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66 results on '"Luc Jaulin"'

1. Thick Fuzzy Sets (TFSs) and Their Potential Use in Uncertain Fuzzy Computations and Modeling

Author

Didier Coquin, Benoit Desrochers, Luc Jaulin, Reda Boukezzoula, Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance (LISTIC), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Equipe ROBotics for EXploration (Lab-STICC_ROBEX), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
0209 industrial biotechnology, Type-2 fuzzy sets (T2FSs), Thick sets (TSs), Computer science, Computation, Fuzzy set, 02 engineering and technology, Interval (mathematics), Fuzzy logic, Upper and lower bounds, [SPI.AUTO]Engineering Sciences [physics]/Automatic, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Dimension (vector space), Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, computer.programming_language, Applied Mathematics, Underwater robot, Cascading Style Sheets, Crisp sets (CSs), Thick fuzzy sets (TFSs), Type-1 fuzzy sets (T1FSs), Computational Theory and Mathematics, Control and Systems Engineering, Robot, 020201 artificial intelligence & image processing, computer, Algorithm
Abstract

International audience; This paper aims at proposing the concept of thick fuzzy sets (TFSs). A TFS is based on the joint use of thick sets (TSs) and -cuts concepts. A TFS is represented by a family of nested TSs. A TS is an uncertain set, which is represented by a pair of crisp sets (CSs). These CSs characterize the upper and lower bounds of the TS. Therefore, a TS can be regarded as an interval of CSs. In this framework, as a type-1 fuzzy set (T1FS) is regarded as a family of nested CSs, a TFS can be represented by a family of nested TSs. Furthermore, according to the vertical dimension, a TFS can be regarded as an interval with T1FS bounds. The potentialities of the TFS concept have been validated using application examples where a real-world application for modeling the zone explored by an underwater robot is given.

Published
2021
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2. Thick gradual intervals: An alternative interpretation of type-2 fuzzy intervals and its potential use in type-2 fuzzy computations

Author

Luc Jaulin, Laurent Foulloy, Reda Boukezzoula, Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance (LISTIC), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)

Subjects
0209 industrial biotechnology, Computer science, Computation, Elementary arithmetic, 02 engineering and technology, Interval (mathematics), Fuzzy logic, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Interval arithmetic, T2FI aggregation operators, 020901 industrial engineering & automation, Operator (computer programming), Artificial Intelligence, Thick intervals and thick gradual intervals, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Representation (mathematics), Interpretation (logic), Extension (predicate logic), Type-1 and type-2 fuzzy intervals, Control and Systems Engineering, 020201 artificial intelligence & image processing, Fuzzy arithmetic and gradual arithmetic, T2FI regression, Algorithm
Abstract

International audience; This paper proposes a new interpretation of type-2 fuzzy intervals (T2FIs) through the joint use of gradual intervals (GIs) and thick intervals (TIs). In this framework, a T2FI is viewed as a thick gradual interval (TGI). This new representation gives an original concept for the manipulation of T2FIs according to the thick gradual representation. Furthermore, this vision allows an extension of the interval arithmetic arsenal and reasoning to the framework of T2FIs. The proposed approach can be regarded as more computationally viable, which will make T2FIs computations more useful in applied scenarios. As an illustration, the proposed concept is used to implement the elementary arithmetic operations on T2FIs. The potentialities of the TGI approach have been validated in the frameworks of T2FI aggregation operators and T2FI regression.

Published
2019
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3. Bracketing backward reach sets of a dynamical system

Author

Luc Jaulin, Benoit Zerr, Thomas Le Mézo, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
0209 industrial biotechnology, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Stability (learning theory), Abstract interpretation, 02 engineering and technology, Dynamical system, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science Applications, Interval arithmetic, Set (abstract data type), 020901 industrial engineering & automation, Interval Computation, Control and Systems Engineering, Backward reach set, 0202 electrical engineering, electronic engineering, information engineering, Basin of attraction, 020201 artificial intelligence & image processing, Statistical physics, Constraint solving, Bracketing, Stability, Mathematics
Abstract

International audience; In this paper, we present a new method for bracketing (i.e., characterizing from inside and from outside) backward reach set of the target region T of a continuous time dynamical system. The principle of the method is to formalize the problem as a constraint network, where the variables are the trajectories (or paths) of the system. The resolution is made possible by using mazes which is a set of paths that contain all solutions of the problem. As a result, we will be able to derive a method able to compute a backward reach set for a huge class of systems without any knowledge of a parametric Lyapunov function and without assuming any linearity for our system. The method will be illustrated on several examples.

Published
2019
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4. A new methodology for solving fuzzy systems of equations: Thick fuzzy sets based approach

Author

Luc Jaulin, Didier Coquin, Reda Boukezzoula, Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance (LISTIC), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Equipe ROBotics for EXploration (Lab-STICC_ROBEX), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
0209 industrial biotechnology, Logic, Fuzzy set, 02 engineering and technology, Fuzzy control system, Interval (mathematics), Cartesian product, Upper and lower bounds, Fuzzy logic, Set (abstract data type), symbols.namesake, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, symbols, 020201 artificial intelligence & image processing, [MATH]Mathematics [math], Projection (set theory), Algorithm, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

This paper presents a new method for solving fuzzy systems of equations (SoEs) where their parameters are represented by fuzzy intervals (FIs). A FI is a normal and convex fuzzy set (FS), where all its α-cuts are crisp intervals (CIs), i.e., conventional intervals. Due to the presence of uncertainty in the left-hand and right-hand sides of these fuzzy SoEs, the solutions are sought neither as FSs, nor as FIs or fuzzy boxes (FBs)—i.e., a Cartesian product of n FIs, but as uncertain FS. In this framework, an uncertain FS is regarded as a thick fuzzy set (TFS). A TFS is a new concept that is based on the joint use of thick sets (TSs) and the α-cuts principle. Therefore, a TS is an uncertain set and is represented by a pair of crisp sets (CSs), which describe its upper and lower bounds, i.e., a TS is an interval of CSs. Moreover, as a FS can be characterized by a family of nested CSs, a TFS can be represented by a family of nested TSs. Furthermore, a TFS can be regarded as an interval with FS boundaries. Nevertheless, in absence of uncertainty in the left-hand side of the fuzzy SoEs, the TFS solution becomes a FS solution. The proposed method is based on a set membership methodology according to paving and set projection techniques. The originality of the proposed approach resides in the fact that it applies whatever the form of the fuzzy system of equations (linear or nonlinear) and allows overcoming the approximation assumption of FS solutions by FIs (or FBs), often supposed in solving fuzzy SoEs. The proposed method has been validated using application examples that are issued from the literature.

Published
2021
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5. Robust Hybrid Interval-Probabilistic Approach for the Kidnapped Robot Problem

Author

Mathias Mantelli, Renata Neuland, Edson Prestes, Mariana Kolberg, Bernardo Hummes, Luc Jaulin, Renan Maffei, Universidade Federal do Rio Grande do Sul [Porto Alegre] (UFRGS), Equipe ROBotics for EXploration (Lab-STICC_ROBEX), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), and This study was financed in part by the Coordenac¸ão de Aperfeic¸oamento de Pessoal de Ńıvel Superior — Brasil (CAPES) — Finance Code 001 and CNPq.

Subjects
0209 industrial biotechnology, Computer science, business.industry, Frame (networking), Probabilistic logic, Mobile robot, 02 engineering and technology, Interval (mathematics), Kidnapped robot problem, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Artificial Intelligence, Control and Systems Engineering, Position (vector), 0202 electrical engineering, electronic engineering, information engineering, Robot, 020201 artificial intelligence & image processing, Computer vision, Artificial intelligence, business, Software, Information Systems
Abstract

International audience; For a mobile robot to operate in its environment it is crucial to determine its position with respect to an external reference frame using noisy sensor readings. A scenario in which the robot is moved to another position during its operation without being told, known as the kidnapped robot problem, complicates global localisation. In addition to that, sensor malfunction and external influences of the environment can cause unexpected errors, called outliers, that negatively affect the localisation process. This paper proposes a method based on the fusion of a particle filter with bounded-error localisation, which is able to deal with outliers in the measurement data. The application of our algorithm to solve the kidnapped robot problem using simulated data shows an improvement over conventional probabilistic filtering methods.

