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1. Comparison of bundle and classical column generation

Author: Olivier Briant, François Vanderbeck, Sophie Michel, Claude Lemaréchal, Nancy Perrot, Ph. Meurdesoif, Optimisation Combinatoire (G-SCOP_OC), Laboratoire des sciences pour la conception, l'optimisation et la production (G-SCOP), Institut National Polytechnique de Grenoble (INPG)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Reformulations based algorithms for Combinatorial Optimization (Realopt), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), OC ( G-SCOP_OC ), Laboratoire des sciences pour la conception, l'optimisation et la production ( G-SCOP ), Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut polytechnique de Grenoble - Grenoble Institute of Technology ( Grenoble INP ) -Institut National Polytechnique de Grenoble ( INPG ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut polytechnique de Grenoble - Grenoble Institute of Technology ( Grenoble INP ) -Institut National Polytechnique de Grenoble ( INPG ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems ( BIPOP ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Laboratoire Jean Kuntzmann ( LJK ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Institut National Polytechnique de Grenoble ( INPG ), Institut de Mathématiques de Bordeaux ( IMB ), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux ( UB ) -Institut Polytechnique de Bordeaux ( Bordeaux INP ) -Centre National de la Recherche Scientifique ( CNRS ), Reformulations based algorithms for Combinatorial Optimization ( Realopt ), Laboratoire Bordelais de Recherche en Informatique ( LaBRI ), Centre National de la Recherche Scientifique ( CNRS ) -École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2-Centre National de la Recherche Scientifique ( CNRS ) -École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2-Institut de Mathématiques de Bordeaux ( IMB ), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux ( UB ) -Institut Polytechnique de Bordeaux ( Bordeaux INP ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Bordeaux ( UB ) -Institut Polytechnique de Bordeaux ( Bordeaux INP ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ), Laboratoire de Mathématiques Appliquées du Havre ( LMAH ), Université Le Havre Normandie ( ULH ), Normandie Université ( NU ) -Normandie Université ( NU ), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Institut de Mathématiques de Bordeaux (IMB), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest
Subjects: [ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC], Mathematical optimization, Linear programming, Bundle algorithm, General Mathematics, 0211 other engineering and technologies, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Travelling salesman problem, Nonsmooth convex optimization, Dantzig-Wolfe decomposition, Vehicle routing problem, MSC : 66K05, 90C25, 90C27, Column generation, 0101 mathematics, Integer programming, Mathematics, Cutting-plane algorithms, 021103 operations research, Stabilized column generation, Bin packing problem, Dantzig–Wolfe decomposition, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Volume algorithm, Lagrangian duality, Software, Cutting-plane method
Abstract: International audience; When a column generation approach is applied to decomposable mixed integer programming problems, it is standard to formulate and solve the master problem as a linear program. Seen in the dual space, this results in the algorithm known in the nonlinear programming community as the cutting-plane algorithm of Kelley and Cheney-Goldstein. However, more stable methods with better theoretical convergence rates are known and have been used as alternatives to this standard. One of them is the bundle method; our aim is to illustrate its differences with Kelley's method. In the process we review alternative stabilization techniques used in column generation, comparing them from both primal and dual points of view. Numerical comparisons are presented for five applications: cutting stock (which includes bin packing), vertex coloring, capacitated vehicle routing, multi-item lot sizing, and traveling salesman. We also give a sketchy comparison with the volume algorithm.
Published: 2006
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2. Discrete-time twisting controller without numerical chattering: analysis and experimental results with an implicit method

Author: Franck Plestan, Olivier Huber, Bernard Brogliato, Vincent Acary, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN), Mines Nantes (Mines Nantes)-École Centrale de Nantes (ECN)-Ecole Polytechnique de l'Université de Nantes (EPUN), Université de Nantes (UN)-Université de Nantes (UN)-PRES Université Nantes Angers Le Mans (UNAM)-Centre National de la Recherche Scientifique (CNRS), ANR-11-BS03-0007,ChaSliM,Vers une commande par modes glissants performante: réduction du chattering, rejet de perturbations, et boite à outils.(2011), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems ( BIPOP ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Laboratoire Jean Kuntzmann ( LJK ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Institut National Polytechnique de Grenoble ( INPG ), Institut de Recherche en Communications et en Cybernétique de Nantes ( IRCCyN ), Mines Nantes ( Mines Nantes ) -École Centrale de Nantes ( ECN ) -Ecole Polytechnique de l'Université de Nantes ( Polytech Nantes ), Université de Nantes ( UN ) -Université de Nantes ( UN ) -PRES Université Nantes Angers Le Mans ( UNAM ) -Centre National de la Recherche Scientifique ( CNRS ), and ANR-11-BS03-0007,ChaSliM,Vers une commande par modes glissants performante: réduction du chattering, rejet de perturbations, et boite à outils. ( 2011 )
Subjects: Discretization, Work (physics), Structure (category theory), implicit discretization, Control engineering, Tracking (particle physics), twisting controller, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Discrete time and continuous time, Control theory, [ INFO.INFO-AU ] Computer Science [cs]/Automatic Control Engineering, electropneumatic actuator, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], sampled-data system, Reduction (mathematics), Mathematics
Abstract: International audience; In this note, we present an implementation of the twisting controller on an electropneumatic plant for a tracking control problem. Implicit and explicit discrete-time twisting controllers are considered, and some implementation details are provided. Experimental results are provided and analyzed. They sustain the theoretical superiority of the implicitly discretized version, as shown in previous work. The main advantages of the implicit method are better tracking and drastic reduction in the input and output chattering. This is achieved without modifying the controller structure compared to its continuous-time version.
Published: 2014
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3. Non Smooth Fracture Dynamics (NSFD)

Author: Vincent Acary, Frédéric Dubois, MONERIE Yann, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems ( BIPOP ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Laboratoire Jean Kuntzmann ( LJK ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Institut National Polytechnique de Grenoble ( INPG ), Réseaux, Moyens Informatiques, Calcul Scientifique ( Remics ), Laboratoire de Mécanique et Génie Civil ( LMGC ), Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ), Institut de Radioprotection et de Sûreté Nucléaire ( IRSN ), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Réseaux, Moyens Informatiques, Calcul Scientifique (Remics), Laboratoire de Mécanique et Génie Civil (LMGC), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), and Institut de Radioprotection et de Sûreté Nucléaire (IRSN)
Subjects: [ INFO.INFO-MO ] Computer Science [cs]/Modeling and Simulation, [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph], [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], [ SPI.MECA.SOLID ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the solides [physics.class-ph], [ SPI.MECA.STRU ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the structures [physics.class-ph], [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [ PHYS.MECA.STRU ] Physics [physics]/Mechanics [physics]/Mechanics of the structures [physics.class-ph], [ PHYS.MECA.SOLID ] Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph]
Abstract: International audience; We present in this work a modeling approach and an associated numerical strategy both devoted to complex mechanical surface interactions. This approach together with the dedicated numerical strategy are referred as Non Smooth Fracture Dynamics (NSFD). From an applied point of view, this work concerns the comprehension, the prediction and the numerical simulation of dynamic fracture for a wide variety of materials and structures. The main contribution is the ability to predict an entire fracture process: crack initiation, growth, propagation of microcracks, coalescence, propagation of a microcrack, final rupture and post fracture behavior (e.g. frictional contact between created fragments after fracture).
Published: 2010

4. Comparison and Coupling of Algorithms for Collisions, contact and friction in rigid multi-body simulations

Author: Renouf, Mathieu, Acary, Vincent, Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] ( LaMCoS ), Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems ( BIPOP ), and Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria )
Subjects: [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph], [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Mechanics of the structures [physics.class-ph], [ SPI.MECA.SOLID ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the solides [physics.class-ph], [ SPI.MECA.STRU ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the structures [physics.class-ph], [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph], [ PHYS.MECA.STRU ] Physics [physics]/Mechanics [physics]/Mechanics of the structures [physics.class-ph], [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the solides [physics.class-ph], [ PHYS.MECA.SOLID ] Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph], [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the structures [physics.class-ph]
Abstract: International audience; Numerous works in computational mechanics are dedicated to multi-body systems. This leads to the use of various methods to simulate the static or dynamic evolution of complex systems. The case of dense multi-contact assemblies is one of the more complex one: the problem have often a large number of unknown and have a infinity of solution due to the definition of the matrix of the system. Moreover this problem become harder when friction or more complex laws are introduced in the system. Thus we need fast and robust solvers to perform mechanical studies. These performances can be increased when the special problem structure is considered (sparse matrices, block structured problem). Our work is based on the Non Smooth Contact Dynamic framework introduced by Moreau. The method uses a time-stepping integrator without explicit event-handling procedure and an unilateral contact impact formulation associated to Coulomb's friction. In this paper we use and compare different iterative algorithms such as Gauss-Seidel, projected conjugate gradient and direct ones as Lemke and Quadratic programming solvers. The efficiency of the methods is compared in terms of complexity, convergence criterion and of CPU time. To illustrate the results, we focus on granular assemblies. 3D frictional contact simulations are performed with ConF&TiS and the Numerics library of the siconos project.
Published: 2006

5. Nonsmooth fracture dynamics using a cohesive zone approach

Author: Acary , Vincent, Monerie , Yann, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems ( BIPOP ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ), Institut de Radioprotection et de Sûreté Nucléaire ( IRSN ), INRIA, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Institut de Radioprotection et de Sûreté Nucléaire (IRSN)
Subjects: Differential inclusion, ACM : G.: Mathematics of Computing/G.1: NUMERICAL ANALYSIS/G.1.8: Partial Differential Equations, Friction, Fracture Dynamics, [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], Nonsmooth behavior, [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph], [ PHYS.MECA.STRU ] Physics [physics]/Mechanics [physics]/Mechanics of the structures [physics.class-ph], Contact Mechanics, [PHYS.MECA.MEMA]Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph], [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph], Damage, ACM: G.: Mathematics of Computing/G.1: NUMERICAL ANALYSIS/G.1.8: Partial Differential Equations, [ PHYS.MECA.MEMA ] Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph], [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Mechanics of the structures [physics.class-ph], [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], Numerical methods, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], [ PHYS.MECA.SOLID ] Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph], Cohesive Zone Model
Abstract: This article is devoted to the comprehension, the prediction and the numerical simulation of dynamic fracture for a wide variety of materials and structures. The main contribution concerns the prediction of the entire fracture process from crack initiation, growth, propagation, and final rupture, to post fracture behavior such as unilateral contact and dry friction interactions between created fragments after fracture. The new Non Smooth Fracture Dynamics (NSFD) approach presented in this paper is thus based on three main features: a) a surface-volumetric multibody approach using mixed boundary conditions between each volumetric finite elements and/or rigid bodies, b) the development of a generic formulation of the cohesive zone models dedicated to a wide variety of materials and physical phenomena, and incorporating unilateral contact and Coulomb's dry friction and c) a specific nonsmooth dynamical framework based on measure differential inclusions and an associated implicit time--integration scheme allowing the numerical treatment of nonsmooth events such as impacts due to unilateral constraints.
Published: 2006

6. 3D frictional contact and impact multibody dynamics. A comparison of algorithms suitable for real-time applications

