Author: "Luc Jaulin" / Topic: computer science - Searchworks@Jio Institute Digital Library Search Results

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1. Interval centred form for proving stability of non-linear discrete-time systems

Author: Auguste Bourgois and Luc Jaulin
Subjects: Discrete system, Nonlinear system, Exponential stability, Discrete time and continuous time, Computer science, FOS: Electrical engineering, electronic engineering, information engineering, Stability (learning theory), Trajectory, Applied mathematics, Context (language use), Systems and Control (eess.SY), Interval (mathematics), Electrical Engineering and Systems Science - Systems and Control
Abstract: In this paper, we propose a new approach to prove stability of non-linear discrete-time systems. After introducing the new concept of stability contractor, we show that the interval centred form plays a fundamental role in this context and makes it possible to easily prove asymptotic stability of a discrete system. Then, we illustrate the principle of our approach through theoretical examples. Finally, we provide two practical examples using our method : proving stability of a localisation system and that of the trajectory of a robot., Comment: In Proceedings SNR 2020, arXiv:2101.05256
Published: 2021
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2. A Novel Thick Ellipsoid Approach for Verified Outer and Inner State Enclosures of Discrete-Time Dynamic Systems

Author: Andreas Rauh and Luc Jaulin
Subjects: Range (mathematics), Nonlinear system, Discrete time and continuous time, Control and Systems Engineering, Control theory, Computer science, Bounded function, Probabilistic logic, Representation (mathematics), Ellipsoid, Interval arithmetic
Abstract: Simulating dynamic systems with bounded uncertainty in initial conditions and selected parameters is a common task for the reliability analysis of closed-loop control structures as well as for a simulation-based parameter identification on the basis of uncertain measurements. However, dealing with bounded uncertainty is not a trivial task. On the one hand, the naive application of interval analysis often leads to excessively large bounds which may yield state enclosures that are by far too pessimistic to be useful in practice. On the other hand, the use of grid-based or probabilistic and Monte-Carlo like simulation approaches suffers from the disadvantage that they do not provide a guarantee of the correctness of the obtained solutions. Using insufficiently many or badly chosen samples may lead to the phenomenon that critical system states are not detected so that the computed results underestimate the range of reachable states. Therefore, a novel ellipsoidal state enclosure technique is presented which does not require the online solution of linear matrix inequalities (LMIs). It uses the newly introduced representation of state domains by means of thick ellipsoids. These domains simultaneously represent inner and outer enclosures of the reachable states and directly provide a measure for the tightness of the obtained results, regardless of whether the system is linear or nonlinear or whether it is stable or not.
Published: 2021
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3. Platooning Control for Heterogeneous Sailboats Based on Constant Time Headway

Author: Christophe Viel, Ulysse Vautier, Jian Wan, Luc Jaulin, 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), and Institut Mines-Télécom [Paris] (IMT)
Subjects: Platooning, 050210 logistics & transportation, Computer science, Mechanical Engineering, 05 social sciences, Control (management), Heterogeneous fleet, Wind direction, Nonlinear control, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science Applications, Vehicle dynamics, Acceleration, Control theory, 0502 economics and business, Automotive Engineering, Path (graph theory), Non-linear control, Trajectory, Autonomous sailboats, Constant (mathematics)
Abstract: International audience; This paper addresses the problem of platooning control for a fleet of heterogeneous sailboats. The platooning maintains a constant time headway (CTH) between sailboats following a circular path, a complex problem for sailboats due to the influence of wind direction. First, the desired acceleration based on the CTH and the sailboat velocity needed to converge to the platooning is defined. Second, a control of sailboat orientation to manage the sailboat acceleration is proposed. The proposed platooning strategy adapts to the specific characteristics of sailboats, which are different from other motorized marine vehicles. Two tack strategies can be used for the method: the first is to regulate the sailboat velocity; the second is to go front of the wind while staying in a short corridor. The desired acceleration for fulfilling the platooning has been derived and validated. The simulation results demonstrate the effectiveness of the proposed approach in comparison with an optimal receding horizon control algorithm.
Published: 2020
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4. 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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5. 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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6. 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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7. 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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8. 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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9. 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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10. 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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11. 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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12. 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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13. 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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14. 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

