, the concept of largest positive invariant set
associated to a nonlinear state equation.
As a result, a new filter and a new smoother will be introduced to estimate efficiently
a trajectory in an Eulerian context.
[187] Brest du 21 au 24 novembre 2017, Hotel Vauban, Brest.
7ème ANF (Action Nationale de Formation) de l'INSU : "Mer et Robotique : l'apport des robots dans les sciences de la mer"
Titre : Théorie de la robotique
Résumé. Un cours sur la robotique sera proposé avec des éléments de simulation, de théorie du contrôle et
des observateurs d'état. Dans une deuxième phase, des vidéos avec des robots marins faits à l'ENSTA-Bretagne seront
montrées et commentées.
[188] 2017, November 26-30, Seminars of Dagstuhl,
Title: Computing positive invariant sets with intervals
Abstract. Given a set X, and a dynamical deterministic system S, the largest invariant set inside X is the set of all x0
such that all trajectories going through x0 stay inside S for all time instant t.
In this presentation, I will show how interval methods can be used to compute
an inner and an outer characterization of an invariant set.
The procedure that will be presented is fast, guaranteed and does not require any interval integration of the dynamics.
The main idea is to use the new notion of maze, which is a composition of graphs, pavings of boxes and polygons.
The set of mazes forms a lattice with respect to the inclusion so that contractor-based methods could be used.
[189] 2017, December 5, Journée 'IPL ModeliScale', Paris.
Title: A new approach for guaranteed integration of nonlinear ODE using positive-invariant set theory
Abstract. Given a nonlinear ODE of the form dx/dt=f(x(t)), and a set of initial vectors X0.
A trajectory x(.) is a solution if x(0) in X0 and if it satisfies the ODE.
The set of solution S is a subset of the set of trajectories, the dimension of which is infinity.
In this talk, we will show how to compute an inner and an outer
approximation of S and what is the meaning such an the inner approximation. The method we propose combines
interval analysis, positive-invariant set theory and constraints-based methods.
[190] 2017, December 7, Ifremer, réunion de lancement COGNAC, Brest.
Title: Depth control of a float
Abstract. In this talk, I will present some basic notions on non-linear control and how it can
be use to control floats in order to be precise and low consuming.
[191] 2017, December 14, Journée MEA. Paris.
Title: Guaranteed following of an isobath
Abstract. The problem is motivated by an experiment we made with an underwater robot
near Brest. In 2013, The robot succeeded to make autonomously a full turn of an island (l'île des morts).
The main stategy for this is to follow an isobath using a low-cost sonar sensor.
We want to prove a priori that the robot with its controller will be able to succeed its mission
without being lost.
The method we propose combines interval analysis, positive-invariant set theory and constraints-based methods.
[155] 22 février -> 04 avril 2016 RobMOOC, 1ere édition.
Authors: Luc Jaulin
Title: RobMOOC : Un MOOC sur la commande non-linéaire des robots.
[156] March 3, 2016 Journée Terre-Air-Mer. Montpellier
Authors: Luc Jaulin, Benoît Zerr (et 15 étudiants)
Title: Guarding a zone against intruders using a group of robots.
Abstract. The talk is motivated by the detection of submarine intruders inside the Bay of Biscay (golfe de Gascogne).
In this project, we consider a group of underwater robots that are able to localize with a given accuracy using a state observer.
We assume that each robot is able to detect any intruder inside a disk of a known radius. Moreover, the speed of the intruders is assumed
to be bounded and is small with respect to that of our robots. The goal of this project is twofold: (1) to characterize a set for which we
can guarantee that there is no intruder (this corresponds to the secure zone) and (2) to find a control strategy for the group of robots in
order to extend the secure zone as much as possible.
[157] Séminaire Plymouth, March 16 , 2016.
Title. Interval analysis for proving properties of dynamical systems with applications to sailboat robotics.
Abstract. This talk presents a rigorous approach combining interval analysis
and Lyapunov theory for stability analysis of uncertain dynamical differential inclusions and then to perform a Lyapunov analysis in
order to cast the stability problem within a set-inversion framework. With this approach, we can show that for all feasible perturbations,
(i) there exists a safe subset A of the state space the system cannot escape as soon as it enters in it and (ii) if the system is outside
A, it cannot stay outside A forever. In a second step, the methodology is used to build reliable robust controllers. An
illustration related to the line following problem of sailboat robots is then provided. After introducing the basic notions on interval
analysis and Lyapunov theory, I will show how these tools can be used for stability analysis of nonlinear systems. Then an
experimental validation that took place on January 2012 will then be presented. On
this experiment, the autonomous sailboat robot Vaimos, has gone from Brest to Douarnenez (more than 100 km).
Video: http://www.youtube.com/watch?v=YdA8gFInY1M
Wiki: https://en.wikipedia.org/wiki/Vaimos.
[158] Journée MRIS, Ecole polytechnique, Paris, 24 mars 2016.
Title: Secure the Bay of Biscay with Robots using interval methods.
Abstract. Last january, a Russian submarine entered inside the Bay of Biscay,
for the first time since the cold war. The talk is motivated by
securing the Bay against submarine intruders. We consider a group
of underwater robots that are able to localize with a given accuracy
using a state observer. We assume that each robot is able to detect
any intruder inside a disk of a known radius. Moreover, the speed of
the intruders is assumed to be bounded and is small with respect to
that of our robots. The goal of this project is twofold: (1) to
characterize a set for which we can guarantee that there is no
intruder (this corresponds to the secure zone) and (2) to find a
control strategy for the group of robots in order to extend the
secure zone as much as possible.
See also the presentation
of the Robotics club.
[158] Pint of Science, 23 mai 2016..
Titre : La robotique dans tous ses états.
[159]
SWIM 2016 Inner approximation of the backward reachable set.
[160] 28 juin 2016. Journée MRIS, ENSTA-Bretagne, Brest.
Title: Bisectable Abstract Domains for the resolution of equations involving complex numbers.
Abstract. The idea of interval arithmetic is to enclose the exact value of a real number inside an interval. Then, computing with intervals will
allow us to enclose the true value for a variable we want to compute. In this talk, I recall the importance of having a lattice structure
for the set of intervals and show that several interval algorithms could be adapted to other types of domains as soon as these domains
have a lattice structure with respect to the inclusion and that we could bisect them. As an illustration, we introduce a new type of
domains, the boxpies, which correspond to the intersection between one box and one pie. We show that boxpies can be used efficiently to
characterize the solution set of constraints involving complex numbers.
[161] 6 juillet 2016. Workshop Réels, Flottants & Vérification, 14h, salle de conférence de l'I3S, Sophia
Title: Characterization of trajectories using constraint programming and abstract interpretation.
Abstract. In this presentation, we consider constraint satisfaction problem
(CSP) where the variables are trajectories (i.e. functions from R into Rn). The constraints of the CSP could be
differential equations, or continuity, or periodicity, etc. A domain of the CSP is called a maze
which is a composition of graphs, pavings of boxes and polygons. The set of mazes forms a lattice with respect to the inclusion and
contractors can be build from each constraint of the CSP. I will show that a propagation can then be used to solve CSPs in
an efficient and guaranteed way.
[162] 19 septembre 2016. Rencontre robotique à l'ISEN de Brest
Title: Compute Capture Sets
[163] COPROD October 2016, Uppsala, Suède
Title. Construction of a mosaic from an underwater video.
Abstract. In this presentation, we will present a new technique for the construction of a mosaic from an underwater
video collected in an underwater environment. The principle is to use proprioceptive data collected by an AUV (here the lock Doppler and
the inertial central) in order to detect feasible loops. The procedure consists in six steps. (1) Use the proprioceptive sensors
only in order to detect all feasible loops. (2) Eliminate all pairs of images that do not correspond to loops. (3) Associate feasible
pairs of images using image processing techniques (4) Contract the feasible trajectories by taking into account the image associations.
(5) Use the trajectory refinement in order to reduce the number of feasible loops. (6) If the contractions are significant enough, goto
Step 3. The resulting fixed point technique is shown to converge. Some test-cases are presented in order to illustrate the efficiency
of the approach.
[163] 11 octobre 2016 -> 10 janvier 2017 KalMOOC, 1ere édition.
Author: Luc Jaulin
Title: KalMOOC : Un MOOC sur le filtre de Kalman.
[164] Lesson. Vendredi 14 octobre 2016, 13h30-17h30.
Title: Calcul par intervalles et applications. Cours de master recherche UBO (Brest).
[165] 8-9 novembre 2016. Journées nationales du GdR Robotique. Paris.
Titre : Combinaison des méthodes ensemblistes avec l'interprétation abstraite pour la robotique
Résumé. Les méthodes ensemblistes à base de calcul par intervalles permettent de résoudre de façon
garantie des problèmes non-linéaires où les variables sont des vecteurs de Rn. Ces variables peuvent par exemple
correspondre à la position d'un robot ou d'amers, à des paramètres de notre robot que l'on cherche à identifier, etc.
Or, dans le monde de la robotique, les variables qui nous intéressent peuvent être d'une autre nature. Par exemple,
ces variables peuvent correspondre à la trajectoire d'un robot, au graphe de mises en correspondance
mesures-amers ou bien à la forme d'un environnement non-structuré (comme une grotte).
Dans de tels cas, un domaine pour représenter une variable inconnue ne peut plus être un simple intervalle
ou un pavé de Rn mais doit être représenté par une structure ensembliste plus complexe. Comme nous le montre
l'interprétation abstraite, afin de pouvoir appliquer les méthodes de propagation, il est important que ces domaines
possède une structure de treillis relativement à l'inclusion.
Nous introduirons ainsi les concepts d'intervalles de graphes, d'intervalles d'ensembles et de labyrinthes
particulièrement adaptés à la robotique. Ensuite nous montrerons comment ces outils peuvent traiter de façon élégantes
des problèmes comme le SLAM en environnement non structuré, l'exploration exhaustive, la planification garantie de
trajectoire sous contrainte d'état, etc.
Quelques illustrations en robotique marine et sous-marine seront présentées afin de montrer l'intérêt et l'efficacité
de l'approche proposée.
[166] 2èmes Journées de l'Automatique (JAMACS) du GDR MACS à Lille, 15,16 novembre.
Title: Secure a zone with robots using a set-membership state observer.
Abstract. Last January, a Russian submarine entered inside the Bay of Biscay,
for the first time since the cold war. This event motivated us to propose an approach to
secure a zone again submarine intruders using a group of underwater robots. We assume that
each robot is able to detect any intruder inside a disk of a known radius. Moreover, the speed of
the intruders is assumed to be bounded. Our goal is twofold: (1) to
characterize a set for which we can guarantee that there is no
intruder (this corresponds to the secure zone) and (2) to find a
control strategy for the group of robots in order to extend the
secure zone as much as possible.
Our contribution is to show that the problem of securing a zone can be solved
using a set-membership observer shared between all robots.
The approach can also be used for other situations, as for instance to guarantee
that there is no intruder (cars, pedestrians, etc), inside a prohibited area.
[167] Journée MRIS à l'ENSTA Paris November 24
Title. Construction of a mosaic from an underwater video with guaranteed data associations.
Abstract. In this presentation, we will present a new technique for the construction of a mosaic from an underwater
video collected in an underwater environment. The principle is to use proprioceptive data collected by an AUV (here the lock Doppler and
the inertial central) in order to detect feasible loops. The procedure consists in six steps. (1) Use the proprioceptive sensors
only in order to detect all feasible loops. (2) Eliminate all pairs of images that do not correspond to loops. (3) Associate feasible
pairs of images using image processing techniques (4) Contract the feasible trajectories by taking into account the image associations.
(5) Use the trajectory refinement in order to reduce the number of feasible loops. (6) If the contractions are significant enough, goto
Step 3. The resulting fixed point technique is shown to converge and to be guaranteed. Some test-cases are presented in
order to illustrate the efficiency of the approach.
[168] December 2, 2016. Workshop on the Validation of Cyberphysic systems, Halmstad.
Title: Guaranteed characterization of trajectories of dynamical systems using contractors.
Abstract. We consider here constraint satisfaction problems
(CSP) where the variables are trajectories (i.e. functions from R into Rn). The constraints of the CSP could be
differential equations, or continuity, or periodicity, etc. A
domain of the CSP is called a maze which is a composition of graphs, pavings of boxes and polygons. A maze can be represented
in the machine and can be handled using well-known algorithms (involving graphs, linear systems or interval analysis).
The set of mazes forms a lattice with respect to the inclusion and contractors for mazes can be build from each constraint of the
CSP. I will show that a propagation can then be used to solve CSPs in an efficient and guaranteed way.
As an illustration, we will consider different problems such as (i) computing the forward reachable set of a dynamical system,
(ii) enclosing the trajectories of hybrid systems and (iii) computing viability kernels.
[138] Journée big sensor à ENSTA Brest, 28 janvier 2015.
Title: Big sensors: collecting measurements with robots.
[139] 19 mars 2015. Journée calcul ensembliste et interprétation abstraite au CNAM.
Title: Contractors in lattices for solving set-valued constraint satisfaction problems.
Abstract.I will consider the resolution of constraint satisfaction problems in
the case where the variables of the problem are subsets of Rn.
In order to use contractor techniques, we will introduce set
intervals, which are sets of subsets of Rn with a lower bound and an upper
bound with respect to the inclusion. Then, we propose an arithmetic
for them. This makes possible to build projection operators that are
then used by the propagation. In order to illustrate the principle
and the efficiency of the approach, a test-case is provided.
[140] Journées robots sous-marins à Ifremer, Toulon le 8 avril 2015.
Title: Localisation and control of a group of underwater robots.
Abstract. The problem to be considered if the localization and the control of a
group of underwater robots. We will assume that (i) only distances
can be measured between robots (ii) the localisation should be solved
in a distributed manner, (iii) the communication between robots is
poor and (iv) the initial conditions of the robots is unknown. To
solve the problem in an efficient and distributed way, we will
consider a set membership method and provide a
comparison with other more conventional techniques based on particle
filters or Kalman filter.
[141] Jeudi 7 mai 2015.
Présentation du projet transverse Big Sensor. Brest, Télécom.
[142] ECA Brest 21 mai 2015
Title: Interval for state estimation.
[143] SWIM'15, Prague, June 9-11 june 2015.
Title: Distributed localization and control of a group of underwater robots using contractor programming.
Abstract. see pdf.
[144] 16-17 juin 2015 à Bourges. JD-MACS
Title. Cours sur le calcul par intervalles et applications.
[145] Seminaire IRISA Rennes, July 9, 2015, 11h.
Title. Interval analysis for proving dynamical properties of mobile robots; application to sailboat robotics.
Abstract. This talk presents a rigorous approach combining interval analysis
and Lyapunov theory for dynamical analysis of robots. The principle of the approach is to represent uncertain systems by
differential inclusions and then to perform a Lyapunov analysis in order to cast our problem within a set-inversion framework. With this
approach, we can show that for all feasible perturbations, (i) there exists a safe subset A of
the state space the system cannot escape as soon as it enters in it and (ii) if the system is outside A,
it cannot stay outside A forever. An illustration related to the line
following problem of sailboat robots is then provided. After introducing the basic notions on interval analysis and Lyapunov
theory, I will show how these tools can be used for stability analysis of nonlinear systems. Then an
experimental validation that took place on January 2012 will then be presented. On this experiment, the autonomous
sailboat robot Vaimos, has gone from Brest to Douarnenez (more than 100 km).
video of Vaimos ,
wiki.