Author: Renouf , Mathieu, Acary , Vincent, Dumont , Georges, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Computer generated images, animation, modeling and simulation (SIAMES), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes, Institut National de Recherche en Informatique et en Automatique (Inria), J.M. Goicolea, J. Cuadrado, J.C. Garcìa Orden, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems ( BIPOP ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ), Computer generated images, animation, modeling and simulation ( SIAMES ), Institut de Recherche en Informatique et Systèmes Aléatoires ( IRISA ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Institut National des Sciences Appliquées - Rennes ( INSA Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Institut National des Sciences Appliquées - Rennes ( INSA Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Centre National de la Recherche Scientifique ( CNRS ) -INRIA Rennes, Institut National de Recherche en Informatique et en Automatique ( Inria ), J.M. Goicolea, J. Cuadrado, J.C. Garcìa Orden, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-INRIA Rennes
Subjects: [ INFO.INFO-MO ] Computer Science [cs]/Modeling and Simulation, [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph], [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], [ SPI.MECA.STRU ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the structures [physics.class-ph], [ PHYS.MECA.STRU ] Physics [physics]/Mechanics [physics]/Mechanics of the structures [physics.class-ph], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract: International audience; During the last decade Virtual Reality has benefited of numerous works dedicated to the modeling and the simulation of multibody systems. Even if a large set of methods are already used by the community of computer graphics and virtual reality, some progresses need still to be made to bridge the gap between accurate mechanical simulation and efficient simulations in real-time of realistic systems. Particularly, the problem of the three dimensional frictional contact with impacts is a key point for the applications with haptic feedback. The work aims at adapting the outstanding methods in computational mechanics to the real-time constraints induced by Virtual Reality. For efficiency reasons, our work is based on the Non Smooth Contact Dynamics (NSCD) framework introduced by Moreau (1988). Two major advantages of the method can be exhibited for the real-time context: the method uses a time-stepping numerical scheme without explicit event-handling procedure and an unilateral contact impact formulation associated with the 3D Coulomb's friction law. In the present paper, we use and compare different iterative algorithms (Non Smooth Gauss-Seidel, projected conjugate gradient, the PATH solver) for complementarity problems with a direct one (Lemke). The efficiency of the methods is compared in terms of complexity, of quality ratio between visual feed-back of solution and convergence criterion and of CPU time keeping in mind the real-time constraint.
Published: 2005

7. Addendum-Erratum to Nonsmooth Modeling and Simulation for Switched Circuits

Author: Brogliato, Bernard, Modélisation, simulation et commande des systèmes dynamiques non lisses (TRIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Subjects: Convex analysis, Siconos software platform, Ideal diodes, Numerical simulation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Switched circuits, Time-stepping methods, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], [SPI.TRON]Engineering Sciences [physics]/Electronics
Abstract: This second version of the Addendum/Erratum corrects some typos present in the monograph.
Published: 2022

8. Solitary waves in the excitable Burridge–Knopoff model

Author: Guillaume James, Arnaud Tonnelier, Jose Eduardo Morales Morales, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF), Modélisation, simulation et commande des systèmes dynamiques non lisses (TRIPOP ), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Guillaume James, Chiara Daraio, Alexander F. Vakakis, INRIA Grenoble - Rhône-Alpes, Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Morales Morales, Jose Eduardo
Subjects: excitable discrete media, Bistability, [SPI] Engineering Sciences [physics], Differential equation, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Excitable media, General Physics and Astronomy, [MATH] Mathematics [math], 01 natural sciences, [PHYS] Physics [physics], 010305 fluids & plasmas, Piecewise linear function, Burridge-Knopoff, [SPI]Engineering Sciences [physics], Lattice (order), lattices differential equations, 0103 physical sciences, systèmes dynamiques, Ondes solitaires, [MATH]Mathematics [math], Solitary waves, 010306 general physics, modèle de Burridge-Knopoff, Mathematics, Stable state, [PHYS]Physics [physics], Applied Mathematics, milieux excitables, [PHYS.MECA]Physics [physics]/Mechanics [physics], Computational Mathematics, Nonlinear system, Lattice dynamical systems, Classical mechanics, Coupling (computer programming), Burridge-Knopoff model, Modeling and Simulation, [PHYS.MECA] Physics [physics]/Mechanics [physics], Ground state
Abstract: The Burridge-Knopoff model is a lattice differential equation describing a chain of blocks connected by springs and pulled over a surface.This model was originally introduced to investigate nonlinear effects arising in the dynamics of earthquake faults. One of the main ingredients of the model is anonlinear velocity-dependent friction force between the blocks and the fixed surface. For some classes of non-monotonic friction forces, the system displays a large response to perturbations above a threshold, which is characteristic of excitable dynamics. Using extensive numerical simulations, we show that this response corresponds to the propagation of a solitary wavefor a broad range of friction laws (smooth or nonsmooth) and parameter values. These solitary waves develop shock-like profiles at large coupling (a phenomenon connected with the existence of weak solutions in a formal continuum limit)and propagation failure occurs at low coupling.We introduce a simplified piecewise linear friction law (reminiscent of the McKean nonlinearity for excitable cells) which allows us to obtain analytical expression of solitary waves and study some of their qualitative properties, such as wavespeed and propagation failure. We propose a possible physical realization of this system as a chain of impulsively forced mechanical oscillators. In certain parameter regimes, non-monotonic friction forces can also give rise to bistability between the ground state and limit-cycle oscillationsand allow for the propagation of fronts connecting these two stable states.; Le modèle de Burridge-Knopoff est un système d’équations différentielles décrivantune chaîne de blocs reliés par des ressorts et tirés sur une surface. Ce modèle a été introduit àl’origine pour étudier les effets non linéaires intervenant dans la dynamique de failles sismiques.L’un des principaux ingrédients du modéle est l’existence d’une force de frottement non linéairequi dépend de la vitesse entre les blocs et la surface fixe. Pour certaines classes de forces defrottement non monotones, le système présente une réponse importante aux perturbations au-dessus d’un certain seuil; une des caractéristiques des systèmes excitables. A l’aide de simulationsnumériques, nous montrons que cette réponse est associée à la propagation d’une onde solitairepour une large gamme de lois de frottement (régulières ou non régulières) et de valeurs deparamètres. Ces ondes solitaires développent des profils de type choc à grand couplage (unphénomène lié à l’existence de solutions faibles dans une limite formelle continue) et un échecde propagation se produit à faible couplage. Nous introduisons une loi de friction simplifiée,linéaire par morceaux (rappelant la non linéarité de McKean pour les cellules excitables), quinous permet d’obtenir l’expression analytique des ondes solitaires et d’étudier certaines de leurspropriétés qualitatives, telles que la vitesse de l’onde et l’échec de propagation. Nous proposonsune réalisation physique possible de ce système comme une chaîne d’oscillateurs mécaniques forcéspar impulsion. Dans certains régimes de paramètres, des forces de frottement non monotonespeuvent également donner lieu à une bistabilité entre un état stationnaire et un cycle limite etpermettre la propagation de fronts reliant ces deux états stables.
Published: 2018
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9. Comparison of several formulations and integration methods for the resolution of DAEs formulations in event-driven simulation of nonsmooth frictionless multibody dynamics

Author: Vincent Acary, Stéphane Garreau, Mounia Haddouni, Bernard Brogliato, Jean-Daniel Beley, ANSYS France, ANSYS, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Subjects: Mathematical optimization, Control and Optimization, Drift-off effect, Numerical time integration, Stability (learning theory), Aerospace Engineering, Context (language use), 010103 numerical & computational mathematics, 01 natural sciences, Projection (linear algebra), symbols.namesake, Contact dynamics, 0103 physical sciences, DAE, 0101 mathematics, 010301 acoustics, Mathematics, Event-driven scheme, Mechanical Engineering, [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], Multibody system, Computer Science Applications, Numerical integration, Impact, Modeling and Simulation, Jacobian matrix and determinant, symbols, Differential algebraic equation
Abstract: International audience; This article is devoted to the comparison of numerical integration methods for nonsmooth multibody dynamics with joints, unilateral contacts and impacts in an industrial context. With an event–driven strategy, the smooth dynamics, which is integrated between two events, may be equivalently formulated as a Differential Algebraic Equation (DAE) of index 1, 2 or 3. It is well-known that these reformulations are no longer equivalent when a numerical time–integration technique is used. The drift-off effect and the stability of the numerical scheme strongly depend on the index of the formulation. But, besides the standard properties of accuracy and stability of the DAE solvers, the event–driven context imposes some further requirements that are crucial for a robust and efficient event-driven strategy. In this article, several state–of–the–art numerical time integration methods for each formulation are compared: the generalized-α scheme for index-3 formulation and stabilized index-2 formulation, (Partitioned) Runge–Kutta Half–Explicit Method of order 5 (HEM5 and PHEM56) for index-2 DAEs with projection techniques, and Runge-Kutta explicit scheme of order 5, the Dormand-Prince scheme (DOPRI5), for index-1 DAEs with projection techniques (MDOP5). We compare these schemes in terms of efficiency, violation of the constraints and the way they handle stiff dynamics on numerous industrial benchmarks, where a CAD software is in this loop. One of the major conclusions is that the index-2 DAEs solvers prove to be better than other schemes to maintain low violations at position and acceleration levels. The best compromise allows us to design efficient event–driven solvers. When the dynamics is stiff, implicit schemes outperform explicit and half-explicit methods whichare sometimes unable to compute the dynamics when the system’s frequency range is wide. Furthermore, in industrial context, some solvers fail to reproduce the properties that they enjoy in theory. This is particularly true for half-explicit schemes when the Jacobian of the constraints has not full rank.
Published: 2017
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10. Dissipative Systems Analysis and Control

Author: Brogliato, B., Lozano, R., Maschke, B., Olav Egeland, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'automatique et de génie des procédés (LAGEP), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-École Supérieure Chimie Physique Électronique de Lyon-Centre National de la Recherche Scientifique (CNRS), Norwegian University of Science and Technology [Trondheim] (NTNU), Norwegian University of Science and Technology (NTNU), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), and Université de Lyon-Université de Lyon-École Supérieure de Chimie Physique Électronique de Lyon (CPE)-Centre National de la Recherche Scientifique (CNRS)
Subjects: 0209 industrial biotechnology, 02 engineering and technology, 01 natural sciences, OJ0061, Adaptive Control, 020901 industrial engineering & automation, Positive Real Systems, 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering, Active Vibration Damping, Kalman-Yakubovich-Popov Lemma, Control Theory, Lagrangian Systems, 010301 acoustics, Circuit Theory, Mechanical Engineering, Passive Systems, Robotics, Control Engineering, Hamiltonian Systems, Feedback Control, Thermodynamics, 020201 artificial intelligence & image processing, Passivity-based Control, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Dissipative Systems, Stability
Abstract: second edition; International audience; Dissipative Systems Analysis and Control (second edition) presents a fully revised and expanded treatment of dissipative systems theory, constituting a self-contained, advanced introduction for graduate students, researchers and practising engineers. It examines linear and nonlinear systems with examples of both in each chapter; some infinite-dimensional examples are also included. Throughout, emphasis is placed on the use of the dissipative properties of a system for the design of stable feedback control laws. The theory is substantiated by experimental results and by reference to its application in illustrative physical cases (Lagrangian and Hamiltonian systems and passivity-based and adaptive controllers are covered thoroughly). The second edition is substantially reorganized both to accommodate new material and to enhance its pedagogical properties. Some of the changes introduced are: * Complete proofs of the main theorems and lemmas. * The Kalman-Yakubovich-Popov Lemma for non-minimal realizations, singular systems, and discrete-time systems (linear and nonlinear). * Passivity of nonsmooth systems (differential inclusions, variational inequalities, Lagrangian systems with complementarity conditions). * Sections on optimal control and H-infinity theory. * An enlarged bibliography with more than 550 references, and an augmented index with more than 500 entries. * An improved appendix with introductions to viscosity solutions, Riccati equations and some useful matrix algebra.
Published: 2020
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11. Gérer les Incertitudes des Robots à Pattes

