References of "Sepulchre, Rodolphe"
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See detailA PDE viewpoint on basic properties of coordination algorithms with symmetries
Sarlette, Alain ULg; Sepulchre, Rodolphe ULg

in Proceedings of the 48th IEEE Conference on Decision and Control (2009, December)

Several recent control applications consider the coordination of subsystems through local interaction. Often the interaction has a symmetry in state space, e.g. invariance with respect to a uniform ... [more ▼]

Several recent control applications consider the coordination of subsystems through local interaction. Often the interaction has a symmetry in state space, e.g. invariance with respect to a uniform translation of all subsystem values. The present paper shows that in presence of such symmetry, fundamental properties can be highlighted by viewing the distributed system as the discrete approximation of a partial differential equation. An important fact is that the symmetry on the state space differs from the popular spatial invariance property, which is not necessary for the present results. The relevance of the viewpoint is illustrated on two examples: (i) ill-conditioning of interaction matrices in coordination/consensus problems and (ii) the string instability issue. [less ▲]

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See detailAutonomous rigid body attitude synchronization
Sarlette, Alain ULg; Sepulchre, Rodolphe ULg; Leonard, Naomi

in Automatica (2009), 45(2), 572-577

Control laws to synchronize attitudes in a swarm of fully actuated rigid bodies, in the absence of a common reference attitude or hierarchy in the swarm, are proposed in [Smith, T. R., Hanssmann, H ... [more ▼]

Control laws to synchronize attitudes in a swarm of fully actuated rigid bodies, in the absence of a common reference attitude or hierarchy in the swarm, are proposed in [Smith, T. R., Hanssmann, H., & Leonard, N.E. (2001). "Orientation control of multiple underwater vehicles with symmetry-breaking potentials". In Proc. 40th IEEE conf. decision and control (pp. 4598–4603); Nair, S., Leonard, N. E. (2007). "Stable synchronization of rigid body networks". In Networks and Heterogeneous Media, 2(4), 595–624]. The present paper studies two separate extensions with the same energy shaping approach: (i) locally synchronizing the rigid bodies’ attitudes, but without restricting their final motion and (ii) relaxing the communication topology from undirected, fixed and connected to directed, varying and uniformly connected. The specific strategies that must be developed for these extensions illustrate the limitations of attitude control with reduced information. [less ▲]

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See detailConsensus optimization on manifolds
Sarlette, Alain ULg; Sepulchre, Rodolphe ULg

in SIAM Journal on Control & Optimization (2009), 48(1), 56-76

The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their ... [more ▼]

The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e., maximizing the consensus) or balance (i.e., minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO(n) and the Grassmann manifold Grass(p,n) are treated as original examples. A link is also drawn with the many existing results on the circle. [less ▲]

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See detailFrom subspace learning to distance learning: a geometrical optimization approach
Meyer, Gilles ULg; Journée, Michel; Bonnabel, Silvère et al

in Proceedings of the 2009 IEEE Workshop on Statistical Signal Processing (SSP2009) (2009)

In this paper, we adopt a differential-geometry viewpoint to tackle the problem of learning a distance online. As this prob- lem can be cast into the estimation of a fixed-rank positive semidefinite (PSD ... [more ▼]

In this paper, we adopt a differential-geometry viewpoint to tackle the problem of learning a distance online. As this prob- lem can be cast into the estimation of a fixed-rank positive semidefinite (PSD) matrix, we develop algorithms that ex- ploits the rich geometry structure of the set of fixed-rank PSD matrices. We propose a method which separately updates the subspace of the matrix and its projection onto that subspace. A proper weighting of the two iterations enables to continu- ously interpolate between the problem of learning a subspace and learning a distance when the subspace is fixed. [less ▲]

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See detailSynchronization in Networks of Identical Linear Systems
Scardovi, Luca; Sepulchre, Rodolphe ULg

in Automatica (2009), 45(11), 2557-2562

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See detailAdaptive Regulation of Vector Controlled Induction Motors
Jadot, Fabrice; Malrait, Francois; Moreno, Javier et al

in IEEE Transactions on Control Systems Technology (2009), 17(3),

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See detailRiemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank
Bonnabel, Silvère; Sepulchre, Rodolphe ULg

in SIAM Journal on Matrix Analysis & Applications (2009), 31(3), 1055--1070

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See detailNonlinear Drillstring Dynamics Analysis
Germay, Christophe; deWouw, Nathan Van; Nijmeijer, Henk et al

in SIAM Journal on Applied Dynamical Systems (2009), 8(2), 527--553

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See detailCoordination on Lie groups
Sarlette, Alain ULg; Bonnabel, Silvère; Sepulchre, Rodolphe ULg

in Proceedings of the 47th IEEE Conference on Decision and Control (2008, December)