[146] Manchester, July 13 2015.
Title: Linear and nonlinear control with intervals.
Abstract : Interval analysis is more and more used to solve
nonlinear problems such as (i) computing all global minimisers of a
nonconvex criterion, (ii) computing all solutions of a set of
nonlinear equations, or (iii) characterizing sets defined by
nonlinear inequalities, ...
Unlike classical numerical approaches (Monte Carlo or local methods, for
instance), the results provided by interval analysis are obtained in
a guaranteed way and in a finite time, even when strong
nonlinearities and discontinuities are involved in the problem. The
purpose of this seminar is to introduce in a pedagogical way the
principles of interval methods and constraint propagation techniques.
Then, it will be show how control problems can be cast into a set
membership framework for which interval methods could be efficient.
Some applications to (i) linear robust control, (ii) nonlinear
control and (iii) control with state constraints will be given.
[147] Sheffield, July 2015
Title: Intervals for state estimation.
Abstract. Interval analysis makes it possible to solve a large class on
nonlinear problems such as (i) computing all global minimisers of a nonconvex criterion, (ii) computing all solutions of a set of
nonlinear equations, (iii) characterizing sets defined by nonlinear inequalities, … Unlike classical numerical approaches (Monte
Carlo or local methods, for instance), the results provided by interval analysis are obtained in a guaranteed way and in a finite
time, even when strong nonlinearities and discontinuities are involved in the problem. Classical interval methods have some
difficulties to deal with problems involving a large number of variables (greater than 10, for instance). This limitation is mainly
due to the bisections involved in the interval algorithms that make the complexity exponential with respect to the number of variables.
Contractor based techniques make it possible to push back this frontier and to deal with high dimensional problems (with more than
1000 variables for instance). The purpose of this presentation is to introduce in a pedagogical way the principles of interval methods and
contractor programming techniques. We will then show how these tools can be used to deal with nonlinear state estimation problems. To
illustrate the efficiency and the robustness of the approach, some applications related to the dynamic localization of actual underwater
robots will be presented.
[148] SMART, 16-18 septembre 2015.
Title: Separators for state estimation.
Abstract. A separator is a pair of two contractors : an inner and an outer
contractors. Separators make it possible to compute an inner and an
outer approximation of a large class of subsets of R^n using a
separator algebra in a way that is similar to the contractor algebra.
In this talk, we will consider a state estimation problem of a
continuous nonlinear system in a bounded error context. For a fixed
time t, separators will be able to compute an inner and an outer
approximations of all state vectors that are consistent with all data
bars.
[149] SMART, 16-18 septembre 2015.
Title: Computing a guaranteed approximation of the viability kernel.
[150] Journées de l'automatique du GdR MACS, les 5 et 6 octobre à Grenoble.
Réunion mixte SDH et MEA
[151] Lesson. Vendredi 9 octobre 2015, 13h30-17h30.
Titre : Calcul par intervalles et applications. Cours de master recherche UBO (Brest).
[152] Teaching in Manchester, Oct 26, 2015
Title: A tutorial on interval analysis with applications to robotics and control.
Abstract. Interval analysis makes it possible to solve a large class of nonlinear problems such as (i) computing all global minimisers of a
nonconvex criterion, (ii) computing all solutions of a set of nonlinear equations, (iii) characterizing sets defined by nonlinear
inequalities, etc. Unlike classical numerical approaches (Monte Carlo or local methods, for instance), the results provided by interval
analysis are obtained in a guaranteed way and in a finite time, even when strong nonlinearities are involved in the problem. The purpose
of this seminar is to introduce in a pedagogical way the principles of interval methods and contractor techniques. Some applications to
control, state estimation, and localization will be given. Moreover, I will introduce the basic concepts on PyIbex, which is a Python
plateform, based on Ibex, to deal easily with interval analysis. During the lab, some exercices on the application of interval
analysis will have to be solved with PyIbex.
[153] November 13 to December 18, 2015.
IAMOOC, 1st edition.
Authors: L. Jaulin, J. Ninin, B. Desrochers
Title: IAMOOC : A MOOC on interval analysis with applications to parameter estimation and robot localization.
[154] 25 novembre 2015. Journée MRIS, Ecole polytechnique, Paris.
Title: Computing the inner and outer approximations of the viability kernel.
Abstract. Since viability theory has been introduced by Jean-Pierre Aubin, almost all methods that
have been developed to approximate the viability kernel are discrete. In this presentation, we will show that interval analysis makes it
possible to bracket the viability kernel of a control dynamic system both from inside and outside. The resulting method is shown to be
simple and efficient. The resolution of some examples taken form the literature will be performed using Ibex (for contractors) and DynIbex
(for guaranteed integration).
[114] Jeudi 6 février 2014
Journée Science Navale .
Titre : Théorie des ensembles et robotique navale autonome.
Résumé. Les robots marins (ou sous marins) évoluent dans un environnement
incertain, appréhendent cet environnement à travers des capteurs entachés d'erreurs. Dans un tel contexte, on souhaite
que les robots prennent des décisions permettant de garantir certaines propriétés (comme la non-collision,
l'accomplissement de la mission, une localisation intègre, etc.). Les ensembles permettent de représenter
une grandeur incertaine. Les ensembles peuvent aussi être manipulés aisément formant ce que l'on appelle le calcul
ensembliste. L'objectif de cette présentation est de donner les principes du calcul ensembliste et de montrer comment il
permet de garantir certaines propriétés des systèmes dynamiques. Quelques applications liées à
la robotique navale seront données :
a) La première est la géo-localisation de mines sous marines (collaboration avec le GESMA).
b) La deuxième application concerne la localisation absolue du robot sous marin (SAUCISSE de l'ENSTA Bretagne) dans un environnement
cartographié à l'aide d'un sonar sectoriel.
c) La troisième application est la détection de boucles dans un contexte sous marin (collaboration avec l'école navale).
d) La dernière application est la commande fiable pour le robot voilier VAIMOS afin garantir que ce dernier restera dans un couloir
imposé (collaboration avec IFREMER).
[115] ENS Cachan. Mardi 18 février 2014, 11h-12h.
Title. Interval methods for proving properties of dynamical systems; application to the
validation of the control lows for the sailboat robot VAIMOS.
Video of the presentation
Abstract. This talk presents an original method combining interval analysis and
Lyapunov theory for stability analysis of uncertain dynamical systems. The principle of the
approach is to represent uncertain systems by differential inclusions and then to perform a Lyapunov analysis in order to cast the
stability problem within a set-inversion framework. With this approach, we can show that for all feasible perturbations, (i) there
exists a safe subset A of the state space the system cannot escape as soon as it enters in it and (ii) if the system is outside A, it
cannot stay outside A forever. In a second step, the methodology is used to build reliable robust controllers. An illustration related to
the line following problem of sailboat robots is then provided. After introducing the basic notions on interval analysis and Lyapunov theory, I will
show how these tools can be used for stability analysis of nonlinear systems. Then an
experimental validation that took place on January 2012 will then be presented. On this experiment, the autonomous
sailboat robot Vaimos, has gone from Brest to Douarnenez (more than 100 km). More details
can be found at
vaimosdouarn.html.
[116] Cardiff. March 5, 2014. Mathematics Colloquium.
Title: Interval analysis for proving properties of dynamical systems; application to sailboat robotics
Abstract. This talk presents a rigorous approach combining interval analysis
and Lyapunov theory for stability analysis of uncertain dynamical systems. The principle of the
approach is to represent uncertain systems by differential inclusions and then to perform a Lyapunov analysis in order to cast the
stability problem within a set-inversion framework. With this approach, we can show that for all feasible perturbations, (i) there
exists a safe subset A of the state space the system cannot escape as soon as it enters in it and (ii) if the system is outside A, it
cannot stay outside A forever. In a second step, the methodology is used to build reliable robust controllers. An illustration related to
the line following problem of sailboat robots is then provided. After introducing the basic notions on interval analysis and Lyapunov theory, I will
show how these tools can be used for stability analysis of nonlinear systems. Then an
experimental validation that took place on January 2012 will then be presented. On this experiment, the autonomous
sailboat robot Vaimos, has gone from Brest to Douarnenez (more than 100 km). Video
: http://www.youtube.com/watch?v=YdA8gFInY1M
Wiki:
https://en.wikipedia.org/wiki/Vaimos.
This talk will be presented in a pedagogical way in order to be easily understood by a public with good notions on mathematics.
[117] Orsay, L2S, journée scientifique en hommage à Eric Walter, 20 Mars 2014
Titre : Panorama des contributions d'Eric Walter.
[118] Orsay, L2S, journée scientifique en hommage à Eric Walter, 20 Mars 2014
Title. Interval analysis for robust control; application to sailboat robotics.
Abstract. This talk presents a rigorous approach combining interval analysis
and Lyapunov theory for stability analysis of uncertain dynamical
systems. The principle of the approach is to represent uncertain systems by differential inclusions
and then to perform a Lyapunov analysis in order to cast the stability problem within a set-inversion framework. With this
approach, we can show that for all feasible perturbations, (i) there exists a safe subset A of the state space the system cannot escape as
soon as it enters in it and (ii) if the system is outside A, it cannot stay outside A forever. In a second step, the methodology is
used to build reliable robust controllers. An illustration related to the line following problem of sailboat robots is then provided.
After introducing the basic notions on interval analysis and Lyapunov theory, I will
show how these tools can be used for stability analysis of nonlinear systems. Then an
experimental validation that took place on January 2012 will then be presented. On this experiment, the autonomous
sailboat robot Vaimos, has gone from Brest to Douarnenez (more than 100 km). Video
: http://www.youtube.com/watch?v=YdA8gFInY1M
Wiki: https://en.wikipedia.org/wiki/Vaimos
This talk will be presented in a pedagogical way in order to be easily understood by a
large public.
[119] Journée MEA-CPNL,Paris. 3 avril 2014
Title: Interval methods: a tutorial.
[120] Journée MEA-CPNL,Paris. 3 avril 2014
Title: Combining interval analysis and nonlinear predictive control to compute capture tubes.
Abstract. Consider an autonomous time dependant nonlinear system dx/dt=f(x,t),
where x belongs to R^n. A tube X(t)
is a function which associates to each t a subset of R^n.
A tube X(t) is said to be a capture tube if the fact that x(t) in X(t)
implies that x(t+t1) in X(t+t1) for all t1>0.
If a candidate capture tube is available, we can check that it is
indeed a capture tube by performing a Lyapunov analysis in order to cast the problem into checking the inconsistency
of a set of nonlinear equations. This inconsistency can then easily
be checked using interval analysis. Now, for many systems such as non
holonomous systems, we rarely have a candidate for a capture tube and
we need to find one. The main contribution of this talk is to show
that a predictive control approach can help us to find such a capture
tube. The main idea if to start from a non-capture tube Z(t)
and to try to find a capture tube which encloses Z(t).
For this, we predict for all t and for all x(t)
in Z(t) within a finite time-horizon window [t,t+t2]
(where t2>0 is fixed) and to show that x(t2)
belongs to Z(t2).
This talk will be presented in a pedagogical way in order to be easily understood by a
public which is not specialist in interval/control methods.
[121] CEA List 6 mai 2014.
Title: Solving set-valued problems; Application to localisation and mapping with robots.
Abstract. In this talk, I will consider the resolution of nonlinear problems in the case where the unknown variables of the
problem are subsets of Rn. In order to use an interval approach, we introduce set intervals,
which are sets of subsets of Rn with a lower bound and an upper
bound with respect to the inclusion. Then, we propose an arithmetic for these set intervals. This will make it possible to build specific
contractors that will be used into a fixed point procedure. As an application, I will consider the range-only SLAM (Simultaneous
Localization And Mapping) problem in the case where (i) the map is unknown and unstructured (i.e., we do not assume that the map is
composed of segments, punctual marks, etc.), and (ii) the trajectory of the robot is also unknown. For the resolution, I will
first to transform the SLAM problem into a hybrid constraint satisfaction problem (CSP) where the variables can either be real
numbers, vectors, trajectories or subsets of Rn. An extension of existing constraint propagation methods is then proposed to solve
hybrid CSPs involving set-valued variables. A simulated test case is then proposed to show the feasibility of the approach.
This talk will be presented in a pedagogical way in order to be easily understood by a
public with good notions on mathematics.
[122] SMART 2014, Manchester. May 21.
Title: Nonlinear state estimation with delays.
Abstract.This talk proposes to use contractor based methods in order to estimate
the trajectory of a robot which is described by nonlinear state equations involving inter-temporal constraints such as delays or
periodicity. The principle of the approach is to represent an uncertain trajectory by an interval function (or a tube) and to apply
contractors derived from the constraint of the system until the fixed point is reached. The method is proved to converge to a tube which
encloses all feasible trajectories. The method will be illustrated on the localization of a group of underwater robots with
unsynchronized clocks. In this problem, we consider that the travel time of the sound that gives us the distances between robots cannot
be neglected. Therefore we cannot suppose that we measure a true distance between robots at the same time, but between robots at
different times.
[123] SWIM 2014, Uppsala. June 11,12.
Title: Separators: a new interval tool to bracket solution sets; application to path planning.
Abstract. Contractor algebra is a numerical tool based on interval analysis which makes it possible to solve many
nonlinear problems arising in control, such as identification, path planning or robust control. More precisely, contractor-based
techniques combined with a paver can provide inner and outer approximations (with subpavings) of solution sets. To compute the
inner subpaving, the De Morgan rules have be used to express the complementary set of the solution set. The task is not so easy and
has never been made automatic, to our knowledge. This talk presents the new notion of separators which is a pair of complementary
contractors and presents the corresponding algebra. Using the separator algebra inside a paver will allow us to get an inner and an
outer approximation of the solution set in a much simpler way than using any other interval approach. Some test cases related to simple
geometrical problems (such as Path Planning) will be provided to illustrate the efficiency of the approach.
[124] IHSEV 2014, Moulin mer. 18-19 juin 2014.
Title: Bilan 'robotique marine' de l'équipe IHSEV
[125] 2014, Nantes, lundi 23 juin. Contraintes et géométrie.
Title: Solving geometrical constraints in space-time.
Abstract.In a Euclidian space, the separation between two points corresponds to their distance which is purely
spatial, and is always positive. In space-time, the separation between two events takes into account not only the spatial separation
between the events, but also their temporal separation. In this talk, we will consider problems involving geometrical constraints in the
space-time. The motion of the objects will be described by differential equations and the clocks attached to each object will be
considered as unknown variables of the problem (equivalently, the clocks are not synchronized).
The principle of the approach is to represent each trajectory of each object as an
interval function (or a tube). Then a contractor-based technique will be used to solve the problem. The method is proved to converge to
tubes which enclose all feasible trajectories for each object. The method will be
illustrated on the localization of a group of underwater robots with unsynchronized clocks. In this problem, we consider that the travel
time of the sound that gives us the distances between robots cannot be neglected. Therefore we cannot suppose that we measure a true
distance between robots at the same time, but between robots at different times.
[126] ICVRAM, 15 juillet 2014. Liverpool.
Title: Inner and outer approximations of probabilistic sets.
[127] Tutorial. Lisbon
Eusipco 2014.
Guaranteed Nonlinear Estimation Using Interval Analysis.
