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115 results on '"Luc Jaulin"'

1. Ellipsoidal Enclosure Techniques for a Verified Simulation of Initial Value Problems for Ordinary Differential Equations

Author

Andreas Rauh, Auguste Bourgois, Luc Jaulin, Julia Kersten, 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), Universität Rostock, 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
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], MathematicsofComputing_NUMERICALANALYSIS, 02 engineering and technology, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 020202 computer hardware & architecture, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Verified simulation of initial value problems, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, 0202 electrical engineering, electronic engineering, information engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], Interval analysis, Uncertain systems, Robustness analysis, Ellipsoidal enclosure techniques
Abstract

International audience; The verified simulation of initial value problems (IVPs) for ordinary differential equations (ODEs) with uncertain parameters is an up-to-date research topic and a basic building block for predictor-corrector type state estimators. Such state estimators are based on a two-stage procedure: First, the continuous-time state equations are evaluated up to the discrete time instant at which new measured data become available. Second, the forecasted state enclosures need to be refined by accounting for the information provided by the available sensors. In this paper, we focus on the first stage by presenting a novel ellipsoidal enclosure technique for continuous-time processes. It is based on thick ellipsoids and temporal Taylor series for a verified integration of ODEs that in combination allow for determining inner and outer bounds for the domains of reachable states. Comparisons with other set-valued integration techniques conclude this paper.

Published
2021
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2. 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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3. 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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4. Restricted Orientation Dubins Path With Application to Sailboats

Author

Ulysse Vautier, Christophe Viel, Robert Hone, Jian Wan, Luc Jaulin, Ming Dai, Plymouth University, 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), and Zhejiang University of Science and Technology

Subjects
0209 industrial biotechnology, Turning, Control and Optimization, Computer science, Biomedical Engineering, 02 engineering and technology, Orientation (graph theory), Topology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science::Robotics, 020901 industrial engineering & automation, Artificial Intelligence, Position (vector), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Motion planning, Path planning, Mechanical Engineering, Indexes, Dubins path, Computer Science Applications, Human-Computer Interaction, Planning, Control and Systems Engineering, Face, Face (geometry), Shortest path problem, Robot, Computer Vision and Pattern Recognition, Robots
Abstract

International audience; This paper develops a geometrical construction of a shortest Dubins path in a discontinuous orientation restricted environment. The method proposed here builds the shortest path from one pose to the other while avoiding a no-go zone in terms of orientation, and being constrained to move forward. Finally, an application to autonomous sailboats is then provided to validate the feasibility of the planned shortest path in a position keeping scenario.

Published
2019
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5. 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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6. Platooning Control for Sailboats Using a Tack Strategy

Author

Christophe Viel, Luc Jaulin, Jian Wan, Ulysse Vautier, Plymouth University, Zhejiang University of Science and Technology, 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), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
Platooning, 0209 industrial biotechnology, Quadrilateral, business.industry, Computer science, Control (management), Robotics, 02 engineering and technology, Mechatronics, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science Applications, Task (project management), Acceleration, 020901 industrial engineering & automation, Autonomous sailboat, Control and Systems Engineering, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Path (graph theory), Non-linear control, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], 14. Life underwater, Artificial intelligence, Underwater, business
Abstract

International audience; This paper addresses the problem of platooning control for a fleet of sailboats. A quadrilateral path is proposed to avoid going into the wind. A tack strategy is defined to go front the wind, stay in a short corridor and regulate the sailboat acceleration, which is a challenging task in comparison to autonomous underwater vehicles (AUVs) or surface vehicles that can use motors for such regulation. Desired acceleration which guarantees to reach the platooning has been derived and validated. A method of regulating the sail angle using a proportional command is proposed to control the sailboat acceleration. Simulation results demonstrate the effectiveness of the proposed approach.