Author: Villa, Nahuel, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), EU 2020 Comanoid Research and Innovation Action (RIA), Universite Grenoble Alpes, Inria Grenoble Rhônes-Alpes, Bernard Brogliato (bernard.brogliato@inria.fr), Pierre-Brice Wieber, and European Project: 645097,H2020 Pilier Industrial Leadership,H2020-ICT-2014-1,COMANOID(2015)
Subjects: mRPI set, Bounded Input Bounded Output, Période d'échantillonnage, Contrôle de l'équilibre, Reference Motion Generation, Robot à Pieds, ACM: H.: Information Systems/H.1: MODELS AND PRINCIPLES, Balance Control, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Legged Robots, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Sampling Period, Minimum Robust Positively Invariant Set, Robust Control, Contrôle robuste
Abstract: Legged robots have a huge potential field of application that ranges from routine and dangerous works, to help in the treatment of children with autism. Nevertheless, employing these complex machines on a real application requires safety guarantees on their functioning. This is traditionally approached by over-sizing the robot design, but, since how resources should be distributed is unknown, these robots are still quite restricted in their capabilities, yet without formal safety guarantees and too expensive for most simple tasks. A quantitative analysis to determine how fast and precise, and therefore how expensive should sensors, actuators and computers be has never been investigated in the existing scientific literature. There is a long theoretical and practical work to be done in this regard and it is the goal of this thesis to initiate this discussion.Based on concepts from robust control theory, considering bounded uncertainties, we propose to quantify the effect of main sources of uncertainty on the balance control of the center of mass of the robot, since it is unstable and fundamental to develop any other task. As a first result, we established conditions to ensure the safe balance of the robot. Then, we provided control choices to reduce the restrictiveness on the motion of the robot and its cost.; Les robots à pattes ont un énorme champ d’applications potentiel, allant des travaux routiniers et dangereux, à l’assistance comme intermédiaires rassurants entre des enfants autistes et leur entourage. Cependant, l’utilisation de ces machines complexes requiert des garanties de sécurité sur leur fonctionnement. Ceci est traditionnellement abordé en sur-dimensionnant la conception du robot. Toutefois, comme la répartition des ressources est inconnue, leurs capacités sont encore assez limitées, sans garanties de sécurité formelles et trop coûteux pour la plupart des tâches simples. Une analyse quantitative visant à déterminer la rapidité et la précision, et donc le coût, des capteurs, des actionneurs et des calculateurs n’a jamais été étudiée dans la littérature scientifique existante. Il y a là tout un travail théorique et pratique qui reste à réaliser et le but de cette thèse est d'initier cette discussion.Sur la base des concepts de la théorie du contrôle robuste, prenant en compte des incertitudes bornées, nous proposons de quantifier l’effet des principales sources d’incertitude sur le contrôle de l'équilibre du centre de gravité du robot, car il est instable et fondamental pour développer toute autre tâche. Comme premier résultat, nous avons déterminé les conditions nécessaires pour assurer l'équilibre du robot en toute sécurité. Ensuite, nous fournissons des choix de contrôle pour réduire le caractère restrictif du mouvement du robot et de son cout.
Published: 2019

12. Managing Uncertainties in Legged Robots

Author: Villa, Nahuel, Modélisation, simulation et commande des systèmes dynamiques non lisses (TRIPOP ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Université Grenoble Alpes, Bernard Brogliato, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Subjects: Prioritization, Legged robot, Mpc, Automatic, Objectifs de commande, Control, Robustness, Robuste, Automatique, Incertitudes, Robot à jambes, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract: Biped and quadruped robots are beginning now to master the skill of walking dynamically in most standard situations. This suggests that more widespread commercial use of such robots will soon be possible. This requires, however, that guarantees are provided about their safety and operational performance. In research prototypes, the risk of failure is usually contained by using very fast and precise (and therefore very expensive) sensors, actuators and computers, resulting in robots that are clearly too expensive for commercial purposes.The dynamics of the Center of Mass (CoM) of these robots over the support feet is unstable, and therefore very sensitive to all sources of uncertainties. But how fast and precise, and therefore how expensive should the sensors, actuators and computers be has never been investigated in the existing scientific literature. A precise quantification of the effect of uncertainties and sampling period on legged balance control seems to be missing, and it is the goal of this paper to initiate this discussion.The balance of legged robots mostly involves motion of their CoM with respect to their feet on the ground. We therefore focus our analysis on the motion of the CoM, considering that other aspects of the motion of the robot, such as precise whole-body joint motion and contact force control, are handled separately, as usual in this field of robotics.We introduced a tube-based Model Predictive Control (MPC) of walking in order to guarantee that all kinematic and dynamic constraints are always satisfied, even in the presence of uncertainties. We considered that uncertainties can take any value between some bounds, generating some tracking error which can be bounded accordingly. Here, we propose to analyze how these bounds are related: how much tracking error can we expect for a given amount of uncertainty? This naturally depends not only on the kind of uncertainty (e.g. on sensors or actuators), but also on the control law and its sampling period.Our findings are validated in experiments and simulations with the torque-controlled humanoid robot Toro developed at DLR. The proposed mathematical derivations and results apply nevertheless indistinctly to biped and quadruped robots.; Les robots bipède et quadrupède commencent à maîtriser la capacité de marcher de manière dynamique dans la plupart des situations standard. Ceci suggère que l'utilisation commerciale plus répandue de tels robots sera bientôt possible. Toutefois, cela nécessite que des garanties soient fournies concernant sa sécurité et ses performances opérationnelles. Dans les prototypes de recherche, le risque d'échec est généralement limité par l'utilisation de capteurs, d'actionneurs et d'ordinateurs très rapides et précis (et donc très coûteux), ce qui aboutit à des robots nettement trop coûteux pour un usage commercial.La dynamique du centre de masse de ces robots aux pieds de support est instable et, par conséquent, très sensible à toutes les sources d'incertitude. Mais la rapidité et la précision, et donc le coût, des capteurs, des actionneurs et des ordinateurs n’ont jamais été étudiés dans la littérature scientifique existante. Il semble y avoir un manque de quantification précise de l'effet des incertitudes et de la période d'échantillonnage dans le contrôle de l'équilibre des jambes, et l'objectif de ce document est d'initier cette discussion.L'équilibre des robots avec les jambes implique principalement le mouvement de leur CoM par rapport à leurs pieds sur le sol. Par conséquent, nous concentrons notre analyse sur le mouvement du centre de gravité, en considérant que d'autres aspects du mouvement du robot, tels que le mouvement précis de l'articulation du corps entier et le contrôle de la force de contact, sont traités séparément, comme d'habitude dans ce domaine. robotique.Nous avons introduit un modèle de contrôle prédictif (MPC) basé sur des tubes de marche afin de garantir que toutes les restrictions cinématiques et dynamiques sont toujours respectées, même en présence d'incertitudes. Nous pensons que les incertitudes peuvent prendre n'importe quelle valeur entre certaines limites, générant une erreur de suivi qui peut être limitée en conséquence. Nous proposons ici d’analyser le lien entre ces limites: quelle erreur de suivi pouvons-nous espérer pour une certaine incertitude? Naturellement, cela dépend non seulement du type d'incertitude (par exemple, des capteurs ou des actionneurs), mais également de la loi de commande et de sa période d'échantillonnage.Nos résultats sont validés par des expériences et des simulations avec le robot humanoïde Toro à contrôle de couple développé en DLR. Cependant, les dérivations et les résultats mathématiques proposés s’appliquent de manière interchangeable aux robots bipèdes et quadruples.
Published: 2019

13. Nonsmooth simulation of dense granular flows with pressure-dependent yield stress

Author: Gilles Daviet, Florence Bertails-Descoubes, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011)
Subjects: Mathematical optimization, Computer simulation, Discretization, Computer science, Applied Mathematics, Mechanical Engineering, General Chemical Engineering, Condensed Matter Physics, Granular material, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 01 natural sciences, Discrete element method, 010305 fluids & plasmas, 010101 applied mathematics, Drucker–Prager yield criterion, 0103 physical sciences, Scalability, Convex optimization, Continuous simulation, General Materials Science, 0101 mathematics
Abstract: International audience; Understanding the flow of granular materials is of utmost importance for numerous industrial applications including the manufacturing, storing and transportation of grain assemblies (such as cement, pills, or corn), as well as for natural risk assessing considerations. Discrete Element Modeling (DEM) methods, which explicitly represent grain-grain interactions, allow for highly-tunable and precise simulations, but they suffer from a prohibitive computational cost when attempting to reproduce large scale scenarios. Continuum models have been recently investigated to overcome such scalability issues, but their numerical simulation still poses many challenges. In this work we propose a novel numerical framework for the continuous simulation of dilatable materials with pressure-dependent (Coulomb) yield stress. Relying upon convex optimization tools, we show that such a macroscopic, nonsmooth rheology can be interpreted as the exact analogous of the solid frictional contact problem at the heart of DEM methods, extended to the tensorial space. Combined with a carefully chosen finite-element discretization, this new framework allows us to avoid regularizing the continuum rheology while benefiting from the efficiency of nonsmooth optimization solvers, mainly leveraged by DEM methods so far. Our numerical results successfully compare to analytic solutions on model problems, and we retrieve qualitative flow features commonly observed in reported experiments of the literature.
Published: 2016
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14. Managing Uncertainties in Legged Robots

Author: Villa, Nahuel, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Université Grenoble Alpes, and Bernard Brogliato
Subjects: Prioritization, Legged robot, Mpc, Automatic, Objectifs de commande, Control, Robustness, Robuste, Automatique, Incertitudes, Robot à jambes, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract: Biped and quadruped robots are beginning now to master the skill of walking dynamically in most standard situations. This suggests that more widespread commercial use of such robots will soon be possible. This requires, however, that guarantees are provided about their safety and operational performance. In research prototypes, the risk of failure is usually contained by using very fast and precise (and therefore very expensive) sensors, actuators and computers, resulting in robots that are clearly too expensive for commercial purposes.The dynamics of the Center of Mass (CoM) of these robots over the support feet is unstable, and therefore very sensitive to all sources of uncertainties. But how fast and precise, and therefore how expensive should the sensors, actuators and computers be has never been investigated in the existing scientific literature. A precise quantification of the effect of uncertainties and sampling period on legged balance control seems to be missing, and it is the goal of this paper to initiate this discussion.The balance of legged robots mostly involves motion of their CoM with respect to their feet on the ground. We therefore focus our analysis on the motion of the CoM, considering that other aspects of the motion of the robot, such as precise whole-body joint motion and contact force control, are handled separately, as usual in this field of robotics.We introduced a tube-based Model Predictive Control (MPC) of walking in order to guarantee that all kinematic and dynamic constraints are always satisfied, even in the presence of uncertainties. We considered that uncertainties can take any value between some bounds, generating some tracking error which can be bounded accordingly. Here, we propose to analyze how these bounds are related: how much tracking error can we expect for a given amount of uncertainty? This naturally depends not only on the kind of uncertainty (e.g. on sensors or actuators), but also on the control law and its sampling period.Our findings are validated in experiments and simulations with the torque-controlled humanoid robot Toro developed at DLR. The proposed mathematical derivations and results apply nevertheless indistinctly to biped and quadruped robots.; Les robots bipède et quadrupède commencent à maîtriser la capacité de marcher de manière dynamique dans la plupart des situations standard. Ceci suggère que l'utilisation commerciale plus répandue de tels robots sera bientôt possible. Toutefois, cela nécessite que des garanties soient fournies concernant sa sécurité et ses performances opérationnelles. Dans les prototypes de recherche, le risque d'échec est généralement limité par l'utilisation de capteurs, d'actionneurs et d'ordinateurs très rapides et précis (et donc très coûteux), ce qui aboutit à des robots nettement trop coûteux pour un usage commercial.La dynamique du centre de masse de ces robots aux pieds de support est instable et, par conséquent, très sensible à toutes les sources d'incertitude. Mais la rapidité et la précision, et donc le coût, des capteurs, des actionneurs et des ordinateurs n’ont jamais été étudiés dans la littérature scientifique existante. Il semble y avoir un manque de quantification précise de l'effet des incertitudes et de la période d'échantillonnage dans le contrôle de l'équilibre des jambes, et l'objectif de ce document est d'initier cette discussion.L'équilibre des robots avec les jambes implique principalement le mouvement de leur CoM par rapport à leurs pieds sur le sol. Par conséquent, nous concentrons notre analyse sur le mouvement du centre de gravité, en considérant que d'autres aspects du mouvement du robot, tels que le mouvement précis de l'articulation du corps entier et le contrôle de la force de contact, sont traités séparément, comme d'habitude dans ce domaine. robotique.Nous avons introduit un modèle de contrôle prédictif (MPC) basé sur des tubes de marche afin de garantir que toutes les restrictions cinématiques et dynamiques sont toujours respectées, même en présence d'incertitudes. Nous pensons que les incertitudes peuvent prendre n'importe quelle valeur entre certaines limites, générant une erreur de suivi qui peut être limitée en conséquence. Nous proposons ici d’analyser le lien entre ces limites: quelle erreur de suivi pouvons-nous espérer pour une certaine incertitude? Naturellement, cela dépend non seulement du type d'incertitude (par exemple, des capteurs ou des actionneurs), mais également de la loi de commande et de sa période d'échantillonnage.Nos résultats sont validés par des expériences et des simulations avec le robot humanoïde Toro à contrôle de couple développé en DLR. Cependant, les dérivations et les résultats mathématiques proposés s’appliquent de manière interchangeable aux robots bipèdes et quadruples.
Published: 2019
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15. Model Predictive Control for biped walking