Published
2021
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6. Enclosing the Sliding Surfaces of a Controlled Swing

Author

Luc Jaulin, Benoit Desrochers, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), DGA Techniques Navales, and Direction générale de l'Armement (DGA)

Subjects
Surface (mathematics), FOS: Computer and information sciences, G.1.0, G.1.7, 0209 industrial biotechnology, Computer Science - Logic in Computer Science, Internet of things, Hybrid systems, Computer science, Computer Science - Artificial Intelligence, Embedded systems, 02 engineering and technology, Interval (mathematics), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science - Robotics, 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Differentiable function, Controllers, Swing, Logic in Computer Science (cs.LO), Artificial Intelligence (cs.AI), Hybrid system, Trajectory, Piecewise, 020201 artificial intelligence & image processing, Robotics (cs.RO)
Abstract

When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution of the closed-loop system is not anymore piecewise differentiable along the trajectory, mainly due to conditional statements inside the controller. This may lead to some unwanted chattering effects than may damage the system. This behavior is difficult to observe even in simulation. In this paper, we propose an interval approach to characterize the sliding surface which corresponds to the set of all states such that the state trajectory may jump indefinitely between two distinct behaviors. We show that the recent notion of thick sets will allows us to compute efficiently an outer approximation of the sliding surface of a given class of hybrid system taking into account all set-membership uncertainties. An application to the verification of the controller of a child swing is considered to illustrate the principle of the approach., Comment: In Proceedings SNR 2020, arXiv:2101.05256

Published
2021
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7. A boundary approach for set inversion

Author

Luc Jaulin, Equipe ROBotics for EXploration (Lab-STICC_ROBEX), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
0209 industrial biotechnology, Artificial intelligence, Set inversion, Computer science, Continuous domains, Boundary, Mathematical analysis, Boundary (topology), 02 engineering and technology, Interval (mathematics), Constraint propagation, Inversion (discrete mathematics), Domain (mathematical analysis), Image (mathematics), [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Set (abstract data type), 020901 industrial engineering & automation, Control and Systems Engineering, Set Inversion, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Interval analysis, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, Volume (compression)
Abstract

In the paper, we present a new interval-based set inversion algorithm which takes into account the continuity of the problem. In the case where the set Y to be inverted has some volume, we show that inverting the boundary ∂ Y of Y is sufficient to reconstruct the preimage X = f − 1 ( Y ) . The inversion of ∂ Y separates the domain of f into two regions : one inside X and one outside. To detect which part is inside or outside, we show that we can retro-propagate the information coming from Y at negligible cost. The efficiency of the approach is illustrated on a localization problem.

Published
2021
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8. Towards a Generic Interval Solver for Differential-Algebraic CSP

Author

Victor Reyes, Bertrand Neveu, Luc Jaulin, Gilles Chabert, Simon Rohou, Alexandre Goldsztejn, Abderahmane Bedouhene, Gilles Trombettoni, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), Laboratoire d'Informatique Gaspard-Monge (LIGM), École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, IRT Jules Vernes, Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Agents, Apprentissage, Contraintes (COCONUT), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Simonis, Helmut, and ANR-16-CE33-0024,CONTREDO,Intervalles et contracteurs pour les systèmes dynamiques(2016)

Subjects
Physics, 050101 languages & linguistics, 05 social sciences, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Interval (mathematics), Solver, Interval arithmetic, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Tree (data structure), [SPI]Engineering Sciences [physics], 0202 electrical engineering, electronic engineering, information engineering, Constraint programming, Initial value problem, 020201 artificial intelligence & image processing, 0501 psychology and cognitive sciences, Boundary value problem, Algorithm, Differential algebraic equation, Interval Analysis, Differential Algebraic Equations
Abstract

International audience; In this paper, we propose an interval constraint programming approach that can handle the differential-algebraic CSP (DACSP), where an instance is composed of real and functional variables (also called dynamic variables or trajectories) together, and differential and/or “static” numerical constraints among those variables. Differential-Algebraic CSP systems can model numerous real-life problems occurring in physics, biology or robotics. We introduce a solver, built upon the Tubex and Ibex interval libraries, that can rigorously approximate the set of solutions of a DACSP system. The solver achieves temporal slicing and a tree search by splitting trajectories domains. Our approach provides a significant step towards a generic interval CP solver for DACSP that has the potential to handle a large variety of constraints. First experiments highlight that this solver can tackle interval Initial Value Problems (IVP), Boundary Value Problems (BVP) and integro-differential equations.

Published
2020
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9. Thick sets, multiple-valued mappings, and possibility theory

Author

Henri Prade, Didier Dubois, Luc Jaulin, Vladik Kreinovich, Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), and Janusz Kacprzyk

Subjects
Possibility theory, 0209 industrial biotechnology, Thick set, Inverse image, Computer science, Multivalued function, Fuzzy set, Uncertainty, Probabilistic logic, 02 engineering and technology, Interval (mathematics), 16. Peace & justice, Set (abstract data type), Algebra, 020901 industrial engineering & automation, Bounded function, 0202 electrical engineering, electronic engineering, information engineering, Interval analysis, [INFO]Computer Science [cs], 020201 artificial intelligence & image processing, Inverse function
Abstract

International audience; Carrying uncertain information via a multivalued function can be found in different settings, ranging from the computation of the image of a set by an inverse function to the Dempsterian transfer of a probabilistic space by a multivalued function. We then get upper and lower images. In each case one handles so-called thick sets in the sense of Jaulin, i.e., lower and upper bounded ill-known sets. Such ill-known sets can be found under different names in the literature, e.g., interval sets after Y. Y. Yao, twofold fuzzy sets in the sense of Dubois and Prade, or interval-valued fuzzy sets, ... Various operations can then be defined on these sets, then understood in a disjunctive manner (epistemic uncertainty), rather than conjunctively. The intended purpose of this note is to propose a unified view of these formalisms in the setting of possibility theory, which should enable us to provide graded extensions to some of the considered calculi.

Published
2020
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10. Set-membership state estimation by solving data association

Author

Benoit Desrochers, Luc Jaulin, Simon Rohou, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), DGA Techniques Navales, Direction générale de l'Armement (DGA), and ANR-16-CE33-0024,CONTREDO,Intervalles et contracteurs pour les systèmes dynamiques(2016)

Subjects
0209 industrial biotechnology, Computer science, Reliability (computer networking), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Sonar, [SPI.AUTO]Engineering Sciences [physics]/Automatic, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Set (abstract data type), 020901 industrial engineering & automation, Position (vector), 0202 electrical engineering, electronic engineering, information engineering, Trajectory, Robot, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], 020201 artificial intelligence & image processing, Underwater, Algorithm, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; This paper deals with the localization problem of a robot in an environment made of indistinguishable landmarks, and assuming the initial position of the vehicle is unknown. This scenario is typically encountered in underwater applications for which landmarks such as rocks all look alike. Furthermore, the position of the robot may be lost during a diving phase, which obliges us to consider unknown initial position. We propose a deterministic approach to solve simultaneously the problems of data association and state estimation, without combinatorial explosion. The efficiency of the method is shown on an actual experiment involving an underwater robot and sonar data.

Published
2020

11. Characterizing Sliding Surfaces of Cyber-Physical Systems

Author

Fabrice Le Bars, Luc Jaulin, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)

Subjects
0209 industrial biotechnology, Information Systems and Management, Computer science, 02 engineering and technology, Management Science and Operations Research, Classification of discontinuities, Theoretical Computer Science, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Sailboats, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Computer Science (miscellaneous), Interval analysis, Electrical and Electronic Engineering, business.industry, Cyber-physical system, Robotics, Sliding surface, Trajectory, Piecewise, Robot, 020201 artificial intelligence & image processing, Computer Vision and Pattern Recognition, Artificial intelligence, business, Software
Abstract

International audience; When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution function of the closed-loop system is not anymore piecewise continuous along the trajectory, mainly due to if statements inside the control algorithm. As a consequence, an unwanted chattering effect may occur. This behavior is often difficult to observe even in simulation. We propose here a set-membership method based on interval analysis to detect different types of discontinuities. One of them is the sliding surface where the state trajectory jumps indefinitely between two distinct behaviors. As an application, we consider the validation of a sailboat controller. We show that our approach is able to detect and explain some unwanted sliding effects that may be observed in rare and specific situations on our actual sailboat robots.

Published
2020
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12. An Interval Approach to Compute Invariant Sets

Author

Thomas Le Mézo, Luc Jaulin, Benoit Zerr, Pôle STIC_OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), and This work has been supported by the French Government Defense procurement and technology agency (DGA - Direction Générale de l'Armement)

Subjects
Lyapunov function, constraint programming, 0209 industrial biotechnology, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Context (language use), 02 engineering and technology, Interval (mathematics), Set (abstract data type), invariant set, symbols.namesake, 020901 industrial engineering & automation, 0202 electrical engineering, electronic engineering, information engineering, State space, Applied mathematics, Limit (mathematics), Electrical and Electronic Engineering, Invariant (mathematics), Mathematics, Discrete mathematics, Computer Science Applications, state equation, limit cycle, Nonlinear system, Control and Systems Engineering, symbols, 020201 artificial intelligence & image processing, interval analysis, Guaranteed integration
Abstract

International audience; This paper proposes an original interval-based method to compute an outer approximation of all invariant sets (such as limit cycles) of a continuous-time non-linear dynamic system which are included inside a prior set of the state space. Contrary to all other existing approaches, our method has the following properties: (i) it is guaranteed (a solution cannot be lost), (ii) it is applicable to a large class of systems without any specific assumption such as the knowledge of a Lyapunov function or any partial linearity, and (iii) there is no need to integrate the system.