Published
2019
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7. Exact bounded-error continuous-time linear state estimator

Author

Simon Rohou, 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), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), and ANR-16-CE33-0024,CONTREDO,Intervalles et contracteurs pour les systèmes dynamiques(2016)

Subjects
0209 industrial biotechnology, General Computer Science, Dynamical systems theory, Mechanical Engineering, 020208 electrical & electronic engineering, 02 engineering and technology, State (functional analysis), Interval (mathematics), Dynamical system, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control and Systems Engineering, Bounded function, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Dynamical systems, 0202 electrical engineering, electronic engineering, information engineering, Trajectory, Applied mathematics, Uncertainty analysis, Electrical and Electronic Engineering, Mathematics
Abstract

International audience; This paper proposes an interval-based method for estimating the state of a linear continuous-time dynamical system. In this work, we assume that the measurements are provided at discrete times and that all errors are bounded. Interval analysis is used to propagate the interval uncertainties continuously over time. The resulting method is guaranteed to never lose any feasible solution and provides an optimal polygonal enclosure of the state trajectory. A reproducible example illustrates the principle of the method.

Published
2021
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8. 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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9. Interval Inspired Approach Based on Temporal Sequence Constraints to Place Recognition

Author

Edson Prestes, Mariana Kolberg, Fernanda Rodrigues, Diego Pittol, Luc Jaulin, Renan Maffei, Renata Neuland, 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), This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and CNPq., 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, Computer science, 02 engineering and technology, Interval (mathematics), Simultaneous localization and mapping, Machine learning, computer.software_genre, Industrial and Manufacturing Engineering, Interval arithmetic, Set (abstract data type), 020901 industrial engineering & automation, Artificial Intelligence, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Electrical and Electronic Engineering, Sequence, business.industry, Mechanical Engineering, Process (computing), Robotics, Agricultural robots, Control and Systems Engineering, Robot, Artificial intelligence, business, computer, Software
Abstract

International audience; Place recognition is an essential task in many robotics applications. Recognizing if the robot is crossing an already visited place may be used to improve its localization and map estimation. A place recognition strategy must be as accurate as possible, despite the challenges related to environment dynamicity. It should avoid generating false positives since even a few erroneous matches may be enough to cause the degradation of the Simultaneous Localization and Mapping (SLAM) process. We propose a novel approach for place recognition inspired by interval analysis theory. Our approach models the known world as a set of intervals based on the robot’s observations. The search to determine whether the current robot location is new or known begins as the robot explores its surroundings. Our approach has three main steps. First, it selects a set of nearest neighbors based on the similarity between the current robot observation and the intervals composing the known world. In the second step, our approach uses temporal constraints to select one element of the set. And finally, the third step is to sweep the selected interval looking for the query best match. We evaluate our proposal by dealing with visual place recognition using only image information and demonstrate its effectiveness using some challenging public datasets.

Published
2021
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10. 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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11. 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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12. 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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13. Non-linear control under state constraints with validated trajectories for a mobile robot towing a trailer

Author

Joris Tillet, Luc Jaulin, Fabrice Le Bars, 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, tank-trailer, Computer science, Lie derivatives, state constraints, Trailer, Mobile robot, 0102 computer and information sciences, 02 engineering and technology, Nonlinear control, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), Nonlinear system, 020901 industrial engineering & automation, 010201 computation theory & mathematics, Control theory, mobile robots, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Robot, Interval analysis, nonlinear control, Towing
Abstract

International audience; In this paper, we propose a set-inversion approach to validate the controller of a nonlinear system that should satisfy some state constraints. We introduce the notion of follow set which corresponds to the set of all output vectors such that the desired dynamics can be followed without violating the state-constraints. This follow set can then be used to choose feasible trajectories that a mobile robot will be able to follow. An illustrative example with a robot towing a trailer is presented. This example is motivated by the safe control of a boat towing a marine magnetique sensor to find wrecks.