Author: Pierre-Brice Wieber, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: Model predictive control, Computer science, Control theory, ComputingMilieux_MISCELLANEOUS, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract: International audience
Published: 2018
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16. Multibody systems with 3D revolute joints with clearances: an industrial case study with an experimental validation

Author: Narendra Akhadkar, Bernard Brogliato, Vincent Acary, Schneider Electric ( SE), Modélisation, simulation et commande des systèmes dynamiques non lisses (TRIPOP ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: Engineering, joint clearance, Control and Optimization, Monte Carlo method, 0211 other engineering and technologies, stabilized combined Moreau–Jean time-stepping scheme, Aerospace Engineering, Unilateral contact, 02 engineering and technology, 01 natural sciences, circuit breaker, sensitivity analysis, Control theory, Robustness (computer science), experimental validation, 0103 physical sciences, unilateral constraints, Contact dynamics, impacts, 010301 acoustics, 021106 design practice & management, business.industry, Mechanical Engineering, Numerical analysis, Revolute joint, [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], Coulomb's friction, Computer Science Applications, Numerical integration, Modeling and Simulation, Coefficient of restitution, business
Abstract: International audience; This article is devoted to the analysis of the influence of the joint clearances in a mechanism of a circuit breaker, which is a forty-two degrees of freedom mechanism made of seven links, seven revolute joints, and four unilateral contacts with friction. Spatial (3D) revolute joints are modelled with both radial and axial clearances taking into account contact with flanges. Unilateral contact, Coulomb's friction and Newton impact laws are modeled within the framework of nonsmooth mechanics without resorting to some regularizations or compliance/damping at contact. The nonsmooth contact dynamics method based on an event-capturing time–stepping scheme with a second order cone complementarity solver is used to perform the numerical integration. Futhermore, the stabilization of the constraints at the position level is made thanks to the stabilized combined projected Moreau–Jean scheme. The nonsmooth modeling approach together with an event–capturing time–stepping scheme allows us to simulate, in an efficient and robust way, the contact and impacts phenomena that occur in joints with clearances. In particular, comparing with the event–detecting time–stepping schemes, the event–capturing scheme enables to perform the time–integration with large number of events (impacts, sliding/sticking transitions, changes in the direction of sliding) and possibly with finite time accumulations with a reasonable time–step length. Comparing with compliant contact models, we avoid stiff problems related with high stiffnesses at contact which generate some issues in contact stabilization and spurious oscillations during persistent contact periods. In the studied mechanisms of the circuit breakers, the numerical methods deals more than seventy contact points without any problems. Furthermore , the number of contact parameters is small : one coefficient of restitution and one coefficient of friction. Though they are sometimes difficult to measure accurately, the sensitivity of the simulation result with respect to contact parameters is low in the mechanism of the circuit breaker. It is demonstrated that this method, thanks to its robustness and efficiency allows to perform a sensitivity analysis using a Monte Carlo method. The numerical results are also validated by careful comparisons with experimental data which show a very good correlation.
Published: 2018
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17. The Contact Dynamics method: A nonsmooth story

Author: Dubois, Frédéric, Acary, Vincent, Jean, Michel, Réseaux, Moyens Informatiques, Calcul Scientifique (Remics), Laboratoire de Mécanique et Génie Civil (LMGC), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de micromécanique et intégrité des structures (MIST), Institut de Radioprotection et de Sûreté Nucléaire (IRSN)-Centre National de la Recherche Scientifique (CNRS), Modélisation, simulation et commande des systèmes dynamiques non lisses (TRIPOP ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Aix Marseille Université (AMU), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)
Subjects: Dynamique des contacts, Nonsmooth dynamics, Méthode par éléments discrets, Loi de Coulomb, Contact Dynamics, Shock, Dynamique non régulière, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], Coulomb law, Chocs, Discrete element method
Abstract: International audience; When velocity jumps are occurring, the dynamics is said to be nonsmooth. For instance, in collections of contacting rigid bodies, jumps are caused by shocks and dry friction. Without compliance at the interface, contact laws are not only non-differentiable in the usual sense but also multi-valued. Modeling contacting bodies is of interest in order to understand the behavior of numerous mechanical systems such as flexible multi-body systems, granular materials or masonry. These granular materials behave puzzlingly either like a solid or a fluid and a description in the frame of classical continuous mechanics would be welcome though far to be satisfactory nowadays. Jean-Jacques Moreau greatly contributed to convex analysis, functions of bounded variations, differential measure theory, sweeping process theory, definitive mathematical tools to deal with nonsmooth dynamics. He converted all these underlying theoretical ideas into an original nonsmooth implicit numerical method called Contact Dynamics (CD); a robust and efficient method to simulate large collections of bodies with frictional contacts and impacts. The CD method offers a very interesting complementary alternative to the family of smoothed explicit numerical methods, often called Distinct Elements Method (DEM). In this paper developments and improvements of the CD method are presented together with a critical comparative review of advantages and drawbacks of both approaches.; Lorsque des sauts de vitesse se produisent, la dynamique est dite non régulière. Par exemple, dans les collections de solides supposés rigides rentrant en contact, les sauts sont causés par les chocs et le frottement sec. L'absence de déformabilité fait que les lois de contact sont, non seulement non différentiables au sens usuel, mais aussi multi-valuées. Élaborer des modèles de solides en contact est un moyen de comprendre le comportement de nombreux systèmes mécaniques tels que les systèmes multi-corps flexibles, les matériaux granulaires ou les maçonneries. Les matériaux granulaires se comportent de manière étrange, soit comme des solides, soit comme des fluides, et une description dans le cadre de la mécanique classique des milieux continus, qui serait souhaitable, est loin d'être encore satisfaisante. Jean-Jacques Moreau a contribué, de façon fondamentale, à l'analyse convexe, à la théorie des fonctions à variations bornées et des mesures différentielles ainsi qu'au processus de rafle, outils mathématiques décisifs pour traiter la dynamique non régulière. Il a converti ces idées théoriques sous-jacentes en une méthode numérique originale appelée Contact Dynamics (CD), qui est une méthode non régulière implicite et aussi une méthode robuste et efficace pour simuler de larges collections de solides avec du contact frottant et des impacts. Le méthode CD offre une alternative très intéressante à la famille de méthodes usuelles régularisées explicites, comme la méthode des éléments distincts (DEM). Dans cet article, des développements et des perfectionnements de la méthode CD sont présentés ainsi qu'une étude critique comparative des avantages et inconvénients des deux approches.
Published: 2018
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18. Experimental Comparisons Between Implicit and Explicit Implementations of Discrete-Time Sliding Mode Controllers: Toward Input and Output Chattering Suppression

Author: Ahcene Boubakir, Vincent Acary, Franck Plestan, Bin Wang, Bernard Brogliato, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN), Mines Nantes (Mines Nantes)-École Centrale de Nantes (ECN)-Ecole Polytechnique de l'Université de Nantes (EPUN), and Université de Nantes (UN)-Université de Nantes (UN)-PRES Université Nantes Angers Le Mans (UNAM)-Centre National de la Recherche Scientifique (CNRS)
Subjects: 0209 industrial biotechnology, Perturbation (astronomy), discrete time, 02 engineering and technology, set-valued controller, Sliding mode control, symbols.namesake, 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Implementation, Mathematics, experiment, sliding mode, 020208 electrical & electronic engineering, Discrete time and continuous time, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], Control and Systems Engineering, Euler's formula, symbols, Sampling time, Robust control, Actuator, Chattering, robust control
Abstract: International audience; This brief presents a set of experimental results concerning the sliding mode control of an electropneumatic system. Two discrete-time control strategies are considered: an explicit and an implicit (that is very easy to implement with a projection on the interval [−1, 1]) Euler discretizations. While the explicit implementation is known to generate numerical chattering , the implicit one is expected to significantly reduce chattering while keeping the accuracy. The experimental results reported in this brief remarkably confirm that the implicit discrete-time sliding mode supersedes the explicit ones, with several important features: chattering in the control input is almost eliminated (while the explicit and saturated controllers behave like high-frequency bang–bang inputs), the input magnitude depends only on the perturbation size and is independent of the controller gain and sampling time.
Published: 2015
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19. Cut-Generating Functions and S-Free Sets

Author: Michele Conforti, Gérard Cornuéjols, Claude Lemaréchal, Jérôme Malick, Aris Daniilidis, Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 (PhLAM), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Tepper School of Business, Carnegie Mellon University [Pittsburgh] (CMU), Departament de Matemàtiques [Barcelona] (UAB), Universitat Autònoma de Barcelona (UAB), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)
Subjects: Discrete mathematics, Convex analysis, Generalized gauges, Optimization problem, Theory, General Mathematics, Integer programming, [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Management Science and Operations Research, Complementarity (physics), Separation, Computer Science Applications, Linear map, S-free sets, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics, Separation problem
Abstract: International audience; We consider the separation problem for sets X that are pre-images of a given set S by a linear mapping. Classical examples occur in integer programming, as well as in other optimization problems such as complementarity. One would like to generate valid inequalities that cut off some point not lying in X, without reference to the linear mapping. To this aim, we introduce a concept: cut-generating functions (cgf) and we develop a formal theory for them, largely based on convex analysis. They are intimately related to S-free sets and we study this relation, disclosing several definitions for minimal cgf's and maximal S-free sets. Our work unifies and puts in perspective a number of existing works on S-free sets; in particular, we show how cgf's recover the celebrated Gomory cuts.
Published: 2015
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20. Periodic Motions of Coupled Impact Oscillators

Author: Vincent Acary, Guillaume James, Franck Pérignon, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Modélisation, simulation et commande des systèmes dynamiques non lisses (TRIPOP ), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Remco Leine, Vincent Acary, Olivier Brüls, and Acary, Vincent
Subjects: Coupling constant, Breather, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MECA]Physics [physics]/Mechanics [physics], Dissipation, 01 natural sciences, Stability (probability), 010305 fluids & plasmas, Nonlinear system, Classical mechanics, Normal mode, 0103 physical sciences, Limit (mathematics), Boundary value problem, [PHYS.MECA] Physics [physics]/Mechanics [physics], 010306 general physics, Mathematics
Abstract: International audience; In this work, we study the existence and stability of time-periodic oscillations in a chain of linearly coupled impact oscillators reminiscent of a model analyzed in [2], for rigid impacts without energy dissipation. We introduce a numerical method allowing to compute branches of time-periodic so- lutions when an arbitrary number of nodes undergo rigid impacts. For this purpose, we reformulate the search of periodic solutions as a boundary value problem incorporating unilateral constraints. We illustrate this numerical approach by computing some families of nonlinear spatially localized modes (breathers) and extended modes.
Published: 2018
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21. Collision avoidance based on separating planes for feet trajectory generation