15. 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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16. 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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17. 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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18. 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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19. 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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20. 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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21. 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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22. 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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23. 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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24. 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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25. 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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26. 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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27. 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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28. 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

29. Marine Robotics and Applications

Author: Benoit Zerr, Marc Carreras, Andrea Caiti, Vincent Creuze, Luc Jaulin, Frédéric Plumet, Annick Billon-Coat, 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), University of Pisa - Università di Pisa, Universitat de Girona (UdG), Image & Interaction (ICAR), 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), Institut des Systèmes Intelligents et de Robotique (ISIR), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Systèmes robotiques Conception et Commande (SYROCO), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), and Springer International Publishing
Subjects: Computer science, business.industry, Marine robotics, Robotics, Propulsion, Sonar, Adaptive sampling, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Underwater environments, Systems engineering, 14. Life underwater, Artificial intelligence, Underwater, business, Collective exploration, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract: OUV; International audience; This book reports on findings at the intersection between two related fields, namely coastal hydrography and marine robotics. On one side, it shows how the exploration of the ocean can be performed by autonomous underwater vehicles; on the other side, it shows how some methods from hydrography can be implemented in the localization and navigation of such vehicles, e.g. for target identification or path finding. Partially based on contributions presented at the conference Quantitative Monitoring of Underwater Environment, MOQESM, held on October 11-12, 2016, Brest, France, this book includes carefully revised and extended chapters presented at the conference, together with original papers not related to the event. All in all, it provides readers with a snapshot of current methods for sonar track registration, multi-vehicles control, collective exploration of underwater environments, optimization of propulsion systems, among others. More than that, the book is aimed as source of inspiration and tool to promote further discussions and collaboration between hydrographers, robotic specialists and other related communities.
Published: 2018
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30. 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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31. 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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32. 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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33. 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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34. Robust Data Processing in the Presence of Uncertainty and Outliers: Case of Localization Problems

Author: Luc Jaulin, Martine Ceberio, Vladik Kreinovich, Anthony Welte, Laboratoire Chrono-environnement ( LCE ), Université Bourgogne Franche-Comté ( UBFC ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Franche-Comté ( UFC ), 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 ( UEB ) -ENSTA Bretagne-Institut Mines-Télécom [Paris]-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 ( UEB ) -ENSTA Bretagne-Institut Mines-Télécom [Paris]-Centre National de la Recherche Scientifique ( CNRS ), Pôle STIC_OSM, ENSTA Bretagne, University of Texas at El Paso - UTEP (USA), 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), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Lab-STICC_ENSTAB_CID_PRASYS, 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), University of Texas [El Paso] (UTEP ), 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: Data processing, Observational error, 010504 meteorology & atmospheric sciences, Computer science, Robust statistics, 010103 numerical & computational mathematics, computer.software_genre, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Interval analysis method, [ SPI.AUTO ] Engineering Sciences [physics]/Automatic, Outlier, Measurement uncertainty, Probability distribution, Entropy (information theory), Data mining, 0101 mathematics, Heuristics, computer, 0105 earth and related environmental sciences
Abstract: International audience; To properly process data, we need to take intoaccount both the measurement errors and the fact that someof the observations may be outliers. This is especially importantin radar-based localization problems, where some signals mayreflect not from the analyzed object, but from some nearby object.There are known methods for dealing with both measurementerrors and outliers in situations in which we have full informationabout the corresponding probability distributions. There are alsoknown statistics-based methods for dealing with measurementerrors in situations when we only have partial informationabout the corresponding probabilities. In this paper, we showhow these methods can be extended to situations in which wealso have partial inf0ormation about the outliers (and even tosituations when we have no information about the outliers). Insome situations in which efficient semi-heuristic methods areknown, our methodology leads to a justification of these efficientheuristics – which makes us confident that our new methods willbe efficient in other situations as well.
Published: 2016