Published
2020
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14. 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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15. 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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16. 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

17. 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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18. Proving the existence of loops in robot trajectories

Author

Luc Jaulin, Clement Aubry, Simon Rohou, and Peter Franek

Subjects
Computational Geometry (cs.CG), FOS: Computer and information sciences, 0209 industrial biotechnology, Loop (graph theory), G.1.5, Computer science, Context (language use), 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Field (computer science), Interval arithmetic, Computer Science::Robotics, Computer Science - Robotics, 020901 industrial engineering & automation, Artificial Intelligence, 0101 mathematics, Electrical and Electronic Engineering, I.2.9, Applied Mathematics, Mechanical Engineering, Modeling and Simulation, Key (cryptography), Trajectory, Computer Science - Computational Geometry, Differential topology, Robot, Robotics (cs.RO), Algorithm, Software
Abstract

In this paper we present a reliable method to verify the existence of loops along the uncertain trajectory of a robot, based on proprioceptive measurements only, within a bounded-error context. The loop closure detection is one of the key points in simultaneous localization and mapping (SLAM) methods, especially in homogeneous environments with difficult scenes recognitions. The proposed approach is generic and could be coupled with conventional SLAM algorithms to reliably reduce their computing burden, thus improving the localization and mapping processes in the most challenging environments such as unexplored underwater extents. To prove that a robot performed a loop whatever the uncertainties in its evolution, we employ the notion of topological degree that originates in the field of differential topology. We show that a verification tool based on the topological degree is an optimal method for proving robot loops. This is demonstrated both on datasets from real missions involving autonomous underwater vehicles and by a mathematical discussion.

Published
2018
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19. Méthode fiable d’estimation d'état non-linéaire impliquant des incertitudes temporelles

Author

Lyudmila Mihaylova, Sandor M. Veres, Luc Jaulin, Fabrice Le Bars, 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), and University of Sheffield [Sheffield]

Subjects
tubes, 0209 industrial biotechnology, Computer science, Computation, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], contractors, Set (abstract data type), 020901 industrial engineering & automation, Bounding overwatch, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], state estimation, Electrical and Electronic Engineering, robotics, non-linear systems, Mobile robot, Nonlinear system, 010201 computation theory & mathematics, Control and Systems Engineering, Bounded function, Trajectory, Local consistency, time uncertainties, constraints, Algorithm, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

This paper presents a new approach to bounded-error state estimation involving time uncertainties. For a given bounded\ud observation of a continuous-time non-linear system, it is assumed that neither the values of the observed data nor their\ud acquisition instants are known exactly. For systems described by state-space equations, we prove theoretically and demonstrate\ud by simulations that the proposed constraint propagation approach enables the computation of bounding sets for the systems’\ud state vectors that are consistent with the uncertain measurements. The bounding property of the method is guaranteed even\ud if the system is strongly non-linear. Compared with other existing constraint propagation approaches, the originality of the\ud method stems from our definition and use of bounding tubes which enable to enclose the set of all feasible trajectories inside\ud sets. This method makes it possible to build specific operators for the propagation of time uncertainties through the whole\ud trajectory. The efficiency of the approach is illustrated on two examples: the dynamic localization of a mobile robot and the\ud correction of a drifting clock.

Published
2018
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20. 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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21. Chain of Set Inversion Problems Application to reachability analysis

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), Pôle STIC_OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), 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
Large class, Discrete mathematics, 0209 industrial biotechnology, State system, Set inversion, Solution set, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Chain (algebraic topology), Control and Systems Engineering, Reachability, 0101 mathematics, Mathematics
Abstract

International audience; This paper deals with the set inversion problem X = f −1 (Y) in the case where f : R n → R m depends on a parameter vector p ∈ R q which is known to be inside a box [p]. We show that for a large class of problems, we can obtain an accurate approximation of the solution set, without bisecting in the p-space. To do this, symbolic methods are required to cast our initial problem into a chain of set-inversion problems, the links of which have some nice properties with respect to p. As an application, we consider the problem of computing the set of all initial states of an uncertain discrete-time state system that reach a target set Y in a given time.