Author: Pierre-Brice Wieber, Stanislas Brossette, Joint Robotics Laboratory [Japan] (CNRS-AIST JRL), National Institute of Advanced Industrial Science and Technology (AIST)-Centre National de la Recherche Scientifique (CNRS), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and Joint Robotics Laboratory (CNRS-AIST JRL )
Subjects: 0209 industrial biotechnology, Mathematical optimization, Optimization problem, Computer science, 02 engineering and technology, Resolution (logic), [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Robustness (computer science), Convergence (routing), 0202 electrical engineering, electronic engineering, information engineering, Trajectory, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], 020201 artificial intelligence & image processing, Collision avoidance, Independence (probability theory)
Abstract: International audience; In this paper, we present a formulation of the collision avoidance constraints that relies on the use of separating planes instead of a distance function. This formulation has the advantage of being defined and continuously differentiable in every situation. Because it introduces additional variables to the optimization problems, making it bigger and potentially slowing down its resolution, we propose a different resolution method that takes advantage of the independence of the variables, to form two subproblems that can be solved efficiently in an alternate problem fashion. We present some preliminary results using this approach in order to highlight its potential and promises in terms of convergence speed and robustness.
Published: 2017
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22. Model Predictive Control of Biped Walking with Bounded Uncertainties

Author: Pierre-Brice Wieber, Nahuel Alejandro Villa, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Subjects: 0209 industrial biotechnology, Bounded Uncertainty, Computer science, 02 engineering and technology, Tracking (particle physics), Biped Walking, Tracking error, Computer Science::Robotics, Model predictive control, 020901 industrial engineering & automation, Control theory, Robustness (computer science), Bounded function, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Robot, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], 020201 artificial intelligence & image processing, Closed Loop MPC, Humanoid robot, Model Predictive Control
Abstract: International audience; A biped walking controller for humanoid robots has to handle together hard constraints, dynamic environments, and uncertainties. Model Predictive Control (MPC) is a suitable and widely used control method to handle the first two issues. Uncertainties on the robot imply a non-zero tracking error when trying to follow a reference motion. A standard solution for this issue is to use tighter constraints by introducing some hand tuned safety margins, for the reference motion generation to ensure that the actual robot motion will satisfy all constraints even in presence of the tracking error. In this article, we find bounds for the tracking error and we show how such safety margins can be precisely computed from the tracking error bounds. Also, a tracking control gain is proposed to reduce the restrictiveness introduced with the safety margins. MPC with these considerations ensure the correct operation of the biped robot under a given degree of uncertainties when it is implemented in open-loop. Nevertheless, the straightforward way to implement an MPC closed-loop scheme fails. We discuss the reasons for this failure and propose a robust closed-loop MPC scheme.
Published: 2017
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23. On solving contact problems with Coulomb friction: formulations and numerical comparisons

Author: Acary, Vincent, Brémond, Maurice, Huber, Olivier, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), SED [Grenoble], Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Wisconsin-Madison, INRIA, and Service Expérimentation et Développement (SED [Grenoble])
Subjects: frottement de Coulomb, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], Systèmes multi–corps, Schémas numériques de résolution, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], nonsmooth Mechanics, Coulomb friction, Mécanique non régulière, contraintes unilatérales, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], numerical methods, unilateral constraints, impact, Multibody systems, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: In this report, we review several formulations of the discrete frictional contact problemthat arises in space and time discretized mechanical systems with unilateral contact andthree-dimensional Coulomb’s friction. Most of these formulations are well–known concepts in theoptimization community, or more generally, in the mathematical programming community. Tocite a few, the discrete frictional contact problem can be formulated as variational inequalities,generalized or semi–smooth equations, second–order cone complementarity problems, or as optimizationproblems such as quadratic programming problems over second-order cones. Thanks tothese multiple formulations, various numerical methods emerge naturally for solving the problem.We review the main numerical techniques that are well-known in the literature and we also proposenew applications of methods such as the fixed point and extra-gradient methods with self-adaptivestep rules for variational inequalities or the proximal point algorithm for generalized equations.All these numerical techniques are compared over a large set of test examples using performanceprofiles. One of the main conclusion is that there is no universal solver. Nevertheless, we are ableto give some hints to choose a solver with respect to the main characteristics of the set of tests; Dans ce rapport, plusieurs formulations du problème discret de contact frottant qui apparaîtdans les systèmes mécaniques avec du contact unilatéral et du frottement de Coulomb, sont présentées.La plupart de ces formulations sont des objets bien connus dans la communauté de l’optimisation, etplus généralement, de la programmation mathématique. Pour en citer quelques uns, le problème decontact frottant peut être formulé comme une inégalité variationnelle, comme une équation non-régulièreou semi–lisse, comme un problème de complémentarité sur des cônes, ou encore comme des problèmesd’optimisation par exemple des problèmes quadratiques sur des cônes du second ordre. Grâce à cesmultiples formulations, de nombreuses méthodes numériques de résolutions émergent naturellement. Ondétaille dans ce rapport les principales techniques numériques bien connues dans la littérature et nousproposons aussi des nouvelles méthodes comme les méthodes de point fixe et d’extra-gradient pour lesinégalités variationnelles avec une règle d’adaptation automatique du pas, ainsi que l’application del’algorithme du point optimal pour les équations généralisées. Toutes ces techniques sont comparées surun grand ensemble de problème–tests en utilisant des profils de performance. Une des conclusions est qu’iln’existe pas de méthode universelle. Néanmoins, on peut donner des conseils pour choisir une méthodeparticulière la mieux adaptée aux caractéristiques d’un problème donné.
Published: 2017

24. Strong recursive feasibility in model predictive control of biped walking

Author: Thierry Fraichard, Matteo Ciocca, Pierre-Brice Wieber, Interaction située avec les objets et environnements intelligents (PERVASIVE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'Informatique de Grenoble (LIG ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011), and European Project: 645097,H2020 Pilier Industrial Leadership,H2020-ICT-2014-1,COMANOID(2015)
Subjects: Scheme (programming language), 0209 industrial biotechnology, Robot kinematics, Linear programming, Computer science, 02 engineering and technology, Constraint (information theory), Model predictive control, 020901 industrial engineering & automation, Terminal (electronics), Control theory, 0202 electrical engineering, electronic engineering, information engineering, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Robot, 020201 artificial intelligence & image processing, Legged robot, computer, computer.programming_language
Abstract: International audience; Realizing a stable walking motion requires satisfying a set of constraints. Model Predictive Control (MPC) is one of few suitable methods to handle such constraints. The capacity to satisfy constraints, which is usually called feasibility, is classically guaranteed recursively. In our applications , an important aspect is that the MPC scheme has to adapt continuously to the dynamic environment of the robot (e.g. collision avoidance, physical interaction). We aim therefore at guaranteeing recursive feasibility for all possible scenarios, which is called strong recursive feasibility. Recursive feasibility is classically obtained by introducing a terminal constraint at the end of the prediction horizon. Between two standard approaches for legged robot, in our applications we favor a capturable terminal constraint. When the robot is not really planning to stop and considers actually making a new step, recursive feasibility is not guaranteed anymore. We demonstrate numerically that recursive feasibility is actually guaranteed, even when a new step is added in the prediction horizon.
Published: 2017
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25. Multivalued robust tracking control of fully actuated Lagrange systems: Continuous and discrete–time algorithms

Author: Miranda-Villatoro, Felix, Brogliato, Bernard, Castaños, Fernando, Departamento de Control Automático (CINVESTAV-IPN), Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV-IPN), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Subjects: finite–time convergence, sliding-mode control, discrete–time, convex analysis, Lyapunov stability, Robust control, trajectory tracking, passivity-based controller, differential inclusion, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Euler–Lagrange systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract: International audience; In this paper the robust trajectory tracking problem of a class of nonlinear systems described by the Euler–Lagrange equations of motion is studied. We start considering a plant under the effects of an unknown external perturbation and also with uncertainties on its parameters. After that a class of passivity-based multivalued control laws is proposed and the well–posedness together with the stability of the closed–loop are established in the continuous–time setting. The discrete–time version of the plant and the controller are studied and well–posedness together with stability results are obtained, using the so-called implicit discretization approach introduced in [1, 2]. Numerical simulations are presented and demonstrate the effectiveness of the proposed discrete-time controller.
Published: 2017
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26. Set-valued discrete-time sliding-mode control of uncertain linear systems

Author: Félix A. Miranda-Villatoro, Bernard Brogliato, Fernando Castaños, Departamento de Control Automático (CINVESTAV-IPN), Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV-IPN), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Subjects: Lyapunov stability, 0209 industrial biotechnology, Discretization, Computer science, 020208 electrical & electronic engineering, Linear system, Differential inclusions, 02 engineering and technology, Linear-quadratic-Gaussian control, Backward Euler method, Sliding mode control, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, sliding-mode control, linear uncertain systems, Differential inclusion, Control and Systems Engineering, Control theory, discrete-time systems, 0202 electrical engineering, electronic engineering, information engineering, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Robust control, robust control
Abstract: International audience; This paper focuses on the discrete-time sliding-mode control problem, that is, given an uncertain linear system under the effect of external matched perturbations, to design a set-valued control law that achieves the robust regulation of the plant and at the same time reduces substantially the chattering effect in both the input and the sliding variables. The cornerstone is the implicit Euler discretization technique together with a differential inclusion framework which allow us to make a suitable selection of the control values that will compensate for the disturbances. Numerical examples confirm the effectiveness of the proposed methodology.
Published: 2017
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27. Prelimenary results on the optimal control of linear complementarity systems

Author: Vieira, Alexandre, Brogliato, Bernard, Prieur, Christophe, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011)
Subjects: Complementarity problems, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Linear optimal control
Abstract: International audience; In this paper, we give some results concerning the quadratic optimal control of linear complementarity systems. We derive first order conditions for this system, that we manage to express as a Mixed Linear Complementarity System. We then use this result to build numerical schemes, which are expressed as Mathematical Problems with Equilibrium Constraints.
Published: 2017
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28. Prelimenary results on the optimal control of linear complementarity systems

Author: Christophe Prieur, Alexandre Vieira, Bernard Brogliato, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011)
Subjects: 0209 industrial biotechnology, Mathematical optimization, Mathematical problem, 010102 general mathematics, 02 engineering and technology, Lemke's algorithm, Linear optimal control, Optimal control, 01 natural sciences, Complementarity (physics), Linear complementarity problem, 020901 industrial engineering & automation, Quadratic equation, Complementarity problems, Control and Systems Engineering, Complementarity theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Mixed complementarity problem, Mathematics
Abstract: International audience; In this paper, we give some results concerning the quadratic optimal control of linear complementarity systems. We derive first order conditions for this system, that we manage to express as a Mixed Linear Complementarity System. We then use this result to build numerical schemes, which are expressed as Mathematical Problems with Equilibrium Constraints.
Published: 2017
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29. 3D Revolute Joint with Clearance in Multibody Systems