[128] Coprod 2014, Wuerzburg, Germany.
Title: Robust Localisation Using Separators.
[129] SCAN 2014
, Wuerzburg
[130] Journée de l'école doctorale SICMA, Brest
4ème Journée des doctorants de l'Ecole Doctorale SICMA, 25 Septembre 2014
Introduction à la robotique.
[131] Lesson. Vendredi 10 octobre 2014, 13h30-17h30.
Titre :Calcul par intervalles et applications. Cours de master recherche UBO (Brest).
[132] MOQESM 2014, 14-15 octobre
Title. Construction of a mosaic from an underwater video using proprioceptive sensors ; an interval analysis approach.
Abstract. In this presentation, we will present a new technique for the construction of a mosaic from an underwater
video collected in an underwater environment. The principle is to use proprioceptive data collected by an AUV (here the lock Doppler and
the inertial central) in order to detect feasible loops. The procedure consists in six steps. (1) Use the proprioceptive sensors
only in order to detect all feasible loops. (2) Eliminate all pairs of images that do not correspond to loops. (3) Associate feasible
pairs of images using image processing techniques (4) Contract the feasible trajectories by taking into account the image associations.
(5) Use the trajectory refinement in order to reduce the number of feasible loops. (6) If the contractions are significant enough, goto
Step 3. The resulting fixed point technique is shown to converge. Some test-cases are presented in order to illustrate the efficiency
of the approach.
[133] MOQESM 2014, 15 octobre
Round table on big sensors, Sea Tech Week, Oct 15, 16h15.
[134] Nantes. Oct 22, 2014.LINA. Séminaires Contraintes et optimisation.
Title. Interval for proving stability properties of dynamical systems; application to sailboat robotics.
Abstract. This talk presents a rigorous approach combining interval analysis
and Lyapunov theory for stability analysis of uncertain dynamical
systems. The principle of the approach is to represent uncertain systems by differential inclusions
and then to perform a Lyapunov analysis in order to cast the stability problem within a set-inversion framework. With this
approach, we can show that for all feasible perturbations, (i) there exists a safe subset A of the state space the system cannot escape as
soon as it enters in it and (ii) if the system is outside A, it cannot stay outside A forever. In a second step, the methodology is
used to build reliable robust controllers. An illustration related to the line following problem of sailboat robots is then provided.
After introducing the basic notions on interval analysis and Lyapunov theory, I will
show how these tools can be used for stability analysis of nonlinear systems. Then an
experimental validation that took place on January 2012 will then be presented. On this experiment, the autonomous
sailboat robot Vaimos, has gone from Brest to Douarnenez (more than 100 km).
video.
wikipedia.
[135] Seminar MBDA, November 27, 2014.
Title. Computing capture tubes.
[136] Journées GDR Paris biorob 28 nov 2014.
Title: Distributed localization of a group of underwater robots.
Abstract.This talk proposes to use contractor based methods in order to estimate
the trajectory of a robot which is described by nonlinear state
equations involving inter-temporal constraints such as delays or
periodicity. The principle of the approach is to represent an
uncertain trajectory by an interval function (or a tube) and to apply
contractors derived from the constraint of the system until the fixed
point is reached. The method is proved to converge to a tube which
encloses all feasible trajectories.The method will be
illustrated on the localization of a group of underwater robots with
unsynchronized clocks. In this problem, we consider that the travel
time of the sound that gives us the distances between robots cannot
be neglected. Therefore we cannot suppose that we measure a true
distance between robots at the same time, but between robots at
different times.
[137] Mexico. December 17, 2014.
Title. Interval analysis for
proving stability properties of mobile robots; application to
sailboat robotics.
Abstract. This talk presents a rigorous approach combining interval analysis
and Lyapunov theory for stability analysis of uncertain dynamical
systems. The principle of the
approach is to represent uncertain systems by differential inclusions
and then to perform a Lyapunov analysis in order to cast the
stability problem within a set-inversion framework. With this
approach, we can show that for all feasible perturbations, (i) there
exists a safe subset A of the state space the system cannot escape as
soon as it enters in it and (ii) if the system is outside A, it
cannot stay outside A forever. In a second step, the methodology is
used to build reliable robust controllers. An illustration related to
the line following problem of sailboat robots is then provided. After
introducing the basic notions on interval analysis and Lyapunov
theory, I will show how these tools can be used for stability
analysis of nonlinear systems. Then an
experimental validation that took place on January
2012 will then be presented. On this experiment, the autonomous
sailboat robot Vaimos,
has gone from Brest to Douarnenez (more than 100 km). Video
: http://www.youtube.com/watch?v=YdA8gFInY1M,
Wiki: https://en.wikipedia.org/wiki/Vaimos,
This talk will be presented in a pedagogical way in order to be easily understood by a large public.
[101] Manchester,
lessons of interval robotics. Control Systems Research Group School of Electrical and Electronic Engineering. March 4,5,6 2013.
Abstract. Interval analysis makes it possible to solve a large class of nonlinear problems such as (i) computing all global
minimizers of a nonconvex criterion, (ii) computing all solutions of a set of nonlinear equations, (iii) characterizing sets defined by
nonlinear inequalities, etc. Unlike classical numerical approaches (Monte Carlo or local methods, for instance), the results provided by
interval analysis are obtained in a guaranteed way and in a finite time, even when strong nonlinearities and discontinuities are
involved in the problem. Unfortunately, classical interval methods have some difficulties to deal with problems
involving a large number of variables (greater than 10, for instance). This limitation is mainly due to the bisections involved
in the interval algorithms that makes the complexity exponential with respect to the number of variables. Constraint propagation
techniques make it possible to push back this frontier and to deal with high dimensional problems (with more than 1000 variables for
instance). Even so, these techniques are no widely known in the interval community. The purpose of the lessons
is to introduce in a pedagogical way the principles of interval methods and constraint propagation techniques. Some applications to state
estimation, SLAM, path planning, nonlinear control... will be presented. Most of these applications are related to robotics, mainly
underwater robotic and sailboat robotics.
Monday 4th of March (2.00pm - 4.00pm): Interval methods (intervals, computing with sets, contractors), applications for stability
analysis of nonlinear systems and for path-planning.
Chapter 1. Intervals,
Chapter2. Subpavings,
Chapter 3. Contractors,
Chapter 8. Path planning.
Tuesday 5th of March (10.00am - 12.00pm): Localization, SLAM and non-linear control.
Chapter 4. Robust estimation,
Chapter 5. Robust observers,
Chapter 6. Interval SLAM,
Chapter 7. Loop detection.
Wednesday: Non-linear control and nonlinear stability. Pratice (SIVIA with IBEX 2.0),
Chapter 9.
Sailboat robotics Chapter 10. Attractors
Videos (associated to the slides above)
Monday 4th of March 2013:
Interval methods (intervals, computing with sets, contractors)
[102]
Workshop Exploration multi-robots.
20 mars 2013 à Lyon, conjointement avec l'événement Innorobo 2013.
Title: Cooperative control, sailboats and underwater robots.
Abstract. This talk proposes interval based methods for the reliable exploration of mobile robots.
For exploration, we will show that a set-membership approach makes it possible to guarantee that all the required space has indeed been
explored. When dealing with a swarm of robots, we will also show that the approach makes it possible to guarantee that no collision between
robots will occur. Moreover, in an underwater environment, we will demonstrate that the collaboration between robots allows a guaranteed
localization of the whole swarm. The feasibility of the approach will be illustrated by some simulations and some actual experiments
involving sailboat robots and underwater robots.
[103] Jeudi 21 mars de 8h30 à 12h30 à Lyon.
Conjointement avec l'événement Innorobo 2013,
Workshop on Recent advances in sensing, localization, and control for underwater robotics
Titre: Loop detection with proprioceptive sensors. Application to underwater robotics.
By: Luc Jaulin, Clément Aubry, Rozenn Desmare.
Abstract: I will present a new set-membership approach for loop detection of mobile robots
in the situation where proprioceptive sensors only are
available. To detect loops, the new concepts of t-plane (which is a two dimensional space with time coordinates) is introduced. Interval
of functions (or tubes) are then used to represent uncertain trajectories and tests are provided in order to remove parts of the
t-plane that do not correspond to any loop. An experiment with an actual underwater robot is proposed in order to illustrate the
principle and the efficiency of the approach.
[104]
MBDA, Paris, 27 Mai 2013
Set membership methods for analysing the robustness of complex systems.
[105]
SWIM 2013, Brest, June 5-7, 2013
Title: Outer approximation of attractors using an interval quantization.
Abstract. An attractor is the set toward which the solutions of a dynamical
system converge. In this talk, the system is described by an
autonomous state equation. When the evolution function f:Rn→Rn,
in nonlinear, interval analysis is needed to
provide guaranteed conclusion. Existing interval-based methods cover
the state space with small boxes and perform interval integration for
each of them, which makes them limited to small dimensional problems.
In this talk, I will shows that an outer approximation of attractors
can be built without any interval integration. The basic idea is to
perform a quantization the state equation into a dynamical graph. The
nodes of this graph are polytopes covering the state space. A test
case related to the station keeping of a non-holonomous robot
illustrates the principle of the approach.
[106] 12-13 juin 2013, Journées démonstrateurs. Angers.
Titre : VAIMOS, un voilier autonome.
[107]
NUMTA 2013. Falerna Calabria, Italy, June 18, 2013.
Title: Parametric global optimization; application to sailboat robotics.
[108] Séminaire à Nantes le 25 juin 2013.
Title: Localization and Mapping in a complex environment: a constraint programming approach.
Abstract. This presentation deals with the simultaneous localization and
mapping (SLAM) problem for a robot. The robot has to build a map of its environment while localizing itself using the partially built
map. SLAM is often referred to as a chicken and egg problem: if the map is known, finding the robot trajectory can be performed using any
suited localization method and if the trajectory is known we can easily build the map. Here, the environment is complex, i.e., we do
not assume that the map is composed of segments, punctual marks, or any other parametric shape. The approach that will be proposed is to
transform the SLAM problem into a hybrid constraint satisfaction problem (CSP) where the variables can either be real numbers,
vectors, trajectories or subsets of Rn. An extension of existing constraint propagation methods is then
proposed to solve hybrid CSPs involving set-valued variables. A simulated test case is then proposed to show the feasibility of the
approach.
[109] Ecole JD-JN MACS. 9-10 juillet 2013 à Strasbourg.
Titre : Méthodes Intervalles et Applications.
[110]
Journée MEA, Paris, 14 novembre 2013.
Title: Pure range-only SLAM with indistinguishable landmarks; a constraint programming approach.
Abstract. This presentation deals with the simultaneous localization and
mapping problem (SLAM) for a robot. The robot has to build a map of
its environment while localizing itself using an the partially built
map. It is assumed that (i) the map is made of punctual static
landmarks, (ii) the landmarks are indistinguishable (which is the
main contribution of this work), (iii) the only exteroceptive
measurements correspond to the distance between the robot and the landmarks.
In our SLAM problem, the
unknown variables have an heterogeneous nature: the landmarks are
vectors of R^2, the trajectories belong to the set of functions from R->Rn, the free space is a subset of R^2 and
the data associations can be represented by a graph G. This talk shows that constraint propagation methods
can easily deal with heterogeneous variables and that solving the SLAM problem amounts to use a fixed point
method with specific contractors. The resulting method will inherit
properties of constraint propagation tools: a polynomial time algorithm which provides guaranteed results.
[111] Séminaire au LIRMM à Montpellier le 21 novembre 2013.
Title: Programmation par contraintes appliquée à la robotique mobile.
Abstract. De nombreux problèmes de la robotique mobile (planification de trajectoire, localisation,
cartographie) peuvent se modéliser par des contraintes ou CSP (Constraint Satisfaction Problem). En robotique, les variables de ces
CSP ont une nature extrêmement variée relativement à ce qui est classiquement considéré dans la communauté
CP (Constraint Programming). En effet, les inconnues du problème (ou les variables du CSP) peuvent être des réels (comme
par exemple des paramètres à identifier), des fonctions (e.g, la trajectoire d'un robot ou une loi de commande), des
ensembles de Rn (e.g., la forme d'un objet ou la carte 3D de l'environnement du robot) ou bien des graphes (représentant
par exemple la mise en correspondance entre des objets détectés). Dans tous les cas considérés, ces variables
appartiennent à des ensembles ordonnés, ou plus précisément des treillis, pour lesquels le concept d'intervalle peut être défini.
On peut ainsi avoir des intervalles de fonctions (ou tubes), des intervalles d'ensembles de Rn ou des intervalles de
graphes. Les contraintes du problème (e.g. la trajectoire est périodique, les deux robots ne se voient pas) sont alors
transformées en opérateurs de contraction, ou contracteurs, capables de contracter les intervalles contenant
les valeurs des variables sans perdre aucune solution. L'élégance, l'efficacité
et la robustesse des méthodes de programmation par contraintes seront démontrées sur plusieurs applications faisant
intervenir des robots réels. Parmi ces applications seront présentées la commande de robots voiliers et la
localisation de mines par des robots sous-marins.
[112] Cycle de conférences en Informatique et Automatique de Lille, Jeudi 28 novembre 2013, 14h à 15h30..
Titre : Calcul ensembliste et robotique navale.
Résumé. Les robots marins (ou sous marin) évoluent dans un environnement
incertain, appréhendent cet environnement en toute autonomie à l'aide de capteurs plus ou moins précis. Dans un tel contexte,
on souhaite que les robots prennent des décisions permettant de garantir certaines propriétés (comme la
non-collision, l'accomplissement de la mission, une localisation intègre, etc.).
Les ensembles permettent de représenter une grandeur incertaine. Les ensembles peuvent aussi être manipulés aisément formant
ce que l'on appelle le calcul ensembliste. L'objectif de cette présentation est de donner les principes du calcul ensembliste et
de montrer comment il permet de garantir certaines propriétés sur les systèmes dynamiques et de valider des lois de commande dans un
contexte incertain. Quelques applications liées à la robotique navale seront données. Plus précisément,
je parlerai de la géo-localisation de mines sous marines, de l'estimation d'état ensembliste pour la localisation d'un
robot sous marin, et de la commande fiable du robot voilier VAIMOS.
[113] Journée MEA, Brest, 5 décembre 2013.
Title. Separators: a new interval tool to bracket solution sets; application to path planning.
Abstract. Contractor algebra is a numerical tool based on interval analysis
which makes it possible to solve many nonlinear problems arising in
control, such as identification, path planning or robust control.
More precisely, contractor-based techniques combined with a paver can
provide inner and outer approximations (with subpavings) of solution
sets. To compute the inner subpaving, the De Morgan rules has be used
to express the complementary set of the solution set. The task is not
so easy and has never been made automatic, to our knowledge. This
talk presents the new notion of separators which is a pair of
complementary contractors and presents the corresponding algebra.
Using the separator algebra inside a paver will allow us to get an
inner and an outer approximation of the solution set in a much
simpler way than using any other interval approach. Some test cases
related to simple geometrical problems (such as Path Planning) will
be provided to illustrate the efficiency of the approach.
[87]
Journée ensembliste MEA + SDH. Jeudi 2 février 2012 à l'ENSTA Paris.
Title: Reliable control using interval analysis. Application to sailboat robotics.