35. 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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36. 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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37. Obstacle Avoidance for an Autonomous Marine Robot—A Vector Field Approach

Author: Silke Schmitt, Fabrice Le Bars, Thomas Latzel, and Luc Jaulin
Subjects: Control algorithm, Automatic Identification System, law, Computer science, Simple (abstract algebra), Control theory, Obstacle avoidance, Robot, Vector field, GeneralLiterature_MISCELLANEOUS, Control methods, Euclidean vector, law.invention
Abstract: A marine robot, especially a sailing boat robot, is exposed to a dynamic environment. This paper presents a simple and efficient obstacle avoidance control algorithm. The presented control method uses vector fields to regulate the marine robot.
Published: 2016
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38. Computing Capture Tubes

Author: Vincent Doze, Gilles Chabert, Luc Jaulin, Jordan Ninin, Mohamed Saad Ibnseddik, Daniel Lopez, Alexandru Stancu, Stéphane Le Ménec, 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, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Lab-STICC_ENSTAB_CID_PRASYS, 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), University Of Manchester Institute (UMIST/Department of Process Integration), University of Manchester [Manchester], MBDA France (MBDA), MBDA France, IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), 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: Nonholonomic system, business.industry, Differential equation, Computer science, Mobile robot, Robotics, Capture tube Contractors Interval arithmetic Robotics Stability, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science::Robotics, Control theory, Trajectory, Robot, Initial value problem, Artificial intelligence, [MATH]Mathematics [math], Differential (infinitesimal), business
Abstract: International audience; Many mobile robots such as wheeled robots, boats, or plane are described by nonholonomic differential equations. As a consequence, they have to satisfy some differential constraints such as having a radius of curvature for their trajectory lower than a known value. For this type of robots, it is difficult to prove some properties such as the avoidance of collisions with some moving obstacles. This is even more difficult when the initial condition is not known exactly or when some uncertainties occur. This paper proposes a method to compute an enclosure (a tube) for the trajectory of the robot in situations where a guaranteed interval integration cannot provide any acceptable enclosures. All properties that are satisfied by the tube (such as the non-collision) will also be satisfied by the actual trajectory of the robot.
Published: 2016
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39. Set-Membership Approach to the Kidnapped Robot Problem

Author: Benoit Desrochers, Simon Lacroix, Luc Jaulin, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Lab-STICC_ENSTAB_CID_IHSEV, OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Équipe Robotique et InteractionS (LAAS-RIS), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Pôle STIC [Brest] (STIC), Pole STIC, ENSTA Bretagne, Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique)
Subjects: 0209 industrial biotechnology, Matching (graph theory), Computer science, business.industry, Raised-relief map, 02 engineering and technology, Interval (mathematics), Kidnapped robot problem, GeneralLiterature_MISCELLANEOUS, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), 020901 industrial engineering & automation, Robustness (computer science), Outlier, 0202 electrical engineering, electronic engineering, information engineering, Robot, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], 020201 artificial intelligence & image processing, Computer vision, Algorithm design, Artificial intelligence, business, Lidar data, Interval Analysis
Abstract: International audience; This article depicts an algorithm which matches the output of a Lidar with an initial terrain model to estimate the absolute pose of a robot. Initial models do not perfectly fit the reality and the acquired data set can contain an unknown, and potentially large, proportion of outliers. We present an interval based algorithm that copes with such conditions, by matching the Lidar data with the terrain model in a robust manner. Experimental validations using different terrain model are reported to illustrate the performance of the method.
Published: 2015