Published
2017
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13. Minkowski Operations of Sets with Application to Robot Localization

Author

Luc Jaulin, Benoit Desrochers, DGA/TN, DGA, Pôle STIC_OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)

Subjects
Computational Geometry (cs.CG), FOS: Computer and information sciences, 0209 industrial biotechnology, Computer Science - Artificial Intelligence, Computer science, ComputerApplications_COMPUTERSINOTHERSYSTEMS, Systems and Control (eess.SY), 02 engineering and technology, Sonar, lcsh:QA75.5-76.95, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science - Robotics, 020901 industrial engineering & automation, Robot localization, Robot Autonome, Minkowski space, FOS: Electrical engineering, electronic engineering, information engineering, 0202 electrical engineering, electronic engineering, information engineering, Contractors, lcsh:Mathematics, localisation d'un robot, Order (ring theory), Resolution (logic), lcsh:QA1-939, Minkowski addition, Minkowski operations, Artificial Intelligence (cs.AI), Computer Science - Computational Geometry, Computer Science - Systems and Control, Robot, 020201 artificial intelligence & image processing, lcsh:Electronic computers. Computer science, interval analysis, Robotics (cs.RO), Algorithm
Abstract

This papers shows that using separators, which is a pair of two complementary contractors, we can easily and efficiently solve the localization problem of a robot with sonar measurements in an unstructured environment. We introduce separators associated with the Minkowski sum and the Minkowski difference in order to facilitate the resolution. A test-case is given in order to illustrate the principle of the approach., In Proceedings SNR 2017, arXiv:1704.02421

Published
2017
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14. Guaranteed Nonlinear Parameter Estimation with Additive Gaussian Noise

Author

Jeremy Nicola, Luc Jaulin, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Olga Kosheleva, Sergey P. Shary, Gang Xiang, Roman Zapatrin, and Janusz Kacprzyk

Subjects
0209 industrial biotechnology, Set inversion, Estimation theory, Set-estimation, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Nonlinear parameter estimation, 02 engineering and technology, Interval arithmetic, Set (abstract data type), Probabilistic estimation, [SPI]Engineering Sciences [physics], symbols.namesake, 020901 industrial engineering & automation, Gaussian noise, Localization, Parameter estimation, 0202 electrical engineering, electronic engineering, information engineering, symbols, Interval analysis, Applied mathematics, 020201 artificial intelligence & image processing, Set estimation, Mathematics
Abstract

International audience; In this paper we propose a new approach for nonlinear parameter estimation under additive Gaussian noise. We provide an algorithm based on interval analysis and set inversion which computes an inner and an outer approximation of a set enclosing the parameter vector with a given probability. The principle of the approach is illustrated by examples related to parameter estimation and range-only localization.

Published
2020
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15. Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System

Author

Luc Jaulin, Andreas Rauh, Swantje Romig, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Department of Mechatronics, and University of Rostock

Subjects
0209 industrial biotechnology, Numerical Analysis, Set inversion, Sliding mode control, Computer science, 02 engineering and technology, Interval (mathematics), Invariant sets, Theoretical Computer Science, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computational Mathematics, Nonlinear system, 020901 industrial engineering & automation, Computational Theory and Mathematics, Bounded function, Lyapunov stability, 0202 electrical engineering, electronic engineering, information engineering, Interval analysis, 020201 artificial intelligence & image processing, Invariant (mathematics), Global optimization, Algorithm
Abstract

In recent years, many applications, as well as theoretical properties of interval analysis have been investigated. Without any claim for completeness, such applications and methodologies range from enclosing the effect of round-off errors in highly accurate numerical computations over simulating guaranteed enclosures of all reachable states of a dynamic system model with bounded uncertainty in parameters and initial conditions, to the solution of global optimization tasks. By exploiting the fundamental enclosure properties of interval analysis, this paper aims at computing invariant sets of nonlinear closed-loop control systems. For that purpose, Lyapunov-like functions and interval analysis are combined in a novel manner. To demonstrate the proposed techniques for enclosing invariant sets, the systems examined in this paper are controlled via sliding mode techniques with subsequently enclosing the invariant sets by an interval based set inversion technique. The applied methods for the control synthesis make use of a suitably chosen Gr&ouml, bner basis, which is employed to solve B&eacute, zout&rsquo, s identity. Illustrating simulation results conclude this paper to visualize the novel combination of sliding mode control with an interval based computation of invariant sets.

Published
2019
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16. Thick gradual sets and their computations: Application for determining the uncertain zone explored by an underwater robot

Author

Luc Jaulin, Benoit Desrochers, Reda Boukezzoula, Laurent Foulloy, Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance (LISTIC), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Equipe ROBotics for EXploration (Lab-STICC_ROBEX), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
0209 industrial biotechnology, Computer science, Fuzzy set, Parameterized complexity, Monotonic function, 02 engineering and technology, Fuzzy control system, Interval (mathematics), Upper and lower bounds, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Artificial Intelligence, Control and Systems Engineering, 0202 electrical engineering, electronic engineering, information engineering, Trajectory, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, Representation (mathematics), Algorithm, ComputingMilieux_MISCELLANEOUS
Abstract

This paper proposes a new concept of thick gradual sets (TGSs), which is based on the notions of thick sets (TSs) and gradual sets (GSs). A TS is an uncertain set, which is represented by a pair of crisp sets (CSs). These CSs represent the upper and lower bounds of the TS. Therefore, a TS can be considered as an interval of CSs. A GS is a CS, which is parameterized by a degree of pertinence and aims to increase the specificity of CSs. Furthermore, a TGS is an interval of GSs, i.e., a pair of lower and upper GSs. In situations when the constraint of monotonicity (consistency) is guaranteed, a GS becomes a type-1 fuzzy set (T1FS) and a TGS can be regarded as a thick fuzzy set (TFS). Moreover, a TFS, which is composed of lower and upper T1FS bounds, can be interpreted as a type-2 fuzzy set (T2FS). According to the TGS representation, this new approach offers an original concept for interpreting, manipulating, and computing some uncertain quantities that cannot be represented by GSs, T1FSs, and/or T2FSs. The potential applications of the TGS concept has been validated using application examples in the frameworks of solving fuzzy systems of equations and uncertain fuzzy regression and through a real-world application where the trajectory of an underwater robot is uncertain and cannot be precisely known because of disturbances induced by the environment. The proposed approach makes it possible to compute the uncertain zone explored by the underwater robot.

Published
2021
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17. Computing a Guaranteed Approximation of the Zone Explored by a Robot

Author

Luc Jaulin, Benoit Desrochers, Délégation générale de l'armement (DGA), Ministère de la Défense, Pôle STIC_OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)

Subjects
0209 industrial biotechnology, Service robots, Computer science, Uncertainty, Trajectory, Probabilistic logic, 02 engineering and technology, Workspace, Space (mathematics), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science Applications, Computer Science::Robotics, 020901 industrial engineering & automation, Dimension (vector space), Control and Systems Engineering, Control theory, Robot sensing systems, 0202 electrical engineering, electronic engineering, information engineering, Robot, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, Simulation
Abstract

International audience; This paper deals with the guaranteed characterization of the part of the space that has been explored by a robot.The main difficulty of the problem is to take into account the uncertainty associated with the trajectory and the fact that thedimension of the visible space at time t may be smaller than that of the workspace. An example involving an experiment made with an actual underwater robot is presented in order to illustrate the efficiency of the approach.

Published
2017
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18. A minimal contractor for the polar equation: Application to robot localization

Author

Benoit Desrochers and Luc Jaulin

Subjects
0209 industrial biotechnology, Mathematical optimization, Computer science, business.industry, ComputerApplications_COMPUTERSINOTHERSYSTEMS, Robotics, 02 engineering and technology, Computer Science::Computers and Society, law.invention, Interval arithmetic, Computer Science::Robotics, 020901 industrial engineering & automation, Artificial Intelligence, Control and Systems Engineering, law, 0202 electrical engineering, electronic engineering, information engineering, Constraint programming, 020201 artificial intelligence & image processing, Cartesian coordinate system, Set theory, Artificial intelligence, Electrical and Electronic Engineering, Polar coordinate system, business, Algorithm
Abstract

Contractor programming relies on a catalog on elementary contractors which need to be as efficient as possible. In this paper, we introduce a new theorem that can be used to build minimal contractors consistent with equations, and another new theorem to derive an optimal separator from a minimal contractor. As an application, we focus on the channeling polar constraint associated to the change between Cartesian coordinates and Polar coordinates. We illustrate our method on the localization problem of an actual underwater robot where both range and goniometric measurements of landmarks are collected.