Abstract. This talk proposes an interval based method for the validation of
reliable and robust navigation rules for mobile robots. The main idea
is to show that for all feasible perturbations, (i) there exists a
safe subset A of the state space such that the robot cannot escape as
soon as it enters in it and (ii) if the robot is outside A, it cannot
stay outside A forever. The methodology will be illustrated on the
line following problem of a sailboat
robot. A validation on actual experiment made on January 2012 is
presented. In this experiment the sailboat robot, named Vaimos,
has gone autonomously from Brest to Douarnenez (around 100 km). More
details on the experiment can be found at
http://www.ensta-bretagne.fr/jaulin/vaimosdouarn.html
[88]
Journée Ifremer. Jeudi 5 avril 2012 à Toulon.
Title: Robotique (sous)-marine et calcul ensembliste.
[89]
Séminaire LAAS.Jeudi 25 avril 2012 à Toulouse
Title. Reliable control using interval analysis. Application to sailboat robotics
Abstract. This talk proposes an interval based method for the validation of
reliable and robust navigation rules for mobile robots. The main idea
is to show that for all feasible perturbations, (i) there exists a
safe subset A of the state space such that the robot cannot escape as
soon as it enters in it and (ii) if the robot is outside A, it cannot
stay outside A forever. The methodology will be illustrated on the
line following problem of a sailboat
robot. A validation on actual experiment made on January 2012 is
presented. In this experiment the sailboat robot, named Vaimos,
has gone autonomously from Brest to Douarnenez (around 100 km). More
details on the experiment can be found at
http://www.ensta-bretagne.fr/jaulin/vaimosdouarn.html
[91]
Journées IHSEV. 11-12 juin à Logona.
Titre. Les Robots voiliers.
[92]
Novosibirsk, 23 sept 2012. Plenary talk at SCAN 2012 for the Moore prize
Moore prize.
Title: Interval analysis and robotics.
[93] IRAuS, le 4 octobre 2012 à Orléans
Titre. Calcul par intervalles pour l'étude de la stabilité dynamique des robots ; application au suivi de
route de robots voiliers.
Résumé. Dans cet exposé, une nouvelle méthode pour l'étude de la stabilité dynamique
des robots sera présentée. Cette méthode possède les propriétés attractives énoncées
ci-dessous.
Elle est numérique et peut donc être utilisée pour une très grande
classe robots.
Elle est rigoureuse. Du fait qu'elle utilise des méthodes ensemblistes, cette méthode apporte une
preuve de stabilité, tout comme pourraient le faire les approches formelles.
Elle est robuste, dans le sens où elle permet de prendre en compte des incertitudes de
nature ensembliste pouvant perturber le robot.
Le principe est de représenter la dynamique du robot avec ses incertitudes par une inclusion différentielle puis ensuite
d'utiliser la théorie de Lyapunov afin de transformer le problème de stabilité en un problème d'inversion
ensembliste. Avec cette approche, nous pourrons montrer qu'il existe un sous ensemble A (appelé domaine de capture) de l'espace d'état
tel que pour toutes les perturbations faisables, (i) le système ne pourra pas s'échapper de A s'il en est rentré et
(ii) si le système est à l'extérieur de A, il va finir par y rentrer. Dans une deuxième phase, la méthodologie
sera étendue pour la conception de régulateurs robustes. Elle sera enfin illustrée sur le problème de
la navigation de robots voiliers autonomes. Pour cela, je décrirai une validation expérimentale qui s'est tenue en Janvier
2012. Dans cette expérience, le robot voilier Vaimos, a effectué une mission de Brest à Douarnenez (plus de 100
km) en autonomie complète. Plus de détails sur cette expérience peuvent être trouvés sur
vaimosdouarn.html.
[94] Friday Oct 18, 2012. IPA, Uppsala
Title. An interval approach for stability analysis of nonlinear systems.
Abstract.
This talk proposes a new interval-based method for robust stability
analysis of nonlinear systems. The principle of the approach is to
represent uncertain systems by differential inclusions and then to
perform a Lyapunov analysis in order to transform the stability
problem within a set-inversion framework. With this approach, we can
show that for all feasible perturbations, (i) there exists a safe
subset A of the state space the system cannot escape as soon as it
enters in it and (ii) if the system is outside A, it cannot stay
outside A forever. In a second step, the methodology is used to build
reliable robust controllers. An illustration related to the line
following problem of sailboat robots is then provided.
An experimental validation that took place on January
2012 will then be presented. On this experiment, the autonomous
sailboat robot Vaimos,
has gone from Brest to Douarnenez (more than 100 km). More details
can be found at
http://www.ensta-bretagne.fr/jaulin/vaimosdouarn.html.
[95] JRA 2012, Nantes. 23 octobre 2012.
Titre. Calcul par intervalles pour l'étude de la stabilité dynamique des robots ;
application au suivi de route de robots voiliers.
Résumé. Dans cet exposé, une nouvelle méthode pour l'étude
de la stabilité dynamique des robots sera présentée. Cette méthode possède les propriétés
attractives énoncées ci-dessous.
Elle est numérique
et peut donc être utilisée pour une très grande classe robots.
Elle est rigoureuse. Du fait qu'elle utilise des méthodes ensemblistes, cette méthode apporte une
preuve de stabilité, tout comme pourraient le faire les
approches formelles.
Elle est robuste, dans le sens où elle permet de prendre en compte des incertitudes de
nature ensembliste pouvant perturber le robot.
Le principe est de représenter la dynamique du robot avec ses incertitudes par une inclusion différentielle puis ensuite
d'utiliser la théorie de Lyapunov afin de transformer le problème de stabilité en un problème d'inversion
ensembliste. Avec cette approche, nous pourrons montrer qu'il existe un sous ensemble A (appelé domaine de capture) de l'espace d'état
tel que pour toutes les perturbations faisables, (i) le système ne pourra pas s'échapper de A s'il en est rentré et
(ii) si le système est à l'extérieur de A, il va finir par y rentrer. Dans une deuxième phase, la méthodologie
sera étendue pour la conception de régulateurs robustes. Elle sera enfin illustrée sur le problème de
la navigation de robots voiliers autonomes. Pour cela, je décrirai une validation expérimentale qui s'est tenue en Janvier
2012. Dans cette expérience, le robot voilier Vaimos, a effectué une mission de Brest à Douarnenez (plus de 100
km) en autonomie complète. Plus de détails sur cette expérience peuvent être trouvés sur
http://www.ensta-bretagne.fr/jaulin/vaimosdouarn.html.
[96] Lesson. Vendredi 16 novembre 2012, 13h30-17h30. Calcul par intervalles et applications. Cours de master recherche UBO (Brest)
[97] Journée du 22 novembre 2012. GT2 du GDR robotique .
Perception et localisation pour les robots marins et sous-marins.
Titre. Calcul par intervalles pour l'étude de la stabilité dynamique des robots ; application au suivi de route de robots voiliers.
Résumé. Dans cet exposé, une nouvelle méthode pour l'étude de la stabilité dynamique des robots sera présentée.
Cette méthode possède les propriétés attractives énoncées ci-dessous.
Elle est numérique et peut donc être utilisée pour une très grande classe robots.
Elle est rigoureuse. Du fait qu'elle utilise des méthodes ensemblistes, cette méthode apporte une
preuve de stabilité, tout comme pourraient le faire les approches formelles.
Elle est robuste, dans le sens où elle permet de prendre en compte des incertitudes de nature ensembliste pouvant perturber le robot.
Le principe est de représenter la dynamique du robot avec ses incertitudes par une inclusion différentielle puis ensuite d'utiliser la théorie de Lyapunov afin de transformer le
problème de stabilité en un problème d'inversion ensembliste. Avec cette approche, nous pourrons montrer qu'il existe
un sous ensemble A (appelé domaine de capture) de l'espace d'état
tel que pour toutes les perturbations faisables, (i) le système ne pourra pas s'échapper de A s'il en est rentré et
(ii) si le système est à l'extérieur de A, il va finir par y rentrer. Dans une deuxième phase, la méthodologie
sera étendue pour la conception de régulateurs robustes. Elle sera enfin illustrée sur le problème de
la navigation de robots voiliers autonomes. Pour cela, je décrirai une validation expérimentale qui s'est tenue en Janvier
2012. Dans cette expérience, le robot voilier Vaimos, a effectué une mission de Brest à Douarnenez (plus de 100
km) en autonomie complète. Plus de détails sur cette expérience peuvent être trouvés sur
www.ensta-bretagne.fr/jaulin/vaimosdouarn.html.
[98] Monday 3 to Thursday 6 december 2012, Porto Alegre, UFRGS, Brazil, lessons of interval robotics (10h).
o 15h-17h, Monday and Tuesday: interval methods (intervals, computing with sets, contractors)
o 15h-17h, Wednesday: Robust state estimation
o 15h-17h, Thursday: SLAM.
o 15h-17h, Friday: Loop detection for SLAM
[99] Friday 7 december 2012, 13h00. Porto Alegre, Brazil, Seminar.
Title. Interval analysis and sailboat robotics.
Abstract. This talk proposes a new interval-based method for robust stability
analysis of nonlinear systems. The principle of the approach is to
represent uncertain systems by differential inclusions and then to
perform a Lyapunov analysis in order to transform the stability
problem within a set-inversion framework. With this approach, we can
show that for all feasible perturbations, (i) there exists a safe
subset A of the state space the system cannot escape as soon as it
enters in it and (ii) if the system is outside A, it cannot stay
outside A forever. In a second step, the methodology is used to build
reliable robust controllers. An illustration related to the line
following problem of sailboat robots is then provided.
[100] Théorie des contracteurs, Lundi 17 décembre 2012. ENSTA Bretagne. Dans le cadre de la formation IBEX 2.0, faite par Gilles Chabert le mardi 18.
[79]. Journée ensembliste MEA.Jeudi 9 décembre 2010.
Title: Fleeting state estimation.
Abstract. This talk deals with nonlinear state estimation where measurements
are available only when some given equality conditions are satisfied.
For this type of problems, which are often met in robot localization
when sonar or radar are involved, the data are qualified as fleeting
because the measurements are available only at some given unknown
dates. A new set-membership approach able to deal efficiently and
reliably with nonlinear estimation with fleeting data is presented.
The main idea to propose an arithmetic for interval functions (or
tubes) and to use this arithmetic to allow a propagation through
constraints involving functions. An illustration related to SLAM with
one rotating telemeter will be given.
[80] Journée IHSEV, ENIB. Jeudi 7 janvier 2011.
Titre : Méthodes ensemblistes pour la robotique.
[81] Présentation du profil robotique à l'ENSTA-Bretagne.
[82] Journée ensembliste MEA + SDH.Jeudi 3 février 2011.
Title: Interval state estimation of a nonlinear hybrid system: the sailboat.
Abstract. This talk deals with the state estimation of a sailboat robot, which is an example
of nonlinear hybrid systems (the mainsheet can be tight or not). This problem is motivated by the
microtransat challenge where small autonomous sailboat robots are designed to cross the Atlantic ocean.
All components of such robots should be robust with respect to all situations (heavy weather,
waves, salt water, low level of energy, long trip, etc.). Two types of sensors can be considered.
(i) Reliable sensors, which could survive to all situations. Such sensors are the GPS, the
compass, the gyrometers and accelerometers. All these sensors are low energy consumers, can be enclosed
inside a waterproof tank and can survive for years. The GPS gives us the position of the boat and new
generation GPS can also return the speed with a good accuracy by using the Doppler effect. Since the
magnetic perturbation inside the ocean can be neglected, the compass measures the north direction with
a rather good accuracy. The gyrometer
returns the rotational speed and the accelerometers make possible to get the roll and pitch of the robot.
(ii) Unreliable sensors, which have a high probability to brake down in case of heavy weather.
Anemometers (device that is used for measuring wind speed), weather vane (which returns the direction
of the wind), dynamometers which measures the forces on the sail or the rudder are considered as
unreliable. They are directly in contact with aggressive natural elements (wind, wave, salt) and can fail down at any time.
On the one hand, to control the robot, it is necessary to know where the wind comes from, what is its power, how strong
are the forces on the sail or on the rudder, if the mainsheet is tight or not, etc. On the other hand, a
reliable boat can only enclose reliable sensors. This talk provides a new method which combines classical nonlinear
observation technique, based on flatness concepts, with interval analysis. The first tool makes possible to transform the
observation problem into equations that have to be solved at each time. Interval analysis gives a
systematic way to solve the inversion problem and makes possible to
take into account some interval uncertainties on the measurement
data.
A youtube video of our sailboat robot can be found at http://www.youtube.com/watch?v=jOjxRPnwQ9g
[83]
ENSTA-Bretagne, Mardi 29 mars 2011
Titre : Méthodes ensemblistes pour la localisation .
[84]
JIME 2011. Jeudi 7 avril 2011.
Titre : Quelques avancées récentes du calcul par intervalles permettant le traitement
robuste de problèmes de grande taille ; applications à la robotique mobile.
Résumé : Le calcul par intervalles est un outil numérique capable de résoudre une grande classe de problèmes non-linéaires,
comme par exemple le calcul de tous les minima globaux d'un critère non-convexe ou bien le calcul de toutes les solutions d'un système
d'équations non linéaires. Contrairement aux méthodes numériques classiques, le résultat est obtenu de façon globale et garantie en un temps fini, même lorsque des
fonctions trigonométriques ou discontinues apparaissent dans le problème.
Malgré, toutes ses bonnes propriétés, le calcul par intervalles est resté relativement confidentiel dans la communauté automaticienne en
raison des préjugés suivants :
Trop couteux. Le nombre de variables doit être faible car sinon le temps de calcul est beaucoup trop grand.
Pas robustes. Lorsque des bornes sur les erreurs de mesures ne sont pas
rigoureusement respectées ou lorsque des données
aberrantes existent, l'ensemble des solutions est vide et le résultat
est difficilement exploitable.
Difficiles mettre en oeuvre.
L'implémentation efficace des méthodes intervalles est laborieuse et demande des connaissances approfondies
en informatique.
Peu d'applications réalistes. Il n'existe pas ou peu d'applications industrielles utilisant le
calcul par intervalles et qui pourraient difficilement fonctionner
sans un tel outil.
Dans cet exposé, nous allons
chercher à démentir ces préjugés.
Les méthodes par intervalles peuvent s'avérer très efficaces même quand le nombre de variables est très
grand (<100 000, par exemple). Il suffit pour cela d'utiliser des
méthodes de propagation de contraintes. Lorsque des données aberrantes sont
présentes, on cherche à être cohérent, non pas avec toutes les mesures, mais avec un maximum d'entre-elles. On
arrive ainsi à obtenir des méthodes d'estimation très robustes. Il existe des outils informatiques (Int4Sci, IntLab, QUIMPER, Alias, Profil Bias, C-XSC, etc.) qui permettent de programmer
rapidement et aisément des algorithmes ensemblistes. Des applications réelles convaincantes utilisant le calcul par
intervalles commencent à voir le jour. Des robots utilisant le calcul par intervalles pour se localiser existent. Le SLAM avec des
méthodes ensemblistes est utilisé pour la localisation de mines sous-marine, etc. Quelques applications en robotique mobile sous-marine (localisation et SLAM) impliquant des robots
réels dans des situations difficiles seront présentées afin d'illustrer ces affirmations. Cet exposé sera présenté de façon pédagogique afin d'être compris dans son
intégralité et sans difficulté par des
non-spécialistes.