Author: Vincent Acary, Narendra Akhadkar, Bernard Brogliato, Schneider Electric ( SE), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Subjects: Computer science, business.industry, Numerical analysis, 02 engineering and technology, Structural engineering, Revolute joint, Multibody system, Degrees of freedom (mechanics), 01 natural sciences, Mechanism (engineering), 020303 mechanical engineering & transports, 0203 mechanical engineering, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], 0103 physical sciences, Contact dynamics, Overall performance, business, 010301 acoustics, Circuit breaker
Abstract: International audience; The aim of this paper is to understand the influence of radial and axial clearance in the revolute joints on the overall performance of a circuit breaker. A circuit breaker mechanism is made of seven links, seven revolute joints with clearance in both radial and axial direction, four unilateral contacts with friction, and it has forty-two degrees of freedom. The Moreau-Jean nonsmooth contact dynamics (NSCD) numerical method is used to perform the simulations. The numerical results are validated by careful comparisons with experimental data.
Published: 2017
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30. Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves

Author: Mariana Haragus, Panayotis G. Kevrekidis, Jesús Cuevas-Maraver, Dimitri J. Frantzeskakis, N. I. Karachalios, Guillaume James, Universidad de Sevilla, Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory (LANL), Department of Mathematics and Statistics [University of Massachusetts], University of Massachusetts System (UMASS), National and Kapodistrian University of Athens (NKUA), University of the Aegean, Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174) (FEMTO-ST), Université de Technologie de Belfort-Montbeliard (UTBM)-Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), ANR-13-BS01-0009,BoND,Frontières, numérique, dispersion.(2013), ANR-11-LABX-0001,ACTION,Systèmes intelligents intégrés au cœur de la matière(2011), Universidad de Sevilla / University of Sevilla, Université de Technologie de Belfort-Montbeliard (UTBM)-Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM)-Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), Universidad de Sevilla. Departamento de Física Aplicada I, Universidad de Sevilla. FQM280: Física no Lineal, and European Union (UE)
Subjects: Physics, Floquet theory, Breather, FOS: Physical sciences, Pattern Formation and Solitons (nlin.PS), Nonlinear Sciences - Pattern Formation and Solitons, 01 natural sciences, Stability (probability), Instability, 010305 fluids & plasmas, Classical mechanics, [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS], 0103 physical sciences, Orbit (dynamics), [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Peregrine soliton, Limit (mathematics), Rogue wave, 010306 general physics
Abstract: International audience; In the present work, we aim at taking a step towards the spectral stability analysis of Peregrine solitons, i.e., wave structures that are used to emulate extreme wave events. Given the space-time localized nature of Peregrine solitons, this is a priori a non-trivial task. Our main tool in this effort will be the study of the spectral stability of the periodic generalization of Peregrine soliton in the evolution variable, namely the Kuznetsov-Ma breather. Given the periodic structure of the latter, we compute the corresponding Floquet multipliers, and examine them in the limit where the period of the orbit tends to infinity. This way, we extrapolate towards the stability of the limiting structure, namely the Peregrine soliton. We find that multiple unstable modes of the background are enhanced, yet no additional unstable eigenmodes arise as the Peregrine limit is approached. We explore the instability evolution also in direct numerical simulations. Lastly, we speculate on the implications of these conclusions towards the stability of the Peregrine soliton structure.
Published: 2017
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31. Traveling waves in a spring-block chain sliding down a slope

Author: Guillaume James, Jose Eduardo Morales Morales, Arnaud Tonnelier, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Subjects: Spinodal, business.product_category, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Front (oceanography), Mechanics, 01 natural sciences, Pulse (physics), Physics::Geophysics, 010101 applied mathematics, Chain (algebraic topology), [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS], Control theory, Spring (device), 0103 physical sciences, Limit (music), 0101 mathematics, Inclined plane, 010306 general physics, business, Mathematics, Block (data storage)
Abstract: International audience; Travelling waves are studied in a spring slider-block model. We explicitly construct front waves (kinks) for a piecewise-linear spinodal friction force. Pulse waves are obtained as the matching of two traveling fronts with identical speeds. Explicit formulas are obtained for the wavespeed and the wave form in the anti-continuum limit. The link with localized waves in a Burridge-Knopoff model of an earthquake fault is briefly discussed.
Published: 2017
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32. Modélisation numérique de structures élancées en présence de contact frottant: de la simulation dynamique à la conception statique inverse

Author: Bertails-Descoubes, Florence, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Université Grenoble Alpes, Fabrice Neyret, and Bertails-Descoubes, Florence
Subjects: direct and inverse modeling, numerical simulation, [INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR], Tiges élastiques minces, Thin elastic rods, contact frottant, simulation numérique, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, frictional contact, modélisation directe et inverse, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]
Published: 2017

33. Visual Servoing Using Model Predictive Control to Assist Multiple Trajectory Tracking

Author: Nicolas Cazy, Paolo Robuffo Giordano, Pierre-Brice Wieber, François Chaumette, Visual servoing in robotics, computer vision, and augmented reality (Lagadic), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE (IRISA-D5), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE (IRISA-D5), Université de Bretagne Sud (UBS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Bretagne Sud (UBS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Rennes – Bretagne Atlantique, and Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: 0209 industrial biotechnology, Robot kinematics, Active perception, Computer science, business.industry, 02 engineering and technology, Visual servoing, Computer Science::Robotics, Model predictive control, 020901 industrial engineering & automation, Control theory, 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, Computer vision, Artificial intelligence, Noise (video), business
Abstract: International audience; We propose in this paper a new active perception scheme based on Model Predictive Control under constraints for generating a sequence of visual servoing tasks. The proposed control scheme is used to compute the motion of a camera whose task is to successively observe a set of robots for measuring their position and improving the accuracy of their localization. This method is based on the prediction of an uncertainty model (due to actuation and measurement noise) for determining which robot has to be observed by the camera. Simulation results are presented for validating the approach.
Published: 2017
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34. Méthodes de Newton non–lisses pour les problèmes de contact frottant dans les systèmes de multi–corps flexibles

Author: Acary, Vincent, Brémond, Maurice, Dubois, Frédéric, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), SED [Grenoble], Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Réseaux, Moyens Informatiques, Calcul Scientifique (Remics), Laboratoire de Mécanique et Génie Civil (LMGC), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Saclay, and Service Expérimentation et Développement (SED [Grenoble])
Subjects: lisses, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], contact unilatéral, frottement de Coulomb, méthodes Newton non
Abstract: International audience; Dans cette contribution, on se propose d’évaluer la performance des méthodes de Newton non–lisses dans le contexte des systèmes multi–corps flexibles (mécanismes, milieux granulaires ou milieux divisés) avec contact et frottement. Les méthodes itératives de type projection (Jacobi ou Gauss-Seidel projeté) sont généralement utilisées pour leurs propriétés de robustesse et de régularisation des systèmes fortement hyper–statiques. On montre que dans le cas des systèmes déformables, les méthodes de Newton permettent d’atteindre de grandes précisions à un coût beaucoup plus faible.
Published: 2017

35. Geometric and numerical aspects of redundancy

Author: Dimitar Dimitrov, Adrien Escande, Pierre-Brice Wieber, Alexander Sherikov, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Joint Robotics Laboratory (CNRS-AIST JRL ), National Institute of Advanced Industrial Science and Technology (AIST)-Centre National de la Recherche Scientifique (CNRS), and Joint Robotics Laboratory [Japan] (CNRS-AIST JRL)
Subjects: 0301 basic medicine, Engineering, Trust region, Mathematical optimization, business.industry, Mobile manipulator, Resolution (logic), Newton's method in optimization, 03 medical and health sciences, 030104 developmental biology, 0302 clinical medicine, Singularity, 030220 oncology & carcinogenesis, Redundancy (engineering), Robot, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Artificial intelligence, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], business, Humanoid robot
Abstract: International audience; If some resources of a robot are redundant with respect to a given objective, they can be used to address other, additional objectives. Since the amount of resources required to realize a given objective can vary, depending on the situation, this gives rise to a limited form of decision making, when assigning resources to different objectives according to the situation. Such decision making emerges in case of conflicts between objectives, and these conflicts appear to be situations of linear dependency and, ultimately, singularity of the solutions. Using an elementary model of a mobile manipulator robot with two degrees of freedom, we show how standard resolution schemes behave unexpectedly and inefficiently in such situations. We propose then as a remedy to introduce carefully tuned artificial conflicts, in the form of a trust region.
Published: 2017
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36. Unilaterally Incompressible Skinning

Author: Mickaël Ly, Florence Bertails-Descoubes, Damien Rohmer, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE ), and Inria - Research Centre Grenoble – Rhône-Alpes
Subjects: ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, buckling, unilateral constraint, skinning, cloth animation, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], ComputingMethodologies_COMPUTERGRAPHICS, complementarity
Abstract: Skinning was initially devised for computing the skin of a character deformed through a skeleton; but it is now also commonly used for deforming tight garments at a very cheap cost. However, unlike skin which may easily compress and stretch, tight cloth strongly resists compression: inside bending regions such as the interior of an elbow, cloth does not shrink but instead buckles, causing interesting folds and wrinkles which are completely missed by skinning methods. Our goal is to extend traditional skinning in order to capture such folding patterns automatically, without sacrificing efficiency. The key of our model is to replace the usual skinning formula — derived from, e.g., Linear Blend Skinning or Dual Quaternions — with a complementarity constraint, making an automatic switch between, on the one hand, classical skinning in zones prone to stretching, and on the other hand, a quasi-isometric scheme in zones prone to compression. Moreover, our method provides some useful handles to the user for directing the type of folds created, such as the fold density or the overall shape of a given fold. Our results show that our method can generate similar complexity of folds compared to full cloth simulation, while retaining interactivity of skinning approaches and offering intuitive user control.
Published: 2017

37. Uncontrolled inexact information within bundle methods

Author: Sofia Zaourar, Welington de Oliveira, Jérôme Malick, Données, Apprentissage et Optimisation (DAO), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Department of Applied Mathematics -- Universidade do Estado do Rio de Janeiro (UERJ), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), The first author gratefully acknowledges the support of the grant 'ANR GeoLMI' and the CNRS Mastodons project 'gargantua/titan'. The second author gratefully acknowledges the support provided by Severo Ochoa Program SEV-2013-0323 and Basque Government BERC Program 2014-2017., and ANR-11-BS03-0011,GEOLMI,Geométrie et algèbre des inégalités matricielles linéaires avec applications en commande(2011)
Subjects: 90C27, Mathematical optimization, Control and Optimization, Optimization problem, L-reduction, Nonsmooth optimization, bundle methods, two-stage stochastic problems, 0211 other engineering and technologies, 65K05, 010103 numerical & computational mathematics, 02 engineering and technology, Management Science and Operations Research, 01 natural sciences, Multi-objective optimization, 90C25, 0101 mathematics, Multi-swarm optimization, Mathematics, Continuous optimization, T57-57.97, 49M27, Applied mathematics. Quantitative methods, 021103 operations research, Probabilistic-based design optimization, QA75.5-76.95, energy optimization, [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO], 90C15, Computational Mathematics, Vector optimization, inexact oracle, Electronic computers. Computer science, Modeling and Simulation, Stochastic optimization, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 49J52, chance-constrained problems
Abstract: International audience; We consider convex nonsmooth optimization problems where additional information with uncontrolled accuracy is readily available. It is often the case when the objective function is itself the output of an optimization solver, as for large-scale energy optimization problems tackled by decomposition. In this paper, we study how to incorporate the uncontrolled linearizations into (proximal and level) bundle algorithms in view of generating better iterates and possibly accelerating the methods. We provide the convergence analysis of the algorithms using uncontrolled linearizations, and we present numerical illustrations showing they indeed speed up resolution of two stochastic optimization problems coming from energy optimization (two-stage linear problems and chance-constrained problems in reservoir management).
Published: 2017
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38. A New Representation of Systems with Frictional Unilateral Constraints and Its Baumgarte-Like Relaxation