40. Rigid Transformation Using Interval Analysis for Robot Motion Estimation

Author: Salvador Pacheco Guteirrez, Mohamed Mustafa, Alexandru Stancu, Eduard Codres, and Luc Jaulin
Subjects: Computer science, business.industry, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Frame of reference, Interval arithmetic, Motion estimation, Robot, Measurement uncertainty, Computer vision, Artificial intelligence, Image sensor, business, Rigid transformation, Stereo camera
Abstract: Rigid transformation is a popular method to estimate the robot motion given two sets of corresponding points seen from two different locations. Range imaging sensors, such as stereo camera and structured-light 3-D scanner, can be used to provide these corresponding points, however, such sensors have measurement uncertainty defined by intervals with upper and lower bounds. This paper presents a new approach to use interval analysis and simultaneously estimate the following: (1) the robot motion and, (2) the position of the landmarks with respect to the initial frame of reference, i.e. The robot initial pose. We will show that using this approach, the uncertainties of the landmark positions decrease over time, which causes the uncertainty of the robot pose to remain bounded. Our approach is illustrated with examples using simulated data, and real data acquired by Kinect sensor.
Published: 2015
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41. Instantaneous Localization

Author: Luc Jaulin
Subjects: Computer science, Orientation (computer vision), business.industry, Degrees of freedom, Kinematics, Multilateration, Inscribed angle, Computer Science::Robotics, Position (vector), Compass, Robot, Computer vision, Artificial intelligence, business
Abstract: Localization consists of finding the position of the robot (in other words, the coordinates of its center as well as its orientation), or more generally all its degrees of freedom. This problem is encountered in navigation, where we need to approximate the position, orientation and speed of the robot. The problem of localization is often considered to be a particular case of state estimation, which will be presented in the following chapters. However, in the case where an accurate state model is not available for our robot, an instantaneous localization often remains possible and may be sufficient for making a decision. Let us take, for instance, the situation in which we are aboard a ship and have just detected a lighthouse whose absolute position and height are known. By measuring the perceived height of the lighthouse and its angle relative to the ship, we may deduce the position of the ship using a compass, without using a state model for the ship. Instantaneous, or model-free localization, is an approach to localization that does not utilize the evolution equation of the robot, in other words it does not seek to make the measures coherent through time. This localization mainly consists of solving equations of geometric nature which are often nonlinear. The variables involved may be position variables or kinematic variables such as speed and accelerations. Since these localization methods are specific and quite far from state estimation methods, we will devote an entire chapter to them. After introducing the main sensors used for localization, we will present goniometric localization (in which the robot uses the angles of perception of landmarks) followed by multilateration which uses distances between the robot and landmarks.
Published: 2015
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42. Towing with sailboat robots

Author: Fabrice Le Bars, 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), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), and NUI Galway
Subjects: 0209 industrial biotechnology, 010505 oceanography, Computer science, Proportional control, 02 engineering and technology, Object (computer science), 01 natural sciences, Square (algebra), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Arbitrarily large, sailboat robot, 020901 industrial engineering & automation, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Trajectory, Robot, controller, Towing, Energy (signal processing), 0105 earth and related environmental sciences, Marine engineering
Abstract: International audience; Moving huge objects floating at the surface of the ocean (such as containersor icebergs) with boats requires many human operators and a lot of energy.This is mainly due to the fact that when humans operate such equipment, time iscostly. Now, when we have time (as when robots operate, for instance), it is possibleto move arbitrarily large objects, for over long distances, with a limited quantity ofenergy. This is a consequence of the fact that in the water, the friction forces areproportional to the square of the speed (i.e., when we go slowly, we have almostno friction). This paper proposes the use of a sailboat robot to tow large objects. Itshows which control law could be used is order to (i) avoid loops inside the towingcable, (ii) avoid collisions between the robot and the towed object, and (iii) movethe object toward the desired direction. The control law is validated on a simulationwhere the object to be towed has to follow a trajectory corresponding to a largecircle.
Published: 2015