This paper studies the coordinated motion of a group of agents evolving on a Lie group. Left- or right-invariance with respect to the absolute position on the group lead to two different characterizations ... [more ▼]

This paper studies the coordinated motion of a group of agents evolving on a Lie group. Left- or right-invariance with respect to the absolute position on the group lead to two different characterizations of relative positions and two associated definitions of coordination (fixed relative positions). Conditions for each type of coordination are derived in the associated Lie algebra. This allows to formulate the coordination problem on Lie groups as consensus in a vector space. Total coordination occurs when both types of coordination hold simultaneously. The discussion in this paper provides a common geometric framework for previously published coordination control laws on SO(3), SE(2) and SE(3). The theory is illustrated on the group of planar rigid motion SE(2). [less ▲]

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See detailClustering behaviors in networks of integrate-and-fire oscillators
Mauroy, Alexandre ULg; Sepulchre, Rodolphe ULg

in Chaos (2008), 18

Clustering behavior is studied in a model of integrate-and-fire oscillators with excitatory pulse coupling. When considering a population of identical oscillators, the main result is a proof of global ... [more ▼]

Clustering behavior is studied in a model of integrate-and-fire oscillators with excitatory pulse coupling. When considering a population of identical oscillators, the main result is a proof of global convergence to a phase-locked clustered behavior. The robustness of this clustering behavior is then investigated in a population of nonidentical oscillators by studying the transition from total clustering to the absence of clustering as the group coherence decreases. A robust intermediate situation of partial clustering, characterized by few oscillators traveling among nearly phase-locked clusters, is of particular interest. The analysis complements earlier studies of synchronization in a closely related model. [less ▲]

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See detailGlobal synchronization on the circle
Sarlette, Alain ULg; Tuna, Sezai Emre; Blondel, Vincent et al

in Proceedings of the 17th IFAC World Congress (2008, July)

The convexity arguments used in the consensus literature to prove synchronization in vector spaces can be applied to the circle only when all agents are initially located on a semicircle. Existing ... [more ▼]

The convexity arguments used in the consensus literature to prove synchronization in vector spaces can be applied to the circle only when all agents are initially located on a semicircle. Existing strategies for (almost-)global synchronization on the circle are either restricted to specific interconnection topologies or use auxiliary variables. The present paper first illustrates this problem by showing that weighted, directed interconnection topologies can be designed to make any reasonably chosen configuration of the agents on the circle a stable equilibrium of a basic continuous-time consensus algorithm. Then it proposes a so-called “gossip algorithm”, which achieves global asymptotic synchronization on the circle with probability 1 for a large class of interconnections, without using auxiliary variables, thanks to the introduction of randomness in the system. [less ▲]

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See detailRobotics and neuroscience: A rhythmic interaction
Ronsse, Renaud; Lefèvre, Philippe; Sepulchre, Rodolphe ULg

in Neural Networks (2008), 21(4), 577-583

At the crossing between motor control neuroscience and robotics system theory, the paper presents a rhythmic experiment that is amenable both to handy laboratory implementation and simple mathematical ... [more ▼]

At the crossing between motor control neuroscience and robotics system theory, the paper presents a rhythmic experiment that is amenable both to handy laboratory implementation and simple mathematical modeling. The experiment is based on an impact juggling task, requiring the coordination of two upper-limb effectors and some phase-locking with the trajectories of one or several juggled objects. We describe the experiment, its implementation and the mathematical model used for the analysis. Our underlying research focuses on the role of sensory feedback in rhythmic tasks. In a robotic implementation of our experiment, we study the minimum feedback that is required to achieve robust control. A limited source of feedback, measuring only the impact times, is shown to give promising results. A second field of investigation concerns the human behavior in the same impact juggling task. We study how a variation of the tempo induces a transition between two distinct control strategies with different sensory feedback requirements. Analogies and differences between the robotic and human behaviors are obviously of high relevance in such a flexible setup. [less ▲]

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See detailStabilization of Planar Collective Motion With Limited Communication
Sepulchre, Rodolphe ULg; Paley, Derek; Leonard, Naomi E.

in IEEE Transactions on Automatic Control (2008), 53(3), 706-719

This paper proposes a designmethodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel ... [more ▼]