Author: Bernard Brogliato, Ryo Kikuuwe, Kyushu University [Fukuoka], Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and Kyushu University
Subjects: 0209 industrial biotechnology, Control and Optimization, Physics::Medical Physics, Aerospace Engineering, Of the form, 02 engineering and technology, 01 natural sciences, symbols.namesake, 020901 industrial engineering & automation, 0103 physical sciences, frictional unilateral constraints, Applied mathematics, Algebraic number, differential algebraic inclusions, 010301 acoustics, Mathematics, Mechanical Engineering, Mathematical analysis, Ode, Baumgarte stabilization, 16. Peace & justice, Computer Science Applications, Mechanical system, Modeling and Simulation, Lagrange multiplier, Ordinary differential equation, Norm (mathematics), symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Differential algebraic equation
Abstract: International audience; This paper proposes a new representation of multibody mechanical systems involving three-dimensional frictional unilateral constraints. The new representation is of the form of a differential algebraic inclusion (DAI) employing a normal cone with a non-Euclidean, singular norm metric. It can be seen as a generalization of a differential algebraic equation (DAE) using Lagrange multipliers, which has been used to represent mechanical systems with equality constraints. The paper also presents an approach to approximate the aforementioned DAI by another form of DAI, which can be equivalently converted into an ordinary differential equation (ODE). The approach can be seen as a generalization of the Baumgarte stabilization, which is originally for DAEs. The new DAI representation and its ODE approximation are illustrated with some simple examples.
Published: 2017
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39. Simulation of Drucker–Prager granular flows inside Newtonian fluids

Author: Daviet, Gilles, Bertails-Descoubes, Florence, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and Daviet, Gilles
Subjects: [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract: Granular-fluid interactions appear in a variety of real-life scenarios ranging from immersed avalanches to ash clouds. We present a continuum-based numerical method for the simulation of such phenomena. Our approach avoids the heavy computational cost inherent to a fluid-solid coupling at the grain scale, while still being able to capture the distinctive regimes governing the collapse of an immersed granular column. To the best of our knowledge, the method presented here is the first to combine fully-coupled two-phase equations for immersed granular flows with an implicit nonsmooth treatment of the Drucker–Prager rheology.
Published: 2017

40. On output regulation in state-constrained systems: An application to polyhedral case

Author: Christophe Prieur, Aneel Tanwani, Bernard Brogliato, GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Grenoble Images Parole Signal Automatique (GIPSA-lab), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)
Subjects: complementarity problems, 0209 industrial biotechnology, Dynamical systems theory, state constraints, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 020208 electrical & electronic engineering, Convex set, Internal model, 02 engineering and technology, internal model principle, Nonlinear control, hybrid systems, Output regulation, [SPI.AUTO]Engineering Sciences [physics]/Automatic, System dynamics, 020901 industrial engineering & automation, Differential inclusion, Control theory, Hybrid system, 0202 electrical engineering, electronic engineering, information engineering, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Uniqueness, Mathematics
Abstract: International audience; This paper deals with the problem of output regulation using the state feedback control laws for a class of nonsmooth dynamical systems where the state is constrained to evolve within some convex set. The formalism of differential inclusions (DIs) is used to describe the system dynamics and the derivation of the state feedback law is based on the internal model principle. We study two types of control laws: firstly, a static control is designed assuming that the entire states of the plant and the exosystem are available for feedback; In the second case, only the error to be regulated is available for feedback and a dynamic compensator is designed. The analyses are based on using the properties of the normal cones associated with convex sets to study the well-posedness (existence and uniqueness of solutions) and the stability of the closed-loop system. As an application, we design a discontinuous controller which guarantees the viability of a predefined polyhedral subset of the state space using the formulation of linear complementarity systems.
Published: 2014
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41. Multi-Objective Control of Robots

Author: Dimitar Dimitrov, Pierre-Brice Wieber, Adrien Escande, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Joint Robotics Laboratory (CNRS-AIST JRL ), National Institute of Advanced Industrial Science and Technology (AIST)-Centre National de la Recherche Scientifique (CNRS), Joint Robotics Laboratory [Japan] (CNRS-AIST JRL), and Centre National de la Recherche Scientifique (CNRS)-National Institute of Advanced Industrial Science and Technology (AIST)
Subjects: Flexibility (engineering), Mathematical optimization, Optimization problem, Linear programming, Process (engineering), Robot, 16. Peace & justice, Set (psychology), Industrial engineering, Field (computer science), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Mathematics, Task (project management)
Abstract: International audience; "Prior to linear programming it was not practical to explicitly state general goals and so objectives were often confused with the ground rules for the solution. (...) Thus the means to attain the objective becomes the objective in itself, which in turn spawns new ground rules as to how to go about attaining the means (...). These means in turn become confused with goals." G. B. Dantzig Even though over 20 years old, the above quote still reflects well a common practice in the field of robotics. That is, not establishing a clear separation between: (i) what one wants to achieve, and (ii) how this must be done. Using high-level goals for posing real-world problems in mathematical terms can be advantageous since, at the level of modeling, one need not consider the particular technique for approaching their solution. In fact, being able to abstract the problem formulation can be viewed as a part of the revolutionary development that followed the birth of the field of linear programming [1], because practitioners could be trained to cast situations (of potentially great complexity) in terms of a set of general goals and rely on available solvers developed by specialists in the fields of numerical analysis and optimization. Such separation leads to a reliable solution process. In this note we argue that the ability to define typical robotic problems in terms of lucid goals is beneficial not only from the point of view of clarity of presentation, but also for efficiency of computations. Our main point is that this can be achieved through the explicit use of multi-objective formulations. By means of several 2014 4 16 Lexicographic Optimization, Task Prioritization, Hierarchical Problems, Inequality Constraints * 1 Rhone-Alpes, 38334 St-Ismier Cedex, France * 2 Tsukuba-shi, Ibaraki examples, we illustrate the advantages of this modeling approach and suggest that, by leveraging standard tools from the field of multi-objective optimization, such formulations can be resolved reliably and efficiently. We summarize some recent developments of (the already classical in the field of robotics) task prioriti-zation, among which the fact that hierarchical problems can be interpreted as a particular type of multi-objective models. 1. Multi-criteria decision making Multi-criteria decision making has been popular for many decades and a variety of optimization techniques for facilitating it has been developed. The ability to handle multiple criteria provides more expressive models , leading to an increase in flexibility and reliability of design, control, and estimation schemes. The key question in many areas is how to define what is a good/desirable behavior of a given process and often the answer involves the specification of multiple conflicting objectives. Conflicting objectives occur naturally in typical robotics problems. For example, consider a ma-nipulator arm mounted on a free-floating base. Then, due to the momentum conservation, the objective of tracking a given end-effector profile would conflict with the objective of preserving the posture of the base. Resolving conflicts between objectives usually requires the participation of a human decision-maker who can express preference relations between alternative solutions. The involvement of a decision-maker can come at different stages of the solution process. In some applications , solving a multi-objective optimization problem is defined as the generation of the pareto-optimal surface , at which point a decision-maker can analyze the results and choose the most appropriate pareto-optimal point. This technique, however, might be inadequate to the needs of other applications e.g., real-time robot
Published: 2014
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42. Super space clothoids

Author: Florence Bertails-Descoubes, Romain Casati, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)
Subjects: Power series, Mathematical analysis, thin elastic rod, Motion (geometry), 020207 software engineering, Geometry, 02 engineering and technology, Kinematics, Orders of magnitude (numbers), Curvature, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 01 natural sciences, Computer Graphics and Computer-Aided Design, Machine epsilon, 010101 applied mathematics, 3D Euler spiral, 0202 electrical engineering, electronic engineering, information engineering, Piecewise, 0101 mathematics, Differential (infinitesimal), power series, ACM: I.: Computing Methodologies/I.3: COMPUTER GRAPHICS/I.3.7: Three-Dimensional Graphics and Realism/I.3.7.0: Animation, Mathematics
Abstract: Thin elastic filaments in real world such as vine tendrils, hair ringlets or curled ribbons often depict a very smooth, curved shape that low-order rod models --- e.g., segment-based rods --- fail to reproduce accurately and compactly. In this paper, we push forward the investigation of high-order models for thin, inextensible elastic rods by building the dynamics of a G 2 -continuous piecewise 3D clothoid: a smooth space curve with piecewise affine curvature. With the aim of precisely integrating the rod kinematic problem, for which no closed-form solution exists, we introduce a dedicated integration scheme based on power series expansions. It turns out that our algorithm reaches machine precision orders of magnitude faster compared to classical numerical integrators. This property, nicely preserved under simple algebraic and differential operations, allows us to compute all spatial terms of the rod kinematics and dynamics in both an efficient and accurate way. Combined with a semi-implicit time-stepping scheme, our method leads to the efficient and robust simulation of arbitrary curly filaments that exhibit rich, visually pleasing configurations and motion. Our approach was successfully applied to generate various scenarios such as the unwinding of a curled ribbon as well as the aesthetic animation of spiral-like hair or the fascinating growth of twining plants.
Published: 2013
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43. Projected event-capturing time-stepping schemes for nonsmooth mechanical systems with unilateral contact and Coulomb’s friction

Author: Vincent Acary, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: Unilateral contact, Computational Mechanics, General Physics and Astronomy, 01 natural sciences, Projection (linear algebra), Modeling and simulation, Flexible multibody dynamics, [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph], Position (vector), Control theory, 0103 physical sciences, Gear-Gupta-Leimkuhler (GGL) technique, 0101 mathematics, 010301 acoustics, Mathematics, Computational contact mechanics, Mechanical Engineering, Multibody system, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Coulomb's friction, Finite element method, Computer Science Applications, 010101 applied mathematics, Impact, Discrete time and continuous time, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], Mechanics of Materials, Differential algebraic equation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; This work addresses the problem of the numerical time-integration of nonsmooth mechanical systems subjected to unilateral contacts, impacts and Coulomb's friction. The considered systems are the space-discretized continuous systems obtained by using a Finite Element Method (FEM) approach or the multi-body systems, or a mix of them as in flexible multibody dynamics. Up to now, two main numerical schemes are available for this purpose: the Moreau-Jean scheme which solves the constraints at the velocity level together with a Newton impact law and the Schatzman-Paoli scheme which directly considers the constraints at the position level. In both schemes, the position and velocity constraints are not both satisfied in discrete time. A first attempt is made by directly using the Gear-Gupta-Leimkuhler (GGL) approach for Differential Algebraic Equations (DAE), that solves, in discrete time, the constraints on both position and velocity levels. The obtained direct projection scheme succeeds in solving in discrete time both position and velocity constraints, but introduces some chattering at contact after a finite accumulation of impacts. The proposed scheme improves the direct projected scheme by combining several steps of activation and projection to avoid the chattering effect. The stability and the local order of the scheme will be discussed. The usefulness of the scheme is demonstrated on several academic examples and is illustrated on an industrial application : the modeling and simulation of an electrical circuit breaker.
Published: 2013
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44. Dynamics of planar rocking-blocks with Coulomb friction and unilateral constraints: comparisons between experimental and numerical data