Published
2016
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19. Range-only SLAM with indistinguishable landmarks; a constraint programming approach

Author

Luc Jaulin, Lab-STICC_ENSTAB_CID_IHSEV, OSM, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)

Subjects
constraint programming, 0209 industrial biotechnology, 02 engineering and technology, Simultaneous localization and mapping, localization, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Interval arithmetic, Computer Science::Robotics, 020901 industrial engineering & automation, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, Redundancy (engineering), Constraint programming, simultaneous localization and mapping, Discrete Mathematics and Combinatorics, Point (geometry), Computer vision, Mathematics, robotics, business.industry, Constraint (information theory), Computational Theory and Mathematics, Computer Science::Computer Vision and Pattern Recognition, Local consistency, Robot, 020201 artificial intelligence & image processing, Artificial intelligence, interval analysis, business, Software
Abstract

International audience; This paper deals with the simultaneous localization and mapping problem (SLAM) for a robot. The robot hasto 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, (iii) the only exteroceptivemeasurements correspond to the distance between the robot and the landmarks. This problem can be takled usingMonte-Carlo approaches, but the resulting method is often trapped in some local minimimum from which it isdifficult to escape without solving the data association problem. The main contribution of this paper is to show that,due to the redundancy of measurements, a constraint-based approach can find a guaranteed enclosure of the globalsolution with a polynomial complexity. A simulated test-case is provided to illustrate the efficiency of the approach.

Published
2015
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20. Fuzzy Matrix Contractor Based Approach for Localization of Robots

Author

Luc Jaulin, Snehashish Chakraverty, Nisha Rani Mahato, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)

Subjects
0209 industrial biotechnology, Mathematical optimization, Orientation (computer vision), Computer science, Gaussian, Frame (networking), 02 engineering and technology, Fuzzy logic, Computer Science::Computers and Society, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science::Robotics, symbols.namesake, Matrix (mathematics), 020901 industrial engineering & automation, Position (vector), 0202 electrical engineering, electronic engineering, information engineering, symbols, Robot, 020201 artificial intelligence & image processing, Pose, ComputingMilieux_MISCELLANEOUS
Abstract

Localization consists of finding the pose of some robots with respect to its position and orientation. In case of localization of a group of robots over a planar surface, each robot is linked with other robots using constraints that may be considered in term of matrix equations. As such, this chapter deals with the localization of group of robots using angle and distance constraints associated with fuzzy matrix contractors. Matrix contractors based on azimuth–distance and bearing-distance constraints help efficient propagation of fuzzy uncertainties through a group of robots for localization purpose when no absolute frame is present. Finally, various groups of robots have been considered for the verification of proposed contractors viz. azimuth, distance, azimuth–distance, and bearing-distance contractors using Gaussian fuzzy uncertainty.

Published
2018

21. Bracketing the solutions of an ordinary differential equation with uncertain initial conditions

Author

Benoit Zerr, Thomas Le Mézo, Luc Jaulin, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), Pôle STIC_OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), DGA, École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)

Subjects
0209 industrial biotechnology, Dynamical systems theory, ODE, Applied Mathematics, Mathematical analysis, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Abstract interpretation, Interval computation, 02 engineering and technology, State (functional analysis), Interval (mathematics), Infinity, Interval arithmetic, Computational Mathematics, 020901 industrial engineering & automation, Bounded function, Ordinary differential equation, Dynamical systems, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Positive invariant set, Bracketing, Mathematics
Abstract

International audience; In this paper, we present a new method for bracketing (i.e., characterizing from inside and from outside) all solutions of an ordinary differential equation in the case where the initial time is inside an interval and the initial state is inside a box. The principle of the approach is to cast the problem into bracketing the largest positive invariant set which is included inside a given set X. Although there exists an efficient algorithm to solve this problem when X is bounded, we need to adapt it to deal with cases where X is unbounded.

Published
2018
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22. An interval space reducing method for constrained problems with particle swarm optimization

Author

Thiago Melo Machado-Coelho, Gustavo Luís Soares, Petr Ekel, Luc Jaulin, Witold Pedrycz, Alexei Manso Correa Machado, Pontifical Catholic University of Minas Gerais [Belo Horizonte], Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), Pôle STIC_OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), University of Alberta, École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)

Subjects
Continuous optimization, 0209 industrial biotechnology, Mathematical optimization, Meta-optimization, Constrained Optimization, Imperialist competitive algorithm, 02 engineering and technology, Evolutionary computation, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Vector optimization, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Particle Swarm Optimization, Derivative-free optimization, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Multi-swarm optimization, Global optimization, Metaheuristic, Software, Interval Analysis, Mathematics
Abstract

International audience; In this paper, we propose a method for solving constrained optimization problems using Interval Analysis combined with Particle Swarm Optimization. A Set Inverter Via Interval Analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a Space Cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified Particle Swarm Optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100,000 runs on a set of well-known benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.

Published
2017
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23. Thick set inversion

Author

Benoit Desrochers, Luc Jaulin, Délégation générale de l'armement (DGA), Ministère de la Défense, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), Pôle STIC_OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)

Subjects
Discrete mathematics, Linguistics and Language, Set inversion, Efficient algorithm, Uncertainty, 010103 numerical & computational mathematics, 02 engineering and technology, Function (mathematics), 01 natural sciences, Language and Linguistics, Interval arithmetic, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Set (abstract data type), Artificial Intelligence, Set function, Index set, 0202 electrical engineering, electronic engineering, information engineering, Constraint programming, Set-Membership methods, 020201 artificial intelligence & image processing, 0101 mathematics, Interval Analysis, Mathematics
Abstract

This paper deals with the set inversion problem X = f − 1 ( Y ) in the case where the function f : R n → R m and the set Y are both uncertain. The uncertainty is treated under the form of intervals. More precisely, for all x, f ( x ) is inside the box [ f ] ( x ) and the uncertain set Y is bracketed between an inner set Y ⊂ and an outer set Y ⊃ . The introduction of new tools such as thick intervals and thick boxes will allow us to propose an efficient algorithm that handles the uncertainty of sets in an elegant and efficient manner. Some elementary test-cases that cannot be handled easily and properly by existing methods show the efficiency of the approach.

Published
2017
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24. Calcul garanti de trajectoires de robots

Author

Luc Jaulin, Sandor M. Veres, Fabrice Le Bars, Lyudmila Mihaylova, Simon Rohou, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Pôle STIC_OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), University of Sheffield [Sheffield], and This work has been supported by the French Direction Générale de l’Armement (DGA) during the UK-France PhD program.

Subjects
0209 industrial biotechnology, Mathematical optimization, ODE, Computer science, Differential equation, General Mathematics, Constraint (computer-aided design), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, tube programming, [SPI.AUTO]Engineering Sciences [physics]/Automatic, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], contractors, 020901 industrial engineering & automation, Differential inclusion, 0202 electrical engineering, electronic engineering, information engineering, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Differential (infinitesimal), Flexibility (engineering), guaranteed integration, business.industry, Ode, Robotics, Mobile robot, Computer Science Applications, mobile robotics, Control and Systems Engineering, Robot, 020201 artificial intelligence & image processing, Artificial intelligence, business, constraints, Software, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

This paper proposes a new method for guaranteed integration of state equations. Within this framework, the variables of interest are trajectories submitted to both arithmetic and differential equations. The approach consists in formalizing a problem thanks to a constraint network and then apply these constraints to sets of trajectories. The contribution of the paper is to provide a reliable framework to enclose the solutions of these differential equations. Its use is shown to be simple, more general and more competitive than existing approaches dealing with guaranteed integration, especially when applied to mobile robotics. The flexibility of the developed framework allows to deal with non-linear differential equations or even differential inclusions built from datasets, while considering observations of the states of interest. An illustration of this method is given over several examples with mobile robots. A contractor-based approach is proposed for guaranteed integration of state equations.The framework is based on the use of tubes as envelopes of feasible trajectories.A dedicated differential contractor is provided to deal with dynamical systems.The use of tubes is well suited for multi-differential and non-linear equations.An illustration of this approach is given over several mobile robotics examples.