Published
2017
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22. 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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23. 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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24. Thick Separators

Author

Luc Jaulin, Benoit Desrochers, Martine Ceberio, Vladik Kreinovich, 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, DGA Techniques navales, and Janusz Kacprzyk

Subjects
0209 industrial biotechnology, 020901 industrial engineering & automation, 010103 numerical & computational mathematics, 02 engineering and technology, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO], 0101 mathematics, 01 natural sciences
Abstract

International audience; If an interval of R is an uncertain real number, a thick set is an uncertain subset of Rn. More precisely, a thick set is an interval of the powerset of Rn equipped with the inclusion ⊂ as an order relation. It can generally be defined by parameters or functions which are not known exactly, but are known to belong to some intervals. In this paper, we show how to use constraint propagation methods in order to compute efficiently an inner and an outer approximations of a thick set. The resulting inner/outer contraction are made using an operator which is called a thick separator. Then, we show how thick separators can be combined in order to compute with thick sets.

Published
2020
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25. 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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26. Design and control of a low-cost autonomous profiling float

Author

Luc Jaulin, Gilles Le Maillot, Thierry Ropert, Aurélien Ponte, 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), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Laboratoire d'Océanographie Physique et Spatiale (LOPS), Institut de Recherche pour le Développement (IRD)-Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), Institut Français de Recherche pour l'Exploitation de la Mer - Brest (IFREMER Centre de Bretagne), Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER), 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), Institut de Recherche pour le Développement (IRD)-Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), 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, low-cost design, Float (project management), 010504 meteorology & atmospheric sciences, Computer science, Control (management), 02 engineering and technology, 01 natural sciences, Industrial and Manufacturing Engineering, Low-cost design, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Extended Kalman filter, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Control theory, depth control, Depth control, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], General Materials Science, Loop design, state feedback, 0105 earth and related environmental sciences, Profiling (computer programming), Mechanical Engineering, Float, Extended Kalman Filter, Key (cryptography), State (computer science), State feedback
Abstract

This paper presents the development made around the SeaBot, a new low-cost profiling float design for shallow water. We introduce a simplified dynamical model of the float and propose a state feedback depth controller coupled with an Extended Kalman Filter (EKF) to estimate model parameters. We show experimental results of the depth control that validate the model and the controller. We finally propose a loop design method to build low-cost floats by highlighting key design choices along with design rules.

Published
2019
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27. 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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28. Estimating the Trajectory of Low-Cost Autonomous Robots Using Interval Analysis: Application to the euRathlon Competition

Author

Elba Antonio, Luc Jaulin, Carlos H. de la Cruz, Fabrice Le Bars, Jorge Cervantes, 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 Franco-Mexicain d'Informatique et d'Automatique (LAFMIA), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV)-Université de Technologie de Compiègne (UTC)-Consejo Nacional de Ciencia y Tecnología [Mexico] (CONACYT)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and Luc Jaulin

Subjects
0209 industrial biotechnology, SIMPLE (military communications protocol), Computer science, business.industry, Ranging, Robotics, Control engineering, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Competition (economics), [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, 010201 computation theory & mathematics, Trajectory, Robot, Artificial intelligence, business, Envelope (motion)
Abstract

International audience; In this paper, we describe a method based on interval arithmetic and contractors to compute an envelope containing the trajectory of a robot from usual proprioceptive and exteroceptive data, using a simple state equation model. To illustrate the applicability of the method, data from the euRathlon 2015, a multi-domain robotics competition, will be processed to build an estimation of the trajectory of a low-cost AUV (Autonomous Underwater Vehicle), navigating with the help of acoustic communication and ranging with an ASV (Autonomous Surface Vehicle).

Published
2018
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29. Secure a Zone from Intruders with a Group Robots

Author

Luc Jaulin, Benoit Zerr, Khadimoullah Vencatasamy, 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), Luc Jaulin, 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, Group (mathematics), Computer science, Real-time computing, Submarine, 02 engineering and technology, 01 natural sciences, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, 0103 physical sciences, Robot, Underwater, 010301 acoustics
Abstract

International audience; The paper proposes new method to secure a zone of the world from intruders using a group a robots. The principle is to control the group in order to form a chain through which no intruder can go without being detected. We use a set membership method based on interval analysis and mathematical morphology to guarantee that no intruder is inside the secure zone. The approach is illustrated by an example where the environment is the Bay of Biscay, the intruder is a submarine and the group of robots consists of small underwater autonomous vehicles.