Author: Hongjian Zhang, Caishan Liu, Bernard Brogliato, State Key Laboratory for Turbulence and Complex Systems (State Key Lab), Zhejiang University, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Centre National de la Recherche Scientifique (CNRS), Department of Civil, Construction and Environmental Engineering, and Marquette University
Subjects: Engineering, Control and Optimization, Free-rocking, Multiple impacts, Base (geometry), Aerospace Engineering, Motion (geometry), Rocking block, 02 engineering and technology, 01 natural sciences, Physics::Geophysics, Planar, 0203 mechanical engineering, 0103 physical sciences, 010301 acoustics, Block (data storage), business.industry, Mechanical Engineering, Dynamics (mechanics), Experimental data, Mechanics, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the structures [physics.class-ph], Computer Science Applications, Mechanical system, Coulomb friction, 020303 mechanical engineering & transports, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], Overturning, Modeling and Simulation, Onset of rocking, business, Excitation
Abstract: International audience; This paper concerns the dynamics of planar rocking blocks, which are mechanical systems subject to two unilateral constraints with friction. A recently introduced multiple impact law that incorporates Coulomb friction is validated through comparisons between numerical simulations and experimental data obtained elsewhere by other authors. They concern the free-rocking motion with no base excitation, and motions with various base ex-citations for the study of the onset of rocking and of the overturning phenomenon. The comparisons made for free-rocking and for the onset of rocking demonstrate that the proposed impact model allows one to correctly predict the block motions. Especially the free-rocking experiments can be used to fit the impact law parameters (restitution and friction coefficients , block width). The free-rocking fitted parameters are then used in the excited-base cases.
Published: 2013
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45. Travelling waves in a spring-block chain sliding down a slope

Author: Morales, José Eduardo Morales, James, Guillaume, Tonnelier, Arnaud, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and INRIA Grenoble - Rhône-Alpes
Subjects: Travelling front, excitability, piecewise-linear differential equations, [PHYS.MECA]Physics [physics]/Mechanics [physics], Physics::Geophysics, block-spring system
Abstract: Travelling waves in a spring-block chain sliding down an inclined plane are studied. For a piecewise-linear spinodal friction force, we construct analytically front waves. Pulse waves are obtained as the matching of two travelling fronts with identical speeds. Explicit formulas are obtained for the wavespeed and the wave form in the anti-continuum limit. The link with propagating phenomena in the Burridge-Knopoff model is briefly discussed.
Published: 2016

46. Localized waves in discrete excitable mechanical systems

Author: Morales Morales, Jose Eduardo, Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Grenoble Alpes, and Guillaume James
Subjects: Piecewise linear dynamical systems, Solitary waves and fronts, Burridge-Knopoff model, Ondes localisées, Equations differentielles avance-Retard, Modèle de Burridge-Knopoff, Systèmes dynamiques linéaires par morceaux, Advance-Delay differential equations, Ondes solitaires et fronts, Systèmes mécaniques excitables, Excitable mechanical systems, Travelling waves, [PHYS.MECA.ACOU]Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph]
Abstract: This thesis analyses localized travelling waves for some classes of nonlinearlattice differential equations describing excitable mechanical systems. Thesesystems correspond to an infinite chain of blocks connected by springs and sliding on a surface in the presence of a nonlinear velocity-dependent friction force. We investigate both the Burridge-Knopoff model (with blocks attached to springs pulled at constant velocity) and a chain of free blocks sliding on an inclined plane under the effect of gravity. For a class of non-monotonic friction functions, both systems display a large response to perturbations above a threshold, one of the main properties of excitable systems. This response induces the propagation of either solitary waves orfronts, depending on the model and parameter regime. We study these localized waves numerically and theoretically for a broad range of friction laws and parameter regimes, which leads to the analysis of nonlinear advance-delay differential equations. Phenomena of propagation failure and oscillations of the travelling wave profile are also investigated. The introduction of a piecewise linear friction function allows one to construct localized waves explicitly in the form of oscillatory integrals and to analyse some of their properties such as shape and wave speed. An existence proof for solitary waves is obtained for the excitable Burridge-Knopoff model in the weak coupling regime.; Cette thèse étudie des ondes localisées pour certaines classes d'équations différentielles non linéaires décrivant des systèmes mécaniques excitables. Ces systèmes correspondent à une chaîne infinie de blocs reliés par des ressorts et qui glissent sur un surface en présence d'une force de frottement non linéaire dépendant de la vitesse. Nous analysons à la fois le modèle de Burridge-Knopoff (avec des blocs attachés à des ressorts tirés à une vitesse constante) et une chaîne de blocs libres glissant sur un plan incliné sous l'effet de la gravité. Pour une classe de fonctions de frottement non-monotones, ces deux systèmes présentent une réponse de grande amplitude à des perturbations au-dessus d'un certain seuil, ce qui constitue l'une des principales propriétés des systèmes excitables. Cette réponse provoque la propagation d'ondes solitaires ou des fronts, en fonction du modèle et des paramètres. Nous étudions ces ondes localisées numériquement et théoriquement pour une grande gamme de lois de frottement et des régimes de paramètres, ce qui conduit à l'analyse d'équations différentielles non linéaires avec avance et retard. Les phénomènes d'extinction de propagation et d'apparition d'oscillations sont également étudiés pour les ondes progressives. L'introduction d'une fonction de frottement linéaire par morceaux permet de construire explicitement des ondes localisées sous la forme d'intégrales oscillantes et d'analyser certaines de leurs propriétés telles que la forme et la vitesse d'ondes. Une preuve de l'existence d'ondes solitaires est obtenue pour le modèle de Burridge-Knopoff pour un couplage faible.
Published: 2016

47. Ondes localisées dans des systèmes mécaniques discrets excitables

Author: Morales Morales, Jose Eduardo, Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Université Grenoble Alpes, Guillaume James, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Subjects: Piecewise linear dynamical systems, Solitary waves and fronts, Burridge-Knopoff model, Ondes localisées, Equations differentielles avance-Retard, Modèle de Burridge-Knopoff, Systèmes dynamiques linéaires par morceaux, Advance-Delay differential equations, Ondes solitaires et fronts, Systèmes mécaniques excitables, Excitable mechanical systems, Travelling waves, [PHYS.MECA.ACOU]Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph]
Abstract: This thesis analyses localized travelling waves for some classes of nonlinearlattice differential equations describing excitable mechanical systems. Thesesystems correspond to an infinite chain of blocks connected by springs and sliding on a surface in the presence of a nonlinear velocity-dependent friction force. We investigate both the Burridge-Knopoff model (with blocks attached to springs pulled at constant velocity) and a chain of free blocks sliding on an inclined plane under the effect of gravity. For a class of non-monotonic friction functions, both systems display a large response to perturbations above a threshold, one of the main properties of excitable systems. This response induces the propagation of either solitary waves orfronts, depending on the model and parameter regime. We study these localized waves numerically and theoretically for a broad range of friction laws and parameter regimes, which leads to the analysis of nonlinear advance-delay differential equations. Phenomena of propagation failure and oscillations of the travelling wave profile are also investigated. The introduction of a piecewise linear friction function allows one to construct localized waves explicitly in the form of oscillatory integrals and to analyse some of their properties such as shape and wave speed. An existence proof for solitary waves is obtained for the excitable Burridge-Knopoff model in the weak coupling regime.; Cette thèse étudie des ondes localisées pour certaines classes d'équations différentielles non linéaires décrivant des systèmes mécaniques excitables. Ces systèmes correspondent à une chaîne infinie de blocs reliés par des ressorts et qui glissent sur un surface en présence d'une force de frottement non linéaire dépendant de la vitesse. Nous analysons à la fois le modèle de Burridge-Knopoff (avec des blocs attachés à des ressorts tirés à une vitesse constante) et une chaîne de blocs libres glissant sur un plan incliné sous l'effet de la gravité. Pour une classe de fonctions de frottement non-monotones, ces deux systèmes présentent une réponse de grande amplitude à des perturbations au-dessus d'un certain seuil, ce qui constitue l'une des principales propriétés des systèmes excitables. Cette réponse provoque la propagation d'ondes solitaires ou des fronts, en fonction du modèle et des paramètres. Nous étudions ces ondes localisées numériquement et théoriquement pour une grande gamme de lois de frottement et des régimes de paramètres, ce qui conduit à l'analyse d'équations différentielles non linéaires avec avance et retard. Les phénomènes d'extinction de propagation et d'apparition d'oscillations sont également étudiés pour les ondes progressives. L'introduction d'une fonction de frottement linéaire par morceaux permet de construire explicitement des ondes localisées sous la forme d'intégrales oscillantes et d'analyser certaines de leurs propriétés telles que la forme et la vitesse d'ondes. Une preuve de l'existence d'ondes solitaires est obtenue pour le modèle de Burridge-Knopoff pour un couplage faible.
Published: 2016

48. Safe navigation strategies for a biped robot walking in a crowd

Author: Dimitar Dimitrov, Nestor Bohorquez, Alexander Sherikov, Pierre-Brice Wieber, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Subjects: 0209 industrial biotechnology, Computer science, 02 engineering and technology, Collision, Mobile robot navigation, 020901 industrial engineering & automation, Crowds, Terminal (electronics), Control theory, 11. Sustainability, 0202 electrical engineering, electronic engineering, information engineering, Robot, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], 020201 artificial intelligence & image processing, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Duration (project management), Simulation, Collision avoidance
Abstract: International audience; Safety needs to be guaranteed before we can introduce robots into our working environments. For a biped robot to navigate safely in a crowd it must maintain balance and avoid collisions. In highly dynamic and unpredictable environments like crowds, collision avoidance is usually interpreted as passive safety, i.e. that the robot can stop before any collision occurs. We show that both balance preservation and passive safety can be analyzed, from the point of view of viability theory, as the ability of the robot to stop safely at some point in the future. This allows us to address both problems with a single model predictive controller with appropriate terminal constraints. We demonstrate that this controller predicts failures (falls and collisions) as early as the duration of the preview horizon. Finally, we propose a new strategy for safe navigation that relaxes the passive safety conditions to allow the robot to avoid a greater number of collisions.
Published: 2016
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49. Comments on 'Chattering-free digital sliding-mode control with state observer anddisturbance rejection'

Author: Yury Orlov, Vincent Acary, Bernard Brogliato, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and Centro de Investigacion Cientifica y de Education Superior de Ensenada [Mexico] (CICESE)
Subjects: zero-order-hold method, 0209 industrial biotechnology, Variable structure control, backward Euler method, Disturbance (geology), Automatic control, sliding-mode, Control engineering, Mistake, 02 engineering and technology, Backward Euler method, Sliding mode control, discrete-time sliding mode, Computer Science Applications, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, State observer, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering, Mathematics
Abstract: International audience; An unfortunate mistake in the proof of Proposition 1 in V. Acary, B. Brogliato, Y. Orlov, IEEE Transactions on Automatic Control, 57(5) 1087-1101, 2012, is corrected.
Published: 2016
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50. A Newton method with always feasible iterates for Nonlinear Model Predictive Control of walking in a multi-contact situation

Author: Pierre-Brice Wieber, Dimitar Dimitrov, Diana Serra, Alexander Sherikov, Camille Brasseur, Dipartimento di Ingegneria Elettrica e delle Tecnologie dell'Informazione [Napoli] (DIETI), Università degli studi di Napoli Federico II, Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems (BIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and University of Naples Federico II = Università degli studi di Napoli Federico II
Subjects: 0209 industrial biotechnology, Mathematical optimization, Computer science, Computation, 020207 software engineering, 02 engineering and technology, Nonlinear control, symbols.namesake, Nonlinear system, Model predictive control, 020901 industrial engineering & automation, Control theory, Iterated function, 0202 electrical engineering, electronic engineering, information engineering, symbols, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Reduction (mathematics), Dynamic balance, Newton's method
Abstract: International audience; In this paper, we present a Nonlinear Model Predictive Control scheme, which is able to generate walking motions in multi-contact situations. Walking up and down stairs with an additional hand support is a typical example, which we address in simulation. Computing such a nonlinear control scheme is usually done with a Newton method, a potentially time-consuming procedure involving iterative linearizations. We propose here a Newton method which is specifically designed to provide at each iteration a feasible solution, always satisfying the (nonlinear) dynamic balance constraints. This results in a significant reduction in computation time, by minimizing the number of necessary iterations to reach a feasible solution.
Published: 2016
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