[85]
Cours Ecole Navale. Brest. Lundi 8 juin 2011.
Title: Sea robotics.
[86]
Swim 2011. June 14 2011, Bourges.
Title: Range-only SLAM with occupancy maps.
Abstract. This talk proposes a new set-membership approach for solving
range-only SLAM (Simultaneous Localization And Mapping) problems in the case where the map is described by an
arbitrary occupancy set (i.e., we do not assume that the map is composed of
segments, punctual marks, etc.). The principle is to transform the SLAM problem into a
hybrid constraint satisfaction problem (CSP) where the variables can either
be real numbers, vectors, trajectories or subsets of Rn.
An extension of existing constraint propagation methods is then proposed to solve hybrid CSPs
involving set-valued variables. A simulated test case is then proposed to show the
feasibility of the approach.
[69]
Greyc,Caen, March 11, 2010.
Title: Nonlinear interval observers
Abstract.
In this talk, I will consider the state estimation of sailboat robot.
This problem is motivated by the Microtransat challenge where small
autonomous sailboat robots are designed to cross the Atlantic ocean.
All components of such robots should be robust with respect to all
situations (heavy weather, waves, salt water, low level of energy,
long trip, etc.). Two types of sensors can be considered.
1) Reliable
sensors, which could survive to all situations. Such sensors are the
GPS, the compass, the gyrometers and accelerometers. All these
sensors are low energy consumers, can be enclosed inside a waterproof
tank and can survive for years. The GPS gives us the position of the
boat and new generation GPS can also return the speed with a good
accuracy by using the Doppler effect. Since the magnetic perturbation
inside the ocean can be neglected, the compass measures the north
direction with a rather good accuracy. The gyrometer returns the
rotational speed and the accelerometers make possible to get the roll
and pitch of the robot.
2) Unreliable
sensors, which have a high probability to brake down in case of heavy
weather. Anemometers (device that is used for measuring wind speed),
weather vane (which returns the direction of the wind), dynamometers
which measures the forces on the sail or the rudder are considered as
unreliable. They are directly in contact with aggressive natural
elements (wind, wave, salt) and can fail down at any time.
On the one hand, to
control the robot, it is necessary to know where the wind comes from,
what is its power, how strong are the forces on the sail or on the
rudder, if the mainsheet is tight or not, etc. On the other hand, a
reliable boat can only enclose reliable sensors.
The aim of the talk is
twofold. The first goal is to show that the variables that could be
measured by the unreliable sensors could be reconstructed dynamically
from the data collected by the reliable sensors. This is new in a
sailboat context. The second goal is to give a new method which
combines classical nonlinear observation techniques, based on
flatness concepts, with interval analysis. The first tool makes
possible to transform the observation problem into equations that
have to be solved at each time whereas interval analysis provides a
systematic way to solve the inversion problem and makes possible to
take into account some interval uncertainties on the measurement data.
Some photos and videos can be found at www.ensta-bretagne.fr/jaulin/mt.html
[70] Mexico March 17, 15h30.
Title: Interval analysis and constraint propagation; applications to control,
estimation and robotics.
Abstract : Interval analysis makes it possible to solve a
large class of nonlinear problems such as (i) computing all global
minimisers of a nonconvex criterion, (ii) computing all solutions of
a set of nonlinear equations, (iii) characterizing sets defined by
nonlinear inequalities, etc.
Unlike classical numerical
approaches (Monte Carlo or local methods, for instance), the results
provided by interval analysis are obtained in a guaranteed way and in
a finite time, even when strong nonlinearities and discontinuities
are involved in the problem. Unfortunately, classical interval
methods have some difficulties to deal with problems involving a
large number of variables (greater than 10, for instance). This
limitation is mainly due to the bisections involved in the interval
algorithms that make the complexity exponential with respect to the
number of variables. Constraint propagation techniques make it
possible to push back this frontier and to deal with high dimensional
problems (with more than 1000 variables for instance). Even so, these
techniques are no widely known in the interval community. The purpose
of this seminar is to introduce in a pedagogical way the principles
of interval methods and constraint propagation techniques. Some
applications to robust control, state estimation, robot calibration,
path planning ... will be given. Moreover, some free windows solvers
(Proj2d, Interval peeler, CIA) combining interval analysis and
constraint propagation and developed by our interval team in Angers
and Brest, will be presented.
[71] Mexico March 19, 15h30.
Title: Nonlinear interval observers.
Abstract.
In this talk, I will consider the state estimation of sailboat robot.
This problem is motivated by the Microtransat challenge where small
autonomous sailboat robots are designed to cross the Atlantic ocean.
All components of such robots should be robust with respect to all
situations (heavy weather, waves, salt water, low level of energy,
long trip, etc.). Two types of sensors can be considered.
1) Reliable sensors, which
could survive to all situations. Such sensors are the GPS, the
compass, the gyrometers and accelerometers. All these sensors are low energy consumers,
can be enclosed inside a waterproof tank and can survive for years.
The GPS gives us the position of the boat and new generation GPS can
also return the speed with a good accuracy by using the Doppler
effect. Since the magnetic perturbation inside the ocean can be
neglected, the compass measures the north direction with a rather
good accuracy. The gyrometer returns the rotational speed and the
accelerometers make possible to get the roll and pitch of the robot.
1) Unreliable sensors,
which have a high probability to brake down in case of heavy weather.
Anemometers (device that is used for measuring wind speed), weather
vane (which returns the direction of the wind), dynamometers which
measures the forces on the sail or the rudder are considered as
unreliable. They are directly in contact with aggressive natural
elements (wind, wave, salt) and can fail down at any time. On the one
hand, to control the robot, it is necessary to know where the wind
comes from, what is its power, how strong are the forces on the sail
or on the rudder, if the mainsheet is tight or not, etc. On the other
hand, a reliable boat can only enclose reliable sensors.
The aim of the talk is
twofold. The first goal is to show that the variables that could be
measured by the unreliable sensors could be reconstructed dynamically
from the data collected by the reliable sensors. This is new in a
sailboat context. The second goal is to give a new method which
combines classical nonlinear observation techniques, based on
flatness concepts, with interval analysis. The first tool makes
possible to transform the observation problem into equations that
have to be solved at each time whereas interval analysis provides a
systematic way to solve the inversion problem and makes possible to
take into account some interval uncertainties on the measurement
data. Some photos and videos can be found at
www.ensta-bretagne.fr/jaulin/mt.html
[72] Angers, May 11, 2010
Title: Image Shape Extraction using Interval Methods.
Abstract.
This talk proposes a new method for recognition of geometrical shapes
(such as lines, circles or ellipsoids) in an image. The main idea is
to transform the problem into a bounded error estimation problem and
then to use an interval-based method which is robust with respect to
outliers. The approach is illustrated on images taken by an
underwater robot where geometrical objects (such as spherical buoy or
cylinders) have to be detected. The results will then be compared to
those obtained by the more classical generalized Hough transform.
[73] Brest. Thales, June 7, 2010.
Title: Multilatération using interval analysis.
Abstract. Multilateration is commonly used in civil and military
surveillance applications to accurately locate targets (such as
aircraft or any stationary emitter) by measuring the time difference
of arrival (TDOA) of a signal from the emitter at three or more
receiver sites. Multilateration can be cast into a set inversion
problem that can be used efficiently in a reliable and robust way
using interval analysis. The purpose of this seminar is to introduce
in a pedagogical way the principles of interval methods and
constraint propagation techniques. Then, in a second step, we will
show how interval techniques can be applied for TDOA localisation of
similar emitters.
[74] Nantes, SWIM 2010. June 15-16, 2010.
Title: Solving set-valued constraint satisfaction problems.
[75] Lesson. Vendredi 13 novembre 2010, 13h30-17h.
Title: Calcul par intervalles et applications. Cours de master recherche UBO (Brest).
[76] Lesson. Ecole Navale. Brest. Mercredi, 7 juillet 2010.
Title: Interval analysis for sea robotics.
[77] SCAN 2010, Lyon. 30 septembre. 2010..
Title: Solving set-valued constraint satisfaction problems.
Abstract.
I will consider the resolution of constraint
satisfaction problems in the case where the variables of the problem
are subsets of Rn. In order to use a constraint propagation
approach, we introduce set intervals,
which are sets of subsets of Rn with a lower bound and an upper
bound with respect to the inclusion. Then, we propose an arithmetic
for them. This makes possible to build projection operators that are
then used by the propagation. In order to illustrate the principle
and the efficiency of the approach, a test-case is provided.
[78] Ifremer 22 novembre 2010. Brest.
Title: Robots voiliers.
[68] Séminaires de DTN, ENSIETA, 19 janvier 2010, Brest.
Titre : Méthodes ensemblistes pour la robotique.
[56] Lesson. Jeudi et vendredi 19-20 mars 2009, Ecole des JD MACS, Angers (4H).
Titre : Calcul par intervalles et contracteurs
pdf.
[57] Mardi 7 avril 2009. Cergy-Pontoise, 10h45.
Journée Intelligence Artificielle Embarquée
Titre: Calcul par intervalles pour la résolution garantie de problèmes non-linéaires.
Résumé: Le calcul par intervalles permet de résoudre une grande classe de problèmes non-linéaires, comme par exemple le calcul de tous les minima
globaux d'un critère non-convexe ou bien le calcul de toutes les solutions d'un système de n équations à n inconnues. Contrairement aux méthodes numériques
classiques (méthodes de MontéCarlo, par exemple), le résultat est obtenu de façon globale et garantie en un
temps fini, même lorsque des fonctions trigonométriques ou discontinues apparaissent dans le problème. Le but de cet
exposé est de donner les principes de base du calcul par intervalles et des techniques de propagation de contraintes. Des
applications en robotique, estimation, et localisation seront présentées. Cet exposé sera présenté
de façon pédagogique afin d'être compris dans son intégralité et sans difficulté par des non-spécialistes.
[58] Mercredi 29 avril 2009, ENSIETA.
Titre : Présentation des activités de robotique à DTN, ENSIETA.
[59] 1-7 juin 2009, DyToComp 2009, Poznan, Pologne.
Title: Interval methods with applications to robotics.
Abstract. Interval analysis makes it possible to solve a large class on
nonlinear problems such as (i) computing all global minimisers of a nonconvex criterion, (ii) computing all solutions of a set of
nonlinear equations, (iii) characterizing sets defined by nonlinear inequalities, … Unlike classical numerical approaches (Monte
Carlo or local methods, for instance), the results provided by interval analysis are obtained in a guaranteed way and in a finite
time, even when strong nonlinearities and discontinuities are involved in the problem. Combined with constraint propagation
techniques, interval methods make possible to deal efficiently with high dimensional problems (with more than 1000 variables for
instance). The purpose of this presentation is to introduce in a pedagogical way the principles of interval constraint propagation
techniques. Some applications to robotics (such as path-planning, dynamic localization, viability analysis) will be given.
[60] 11-12 juin 2009. SWIM'09.
Title: Probabilistic set-membership estimation.
Abstract. Interval constraint propagation methods have been shown to be
efficient and reliable to solve difficult nonlinear bounded error estimation problems. However they are considered as unsuitable in a
probabilistic context, where the approximation of a probability density function by a set cannot be accepted as reliable. This talk
shows how probabilistic estimation problems can be transformed into a set estimation problem by assuming that some rare events will never
happen. Since the probability of occurrence of those rare events can be computed, we can give some prior lower bounds for the probability
associated to solution set of the corresponding set estimation problem. The approach will be illustrated on a parameter estimation
problem and on the dynamic localization of an underwater robot.
[61] 25 juin 2009. DGA - Journée Technique ERA 2009, Paris.
Titre : Méthodes ensemblistes pour la localisation et la cartographie robuste dans
un contexte de robotique sous-marine.
Résumé : Un robot sous-marin est généralement muni d'un écho-sondeur pour mesurer sa distance au fond, d'un capteur de
pression pour mesurer sa profondeur, d'un loch-doppler pour mesurer sa vitesse, d'une centrale inertielle pour mesurer son orientation et
d'un GPS pour se localiser lorsqu'il se trouve à la surface. Pourtant, malgré tous ces capteurs, une dérive apparaît
lorsque le robot reste trop longtemps sous l'eau et le robot finit par se perdre. Une approche permettant des recalages en cours de
mission consiste à observer attentivement son environnement et de chercher à se localiser tout en reconstituant une carte de
la zone parcourue. C'est l'approche SLAM (Simultaneaous Localization And Mapping) qui a déjà montré ses potentialités
dans le domaine de la robotique terrestre et aérienne. A l'heure actuelle, on peut dire que les méthodes fondées
sur le filtre de Kalman étendu fonctionnent correctement si les conditions suivantes sont satisfaites : (i) le modèle
d'évolution du robot est quasi-linéaire, (ii) les amers détectés ont une nature ponctuelle, (iii) à
chaque détection, le robot est capable de localiser les amers détectés dans son propre repère, (iv) le robot
est capable de distinguer les amers les uns des autres sans se tromper, (v) le robot rencontre plusieurs fois un nombre suffisamment
important d'amers. Lorsque le modèle d'évolution du robot est non-linéaire des méthodes plus récentes
comme le filtrage particulaire ou les méthodes ensemblistes parviennent à résoudre le problème du SLAM de
façon satisfaisante. Cependant en milieu sous-marin, les hypothèses qui rendent les approches de type Kalman adaptées
sont rarement respectées. (i) Les équations d'état d'un robot sous-marin sont souvent fortement non linéaires,
(ii) les amers ont rarement une nature ponctuelle (les câbles sous-marins, les rides de sable, les zones rocheuses, etc. sont
considérés comme des amers) (iii) on est rarement capables de positionner l'amer détecté dans le repère
du robot, (iv) les amers ne sont pas facilement distinguables les uns des autres, (v) le nombre d'amers fiables est faible et cela se
traduit en pratique par des erreurs d'appariement entre les amers, (vi) il existe de nombreuses données aberrantes, que l'on ne peut
détecter que de façon dynamique (les informations qui nous permettront de montrer qu'une donnée est aberrante se
trouvent souvent dans un futur plus ou moins proche). Les approches ensemblistes utilisent principalement le calcul par intervalles et
les méthodes de propagation de contraintes. Elles peuvent résoudre avec efficacité des problèmes
impliquant un grand nombre d'équations ou inéquations non-linéaires où interviennent des contraintes
discrètes (c'est-Ã -dire, faisant intervenir des variables booléennes ou entières). Le but de cet
exposé est de donner les principes de base du calcul par intervalles et des techniques de propagation de contraintes. Dans
le contexte du SLAM, nous montrerons comment elles permettent par exemple la mise en correspondance automatique des amers détectés,
la détection dynamique des données aberrantes et la prise en compte des non-linéarités. Des illustrations
de l'approche sur des robots réels seront présentées.
[62] Munich, 9-15 september 2009.
Second Workshop on Principles and Methods of Statistical Inference
with Interval Probability (WPMSIIP'09). Tuesday 15, 10h.
Title: Probabilistic set-membership estimation.
Abstract. Interval constraint propagation methods have been shown to be
efficient and reliable to solve difficult nonlinear bounded error
estimation problems. However they are considered as unsuitable in a
probabilistic context, where the approximation of a probability
density function by a set cannot be accepted as reliable. This talk
shows how probabilistic estimation problems can be transformed into a
set estimation problem by assuming that some rare events will never
happen. Since the probability of occurrence of those rare events can
be computed, we can give some prior lower bounds for the probability
associated to solution set of the corresponding set estimation
problem. The approach will be illustrated on a parameter estimation
problem and on the dynamic localization of an underwater robot.
