Journée "calcul ensembliste pour la
navigation et la localisation"
Groupe de travail MEA (méthodes ensemblistes pour
l’automatique)
Cette journée thématique s'est tenue le jeudi 2 février 2012 à l'ENSTA-Paristech (www.ensta-paristech.fr) au 32 Boulevard Victor, 75015 Paris.
Contexte. La localisation et la navigation d'un mobile dans un environnement contraint (milieux urbains, intérieurs, souterrains, sous-marins, ...) sont des enjeux majeurs qui intéressent particulièrement la DGA. Les solutions utilisées actuellement sont principalement basées sur des techniques multi-capteurs probabilistes. Pourtant, les approches ensemblistes semblent pouvoir jouer un rôle important dans ce domaine et il semble opportun de faire un point sur ce que les développements récents de ces méthodes peuvent apporter pour résoudre ces problèmes difficiles. Cette journée sera l'occasion d'aborder le problème de localisation et la navigation avec des approches ensemblistes.
Inscription.
Il vous suffit d'envoyer un mail aux organisateurs
(eva.cruck@dga.defense.gouv.fr, luc.jaulin@ensta-bretagne.fr,
nacim.ramdani@univ-orleans.fr).
Organisateurs : Eva Crück (DGA), Nacim Ramdani et Luc Jaulin.
Programme.
9H30. Accueil café.
10H00.
Quelques mots pour présenter la démarche dans laquelle s'inscrit cette journée
du point de vue de la DGA
Oratrice : Eva Crück. DGA (Direction Générale de l'Armement).
10H15. Utilisation des techniques ensemblistes
pour la localisation radio hybride en indoor. Slides.
Film.
Orateur : Bernard Uguen (IETR).
Abstract. Si les techniques de localisation en extérieur sont désormais très fiables et permettent d’atteindre de grandes précisions de positionnement, aucun système ne permet encore d’égaler de telles performances en indoor. Ainsi, tout l’enjeu de la recherche dans la localisation indoor est en réalité d’obtenir des précisions équivalentes à celle que l’on peut obtenir en extérieur à l’aide d’un GPS. A défaut de pouvoir s’appuyer sur un système dédié ou qu’il n’en émerge un, les recherches actuelles tendent compenser ce manque par l’utilisation mutualisée des architectures existantes. L’utilisation de cette hétérogénéité est d’autant plus pertinente du fait de la multiplication des techniques de connexion radio disponible sur les terminaux mobiles (3G, LTE-A, Wifi, Bluetooth,UWB IEEE 802.15.4a...). Toutefois, au delà des informations radio, il existe d’autres informations directement disponibles pouvant aider à la localisation mais souvent peu exploitées en pratiques. Ces informations peuvent liées à la connaissance à priori de l’environnement physique (plan de bâtiment), à la capacité d’un terminal à connaître son orientation (accéléromètres, gyroscopes), …. Malgré la diversité et la richesse de ces informations, il n’existe pas encore de solution simple et directe pour toutes les utiliser dans le problème du positionnement.Parallèlement, les méthodes de localisation ensemblistes permettent de transformer naturellement n’importe quel type d’information (radio, physique,…) en une contrainte limitant une zone de l’espace. Une telle description apporte alors un cadre naturel à la fusion de contraintes hétérogènes, et permet in fine d’améliorer la précision du positionnement. Ainsi, dans le cadre du projet européen WHERE 2, nos recherches sont principalement axées sur les solutions permettant d’intégrer les méthodes ensemblistes dans un contexte radio mobile, et sur le développent d’outils de simulation indoor permettant de valider l’intérêt de ces méthodes par rapport à des approches plus classiques, notamment dans des scénarios coopératifs.
10h30. Reliable control using interval analysis. Application to sailboat
robotics. Slides. Paper.
Speaker. Luc Jaulin
(ENSTA-Bretagne, LabSticc).
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
11h00. Set membership methods applied to underwater robotics. Slides.
Speaker. Fabrice Le Bars and Jan Sliwka (ENSTA-Bretagne, LabSticc).
Abstract. In this talk we will present the recent
developments in set membership methods for the localization and SLAM of
underwater robots. We will present the theory used to solve such problems in a
more general context which is the CSP (Constraint Satisfaction Problem). As
such we will introduce following new set entities: set polynomials (polynomials
with set coefficients), interval accumulators and tubes (interval of
functions), used to represent the solutions. Set polynomials and accumulators
are used to solve problems when there is inconsistent information (the case of
outliers in the sensor measurements). An application to robust localization of
our school's underwater robots (“Sauci'sse” AUV &
“Sterne” Glider) will be presented. The tubes are used to solve a
SLAM problem found during mine detection experiments performed by AUVs "Redermor"
and "Daurade" of the DGA. GESMI, a mine localization software will be
presented.
11h50 Guaranteed robust distributed estimation in a network of sensors. Slides.
Paper.
Speaker. Michel Kieffer (joint Work with Jean-Benoist
Léger).
Abstract. This talk presents a guaranteed robust
bounded-error distributed estimation algorithm. It may be employed to perform
parameter estimation from data collected in a network of wireless sensors. The
algorithm is robust to an arbitrary number of outliers. Using interval analysis, one is able, provided that the
network is connected, to evaluate at
each sensor, an outer approximation of the set of all parameter values which are consistent with a
given number of measurements, and with
noise bounds. An application to a robust distributed source localization
problem is considered.