Published
2018
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30. 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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31. Comparison of Kalman and Interval Approaches for the Simultaneous Localization and Mapping of an Underwater Vehicle

Author

Jeremy Nicola, Luc Jaulin, iXBLUE (Entreprise), 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), Luc Jaulin, 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, 02 engineering and technology, Kalman filter, Interval (mathematics), Simultaneous localization and mapping, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Domain (software engineering), Beacon, Set (abstract data type), [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, 0103 physical sciences, Outlier, State observer, 010301 acoustics, Algorithm
Abstract

International audience; In this paper we compare the use of a Kalman filter and a Robust State Observer for the localization and mapping of an underwater vehicle using range-only measurements between the vehicle and a set of beacons lying on the seafloor. As expected, we show that the Kalman filter performs great when we have a reasonably good prior information on the location of the vehicle and the beacons. Based on set-membership methods, the Robust State Observer demonstrates an outstanding capacity to provide consistent estimates (where the true solution is in the estimated confidence domain) in the presence of outliers at the cost of a very coarse precision. The source of this lack of precision will be discussed.

Published
2017
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32. 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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33. Position keeping control of an autonomous sailboat

Author

Ulysse Vautier, Jian Wan, Christophe Viel, 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), 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, 010505 oceanography, Computer science, Control (management), 02 engineering and technology, Nonlinear control, 01 natural sciences, Stability (probability), autonomous sailboat, Acceleration, 020901 industrial engineering & automation, non-linear control, Control and Systems Engineering, Position (vector), Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Position keeping, Point (geometry), Tacking, 0105 earth and related environmental sciences
Abstract

International audience; This paper addresses the problem of reaching and keeping a target position for a sailboat. A method to control sail angle is proposed, using an adaptive adjustment of the sail to regulate the acceleration of the sailboat. A tacking strategy is defined to navigate into the wind, arrive upwind to slow down the boat and then to stay close to the target point. Simulation results show the effectiveness of the proposed approach. The stability of the sailboat using the proposed control has been proven.

Published
2018
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34. Validated Enclosure of Uncertain Nonlinear Equations Using SIVIA Monte Carlo

Author

Nisha Rani Mahato, Snehashish Chakraverty, Jean Dezert, Luc Jaulin, National Institute of Technology Rourkela, 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), DTIS, ONERA, Université Paris Saclay (COmUE) [Palaiseau], and ONERA-Université Paris Saclay (COmUE)

Subjects
Van der Pol oscillator, Dynamical systems theory, Set inversion, Differential equation, Monte Carlo method, 020206 networking & telecommunications, 02 engineering and technology, Interval (mathematics), SIVIA Monte Carlo, Nonlinear oscillator, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear system, [SPI]Engineering Sciences [physics], 020303 mechanical engineering & transports, Uncertain nonlinear equations, 0203 mechanical engineering, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Dependency problem, Contractor, Mathematics
Abstract

International audience; The dynamical systems in various science and engineering problems are often governed by nonlinear equations (differential equations). Due to insufficiency and incompleteness of system information, the parameters in such equations may have uncertainty. Interval analysis serves as an efficient tool for handling uncertainties in terms of closed intervals. One of the major problems with interval analysis is handling “dependency problems” for computation of the tightest range of solution enclosure or exact enclosure. Such dependency problems are often observed while dealing with complex nonlinear equations. In this regard, initially, two test problems comprising interval nonlinear equations are considered. The Set Inversion via Interval Analysis (SIVIA) along with the Monte Carlo approach is used to compute the exact enclosure of the test problems. Further, the efficiency of the proposed approach has also been verified for solving nonlinear differential equation (Van der Pol oscillator) subject to interval initial conditions.