[63] Bagneux, 8 octobre 2009
Titre : Réalisation d'un robot sous-marin autonome.
[64] LIRMM, 20 octobre 2009
Title: Some applications of interval analysis to sea robotics.
Abstract.
In this talk, I will present some applications of interval analysis to sea robotics.
The first application is the Simultaneous Localization and Mapping (SLAM) of
an underwater robot which has to move inside the ocean. The four-meter long robot, build by the GESMA (Groupe d'étude
sous-marine de l'Atlantique) is equipped with many sensors (such as sonars, Loch-Doppler, gyrometers, etc.) which provide the data. The
approach will be illustrated on a two-hour experiment made in the Douarnenez bay.
The second application is the localization of an underwater robot inside a
swimming pool using mechanical sonar. The main difficulty of the localization is due the large number of outliers generated by the
sonar during the mission. A robust interval observer will be presented and its efficiency will be illustrated on a localization
of the robot SAUC'ISSE during the SAUCE competition. A presentation movie can be found
here.
The last application is a wind observer that we want to implement on our
actual sailboat robot (photos and videos of our robot can be found
here)
in order avoid using anemometers which cannot be considered as reliable.
[65] ITT'09, ENSTA, Paris 27 octobre 2009
Title: Analyse par intervalles pour la robotique mobile.
[66]
UTC, 19 novembre 2009
Title: Some applications of interval analysis to sea robotics.
Abstract. In this talk, I will present some applications of interval analysis
to sea robotics. The first application is the Simultaneous Localization and Mapping (SLAM) of an underwater
robot which has to move inside the ocean. The four-meter long robot, build by the GESMA (Groupe d'étude
sous-marine de l'Atlantique) is equipped with many sensors (such as sonars, Loch-Doppler, gyrometers, etc.) which provide the data. The
approach will be illustrated on a two-hour experiment made in the Douarnenez bay.
The second application is the localization of an underwater robot inside a swimming pool using mechanical sonar. The main difficulty of the
localization is due the large number of outliers generated by the sonar during the mission. A robust interval observer will be
presented and its efficiency will be illustrated on a localization of the robot SAUC'ISSE during the SAUCE competition. A presentation
movie can be found at http://www.youtube.com/watch?v=LWsRCn1vuBk.
The last application is a wind observer that we want to implement on our actual sailboat robot (photos and videos of our robot can be found
here)
in order avoid using anemometers which cannot be considered as reliable.
[67] Journée ensembliste MEA. Jeudi 3 décembre 2009.
Title: New approach for interval state estimation. Estimation to sailboat robotics.
Abstract. This talk deals with the state estimation of sailboat robot. This problem is motivated by the microtransat
challenge where small autonomous sailboat robots are designed to cross the Atlantic ocean. All components of such robots should be
robust with respect to all situations (heavy weather, waves, salt water, low level of energy, long trip, etc.). Two types of sensors can
be considered.
(i) Reliable sensors, which could survive to all situations. Such sensors are the GPS, the
compass, the gyrometers and accelerometers. All these sensors are low energy consumers, can be enclosed inside a waterproof tank and can
survive for years. The GPS gives us the position of the boat and new generation GPS can also return the speed with a good accuracy by
using the Doppler effect. Since the magnetic perturbation inside the ocean can be neglected, the compass measures the north direction with
a rather good accuracy. The gyrometer returns the rotational speed and the accelerometers make possible to get the roll and pitch of the
robot.
(ii) Unreliable sensors, which have a high probability to brake down in case of heavy weather.
Anemometers (device that is used for measuring wind speed), weather vane (which returns the direction of the wind), dynamometers which
measures the forces on the sail or the rudder are considered as unreliable. They are directly in contact with aggressive natural
elements (wind, wave, salt) and can fail down at any time. On the one hand, to
control the robot, it is necessary to know where the wind comes from, what is its power, how strong are the forces on the sail or on the
rudder, if the mainsheet is tight or not, etc. On the other hand, a reliable boat can only enclose reliable sensors. This talk provides a
new method which combines classical nonlinear observation technique, based on flatness concepts, with interval analysis. The first tool
makes possible to transform the observation problem into equations that have to be solved at each time. Interval analysis gives a
systematic way to solve the inversion problem and makes possible to take into account some interval uncertainties on the measurement
data.
video of our sailboat robot.
[45] Jeudi 13 mars 2008, Angers
Title: Contractors and QUIMPER language.
Abstract. QUIMPER is a new programming language devoted to set computation. It makes possible to implement a large class of interval-based
algorithms in a very easy way. This language has been implemented in C++ using the IBEX interval library. After introducing briefly some
fundamental notions related to contractors the QUIMPER language will be presented. Some examples taken from the control and estimation
literature will then be treated with QUIMPER.
[46]
27 mai 2008, LEST, Brest
Titre : Calcul par intervalles pour la résolution garantie de problèmes non-linéaires.
Résumé : Le calcul par intervalles permet de résoudre une grande classe de problèmes non-linéaires, comme par exemple le
calcul de tous les minima globaux d'un critère non-convexe ou bien le calcul de toutes les solutions d'un système de n
équations à n inconnues. Contrairement aux méthodes numériques classiques (méthodes de MontéCarlo,
par exemple), le résultat est obtenu de façon globale et garantie en un temps fini, même lorsque des fonctions
trigonométriques ou discontinues apparaissent dans le problème. Le but de cet exposé est de donner les
principes de base du calcul par intervalles et des techniques de propagation de contraintes. Des applications en robotique,
estimation, et localisation seront présentées.
[47]
Lesson. Vendredi 14 juin 2008, 13h30-17h.
Titre : Calcul par intervalles et applications. Cours de master recherche UBO (Brest).
[48]
4 juin 2008, demi-journée industrielle, JFPC, Nantes
Titre : Programmation par contraintes pour la localisation d'un robot sous-marin.
Résumé : La programmation par contraintes est de plus en plus utilisée en robotique pour deux raisons principales.
La première raison est que de nombreux problèmes issus de la robotique se formulent naturellement en termes de contraintes
faisant généralement intervenir des variables discrètes et continues. La deuxième raison est que les systèmes
de contraintes impliqués se résolvent avec une très grande efficacité avec des méthodes de propagation de
contraintes. Le but de cet exposé est de présenter de façon pédagogique quelques exemples issus de
robotique où la programmation par contrainte a son intérêt. En particulier nous montrerons un robot sous-marin autonome qui
utilise en temps réels une méthode de propagation de contraintes sur les intervalles pour se localiser, et ceci alors que
de très nombreuses données aberrantes perturbent fortement le système de contraintes courant.
[49] SWIM 08, Montpellier
Title: Resolution of nonlinear interval problems using symbolic interval arithmetic.
Abstract. An interval-valued problem is a problem where the unknown variables take interval values. Such a problem can be defined by interval
constraints, such as the interval X=[a,b] is a subset of X*X. Interval valued problems often appear when we want to analyze a
priori the behaviour of an interval solver. To solve interval-valued problems, we propose to transform the constraints on intervals into
constraints on their bounds. For instance, the previous interval constraint (X is a subset of X*X) can be transformed into the
following bound constraint a>min(a*a,a*b,b*b) and b<max(a*a,a*b,b*b). Classical interval solvers can then be
used to solve the resulting bound constraints. The procedure which transforms interval constraints into equivalent bound constraints can
be facilitated by using symbolic interval arithmetic. While classical intervals can be defined as a pair of two real numbers, symbolic
intervals can be defined as a pair of two symbolic expressions. An arithmetic similar to classical interval arithmetic can be defined
for symbolic intervals. The approach will be motivated by several examples related to estimation and experimental design.
[50] SWIM 08, Montpellier.
Title: Interval and Boolean constraint propagation for simultaneous localization and map building.
Abstract.
The SLAM (Simultaneous localization and map building) problem asks if it is possible for an autonomous robot to move in an unknown
environment and build a map of this environment while simultaneously using this map to compute its location. During the talk, it will be
shown that, when the landmarks are identical and when outliers occur, the general SLAM problem can be cast into a constraint satisfaction
problem (CSP) where Boolean and numerical variables occur. The corresponding CSP is nonlinear and classical nonlinear methods have some difficulties to
deal with this type of problems in a reliable way. A basic interval constraint propagation algorithm to solve the CSP will
be proposed. The efficiency of the approach will be illustrated on a two-hour experiment where an actual underwater robot is involved.
This four-meter long robot build by the GESMA (Groupe d'étude sous-marine de l'Atlantique) is equipped with many sensors (such as
sonars, Loch-Doppler, gyrometers, etc.) which provide the data.
[51] Cours. Vendredi 21 novembre 2008, 14h, Amphi A 301 à l'ENSPS, Strasbourg.
Titre: Calcul par intervalles pour la résolution garantie de problèmes non-linéaires.
Résumé: Le calcul par intervalles permet de résoudre une grande classe de problèmes
non-linéaires, comme par exemple le calcul de tous les minima globaux d'un critère non-convexe ou bien le calcul de toutes
les solutions d'un système de n équations à n inconnues. Contrairement aux méthodes numériques classiques (méthodes de MontéCarlo, par exemple), le
résultat est obtenu de façon globale et garantie en un temps fini, même lorsque des fonctions trigonométriques
ou discontinues apparaissent dans le problème. Le but de cet exposé est de donner les principes de base du calcul
par intervalles et des techniques de propagation de contraintes. Des applications en robotique, estimation, et localisation seront
présentées.
[52] 22 octobre 2008, workshop du PEA action, LAAS, Toulouse.
Titre : Méthodes ensemblistes pour la localisation et la cartographie dans un contexte de robotique sous-marine.
Résumé : Un robot sous-marin est généralement muni d'un écho-sondeur pour mesurer sa distance au fond, d'un
capteur de pression pour mesurer sa profondeur, d'un loch-doppler pour mesurer sa vitesse, d'une centrale inertielle pour mesurer son
orientation et d'un GPS pour se localiser lorsqu'il se trouve à la surface. Pourtant, malgré tous ces capteurs, une dérive
apparaît lorsque le robot reste trop longtemps sous l'eau et le robot finit par se perdre. Une approche permettant des recalages en
cours de mission consiste à observer attentivement son environnement et de chercher à se localiser tout en
reconstituant une carte de la zone parcourue. C'est l'approche SLAM (Simultaneaous Localization And Mapping) qui a déjÃ
montré ses potentialités dans le domaine de la robotique terrestre et aérienne. A l'heure actuelle, on peut
dire que les méthodes fondées sur le filtre de Kalman étendu fonctionnent correctement si les conditions suivantes
sont satisfaites : (i) le modèle d'évolution du robot est quasi-linéaire, (ii) les amers détectés ont
une nature ponctuelle, (iii) à chaque détection, le robot est capable de localiser les amers détectés dans
son propre repère, (iv) le robot est capable de distinguer les amers les uns des autres sans se tromper, (v) le robot rencontre
plusieurs fois un nombre suffisamment important d'amers. Lorsque le modèle d'évolution du robot est non-linéaire des
méthodes plus récentes comme le filtrage particulaire ou les méthodes ensemblistes parviennent à résoudre
le problème du SLAM de façon satisfaisante. Cependant en milieu sous-marin, les hypothèses qui rendent les approches
de type Kalman adaptées sont rarement respectées. (i) Les équations d'état d'un robot sous-marin sont souvent
fortement non linéaires, (ii) les amers ont rarement une nature ponctuelle (les câbles sous-marins, les rides de sable,
les zones rocheuses, etc. sont considérés comme des amers) (iii) on n'est rarement capables de positionner l'amer détecté
dans le repère du robot, (iv) les amers ne sont pas facilement distinguables les uns des autres, (v) le nombre d'amers fiables est
faible et cela se traduit en pratique par des erreurs d'appariement entre les amers, (vi) il existe de nombreuses données
aberrantes, que l'on ne peut détecter que de façon dynamique (les informations qui nous permettront de montrer qu'une
donnée est aberrante se trouvent souvent dans un futur plus ou moins proche). Les approches ensemblistes utilisent principalement le
calcul par intervalles et les méthodes de propagation de contraintes. Elles peuvent résoudre avec efficacité des
problèmes impliquant un grand nombre d'équations ou inéquations non-linéaires où interviennent des
contraintes discrètes (c'est-Ã -dire, faisant intervenir des variables booléennes ou entières). Le but de
cet exposé est de donner les principes de base du calcul par intervalles et des techniques de propagation de contraintes. Dans
le contexte du SLAM, nous montrerons comment elles permettent par exemple la mise en correspondance automatique des amers détectés,
la détection dynamique des données aberrantes et la prise en compte des non-linéarités. Des illustrations
de l'approche sur des robots réels seront présentées. Enfin, dans un contexte où plusieurs robots, qui communiquent
entre eux, sont impliqués dans la mission, nous donnerons des pistes pour montrer comment distribuer les calculs entre les robots
et représenter l'information afin que le système complet (constitué de tous les robots) puisse résoudre
le problème du SLAM de façon collective.
[53] Lundi 27 octobre 2008, Belo Horizonte, Brésil.
Title: Interval analysis and constraint propagation; applications to control,
estimation and robotics.
Abstract. Interval analysis makes it possible to solve a large class of nonlinear problems such as (i) computing all global minimisers of a
nonconvex criterion, (ii) computing all solutions of a set of nonlinear equations, (iii) characterizing sets defined by nonlinear
inequalities, … Unlike classical numerical approaches (Monte Carlo or local methods, for instance), the results provided by
interval analysis are obtained in a guaranteed way and in a finite time, even when strong nonlinearities and discontinuities are
involved in the problem. Unfortunately, classical interval methods have some difficulties to deal with problems involving a large number
of variables (greater than 10, for instance). This limitation is mainly due to the bisections involved in the interval algorithms that
make the complexity exponential with respect to the number of variables. Constraint propagation techniques make it possible to push
back this frontier and to deal with high dimensional problems (with more than 1000 variables for instance). Even so, these techniques are
no widely known in the interval community. The purpose of this seminar is to introduce in a pedagogical way the principles of
interval methods and constraint propagation techniques. Some applications to robust control, state estimation, robot calibration,
path planning ... will be given. Moreover, some free windows solvers (Proj2d, Interval peeler, CIA) combining interval analysis and
constraint propagation and developed by our interval team in Angers and Brest, will be presented.
[54] Jeudi 13 novembre 2008 de 10h-17h, à l'ENSAM Paris Journée MEA.
Title: Image Shape Extraction using Interval Methods.
Abstract. This talk proposes a new method for recognition of geometrical shapes (such as lines, circles or ellipsoids) in an image. The main idea is
to transform the problem into a bounded error estimation problem and then to use an interval-based method which is robust with respect to
outliers. The approach is illustrated on images taken by an underwater robot where geometrical objects (such as spherical buoy or
cylinders) have to be detected. The results will then be compared to those obtained by the more classical generalized Hough transform.
[55] Jeudi 20 novembre 2008 .
.
Journées de Rencontre 'Mathématiques, Entreprises et Innovations' UHA- Mulhouse.
Titre : Calcul par intervalles : état de l'art et applications industrielles.