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12h40. Déjeuner buffet (offert par la DGA)
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13h40. On the use of GPS and 3D Road Surface Maps for the Navigation of Road
Vehicles in Urban Environments. Slides.
Speaker. Phillippe
Bonnifait, Heudiasyc,
Abstract. Positioning is of prime
importance in mobile robotics and more specifically for intelligent vehicle
applications. When position information is used in a safety-critical context,
like autonomous vehicle navigation, an integrity method is needed to check that
the positioning error stays within the limits specified for the mission. In
aeronautical navigation, protection levels are defined as bounds on the
position error associated to a given integrity risk. This work aims to compute
a confidence domain in which the user in guaranteed to be located with a given
integrity risk. The possible presence of outliers is handled by the use of
robust set-membership methods.
Sensor measurements and model parameters are prone to errors, which are
often modeled by their probability distribution. In the set-membership working
frame, errors can be represented by intervals, thus making the assumption of
bounded errors. When guaranteed error bounds are unknown or too pessimistic,
error bounds associated with a risk can be used. The risk taken on measurements
is then propagated to the computed confidence domain.
Global navigation satellite systems enable high precision absolute
positioning in open sky environments, but measurements suffer from multipath
and non-line-of-sight propagation in urban areas. Robustness to outliers is
thus needed. To counter the lack of visible satellites in urban canyons,
position is constrained by a 3D map of the drivable space and by using the
proprioceptive sensors embedded in recent vehicles.
This talk presents three positioning methods based on a robust set
inversion via interval analysis with GPS pseudorange measurements:
• Snapshot computation of a position confidence domain, with GPS
measurements and altitude constraint from a digital elevation model.
• Use of a precise 3D model of the drivable space as a positioning
constraint, and observation of the GPS receiver's clock drift.
• Robust pose estimation from a sliding horizon of positions and
proprioceptive measurements, constrained by a 3D map.
These positioning methods have been implemented in real-time and tested
with real data in difficult environments for satellite positioning.
14h30. Fault tolerant control based on
set-theoretic methods. Application for multi-sensor systems. Slides.
Speaker. Sorin Olaru (Supélec).
Abstract. The talk will be dedicated to the
analysis and design of fault tolerant control (FTC) schemes through the use of
set-theoretic methods. In the framework of multisensor schemes, the faults
appearance and the modalities to accurately detect them are investigated as
well as the design of control laws which assure the closed-loop stability. By
using invariant/contractive sets to describe the residual signals, a fault
detection and isolation (FDI) mechanism with reduced computational demands is
implemented based on set-separation. A dual mechanism, implemented by a
recovery block, which certificates previously fault-affected sensors is also
studied. From a broader theoretical perspective, we point to the conditions
which allow the inclusion of {FDI} objectives in the control law design. This
leads to static feedback gains synthesis by means of numerically attractive
optimization problems. Depending on the parameters selected for tuning, is
shown that the FTC design can be completed by a reference governor or a
predictive control scheme which adapts the state trajectory and the feedback
control action in order to assure {FDI}.
When necessary, the specific issues
originated by the use of set-theoretic methods are detailed and various
improvements are proposed towards: invariant set construction, mixed integer
programming (MIP), stability for switched systems (dwell-time notions).
15h20. Reachability analysis for navigation and
motion planning. Slides.
Speaker. Anna Desilles (ENSTA Paritech).
Abstract. The goal of this talk is to introduce the
capture and reachability problems for a general non-linear constrained
dynamical system and two sets associated with these problems: the capture basin
and the reachable set. We show how to compute these sets using two different
approaches.
The
first one is the viability theory. It gives a characterization of a capture
basin (or reachable set) in terms of set-valued analysis. The viability
algorithm constructs an approximation of the capture basin under very general
assumptions on the dynamical system.
The
second approach is based on an optimal control framework and on solving
Hamilton-Jacobi (HJ) equations. The capture basin is characterized as a level
set of the value function of some optimal control problem. It can be computed
using the numerical methods for HJB PDE. This approach provides a very
efficient tool for treating many cases encountered in real applications and can
be extended to general situations including moving targets and/or obstacles
problems, dynamical systems under uncertainties, or differential games. We
illustrate each approach with numerical examples from different applications
(motion planning with obstacles, collision).
16h10. Estimation à erreurs bornées
et guidage-pilotage des aéronefs autonomes en milieu perturbé. Slides.
Orateurs. Julien Marzat (ONERA), Hélène Piet-Lahanier (ONERA), Houria Siguerdidjane (Supélec).
Résumé. Nous présentons deux applications des méthodes de caractérisation d'ensembles de variation sous hypothèse d'erreur bornées pour l'élaboration de lois de guidage pour véhicule autonome. La première application a pour objet l'analyse de la navigation d'un drone de taille faible en présence de vent. La prédiction de l'ensemble de variation admissible de l'état de ce drone en absence de vent est utilisée pour détecter l'occurrence d'une rafale dont l'effet perturbateur rend incompatibles la prédiction et les mesures de position vitesse attitude fournies par les capteurs embarqués. Des lois de guidage permettant de pallier cet effet perturbateur ont été proposées dans ce contexte. La deuxième application concerne la localisation et la prédiction de la position d'une cible manoeuvrante sous hypothèse de limitations de facteur de charge. Une loi de guidage permettant de préserver les possibilités de ralliement de la cible par un intercepteur est finalement présentée.