43. Kalman Filter

Author: Luc Jaulin
Subjects: business.industry, Computer science, State vector, Robotics, Context (language use), Kalman filter, Computer Science::Robotics, Nonlinear system, Position (vector), Control theory, Linearization, Robot, Artificial intelligence, business
Abstract: In Chapters 2 and 3 we have looked at tools for controlling robots in a nonlinear manner. For this purpose, we have assumed that the state vector was completely known. However, this is not the case in practice. This vector must be estimated from sensor measurements. In the case where the only unknown variables are associated with the position of the robot, Chapter 5 gives guidelines to find them. In the more general case, filtering or state observation seeks to reconstruct this state vector as well as possible from all the data measured on the robot throughout time by taking into account the state equations. The aim of this chapter is to show how such reconstruction is performed, within a stochastic context in which the system to observe is assumed to be linear. This is the purpose of the Kalman filter [KAL 60], which will be discussed in this chapter. The Kalman filter is used in numerous mobile robotics applications, even though the robots in question are strongly nonlinear. For such applications, the initial conditions are assumed to be relatively well known in order to allow a reliable linearization.
Published: 2015
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44. Feedback Linearization

Author: Luc Jaulin
Subjects: Range (mathematics), Nonlinear system, Finite-state machine, Control theory, Computer science, State space, State vector, Robot, Workspace, Feedback linearization
Abstract: Due to their multiple rotation capabilities, robots are considered to be strongly nonlinear systems. In this chapter, we will look at designing nonlinear controllers in order to constrain the state vector of the robot to follow a fixed forward path or to remain within a determined area of its workspace. In contrast to the linear approach, which offers a general methodology but is limited to the neighborhood of a point of the state space, nonlinear approaches only apply to limited classes of systems, but they allow us to extend the effective operating range of the system. Indeed, there is no general method of globally stabilizing nonlinear systems. However, there is a multitude of methods that apply to particular cases. The aim of this chapter is to present one of the more representative theoretical methods (whereas in the following chapter, we will be looking at more pragmatic approaches). This method is called feedback linearization and it requires knowledge of an accurate and reliable state machine for our robot. The robots considered here are mechanical systems whose modeling can be found in. We will assume in this chapter that the state vector is entirely known. In practice, it has to be approximated from sensor measurements. We will see in Chapter 7 how such an approximation is performed.
Published: 2015
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45. Introduction to the Algebra of Separators with Application to Path Planning

Author: Benoit Desrochers, 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), 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 Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Pôle STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), and Billon-Coat, Annick
Subjects: Mathematical optimization, Computer science, set characterization, Solution set, Separator (oil production), Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Algebra, Nonlinear system, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Artificial Intelligence, Control and Systems Engineering, separators, Motion planning, Contractors, Electrical and Electronic Engineering, Robust control, interval analysis, path planning
Abstract: International audience; Contractor algebra is a numerical tool based on interval analysis which makes it possible to solve many nonlinear problems arising in robotics, such as identification, path planning or robust control. This paper presents the new notion of separators which is a pair of complementary contractors and presents the corresponding algebra. Using the separator algebra inside a paver will allow us to get an inner and an outer approximation of the solution set in a much simpler way than using any other interval approach. A path planning problem will then be considered in order to illustrate the principle of the approach.
Published: 2014

46. Robotic Sailing 2013

Author: Fabrice Le Bars and Luc Jaulin
Subjects: 0209 industrial biotechnology, 020901 industrial engineering & automation, Computer science, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, 02 engineering and technology
Published: 2014
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47. Cooperative localization of underwater robots with unsynchronized clocks

Author: Luc Jaulin, Aymeric Bethencourt, Lab-STICC_ENSTAB_CID_IHSEV, OSM, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), 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, Technology, Computer science, Cognitive Neuroscience, Real-time computing, 0102 computer and information sciences, 02 engineering and technology, Interval (mathematics), Constraint satisfaction, 01 natural sciences, Sonar, Clock synchronization, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science::Robotics, Behavioral Neuroscience, 020901 industrial engineering & automation, Developmental Neuroscience, Artificial Intelligence, Interval analysis, AUV, Constraint satisfaction problem, Human-Computer Interaction, 010201 computation theory & mathematics, Localization, Trajectory, Robot, Group of underwater robots
Abstract: This paper proposes an interval based approach for localizing a group of underwater robots with unsynchronized clocks. We use sonar communication and consider that the travel time of the sonar waves cannot be neglected, e.g. when the robots are fast and far-spaced. Therefore we cannot suppose that we measure a true distance between robots at the same time, but between robots at di􀉼erent times. Moreover, as the clocks of the robots are unsynchronized, the emitting and receiving times of the sonar waves are uncertain. To solve this problem, we cast the state equations of our robots as a constraint satisfaction problem and consider the sonar measurements as intertemporal constraints on uncertain times. We introduce the notion of interval of function to encompass the robots trajectory and clock with their uncertainty. We then use interval propagation to successively contract these intervals around the true position and clock of the robots. Several test cases are provided, with both simulated and experimental results.
Published: 2013
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48. 3D Reconstruction Using Interval Methods on The Kinect Device Coupled With an IMU