This paper proposes a designmethodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and time-invariant or timevarying. The emphasis of this paper is to show how previous results assuming all-to-all communication can be extended to a general communication framework. [less ▲]

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See detailGeometric framework for coordination on Lie groups
Sarlette, Alain ULg; Bonnabel, Silvère ULg; Sepulchre, Rodolphe ULg

Conference (2008, March)

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See detailControl of Bimanual Rhythmic Movements: Trading Efficiency for Robustness Depending on the Context
Ronsse, R.; Thonnard, J. L.; Lefevre Philippe et al

in Experimental Brain Research = Experimentelle Hirnforschung = Expérimentation Cérébrale (2008)

This paper investigates how the efficiency and robustness of a skilled rhythmic task compete against each other in the control of a bimanual movement. Human subjects juggled a puck in 2D through impacts ... [more ▼]

This paper investigates how the efficiency and robustness of a skilled rhythmic task compete against each other in the control of a bimanual movement. Human subjects juggled a puck in 2D through impacts with two metallic arms, requiring rhythmic bimanual actuation. The arms kinematics were only constrained by the position, velocity and time of impacts while the rest of the trajectory did not influence the movement of the puck. In order to expose the task robustness, we manipulated the task context in two distinct manners: the task tempo was assigned at four different values (hence manipulating the time available to plan and execute each impact movement individually); and vision was withdrawn during half of the trials (hence reducing the sensory inflows). We show that when the tempo was fast, the actuation was rhythmic (no pause in the trajectory) while at slow tempo, the actuation was discrete (with pause intervals between individual movements). Moreover, the withdrawal of visual information encouraged the rhythmic behavior at the four tested tempi. The discrete versus rhythmic behavior give different answers to the efficiency/robustness trade-off: discrete movements result in energy efficient movements, while rhythmic movements impact the puck with negative acceleration, a property preserving robustness. Moreover, we report that in all conditions the impact velocity of the arms was negatively correlated with the energy of the puck. This correlation tended to stabilize the task and was influenced by vision, revealing again different control strategies. In conclusion, this task involves different modes of control that balance efficiency and robustness, depending on the context. [less ▲]

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See detailContinuous-time susbspace flows related to the symmetric eigenvalue problem
Absil, Pierre-Antoine; Sepulchre, Rodolphe ULg; Mahony, Robert

in Pacific Journal of Optimization (2008), 4(2), 179--194

The classes of continuous-time flows on Rn×p that induce the same flow on the set of p-dimensional subspaces of Rn are described. The power flow is briefly reviewed in this framework, and a subspace ... [more ▼]

The classes of continuous-time flows on Rn×p that induce the same flow on the set of p-dimensional subspaces of Rn are described. The power flow is briefly reviewed in this framework, and a subspace generalization of the Rayleigh quotient flow [Linear Algebra Appl. 368C, 2003, pp. 343–357] is proposed and analyzed. This new flow displays a property akin to deflation in finite time. [less ▲]

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See detailSTABILIZATION OF THREE-DIMENSIONAL COLLECTIVE MOTION
Scardovi, Luca; Leonard, N. E.; Sepulchre, Rodolphe ULg

in Communications in Information and Systems (2008), 8(4), 473-500

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the ... [more ▼]

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the stabilization problem is reduced to a consensus problem on the Lie algebra. The resulting equilibria correspond to parallel, circular and helical formations. We first derive the stabilizing control laws in the presence of all-to-all communication. Providing each agent with a consensus estimator, we then extend the results to a general setting that allows for unidirectional and time-varying communication topologies. [less ▲]

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See detailSpatial Models of Bistability in Biological Collectives
Paley, Derek; Leonard, Naomi; Sepulchre, Rodolphe ULg et al

in Proceedings of the 46th IEEE Conference on Decision and Control (2007, December)

We explore collective behavior in biological systems using a cooperative control framework. In particular, we study a hysteresis phenomenon in which a collective switches from circular to parallel motion ... [more ▼]

We explore collective behavior in biological systems using a cooperative control framework. In particular, we study a hysteresis phenomenon in which a collective switches from circular to parallel motion under slow variation of the neighborhood size in which individuals tend to align with one another. In the case that the neighborhood radius is less than the circular motion radius, both circular and parallel motion can occur. We provide Lyapunov-based analysis of bistability of circular and parallel motion in a closed-loop system of selfpropelled particles with coupled-oscillator dynamics. [less ▲]

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