Published
2017
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25. Phase Based Localization for Underwater Vehicles Using Interval Analysis

Author

Jonathan Grimsdale, Mohamed Saad Ibn Seddik, Luc Jaulin, Lab-STICC_ENSTAB_CID_IHSEV, OSM, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), and Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Heading (navigation), Particle Filters, Computer science, GPS, Acoustics, USBL, LBL, 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Interval arithmetic, 020901 industrial engineering & automation, Sine wave, CSP, 0202 electrical engineering, electronic engineering, information engineering, Underwater, Contractor, Sequential Monte Carlo, Underwater Localization, Interval Analysis, Simulation, Acoustic Localization, Time Constraint Satisfaction Problem, business.industry, Long baseline acoustic positioning system, Applied Mathematics, Constraint satisfaction, TCSP, Computational Mathematics, Computational Theory and Mathematics, Global Positioning System, 020201 artificial intelligence & image processing, Particle filter, business, Constraint Satisfaction
Abstract

International audience; This paper addresses the common issue of locating an Underwater Vehicle (UV). Usually, the positioning of a vehicle is based on the propagation of electromagnetic waves, using systems such as the Global Positioning System (GPS). However, water, and particularly salty water, makes the use of electromagnetic waves impractical due to the attenuation caused by the high conductivity of the medium. Hence, the most reliable way to transmit information underwater is by using sound waves and many technologies have emerged to solve the positioning problem in this way. Technologies such as Long BaseLine (LBL), Short BaseLine (SBL) and Ultra-Short BaseLine (USBL) are the most frequently used underwater. These technologies are based on the use of multiple emitters in the case of LBL and SBL, or multiple receivers in the case of USBL. This paper describes a way of finding a vehicle location, on-board, based on the measurement at the vehicle by a single receiver of the phase of an acoustic sine wave transmitted from a single emitter that is at a fixed and known location. The method also uses other proprioceptive measurements: vehicle's velocity and heading. An algorithm based on contractors and bisections scatters the solution space searching for all possible solutions (positions in this case) to the set of equations. Moreover, this paper introduces the Time Constraint Satisfaction Problem (TCSP). Indeed, the proposed algorithm does not compute the solutions from measurements at a single point in time, rather it uses a set of measurements taken over a time window and stored in a buffer. As a result, the location is not only known at the latest instant but the past locations can be tracked back over the length of the chosen time window.

Published
2014
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26. Contractor programming

Author

Gilles Chabert, Luc Jaulin, Laboratoire d'Informatique de Nantes Atlantique (LINA), Centre National de la Recherche Scientifique (CNRS)-Mines Nantes (Mines Nantes)-Université de Nantes (UN), Développement des Technologies Nouvelles (DTN), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
Constraint processing, 0209 industrial biotechnology, Linguistics and Language, Mathematical optimization, Set inversion, Formalism (philosophy), Intersection (set theory), Computer science, Solution set, 02 engineering and technology, Programming languages, Space (commercial competition), Solver, Deadlock, Solver design, Language and Linguistics, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Set (abstract data type), 020901 industrial engineering & automation, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, Interval methods, 020201 artificial intelligence & image processing
Abstract

WOS; International audience; This paper describes a solver programming method, called "contractor programming", that copes with two issues related to constraint processing over the reals. First, continuous constraints involve an inevitable step of solver design. Existing softwares provide an insufficient answer by restricting users to choose among a list of fixed strategies. Our first contribution is to give more freedom in solver design by introducing programming concepts where only configuration parameters were previously available. Programming consists in applying operators (intersection, composition, etc.) on algorithms called "contractors" that are somehow similar to propagators. Second, many problems with real variables cannot be cast as the search for vectors simultaneously satisfying the set of constraints, but a large variety of different outputs may be demanded from a set of constraints (e.g., a paving with boxes inside and outside of the solution set). These outputs can actually be viewed as the result of different "contractors" working concurrently on the same search space, with a bisection procedure intervening in case of deadlock. Such algorithms (which are not strictly speaking solvers) will be made easy to build thanks to a new branch & prune system, called "paver". Thus, this paper gives a way to deal harmoniously with a larger set of problems while giving a fine control on the solving mechanisms. The contractor formalism and the paver system are the two contributions. The approach is motivated and justified through different cases of study. An implementation of this framework named Quimper is also presented.

Published
2009
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27. A Nonlinear Set Membership Approach for the Localization and Map Building of Underwater Robots

Author

Luc Jaulin

Subjects
0209 industrial biotechnology, business.industry, Mobile robot, Robotics, 02 engineering and technology, Simultaneous localization and mapping, Constraint satisfaction, Computer Science Applications, Interval arithmetic, Computer Science::Robotics, Set (abstract data type), 020901 industrial engineering & automation, Control and Systems Engineering, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Artificial intelligence, Electrical and Electronic Engineering, Particle filter, business, Algorithm, Constraint satisfaction problem, Mathematics
Abstract

This paper proposes a set membership method based on interval analysis to solve the simultaneous localization and map building (SLAM) problem. The principle of the approach is to cast the SLAM problem into a constraint satisfaction problem for which interval propagation algorithms are particularly powerful. The resulting propagation method is illustrated on the localization and map building of an actual underwater robot.

Published
2009
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28. Set-Membership Approach to the Kidnapped Robot Problem

Author

Benoit Desrochers, Simon Lacroix, Luc Jaulin, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Lab-STICC_ENSTAB_CID_IHSEV, OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Équipe Robotique et InteractionS (LAAS-RIS), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Pôle STIC [Brest] (STIC), Pole STIC, ENSTA Bretagne, Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique)

Subjects
0209 industrial biotechnology, Matching (graph theory), Computer science, business.industry, Raised-relief map, 02 engineering and technology, Interval (mathematics), Kidnapped robot problem, GeneralLiterature_MISCELLANEOUS, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), 020901 industrial engineering & automation, Robustness (computer science), Outlier, 0202 electrical engineering, electronic engineering, information engineering, Robot, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], 020201 artificial intelligence & image processing, Computer vision, Algorithm design, Artificial intelligence, business, Lidar data, Interval Analysis
Abstract

International audience; This article depicts an algorithm which matches the output of a Lidar with an initial terrain model to estimate the absolute pose of a robot. Initial models do not perfectly fit the reality and the acquired data set can contain an unknown, and potentially large, proportion of outliers. We present an interval based algorithm that copes with such conditions, by matching the Lidar data with the terrain model in a robust manner. Experimental validations using different terrain model are reported to illustrate the performance of the method.

Published
2015

29. Quantified Set Inversion Algorithm with Applications to Control

Author

Luc Jaulin, Miguel A. Sainz, Josep Vehí, Pau Herrero, Ensta Bretagne, Stic Rems, Extraction et Exploitation de l'Information en Environnements Incertains (E3I2), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
0209 industrial biotechnology, Mathematical optimization, Set inversion, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, Applied Mathematics, Linear system, Solution set, 02 engineering and technology, Constraint satisfaction, Interval arithmetic, Computational Mathematics, Range (mathematics), 020901 industrial engineering & automation, Modal, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Control (linguistics), [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Algorithm, ComputingMilieux_MISCELLANEOUS, Software, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing, Mathematics
Abstract

In this paper, a new algorithm based on Set Inversion techniques and Modal Interval Analysis is presented. This algorithm allows one to solve problems involving quantified constraints over the reals through the characterization of their solution sets. The presented methodology can be applied to a wide range of problems involving uncertain (non)linear systems. Finally, an advanced application is solved.

Published
2005
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30. Set Computation for Nonlinear Control

Author

Stefan Ratschan, Laurent Hardouin, Luc Jaulin, Ensta Bretagne, Stic Rems, Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), and Centre National de la Recherche Scientifique (CNRS)-Université d'Angers (UA)

Subjects
0209 industrial biotechnology, Mathematical optimization, Sequence, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, Applied Mathematics, Computation, 02 engineering and technology, Nonlinear control, Constraint satisfaction, Interval arithmetic, Computational Mathematics, Nonlinear system, 020901 industrial engineering & automation, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, 0202 electrical engineering, electronic engineering, information engineering, Local consistency, 020201 artificial intelligence & image processing, Robust control, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Algorithm, ComputingMilieux_MISCELLANEOUS, Software, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing, Mathematics
Abstract

This paper proposes a new approach to solve the problem of finding a control sequence for a nonlinear discrete-time system that should satisfy given set-membership specifications on the state and the output vectors. This approach is based on set computation and constraint propagation. Two illustrative examples are provided. The approach is then extended to deal with the robust control problem of nonlinear discrete-time systems.