Résumé. Le calcul par intervalles permet de résoudre une grande classe de problèmes non-linéaires, comme par exemple le
calcul de tous les minima globaux d'un critère non-convexe ou bien le calcul de toutes les solutions d'un système de n
équations à n inconnues. Contrairement aux méthodes numériques classiques (méthodes de MontéCarlo, par exemple), le résultat est obtenu de façon globale
et garantie en un temps fini, même lorsque des fonctions trigonométriques ou discontinues apparaissent dans le
problème. Le but de cet exposé est de donner les principes de base du calcul par intervalles et des techniques de
propagation de contraintes. Des applications en robotique, estimation, et localisation seront présentées. Cet
exposé sera présenté de façon pédagogique afin d'être compris dans son intégralité et sans
difficulté par des non-spécialistes.
[33] Vendredi 19 janvier 2007, Sophia-Antipolis, I3S, Coprin.
Titre : Nouveau test intérieur pour un ensemble défini par des égalités existentiellement quantifiées ; application à commande de robots.
Résumé. Dans cet exposé, je m'intéresserai à la caractérisation de sous-ensembles de Rndéfinis comme
des projections de contraintes égalités. Nous allons nous placer dans la situation (qui se produit fréquemment) où
l'ensemble à caractériser admet un intérieur et un extérieur. De nombreuses méthodes efficaces
(utilisant par exemple la propagation de contraintes sur les intervalles) permettent d'obtenir une caractérisation
extérieure de notre ensemble. En revanche, sauf dans des cas bien particuliers, la caractérisation intérieure est
beaucoup plus difficile. Le but de cet exposé est de proposer un nouveau intérieur (issu d'une collaboration avec A.
Goldsztejn) qui nous permettra d'obtenir une caractérisation intérieure de notre ensemble, et ceci même lorsque les
variables existentielles sont partagées entre les égalités. Les notions et les résultats seront illustrés à
travers des exemples issus de la robotique (voilier et robot escaladeur).
[34] February 12, 2007, AUV'06, Brest.
Title: Localization of an AUV using interval analysis.
[35] March 7, 2007, Heriot-Watt University
Title: Interval constraint propagation techniques for the simultaneous localization and map building of an actual
underwater robot.
Abstract. The SLAM (Simultaneous localization and map building) problem asks if it is possible for an autonomous robot to move in an unknown
environment and build a map of this environment while simultaneously using this map to compute its location. During the talk, I will show
that a general SLAM problem can be cast into a constraint satisfaction problem (CSP). The corresponding CSP is nonlinear and
classical nonlinear methods have some difficulties to deal with this type of problems in a reliable way. After a brief presentation of
interval analysis, I will propose to use a basic interval constraint propagation algorithm, to solve the CSP. The efficiency of the
approach will be illustrated on a two-hour experiment where an actual underwater robot is involved. This four-meter long robot build by the
GESMA (Groupe d'étude sous-marine de l'Atlantique) is equipped with many sensors (such as sonars, Loch-Doppler, gyrometers, etc.)
which provide the data. The corresponding algorithm will be able to provide an accurate envelope for the trajectory of the robot and to
compute sets which contain some detected mines in less than one minute.
[36] Mardi 23 avril 2007, ENSIETA, Brest (Journée sur les nouvelles technologies de la sécurité en mer).
Titre: Anticollision : difficultés et méthodes.
[37] Lundi 14 mai 2007, LIP, Lyon.
Titre : Calcul par intervalles, applications en robotique.
[38] Lesson. 15 mai 2007,
Titre : Calcul par intervalles et applications, 2h30. Au master recherche de l'ENS Lyon.
[39] Jeudi 14 juin 2007, GESMA, Brest
Workshop sur la navigation sur amers en milieu sous-marin
Titre : Evaluation de performance en navigation.
[40] Jeudi 19 juillet 2007, Paris, GT calcul ensembliste du GDR Macs.
Title: Interval controllers.
Abstract : An interval controller is a controller that uses interval computation to control a plant. In control theory, interval
analysis is often used for offline nonlinear state/parameter estimation and for the conception of controllers for linear/
nonlinear systems. But interval computation is rarely used by the controller itself : I don't know any actual system which is
controlled by an interval controller; I don't know any actual robot which uses interval arithmetic during its mission. The aim of this
talk is to provide some examples where using intervals inside the controller could make the controller more reliable, more robust with
respect to outliers, etc. than it could be without intervals. As an illustration, the control of an underwater robot inside a swimming
pool will be considered. The robot localizes itself with a sonar and has to execute a mission inside the pool. This robot has been built
at ENSIETA School for the SAUC'E competition (Studient Autonomous Underwater Challenge European) that will take place in England July 14th 2007.
[41] Lundi 30 juillet 2007, Girona.
Title: SAUC'ISSE: our interval underwater robot.
[42] Lundi 1er octobre 2007, Lyon, GT calcul ensembliste du GDR Macs.
Title: Calcul par intervalles, propagation de contraintes et applications.
[43] Jeudi22 novembre 2007, Paris
Title: Resolution of nonlinear interval problems using symbolic interval
arithmetic
Abstract. An interval-valued problem is a problem where the unknown variables take interval values. Such a problem can be defined by interval
constraints, such as the interval X=[a,b] is a subset of X*X. Interval valued problems often appear when we want to analyze a
priori the behavior of an interval solver. To solve interval-valued problems, we propose to transform the constraints on intervals into
constraints on their bounds. For instance, the previous interval constraint (X is a subset of X*X) can be transformed into the
following bound constraint a>min(a*a,a*b,b*b) and b<max(a*a,a*b,b*b). Classical interval solvers can then be
used to solve the resulting bound constraints. The procedure which transforms interval constraints into equivalent bound constraints can
be facilitated by using symbolic interval arithmetic. While classical intervals can be defined as a pair of two real numbers, symbolic
intervals can be defined as a pair of two symbolic expressions. An arithmetic similar to classical interval arithmetic can be defined
for symbolic intervals. The approach will be motivated by several examples related to estimation and experimental design.
[44] mercredi 19 décembre 2007, GESMA, Brest
Titre : SLAM en robotique sous-marine.
[28] Jeudi 18 mai 2006, Journées calcul ensembliste (ENSAM)
Titre : Interval constraint propagation for the SLAM (Simultaneous Localization And Mapping) of a submarine robot.
[29] Jeudi 8 juin 2006, Concours de robotique microtransat (ENSICA)
Title: Control of a sailboat and robotics in ENSIETA
[30] Mardi 5 Décembre 2006, Vienne.
GICOLAG Workshop (Global optimization - Integrating Convexity, Optimization,
Logic and Algebraic Geometry).
Title: Interval constraints propagation techniques for the simultaneous localization and map building of an actual underwater robot.
Abstract. The SLAM (Simultaneous localization and map building) problem asks if it is possible for an autonomous robot to move in an unknown
environment and build a map of this environment while simultaneously using this map to compute its location. During the talk, I will show
that a general SLAM problem can be cast into a huge constraint satisfaction problem (CSP) where the variables are vectors/matrices
and where domains are interval vectors/interval matrices. The corresponding CSP is nonlinear and classical nonlinear methods have
some difficulties to deal with this type of problems in a reliable way. Then, I will propose to use a basic interval constraint
propagation algorithm, adapted to vector/matrix constraints, to solve the CSP. The efficiency of the approach will be illustrated on a
two-hour experiment where an actual underwater robot is involved. This four-meter long robot build by the GESMA (Groupe d'étude
sous-marine de l'Atlantique) is equipped with many sensors (such as sonars, Loch-Doppler, gyrometers, etc.) which provide the data. The
corresponding algorithm will be able to provide an accurate envelope for the trajectory of the robot and to compute sets which contain
some detected mines in less than one minute.
[31] Lundi 18 décembre 2006, 14h, Orléans, LIFO.
Titre : Arithmétique par intervalles et applications en robotique.
Résumé : L'arithmétique des intervalles est un outil numérique permettant la résolution propre et efficace d'une grande
classe de problèmes non-linéaires sur les domaines continus, comme par exemple le calcul de tous les minima globaux d'un
critère non-convexe ou bien le calcul de toutes les solutions d'un système d'équations non-linéaires.
Contrairement aux méthodes numériques classiques (méthodes de Newton ou de MontéCarlo, par exemple), la
solution est caractérisée avec une précision arbitraire, de façon globale et en un temps fini. Ceci
s'applique même lorsque des fonctions trigonométriques ou non-continues apparaissent dans notre problème. Cependant,
les méthodes par intervalles classiques deviennent difficilement applicables lorsque le nombre de variables devient
élevé, (supérieur à 10 par exemple), principalement à cause de la complexité exponentielle
des problèmes traités. L'utilisation de techniques de propagation de contraintes permet de repousser largement cette
barrière et autorise ainsi le traitement de problèmes de plus grandes dimensions (supérieures à 1000 par
exemple). Dans cet exposé je présenterai, tout d'abord, de façon brève et pédagogique les principes de
base de l'arithmétique des intervalles et des techniques de propagation de contraintes sur les domaines continus. Ensuite,
quelques applications du calcul par intervalles en robotique seront montrées, comme par exemple
1. la planification de chemin pour un robot mobile,
2. l'étude de la topologie d'un espace de configuration d'un robot,
3. et la localisation d'un sous-marin
démineur.
[32] December 21, 2006, 11h, University of Girona.
Title: Interval constraint propagation techniques for the simultaneous localization and map building of an actual underwater robot.
Abstract. The SLAM (Simultaneous localization and map building) problem asks if it is possible for an autonomous robot to move in an unknown
environment and build a map of this environment while simultaneously using this map to compute its location. During the talk, I will show
that a general SLAM problem can be cast into a constraint satisfaction problem (CSP). The corresponding CSP is nonlinear and
classical nonlinear methods have some difficulties to deal with this type of problems in a reliable way. After a brief presentation of
interval analysis, I will propose to use a basic interval constraint propagation algorithm, to solve the CSP. The efficiency of the
approach will be illustrated on a two-hour experiment where an actual underwater robot is involved. This four-meter long robot build by the
GESMA (Groupe d'étude sous-marine de l'Atlantique) is equipped with many sensors (such as sonars, Loch-Doppler, gyrometers, etc.)
which provide the data. The corresponding algorithm will be able to provide an accurate envelope for the trajectory of the robot and to
compute sets which contain some detected mines in less than one minute.
[27] Workshop franco-japonais sur la programmation par contraintes du 14 au 16 novembre 2005.
Title: Nonlinear control using interval constraint propagation
Abstract. Interval methods combined with constraints propagation techniques have been shown to
be very efficient to deal in a reliable way with control problems when the system to be considered is described by linear differential
equations. The main idea is to transform the linear differential equation problem into a set of nonlinear inequalities by using the
notions of characteristic polynomial and Routh criterion and then to use classical interval algorithms. Now, most systems that can be
encountered in practice can only be described properly by nonlinear differential equations and the notion of characteristic polynomial
does not exist anymore. For such nonlinear systems, interval methods have rarely been used to solve any realistic control problems. The
aim of this talk is to present three recent realistic applications related to nonlinear control where interval constraint propagation
methods have been successful. The first application results from a collaboration with M. Dao, M. Lhommeau, P. Herrero, J. Vehi and M.
Sainz. The problem to be considered is to control a sailboat in order to go in the right direction, to the right speed, or to go as fast as
possible. The second application is the control of a wheeled stair-climbing robot that we are building with some colleagues from
the ENSIETA engineering school in Brest. Masses supported by the robot have to be moved in order to avoid any sliding of the wheels.
The last application is related to a collaboration with the GESMA (Groupe d'Etude Sous Marine Atlantique). The application concerns the
control and the localization of an AUV (Autonomous Underwater Vehicle). The sensors that are available are a camera to be used in
deep water, a GPS at the surface of the ocean and an accelerometer that can always be used. For such
control problems where strong nonlinearities occur, conventional control methods fail to provide any reliable controller whereas
constraints satisfaction techniques seem to be adapted.
[26] Mercredi 8 novembre 2005, Nice-Sophia Antipolis, I3S.
Title: Nonlinear control of robots using interval constraint propagation
Abstract : Interval methods combined with constraints propagation techniques have been shown to be very efficient to deal
in a reliable way with control problems when the system to be considered is described by linear differential equations. The main
idea is to transform the linear differential equation problem into constraint satisfaction problems (CSP) over continuous domains by
using the notions of characteristic polynomial and Routh criterion. Now, most systems that can be encountered in robotics can only be
described properly by nonlinear differential equations and the notion of characteristic polynomial does not exist anymore. For such
nonlinear systems, interval methods have rarely been used to solve any realistic control problems. The aim of this talk is to present
two recent applications related to nonlinear control of robots where interval constraint propagation methods have been successful. The
first application results from a collaboration with M. Dao, M. Lhommeau, P. Herrero, J. Vehi and M. Sainz. The problem to be
considered is to control a sailboat in order to go in the right direction, to the right speed, or to go as fast as possible. The
second application is the control of a wheeled stair-climbing robot that we are building with some colleagues from the ENSIETA
engineering school in Brest. Masses supported by the robot have to be moved in order to avoid any sliding of the wheels. For such control
problems where strong nonlinearities occur, conventional control methods fail to provide any reliable controller whereas constraints
satisfaction techniques seem to be adapted.
[25] Lesson. 12-16 septembre 2005, Control summer school of Grenoble.
Title: Set computation and its applications to identification, observation, control and robotics
Dépliant.
[24] Vendredi 26 septembre 2005, Int 05 workshop in Copenhagen, Denmark,
Title: Nonlinear control using interval constraint propagation
Abstract. Interval methods combined with constraints propagation techniques have been shown to be very efficient to deal
in a reliable way with control problems when the system to be considered is described by linear differential equations. The main
idea is to transform the linear differential equation problem into a set of nonlinear inequalities by using the notions of characteristic
polynomial and Routh criterion and then to use classical interval algorithms. Now, most systems that can be encountered in practice can
only be described properly by nonlinear differential equations and the notion of characteristic polynomial does not exist anymore. For
such nonlinear systems, interval methods have rarely been used to solve any realistic control problems. The aim of this talk is to
present two recent realistic applications related to nonlinear control where interval constraint propagation methods have been
successful. The first application results from a collaboration with M. Dao, M. Lhommeau, P. Herrero, J. Vehi and M. Sainz. The problem to
be considered is to control a sailboat in order to go in the right direction, to the right speed, or to go as fast as possible. The
second application is the control of a wheeled stair-climbing robot that we are building with some colleagues from the ENSIETA
engineering school in Brest. Masses supported by the robot have to be moved in order to avoid any sliding of the wheels. For such control
problems where strong nonlinearities occur, conventional control methods fail to provide any reliable controller whereas constraints
satisfaction techniques seem to be adapted.
[22] Mercredi 15 septembre 2004, 11h-11h45. Brest.
Titre : Calcul par intervalles pour la résolution garantie de problèmes non-linéaires.