Author: Luc Jaulin, Aymeric Bethencourt, Lab-STICC_ENSTAB_CID_IHSEV, OSM, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), and Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: 0209 industrial biotechnology, Computer science, Point cloud, lcsh:TK7800-8360, 02 engineering and technology, RANSAC, lcsh:QA75.5-76.95, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Interval Methods, 020901 industrial engineering & automation, Artificial Intelligence, Inertial measurement unit, 0202 electrical engineering, electronic engineering, information engineering, Computer vision, Contractors, Kinect, VSLAM, business.industry, lcsh:Electronics, 3D reconstruction, Iterative closest point, IMU, Computer Science Applications, Transformation (function), 020201 artificial intelligence & image processing, lcsh:Electronic computers. Computer science, Artificial intelligence, 3D Reconstruction, business, Software
Abstract: WOS; International audience; The principle behind VSLAM applications like 3D object reconstruction or indoor mapping is to estimate the spatial transformation between two large clouds of points, which represent two poses of the same scene. They can further be processed to obtain detailed surfaces. Since its introduction in 1992, the standard algorithm for finding the alignment between two point clouds is ICP (Iterative Closest Point) and its variants, combined with RANSAC (RANdom SAmple Consensus). This paper presents a new approach using interval analysis. The idea is to define large intervals for the transformation parameters between the poses then to successively contract those intervals using the equations of the transformation of corresponding points between the poses. To contract those intervals faster, we added an IMU (Inertial Measurement Unit) to our system so the initial intervals of the parameters are already small before applying the contractions. We implemented our algorithm using the middleware ROS (Robot Operating System) and stated our performances.
Published: 2013
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49. A Simple Controller for Line Following of Sailboats

Author: Fabrice Le Bars and Luc Jaulin
Subjects: Computer Science::Robotics, Control theory, Simple (abstract algebra), Computer science, Computation, Line (geometry), Robot, Collision avoidance, Power (physics), Interval arithmetic
Abstract: This paper proposes a simple controller for sailboat robots. The resulting controller is simple to implement and its parameters are easy to tune. Its complexity is low enough to be applicable for sailing robots with very limited computation power. The presentation contains all the necessary details to allow a fast and reliable implementation of a sailboat robot controller which follows a line. The paper also presents a simple collision avoidance strategy based on interval analysis.
Published: 2013
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50. An experimental validation of a robust controller with the VAIMOS autonomous sailboat

Author: Luc Jaulin, Fabrice Le Bars, Lab-STICC_ENSTAB_CID_IHSEV, OSM, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), and Billon-Coat, Annick
Subjects: 0209 industrial biotechnology, SIMPLE (military communications protocol), Computer science, Process (computing), Control engineering, 02 engineering and technology, Experimental validation, turbidity, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, sailboat robot, [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Trajectory, Robot, 020201 artificial intelligence & image processing, Tweaking
Abstract: International audience; A sailboat is a strongly non-linear system that however has been proven to be easily controllable. Indeed, its mechanical design comes from an evolution from thousands of years with two main concerns: having a fast, reliable and ef cient vehicle while being easily controlled by humans. This article describes the functioning, the validation process and the performances of a simple controller, inspired from what navigators do, through tests made on the sailboat robot VAIMOS built by IFREMER for oceanography. This controller requires tweaking few parameters with real physical meaning while ensuring accurate trajectory following, needed to make oceanographic measurements in a speci c area.
Published: 2012

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