Published
2004
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31. Guaranteed robust nonlinear estimation with application to robot localization

Author

Luc Jaulin, E. Walter, Dominique Meizel, Michel Kieffer, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), Centre National de la Recherche Scientifique (CNRS)-Université d'Angers (UA), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), and Gerard, Marie-Françoise

Subjects
0209 industrial biotechnology, Mathematical optimization, [SPI] Engineering Sciences [physics], 02 engineering and technology, nonlinear estimation, Interval arithmetic, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, robot localization, Robustness (computer science), 0202 electrical engineering, electronic engineering, information engineering, bounded-error etsimation, Electrical and Electronic Engineering, Mathematics, Set inversion, set estimation, outliers, Estimator, robust estimation, set inversion, Computer Science Applications, Human-Computer Interaction, Data point, Control and Systems Engineering, Outlier, 020201 artificial intelligence & image processing, Set estimation, Robust control, interval analysis, Software, Information Systems
Abstract

International audience; when rliable prior bounds on the acceptable erors between the data and corresponding model outputs are availabl, bounded-error estimation techniques make it possible to characterize the set of all acceptable parameter vectors in a guaranteed way, ven when the model is nonlinear and the number of data points small. However, when the data may contain outliers, i.e., data points for which these bounds should be violated, this set may turn out to be empty, or a least unrealistically small. The outlier minimal number estimator (OMNE) has been designed to deal with such a situation, by minimizing the number of data points considered as outliers. OMNE has been shown in previous papers to be remarkbly robust, even to a majority of outliers. Up to now, it was implemented by random scanning, so its results could not be guaranteed. In this paper, a new algorithm based on set inversion via interval analysis provides a guaranteed OMNE, which is applied to the initial localization of an actual robot in a partially known 2D environment. The difficult problems of associating range data to landmarks of the environment and of detecting potential outliers are solved as by-products of the procedure.

Published
2002
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32. Solving non-linear constraint satisfation problems involving time-dependant functions

Author

Aymeric Bethencourt, Luc Jaulin, Lab-STICC_ENSTAB_CID_IHSEV, OSM, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), and Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Mathematical optimization, Applied Mathematics, 02 engineering and technology, Resolution (logic), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computational Mathematics, Nonlinear system, 020901 industrial engineering & automation, Test case, Computational Theory and Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Interval analysis Constraint satisfaction problem Tubes Time dependant functions Primary 65G40 Secondary 65G30, Order (group theory), 020201 artificial intelligence & image processing, Dependant, Constraint satisfaction problem, Mathematics
Abstract

International audience; In this paper, we consider the resolution of non-linear constraint satisfaction problems where the variables of the systems are trajectories (functions from R to Rn). We introduce the notion of tubes as intervals of functions, for which the lower and upper bounds are trajectories with respect to the inclusion. We then define basic operators and prove propositions verified by tubes. We show the possibility to build contractors on tubes and propagate constraints to solve problems involving time-dependant functions as the unknown variables.We show that the approach is particularly powerful when inter-temporal equations (e.g. delays) are involved. Finally, in order to illustrate the principle and efficiency of the approach, several test cases are provided.

Published
2014
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33. Robotic Sailing 2013

Author

Fabrice Le Bars and Luc Jaulin

Subjects
0209 industrial biotechnology, 020901 industrial engineering & automation, Computer science, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, 02 engineering and technology
Published
2014
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34. 3D Reconstruction Using Interval Methods on The Kinect Device Coupled With an IMU

Author

Luc Jaulin, Aymeric Bethencourt, Lab-STICC_ENSTAB_CID_IHSEV, OSM, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), and Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Computer science, Point cloud, lcsh:TK7800-8360, 02 engineering and technology, RANSAC, lcsh:QA75.5-76.95, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Interval Methods, 020901 industrial engineering & automation, Artificial Intelligence, Inertial measurement unit, 0202 electrical engineering, electronic engineering, information engineering, Computer vision, Contractors, Kinect, VSLAM, business.industry, lcsh:Electronics, 3D reconstruction, Iterative closest point, IMU, Computer Science Applications, Transformation (function), 020201 artificial intelligence & image processing, lcsh:Electronic computers. Computer science, Artificial intelligence, 3D Reconstruction, business, Software
Abstract

WOS; International audience; The principle behind VSLAM applications like 3D object reconstruction or indoor mapping is to estimate the spatial transformation between two large clouds of points, which represent two poses of the same scene. They can further be processed to obtain detailed surfaces. Since its introduction in 1992, the standard algorithm for finding the alignment between two point clouds is ICP (Iterative Closest Point) and its variants, combined with RANSAC (RANdom SAmple Consensus). This paper presents a new approach using interval analysis. The idea is to define large intervals for the transformation parameters between the poses then to successively contract those intervals using the equations of the transformation of corresponding points between the poses. To contract those intervals faster, we added an IMU (Inertial Measurement Unit) to our system so the initial intervals of the parameters are already small before applying the contractions. We implemented our algorithm using the middleware ROS (Robot Operating System) and stated our performances.

Published
2013
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35. An experimental validation of a robust controller with the VAIMOS autonomous sailboat

Author

Luc Jaulin, Fabrice Le Bars, Lab-STICC_ENSTAB_CID_IHSEV, OSM, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), and Billon-Coat, Annick

Subjects
0209 industrial biotechnology, SIMPLE (military communications protocol), Computer science, Process (computing), Control engineering, 02 engineering and technology, Experimental validation, turbidity, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, sailboat robot, [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Trajectory, Robot, 020201 artificial intelligence & image processing, Tweaking
Abstract

International audience; A sailboat is a strongly non-linear system that however has been proven to be easily controllable. Indeed, its mechanical design comes from an evolution from thousands of years with two main concerns: having a fast, reliable and ef cient vehicle while being easily controlled by humans. This article describes the functioning, the validation process and the performances of a simple controller, inspired from what navigators do, through tests made on the sailboat robot VAIMOS built by IFREMER for oceanography. This controller requires tweaking few parameters with real physical meaning while ensuring accurate trajectory following, needed to make oceanographic measurements in a speci c area.

Published
2012

36. Color-based underwater object recognition using water light attenuation

Author

Isabelle Quidu, Luc Jaulin, Stéphane Bazeille, École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Lab-STICC_ENSTAB_CID_SFIIS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Pôle STIC_OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), and Lab-STICC_ENSTAB_CID_IHSEV

Subjects
underwater robot, Color normalization, Computer science, Vision, Computational Mechanics, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 010309 optics, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Artificial Intelligence, Robustness (computer science), 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering, Computer vision, Underwater, Engineering (miscellaneous), business.industry, Mechanical Engineering, Attenuation, Cognitive neuroscience of visual object recognition, Light attenuation, color, Obstacle, Video tracking, 020201 artificial intelligence & image processing, Artificial intelligence, business, light attenuation, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract

International audience; Abstract--In this article we present a new approach for object recognition in a robotic underwater context. Color is an attractive feature because of its simplicity and its robustness to scale changes, object positions and partial occlusions. Unfortunately, in the underwater medium, the colors are modified by attenuation and are not constant with the distance. To perform a color-based recognition of an object, we develop an algorithm robust with respect to the attenuation which takes into account the light modification during its path between the light source and the camera. Therefore, a given underwater object can be identified in an image by detecting all the colors compatible with its prior known color. Our method is fast, robust and needs a very few computers resources. We successfully used it when experimenting in the sea using a system we built. It is suitable for robotic applications where computers resources are limited and shared between various embedded devices. This novel concept enables the use of the color in many applications such as target interception, object tracking or obstacle detection.

Published
2012
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37. Solving set-valued constraint satisfaction problems

Author

Luc Jaulin, Lab-STICC_ENSTAB_CID_IHSEV, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Pôle STIC_OSM, and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
0102 computer and information sciences, 02 engineering and technology, Constraint satisfaction, 01 natural sciences, Upper and lower bounds, Theoretical Computer Science, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Combinatorics, Constraint logic programming, 0202 electrical engineering, electronic engineering, information engineering, Interval analysis, Contractors, Set intervals, Constraint satisfaction problem, Mathematics, Discrete mathematics, Numerical Analysis, Hybrid algorithm (constraint satisfaction), Order (ring theory), Constraint propagation, Computer Science Applications, Computational Mathematics, Computational Theory and Mathematics, 010201 computation theory & mathematics, Constraint graph, Local consistency, 020201 artificial intelligence & image processing, Software
Abstract

In this paper, we consider the resolution of constraint satisfaction problems in the case where the variables of the problem are subsets of $${\mathbb{R}^{n}}$$. In order to use a constraint propagation approach, we introduce set intervals (named i-sets), which are sets of subsets of $${\mathbb{R}^{n}}$$ with a lower bound and an upper bound with respect to the inclusion. Then, we propose basic operations for i-sets. This makes possible to build contractors that are then used by the propagation to solve problem involving sets as unknown variables. In order to illustrate the principle and the efficiency of the approach, a testcase is provided.