Published
2018
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35. 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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36. 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

37. 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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38. Robust set-membership parameter estimation of the glucose minimal model

Author

Pau Herrero, Christofer Toumazou, Benoît Delaunay, Nick Oliver, Luc Jaulin, and Pantelis Georgiou

Subjects
0209 industrial biotechnology, Computational complexity theory, Set inversion, Estimation theory, Computer science, 030209 endocrinology & metabolism, 02 engineering and technology, Fault detection and isolation, Interval arithmetic, Minimal model, Set (abstract data type), 03 medical and health sciences, 020901 industrial engineering & automation, 0302 clinical medicine, Control and Systems Engineering, Robustness (computer science), Signal Processing, Electrical and Electronic Engineering, Algorithm
Abstract

The minimal model of glucose-insulin dynamics is currently being used in several diabetes-related applications, such as investigating the glucose metabolism, and in the developments of model predictive controllers and fault detection techniques for automatic blood glucose control i.e., artificial pancreas. Different approaches have been proposed to identify this model, but none of them is capable of providing guaranteed robust enclosures for its parameters, something very desired in applications such as the artificial pancreas, where robustness is paramount. This paper presents a novel approach for guaranteed set-membership parameter estimation of the minimal model based on the well-renowned Set Inversion via Interval Analysis SIVIA algorithm. Because the computational complexity of this algorithm is the main barrier for its applicability, an efficient vectorial implementation of SIVIA was employed. Clinical data from a standard intravenous glucose tolerance test were used to prove the validity of the presented approach. Finally, Modal Interval Analysis was used to reduce the numerical overestimation due to the dependency problem of interval arithmetic and significantly speeding up the computations. Copyright © 2015 John Wiley & Sons, Ltd.

Published
2015
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39. 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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40. 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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41. 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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42. 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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43. An Interval Approach for Stability Analysis: Application to Sailboat Robotics

Author

Luc Jaulin, F. Le Bars, 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
0209 industrial biotechnology, Engineering, Stability (learning theory), 02 engineering and technology, Interval (mathematics), 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 010305 fluids & plasmas, Interval arithmetic, 020901 industrial engineering & automation, 0103 physical sciences, State space, Motion planning, sailboat, Electrical and Electronic Engineering, robotics, business.industry, viability, Robotics, Control engineering, Mobile robot, stability, line following, Computer Science Applications, Control and Systems Engineering, Robot, differential inclusion, Artificial intelligence, interval analysis, business
Abstract

wos; International audience; Abstract--This paper proposes an interval based method for the validation of reliable and robust navigation rules for mobile robots. The main idea is to show that for all feasible perturbations, there exists a safe subset of the state space such that the system cannot escape. The methodology is illustrated on the line following problem of a sailboat and then validated on an actual experiment where an actual sailboat robot, named Vaimos, sails autonomously from Brest to Douarnenez (more than 100 km).

Published
2013
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44. Guaranteed Characterization of the Explored Space of a Mobile Robot by using Subpavings

Author

Vincent Drevelle, Benoit Zerr, Luc Jaulin, Billon-Coat, Annick, 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, Computer science, Mobile robot, 02 engineering and technology, Space (commercial competition), exploration, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, mobile robots, 0103 physical sciences, Trajectory, mapping, Underwater, interval analysis, uncertainty, sets, 010301 acoustics
Abstract

International audience; This paper proposes a method to characterize the space explored by a mobile robot during a mission. Because of localization uncertainty, the area osculated by a sensor at a given time is uncertain too. The problem is modeled by using intervals to represent trajectory uncertainties and a "visibility function" to describe the area in view at a given time. A set-inversion method is then applied to compute a "guaranteed visible area" and a "possible visible area" with respect to positioning uncertainty. A bracketing of the actual explored area between a "guaranteed explored area" and a "possible explored area" for the whole mission is finally obtained by respectively taking the union of the guaranteed and possible areas. Results from a simulated underwater exploration mission are presented

Published
2013
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45. Interval Robust Multi-objective Algorithm

Author

Roberta Parreiras, Carlos Andrey Maia, Luc Jaulin, João A. Vasconcelos, Gustavo Luís Soares, Développement des Technologies Nouvelles (DTN), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)