Résumé : Le calcul par intervalles permet de résoudre une grande classe de problèmes
non-linéaires, comme par exemple le calcul de tous les minima globaux d'un critère non-convexe ou bien le calcul de toutes
les solutions d'un système de n équations à n inconnues. Contrairement aux méthodes numériques classiques (méthodes de MontéCarlo, par exemple), le
résultat est obtenu de façon globale et garantie en un temps fini, même lorsque des fonctions trigonométriques ou discontinues apparaissent dans le problème. L'efficacité
des méthodes par intervalles a été grandement améliorée grâce des techniques venues de l'informatique comme la propagation de contraintes, l'analyse
syntaxique ou la différentiation automatique. Le but de cet exposé est de donner les principes de base du calcul par
intervalles et des techniques de propagation de contraintes. Une application sur la localisation dynamique d'un robot à roues à partir de télémètres à ultrasons sera
présentée. Cet exposé sera présenté de façon pédagogique afin d'être compris dans son intégralité et sans difficulté par des non-spécialistes.
[23] Jeudi 23 septembre 2004
Title: Bayesian estimation using interval analysis.
[23] Mardi 14 décembre 2004, 14h , Séminaire au laboratoire de mathématiques de l'université de Bretagne occidentale.
Titre : L'arithmétique des intervalles pour l'étude de propriétés topologiques d'un ensemble défini par des inégalités
Résumé : L'arithmétique des intervalles est un outil numérique permettant la résolution propre et efficace d'une grande
classe de problèmes non-linéaires, comme par exemple le calcul de tous les minima globaux d'un critère non-convexe ou
bien le calcul de toutes les solutions d'un système d'équations non-linéaires. Contrairement aux méthodes
numériques classiques (méthodes de Newton ou de MontéCarlo, par exemple), la solution est caractérisée
avec une précision arbitraire, de façon globale et en un temps fini. Ceci s'applique même lorsque des fonctions
trigonométriques ou non-continues apparaissent dans notre problème. Le but de cet exposé est de présenter
de façon brève et pédagogique les principes de base de l'arithmétique par intervalles. Ensuite, nous
montrerons qu'en combinant les techniques de calcul par intervalles avec la théorie des graphes, il est possible d'étudier
quelques propriétés topologiques (comme par exemple compter le nombre de composantes connexes ou calculer le type
d'homotopie) d'ensembles définis par des inégalités. à titre d'illustration, quelques exemples académiques
issus de l'automatique et la robotique seront traités. Des logiciels de résolution que nous avons développés
seront présentés. Ces logiciels sont disponibles gratuitement et utilisent les méthodes présentées
dans l'exposé.
[21] Mardi 7 septembre 2004, Department of Computer Science, University of Texas, El Paso
Title: Interval analysis and constraint propagation; applications to control, estimation and robotics.
Abstract. Interval analysis makes it possible to solve a large class of nonlinear problems such as (i) computing all global
minimizers of a nonconvex criterion, (ii) computing all solutions of a set of nonlinear equations, (iii) characterizing sets defined by
nonlinear inequalities, etc. Unlike classical numerical approaches (Monte Carlo or local methods, for instance), the results provided by
interval analysis are obtained in a guaranteed way and in a finite time, even when strong nonlinearities and discontinuities are
involved in the problem. Unfortunately, classical interval methods have some difficulties to deal with problems involving a large number
of variables (greater than 10, for instance). This limitation is mainly due to the bisections involved in the interval algorithms that
makes the complexity exponential with respect to the number of variables. Constraint propagation
techniques make it possible to push back this frontier and to deal with high dimensional problems (with more than 1000 variables for
instance). Even so, these techniques are no widely known in the interval community. The purpose of this seminar is to introduce in a
pedagogical way the principles of interval methods and constraint propagation techniques. Some applications to robust control, state
estimation, robot calibration, path planning, etc. will be given. Moreover, some free windows solvers (Proj2d, Interval peeler, CIA)
combining interval analysis and constraint propagation and developed by our interval team in Angers and Brest, will be presented.
[20] Lesson. 26 février 2004, Ecole des mines de Saint Etienne.
Titre : Calcul par intervalles et propagation de contraintes pour l'optimisation globale, 3 hours.
[18] Mercredi 19 novembre 2003,
14h00,16h00, LIRMM, Montpellier, le cadre des conférences pour les élèves de DEA.
Titre : Calcul ensembliste pour l'automatique et ses applications en identification, commande et
robotique.
Résumé : Lorsque les incertitudes de modélisation, les perturbations ou les bruits de mesure
intervenant sur le système sont représentés par des ensembles (et non pas par des lois de probabilité), de
nombreux problèmes d'automatique peuvent se ramener à la caractérisation d'un ensemble défini par des
inégalités qui peuvent être non-linéaires. Les méthodes ensemblistes forment une panoplie d'outils
capables de caractériser un tel ensemble, de lui trouver un point (éventuellement optimal) intérieur, de lui
trouver sur-ensemble (pavé, ellipsoïde, zonotope), de montrer qu'il est ou qu'il n'est pas vide, etc. Le calcul par
intervalles est un de ces outils. Il permet de résoudre une grande classe de problèmes non-linéaires, comme par
exemple le calcul de tous les minima globaux d'un critère non-convexe ou bien le calcul de toutes les solutions d'un système
de n équations à n inconnues. Contrairement aux méthodes numériques classiques (méthodes de
MontéCarlo, par exemple), le résultat est obtenu de façon globale et garantie en un temps fini, même lorsque
des fonctions trigonométriques ou discontinues apparaissent dans le problème. L'efficacité des méthodes par
intervalles a été grandement améliorée grâce à l'utilisation de techniques de propagation de
contraintes, récemment introduites en automatique. Le traitement de problèmes de plusieurs milliers de variables est
désormais envisageable. Le but de cet exposé est de présenter de façon brève et pédagogique
les principes de base du calcul ensembliste et des techniques de propagation de contraintes. Quelques applications en automatique
(commande robuste et estimation de paramètres et d'état) et en robotique (localisation et planification de chemins) seront
données. Des logiciels de résolution gratuits, utilisant le calcul par intervalles, seront présentés.
[16] Jeudi 26 juin 2003, JNA'03, session plénière, Valenciennes.
Titre : Calcul ensembliste pour l'automatique et ses applications en identification, diagnostic, et robotique.
Résumé : Lorsque les incertitudes de modélisation, les perturbations ou les bruits de mesure intervenant sur le système sont
représentés par des ensembles (et non pas par des lois de probabilité), de nombreux problèmes d'automatique
peuvent se ramener à la caractérisation d'un ensemble défini par des inégalités qui peuvent être
non-linéaires. Les méthodes ensemblistes forment une panoplie d'outils capables de caractériser un tel ensemble, de
lui trouver un point (éventuellement optimal) intérieur, de lui trouver sur-ensemble (pavé, ellipsoïde, zonotope),
de montrer qu'il est ou qu'il n'est pas vide, etc. Le calcul par intervalles est un de ces outils. Il permet de résoudre une
grande classe de problèmes non-linéaires, comme par exemple le calcul de tous les minima globaux d'un critère
non-convexe ou bien le calcul de toutes les solutions d'un système de n équations à n inconnues. Contrairement aux
méthodes numériques classiques (méthodes de MontéCarlo, par exemple), le résultat est obtenu de
façon globale et garantie en un temps fini, même lorsque des fonctions trigonométriques ou discontinues apparaissent
dans le problème. L'efficacité des méthodes par intervalles a été grandement améliorée
grâce à l'utilisation de techniques de propagation de contraintes, récemment introduites en automatique. Le
traitement de problèmes de plusieurs milliers de variables est désormais envisageable. Le but de cet exposé est de
présenter de façon brève et pédagogique les principes de base du calcul ensembliste et des techniques de
propagation de contraintes. Quelques applications en automatique (commande robuste et estimation de paramètres et d'état)
et en robotique (localisation et planification de chemins) seront données. Des logiciels de résolution gratuits,
utilisant le calcul par intervalles, seront présentés.
[15] Lesson. 18 Mars 2003, Ecole des mines de Saint Etienne.
Titre : Calcul par intervalles et propagation de contraintes pour l'optimisation globale, 3 hours.
Lecturers: L. Jaulin (LISA, Univ. d'Angers) et Pascal Roustant (AC système).
[14] Mardi 28 janvier 2003, Séminaire du LAAS (Toulouse).
Titre : Méthodes par intervalles pour la résolution globale et garantie de problèmes non
convexes ; application à l'automatique et à la robotique.
Résumé : Le calcul par intervalles permet de résoudre une grande classe de problèmes non-linéaires, comme par exemple le calcul de tous les minima
globaux d'un critère non-convexe ou bien le calcul de toutes les solutions d'un système de n équations à n
inconnues. Contrairement aux méthodes numériques classiques (méthodes de MontéCarlo, par exemple), le
résultat est obtenu de façon globale et garantie en un temps fini, même lorsque des fonctions trigonométriques
ou discontinues apparaissent dans le problème. Cependant, les méthodes par intervalles classiques deviennent
inapplicables lorsque le nombre de variables devient élevé, (supérieur à 10 par exemple), principalement à
cause de la complexité exponentielle des problèmes traités. L'utilisation de techniques de propagation de
contraintes permet de repousser largement cette barrière et autorise ainsi le traitement de problèmes plus grandes
dimensions (supérieures à 1000 par exemple). Le but de cet exposé est de présenter de façon brève
et pédagogique les principes de base du calcul par intervalles et des techniques de propagation de contraintes. Quelques
applications en automatique (commande robuste et estimation d'état) et en robotique (localisation et planification de chemins) seront
données. Des logiciels de résolution gratuits, utilisant le calcul par intervalles, seront présentés.
[13] Mercredi 22 janvier 2003, 10h,
Journées Nationales de Calcul Formel 2003 CIRM, Luminy, 20-24 janvier 2003.
Titre : Méthodes par intervalles, propagation de contraintes et calcul formel : principes et applications.
Actes.
[17] Jeudi 3 juillet 2003
9h30,10h30, Institut de Mathématiques Appliquées (IMA), Université Catholique d'Angers
Titre : Calcul ensembliste pour l'automatique et ses applications en identification, diagnostic, et robotique.
[12] Mardi 10 décembre 2002, Séminaire MATHINFO de l'E.S.I-E-A 16h30 - 18h30 (Amphi A, rue Vésale).
Titre : L'arithmétique des intervalles pour la résolution numérique (mais
garantie) de systèmes d'équations non-linéaires. Pour plus d'informations, voir
http://professeurs.esiea.fr/erra/ESIEA-MATHINFO.html
[11] 20 Novembre 2002,
Séminaire d'Automatique de Paris, Conservatoire National des Arts et Métiers (CNAM).
Titre : Méthodes par intervalles : Principes et applications.
Résumé : Le calcul par intervalles permet de résoudre proprement et efficacement une grande classe de problèmes non-linéaires,
comme par exemple le calcul de tous les minima globaux d'un critère non-convexe ou bien le calcul de toutes les solutions d'un système
de n équations à n inconnues. Contrairement aux méthodes numériques classiques (méthodes de
MontéCarlo, par exemple), le résultat est obtenu de façon globale et garantie en un temps fini, même lorsque
des fonctions trigonométriques ou non-continues apparaissent dans notre problème. Cependant, les méthodes par
intervalles classiques deviennent inapplicables lorsque le nombre de variables devient élevé, (supérieur à 10
par exemple), principalement à cause de la complexité exponentielle des problèmes traités. L'utilisation de
techniques de propagation de contraintes permet de repousser largement cette barrière et autorise ainsi le traitement de
problèmes plus grandes dimensions (supérieures à 1000 par exemple). Le but de cet exposé est de présenter
de façon brève et pédagogique les principes de base du calcul par intervalles et des techniques de propagation de
contraintes. Quelques applications en automatique et en robotique seront données. Des outils logiciels de résolution
gratuits, utilisant le calcul par intervalles, seront présentés. Ils seront alors utilisés pour la résolution de
problèmes de commande robuste et d'estimation d'état.
[10] 8 novembre 2002, UTC, Eudiasyc (Compiègne), séminaire du thème SPC
Titre : Intervalles et propagation de contraintes, applications en automatique et en robotique.
Résumé : Le calcul par intervalles permet de résoudre proprement et efficacement une grande classe de problèmes non-linéaires,
comme par exemple le calcul de tous les minima globaux d'un critère non-convexe ou bien le calcul de toutes les solutions d'un système
de n équations à n inconnues. Contrairement aux méthodes numériques classiques (méthodes de
MontéCarlo, par exemple), le résultat est obtenu de façon globale et garantie en un temps fini, même lorsque des fonctions trigonométriques ou non-continues apparaissent
dans notre problème. Cependant, les méthodes par intervalles classiques deviennent inapplicables lorsque le nombre
de variables devient élevé, (supérieur à 10 par exemple), principalement à cause de la complexité exponentielle des problèmes traités. L'utilisation de
techniques de propagation de contraintes permet de repousser largement cette barrière et autorise ainsi le traitement de
problèmes plus grandes dimensions (supérieures à 1000 par exemple). Le but de cet exposé est de présenter
de façon brève et pédagogique les principes de base du calcul par intervalles et des techniques de propagation de
contraintes. Quelques applications en automatique et en robotique seront données.
[9] Lesson. May 6-10 2002,
Interval and constraint propagation methods for control, 10 hours.
Lecturers: L. Jaulin
Titre : Departement d'Electronica, Informatica i Automatica, Institut d'Informatica i Aplicacions, Universitat de Girona.
[8] 6 décembre 2001, LESIR (Cachan)
Titre : Application des méthodes de propagation de contraintes à l'automatique.
[7] Lesson. November 2001.
Titre : Interval analysis for identification, state estimation and robust control, Belgique.
Lecturers: L. Jaulin, M. Kieffer and E. Walter.
[6] 4 avril 2001, IRCYN (Nantes).
Titre : Méthodes par intervalles : Principes et applications
Résumé : Le calcul par intervalles permet de résoudre proprement et efficacement une grande classe de problèmes non-linéaires, comme par
exemple le calcul de tous les minima globaux d'un critère non-convexe ou bien le calcul de toutes les solutions d'un système
de n équations à n inconnues. Contrairement aux méthodes numériques classiques (méthodes de Monté-Carlo, par exemple), le résultat est obtenu de
façon globale et garantie en un temps fini, même lorsque des fonctions trigonométriques ou non-continues apparaissent
dans notre problème. Cependant, les méthodes par intervalles classiques deviennent inapplicables lorsque le nombre de
variables devient élevé, (supérieur à 10 par exemple), principalement à cause de la complexité
exponentielle des problèmes traités. L'utilisation de techniques de propagation de contraintes permet de repousser
largement cette barrière et autorise ainsi le traitement de problèmes plus grandes dimensions (supérieures à
50 par exemple). Le but de cet exposé est de présenter de façon brève et pédagogique les principes de
base du calcul par intervalles et des techniques de propagation de contraintes. Quelques applications en automatique et en robotique seront données.
[5] 7 juin 2001, CEMIF (Evry).
Titre : Propagation de contraintes sur les intervalles; application à l'estimation à erreurs bornées.
[4] Decembre, 2000, EPFL (Lauzanne, Suisse) :
Titre : 2k trees and interval computation, application to set estimation.
[3] 14 octobre 1999, IRIN (Nantes).
Titre : Analyse par intervalles pour le calcul ensembliste ; Application à la robotique.
[2] 7 janvier 1999, ENSAM (Paris)
Titre : Analyse par intervalles - Application à l'estimation à erreurs bornées - Application à la localisation de robots.
[1] 23 juin 1998, exposé au GDR Alp Analyse par intervalles
Titre : application a la localisation d'un robot, L. Jaulin (LISA, Angers).