Published
2012
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38. Set-membership state estimation with fleeting data

Author

Jan Sliwka, Olivier Reynet, Fabrice Le Bars, Luc Jaulin, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (UMR 3192) (Lab-STICC), Université européenne de Bretagne - European University of Brittany (UEB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Télécom Bretagne-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université européenne de Bretagne - European University of Brittany (UEB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Institut Brestois du Numérique et des Mathématiques (IBNM), and Université de Brest (UBO)-Télécom Bretagne-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Département STIC [Brest] (STIC)

Subjects
0209 industrial biotechnology, Engineering, ComputerApplications_COMPUTERSINOTHERSYSTEMS, 02 engineering and technology, computer.software_genre, Sonar, law.invention, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science::Robotics, Set (abstract data type), Physics::Popular Physics, 020901 industrial engineering & automation, Robot localization, law, Fleeting data, 0202 electrical engineering, electronic engineering, information engineering, Interval analysis, Laser rangefinder, Electrical and Electronic Engineering, Radar, Estimation, business.industry, Observer, Set-membership estimation, Nonlinear system, Control and Systems Engineering, Localization, 020201 artificial intelligence & image processing, Artificial intelligence, Data mining, State (computer science), business, computer
Abstract

WOS; International audience; This paper deals with offline 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. In this paper, the first approach able to deal with nonlinear estimation with fleeting data is presented. An illustration related to offline robot localization with a laser rangefinder will be given.

Published
2012
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39. A non-linear set-membership approach for the control of Discrete Event Systems

Author

Luc Jaulin, Laurent Hardouin, Mehdi Lhommeau, Billon-Coat, Annick, Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), Université d'Angers (UA), Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université d'Angers (UA), Lab-STICC_ENSTAB_CID_IHSEV, OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), and Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Interval Arithmetic, 0209 industrial biotechnology, Mathematical optimization, Event (computing), Linear system, Min-Max-Plus, 02 engineering and technology, General Medicine, Max-plus algebra, Domain (software engineering), Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Max-plus Algebra, Set (abstract data type), Nonlinear system, 020901 industrial engineering & automation, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Timed Event Graphs, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Constraint Satisfaction Problem, Constraint satisfaction problem, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

International audience; A variety of problems in non-linear time-evolution systems such as manufacturing plants, operations research, computer networks, etc., can be modelled as min-max-plus systems in which operations of min, max and addition appear simultaneously. It is well know that systems with only maximum (or minimum) constraints can be modelled as max-plus system and handled by max-plus algebra which changes the original non-linear system into linear system in this framework. Several authors have developed methods, in max-plus algebra, to compute control for max-plus systems. In general, these methods use the residuation theory to design a just-in- time control such that the output of the controlled system is, on the one hand, less than the desired reference signal but as close as possible to the given reference and, on the other hand, the control is delayed as much as possible. In this paper, we consider min-max-plus systems which are extensions of max-plus systems and non-linear even in the max-plus algebra view. We proposes a new approach to solve the just-in-time control problem for a non-linear min-max- plus system. This problem is cast into the more general framework of constraint satisfaction problems. This makes it possible to propose a new algorithm that contracts the feasible domains for each uncertain variable optimally (i.e., no smaller domain could be obtained) and e ciently.

Published
2012

40. Processing Interval Sensor Data in the Presence of Outliers, with Potential Applications to Localizing Underwater Robots

Author

Martine Ceberio, Luc Jaulin, Jan Sliwka, Vladik Kreinovich, Extraction et Exploitation de l'Information en Environnements Incertains (E3I2), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Département STIC [Brest] (STIC), Laboratoire d'Informatique de Nantes Atlantique (LINA), and Centre National de la Recherche Scientifique (CNRS)-Mines Nantes (Mines Nantes)-Université de Nantes (UN)

Subjects
0209 industrial biotechnology, Computer science, Reliability (computer networking), Value (computer science), 02 engineering and technology, Interval (mathematics), Machine learning, computer.software_genre, Upper and lower bounds, interval uncertainty, [SPI.AUTO]Engineering Sciences [physics]/Automatic, underwater robots, 020901 industrial engineering & automation, 0202 electrical engineering, electronic engineering, information engineering, Observational error, business.industry, outliers, Mobile robot, sensor data, Outlier, Measurement uncertainty, 020201 artificial intelligence & image processing, Artificial intelligence, business, computer, Algorithm
Abstract

International audience; Measurements are never absolutely accurate, the measurement result ex is, in general, different from the actual (unknown) values x of the corresponding quantity. In many practical problems, we only know upper bounds Δ on the measurement errors Δx def = ex x. In such situations, once we know the measurement result, the only conclusion that we can make about the actual value x is that this value belongs to the interval [exΔ; ex+Δ]. There exist many efficient algorithms for processing such interval data. However, these algorithms usually assume that all the measurement results are valid. In reality, due to factors such as sensor malfunction, some measurement results may be way off (outliers), for which the difference between ex and x is much larger than the upper bound Δ on the measurement error. In this paper, we overview the algorithmic problems related to processing interval sensor data in the presence of outliers. Our case study - for which we develop and analyze these algorithms - is localization of underwater robots, a problem in which a significant number of measurement results are outliers

Published
2011

41. Range-Only SLAM With Occupancy Maps: A Set-Membership Approach

Author

Luc Jaulin, Extraction et Exploitation de l'Information en Environnements Incertains (E3I2), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), and Département STIC [Brest] (STIC)

Subjects
0209 industrial biotechnology, Mathematical optimization, simultaneous localization and mapping (SLAM), 02 engineering and technology, Simultaneous localization and mapping, localization, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), 020901 industrial engineering & automation, set-membership estimation, 0202 electrical engineering, electronic engineering, information engineering, interval propagation, Interval analysis, Electrical and Electronic Engineering, Constraint satisfaction problem, Mathematics, Real number, Extension (predicate logic), Computer Science Applications, Range (mathematics), Control and Systems Engineering, Local consistency, 020201 artificial intelligence & image processing, occupancy map, Algorithm
Abstract

WOS; International audience; This paper proposes a new set-membership approach to solve range-only simultaneous localization and mapping (SLAM) 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.

Published
2011
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42. Capture basin approximation using interval analysis

Author

Laurent Hardouin, Mehdi Lhommeau, Luc Jaulin, Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), Centre National de la Recherche Scientifique (CNRS)-Université d'Angers (UA), Extraction et Exploitation de l'Information en Environnements Incertains (E3I2), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
0209 industrial biotechnology, Mathematical optimization, Viability theory, ComputingMethodologies_SIMULATIONANDMODELING, 02 engineering and technology, Structural basin, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), 020901 industrial engineering & automation, 0202 electrical engineering, electronic engineering, information engineering, viability theory, Electrical and Electronic Engineering, Physics::Atmospheric and Oceanic Physics, Mathematics, capture basin, State (functional analysis), 16. Peace & justice, guaranteed numerical integration, Numerical integration, Nonlinear system, Control and Systems Engineering, Signal Processing, 020201 artificial intelligence & image processing, Finite time, nonlinear systems, interval analysis, Algorithm
Abstract

WOS; International audience; This paper proposes a new approach for computing the capture basin C of a target T. The capture basin corresponds to the set of initial state vectors such that the target could be reached in finite time via an appropriate control input, before possibly leaving the target. Whereas classical capture basin characterization does not provide any guarantee on the set of state vectors that belong to the capture basin, interval analysis and guaranteed numerical integration allow us to avoid any indetermination. We present an algorithm that is able to provide guaranteed approximation of the inner C− and the outer C+ of the capture basin, such that C−⊆C⊂C+. In order to illustrate the principle and the efficiency of the approach, a testcase on the 'car on the hill' problem is provided.

Published
2011
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43. Probabilistic Set-Membership State Estimator

Author

Luc Jaulin, Lab-STICC_ENSTAB_CID_IHSEV, OSM, Extraction et Exploitation de l'Information en Environnements Incertains (E3I2), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Département STIC [Brest] (STIC), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
0209 industrial biotechnology, Computer science, Probabilistic logic, Estimator, 02 engineering and technology, Interval (mathematics), 16. Peace & justice, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Efficient estimator, Outlier, Stein's unbiased risk estimate, 0202 electrical engineering, electronic engineering, information engineering, Local consistency, 020201 artificial intelligence & image processing, Probabilistic analysis of algorithms, Algorithm
Abstract

International audience; Interval constraint propagation methods have been shown to be efficient, robust and reliable to solve difficult nonlinear bounded-error state 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 paper proposes a new probabilistic approach which makes it possible to use classical set-membership observers which are robust with respect to outliers. The approach is illustrated on a localization of robots in situations where there exist a large number of outliers.