Subjects
Continuous optimization, 0209 industrial biotechnology, Mathematical optimization, Robust Pareto frontier, 021103 operations research, Optimization problem, Robust Multi-objective optimization, Applied Mathematics, Probabilistic-based design optimization, Interval Analysis Genetic algorithm, 0211 other engineering and technologies, Robust optimization, 02 engineering and technology, Multi-objective optimization, Stochastic programming, Vector optimization, 020901 industrial engineering & automation, Test functions for optimization, Algorithm, Analysis, Mathematics
Abstract

WOS; International audience; This paper introduces a method for solving multi-objective optimization problems in uncertain environment. When the uncertainty factors of the optimization problem can be included into the mathematical model, through bounded intervals, [I]RMOA (Interval Robust Multi-objective Algorithm) can find an enclosure of the robust Pareto frontier. In this approach, the robust Pareto solutions are the ones that have the best performance when the worst case scenario, characterized by the uncertainty parameters, is considered. [I]RMOA has some positive aspects: it does not require the calculus of derivatives; it has only two input parameters; it is a reliable tool for solving different robust optimization problems, which can be nonlinear and discontinuous or have nonconvex Pareto frontier, for instance. The success of the method depends only on the quality of the objective inclusion functions and the precision parameters. Its disadvantage lies in the fact that it requires high computational effort, when high-dimensional problems are considered or when a very accurate enclosure is needed. Two analytical robust test functions are proposed to be treated by [I]RMOA and to validate the results provided by a stochastic multi-objective optimization method. The results are satisfactory.

Published
2009
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46. 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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47. 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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48. An Interval-Based Target Tracking Approach for Range-Only Multistatic Radar

Author

João A. Vasconcelos, Andreas Arnold-Bos, Carlos Andrey Maia, Luc Jaulin, and Gustavo Luís Soares

Subjects
0209 industrial biotechnology, Computer science, ComputerApplications_COMPUTERSINOTHERSYSTEMS, Fire-control radar, 02 engineering and technology, law.invention, 020901 industrial engineering & automation, law, Radar imaging, 0202 electrical engineering, electronic engineering, information engineering, Computer vision, Electrical and Electronic Engineering, Radar, Remote sensing, Low probability of intercept radar, Radar tracker, business.industry, 020206 networking & telecommunications, Radar lock-on, Electronic, Optical and Magnetic Materials, Man-portable radar, Bistatic radar, Multistatic radar, Artificial intelligence, Particle filter, business
Abstract

This paper investigates the use of interval analysis to solve the problem of maneuvering target tracking, using range-only measures collected by a multistatic radar. The problem consists in one transmitter, and some receivers working together as a multistatic radar. The radar process is plagued by several uncertainty sources that affect directly the receivers' measures. As a result, target tracking can be both imprecise and unreliable. This study presents the tracking using an interval-based approach that computes the set of all feasible configurations for the target which are consistent with the measures. The algorithm is compared to a conventional tracking method: particle filtering.

Published
2008
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49. An interval approach to solve an initial value problem

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), 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), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), 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), 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, Discretization, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], MathematicsofComputing_NUMERICALANALYSIS, Mathematics::Analysis of PDEs, Ode, 0102 computer and information sciences, 02 engineering and technology, Interval (mathematics), 16. Peace & justice, 01 natural sciences, 020901 industrial engineering & automation, Initial value problems, 010201 computation theory & mathematics, Ordinary differential equation, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, State space, Initial value problem, Vector field, Set theory, Vector fields, Ordinary differential equations, Mathematics
Abstract

International audience; This paper proposes an original guaranteed interval-based method to solve an Initial Value Problem (IVP) for ordinary differential equations (ODE). Our method uses the geometrical properties of the vector field given by the ODE and a state space discretization to compute an enclosure of the trajectories set that verifies the IVP problem.

Published
2016
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50. Quantitative Monitoring of the Underwater Environment

Author

Nathalie Debese, Luc Jaulin, Vincent Creuze, Benoit Zerr, Isabelle Quidu, and Benoit Clement

Subjects
0211 other engineering and technologies, Environmental science, 020101 civil engineering, 02 engineering and technology, Underwater, 021101 geological & geomatics engineering, 0201 civil engineering, Marine engineering
Published
2016
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