Published
2011
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44. Using interval methods in the context of robust localization of underwater robots

Author

Jan Sliwka, Luc Jaulin, Fabrice Le Bars, Olivier Reynet, Billon-Coat, Annick, Extraction et Exploitation de l'Information en Environnements Incertains (E3I2), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
0209 industrial biotechnology, Context (language use), 02 engineering and technology, Machine learning, computer.software_genre, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science::Robotics, 020901 industrial engineering & automation, 0202 electrical engineering, electronic engineering, information engineering, Computer vision, Constraint satisfaction problem, Mathematics, Interval methods, business.industry, Binary image, Mobile robot, Robotics, Data set, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Outlier, Local consistency, 020201 artificial intelligence & image processing, Artificial intelligence, business, computer
Abstract

International audience; In this paper we will apply interval methods to solve the problem of robust localization of an underwater robot. The localization problem is cast into a constraint satisfaction problem (CSP) where constraint propagation algorithms are particularly efficient. The method is designed to work in real environments with numerous outliers. Besides, we used a new approach to represent the map by a binary image. This allow us to represent even unstructured maps. We tested the algorithm on a real data set gathered by an underwater robot in a marina located in Costa Brava.

Published
2011

45. Probabilistic set-membership approach for robust regression

Author

Luc Jaulin, Développement des Technologies Nouvelles (DTN), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), and Grandjean, Hervé

Subjects
Statistics and Probability, 0209 industrial biotechnology, Mathematical optimization, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], probability, Interval estimation, [SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], 02 engineering and technology, Interval (mathematics), [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], 020901 industrial engineering & automation, set-membership estimation, 0202 electrical engineering, electronic engineering, information engineering, Rare events, Interval analysis, [PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Mathematics, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], Estimation theory, Probabilistic logic, Solution set, Density estimation, 16. Peace & justice, robust regression, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 020201 artificial intelligence & image processing, Set estimation
Abstract

NonWOS; International audience; 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 paper 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.

Published
2010

46. Guaranteed set-point computation with application to the control of a sailboat

Author

Pau Herrero, Luc Jaulin, Josep Vehí, Miguel A. Sainz, Extraction et Exploitation de l'Information en Environnements Incertains (E3I2), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Universitat de Girona, and Universitat de Girona (UdG)

Subjects
0209 industrial biotechnology, Mathematical optimization, Class (set theory), feedback linearization, Set inversion, 02 engineering and technology, Solver, Nonlinear control, 16. Peace & justice, Computer Science Applications, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), 020901 industrial engineering & automation, non-linear control, Control and Systems Engineering, Quantifier elimination, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Feedback linearization, interval analysis, Algorithm, set computation, Mathematics
Abstract

WOS; International audience; The problem of characterizing in a guaranteed way the set of all feasible set-points of a control problem is known to be difficult. In the present work, the problem to be solved involves non-linear equality constraints with variables affected by logical quantifiers. This problem is not solvable by current symbolic methods like quantifier elimination, which is commonly used for solving this class of problems. We propose the utilization of guaranteed set-computation techniques based on interval analysis, in particular a solver referred to as Quantified Set Inversion (QSI). As an application example, the problem of simultaneously controlling the speed and the orientation of a sailboat is presented. For this purpose, the combination of QSI solver and feedback linearization techniques is employed.

Published
2010
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47. Resolution of nonlinear interval problems using symbolic interval arithmetic

Author

Luc Jaulin, Gilles Chabert, Développement des Technologies Nouvelles (DTN), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
0209 industrial biotechnology, Computer science, Partition of an interval, 02 engineering and technology, Interval arithmetic, 020901 industrial engineering & automation, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, Interval analysis, Interval order, Quantified problems, Electrical and Electronic Engineering, Symbolic intervals, Computer Science::Databases, Real number, Discrete mathematics, Nonlinear problems, Solver, Constraint propagation, Expression (mathematics), Constraint (information theory), Control and Systems Engineering, Local consistency, Interval (graph theory), 020201 artificial intelligence & image processing, Algorithm
Abstract

WOS; International audience; An interval problem is a problem where the unknown variables take interval values. Such a problem can be defined by interval constraints, such as “the interval [a,b]subset of[a,b]2”. Interval problems often appear when we want to analyze the behavior of an interval solver. To solve interval problems, we propose to transform the constraints on intervals into constraints on their bounds. For instance, the previous interval constraint [a,b]subset of[a,b]2 can be transformed into the following bound constraints “a≥min(a2,ab,b2) and b≤max(a2,ab,b2)”. 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 illustrated on several applications.

Published
2010
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48. Interval SLAM for underwater robots; a new experiment

Author

Luc Jaulin, Fabrice Le Bars, Alain Bertholom, Jan Sliwka, Billon-Coat, Annick, Extraction et Exploitation de l'Information en Environnements Incertains (E3I2), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Département STIC [Brest] (STIC), Groupe d'Etudes Sous-Marines de l'Atlantique (DGA/DET/GESMA), and DGA

Subjects
0209 industrial biotechnology, Engineering, underwater robot, constraint propagation, 02 engineering and technology, Interval (mathematics), Simultaneous localization and mapping, localization, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, set-membership estimation, 0202 electrical engineering, electronic engineering, information engineering, Computer vision, Constraint satisfaction problem, business.industry, Submarine, [SPI.AUTO] Engineering Sciences [physics]/Automatic, SLAM, Local consistency, Robot, Underwater robot, 020201 artificial intelligence & image processing, Artificial intelligence, business, interval analysis
Abstract

International audience; This paper provides a new submarine experiment and shows the results of an interval SLAM (Simultaneous Localization And Mapping) method. The SLAM problem is cast into a constraint satisfaction problem where interval propagation algorithms are particularly efficient. The resulting method is applied to the localization of a submarine robot from the GESMA (Groupe d'Etudes Sous-Marines de l'Atlantique), the Daurade during an experiment in the Douarnenez bay, in Brittany (France).

Published
2010

49. A Priori Error Analysis and Spring Arithmetic

Author

Gilles Chabert, Luc Jaulin, Laboratoire d'Informatique de Nantes Atlantique (LINA), Centre National de la Recherche Scientifique (CNRS)-Mines Nantes (Mines Nantes)-Université de Nantes (UN), Développement des Technologies Nouvelles (DTN), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
AMS 65G40, Applied Mathematics, global optimization, 020207 software engineering, 02 engineering and technology, Function (mathematics), interval arithmetic, Image (mathematics), Interval arithmetic, Computational Mathematics, Nonlinear system, Singularity, Linearization, Error analysis, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Arithmetic, Global optimization, Algorithm, Affine arithmetic, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

WOS; International audience; Error analysis is defined by the following concern: bounding the output variation of a (nonlinear) function with respect to a given variation of the input variables. This paper investigates this issue in the framework of interval analysis. The classical way of analyzing the error is to linearize the function around the point corresponding to the actual input, but this method is local and not reliable. Both drawbacks can be easily circumvented by a combined use of interval arithmetic and domain splitting. However, because of the underlying linearization, a standard interval algorithm leads to a pessimistic bound, and even simply fails (i.e., returns an infinite error) in case of singularity. We propose an original nonlinear approach where intervals are used in a more sophisticated way through the so-called "springs". This new structure allows to represent an (infinite) set of intervals constrained by their midpoints and their radius. The output error is then calculated with a spring arithmetic in the same way as the image of a function is calculated with interval arithmetic. Our method is illustrated on two examples, including an application of geopositioning.

Published
2009
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50. Hull Consistency under Monotonicity

Author

Gilles Chabert, Luc Jaulin, Laboratoire d'Informatique de Nantes Atlantique (LINA), Centre National de la Recherche Scientifique (CNRS)-Mines Nantes (Mines Nantes)-Université de Nantes (UN), Développement des Technologies Nouvelles (DTN), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), and Ian P. Gent

Subjects
Mathematical optimization, 021103 operations research, 0211 other engineering and technologies, ComputerApplications_COMPUTERSINOTHERSYSTEMS, 02 engineering and technology, Interval (mathematics), Computer Science::Computers and Society, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Interval arithmetic, Constraint (information theory), Monotone polygon, Consistency (statistics), 0202 electrical engineering, electronic engineering, information engineering, Constraint programming, 020201 artificial intelligence & image processing, Constraint satisfaction problem, Variable (mathematics), Mathematics
Abstract

International audience; We prove that hull consistency for a system of equations or inequalities can be achieved in polynomial time providing that the underlying functions are monotone with respect to each variable. This result holds including when variables have multiple occurrences in the expressions of the functions, which is usually a pitfall for interval-based contractors. For a given constraint, an optimal contractor can thus be enforced quickly under monotonicity and the practical significance of this theoretical result is illustrated on a simple example.

Published
2009
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