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Nonlinear Drillstring Dynamics Analysis ; ; et al in SIAM Journal on Applied Dynamical Systems (2009), 8(2), 527--553 Detailed reference viewed: 29 (5 ULg)Coordination on Lie groups Sarlette, Alain ; ; Sepulchre, Rodolphe 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 ▲] Detailed reference viewed: 42 (16 ULg)Modulation of Burst Firing by KCNQ Channels in Dopaminergic Neurons: Further Mechanistic Modeling and Experimental Findings Waroux, Olivier ; ; Drion, Guillaume et al Poster (2008, November) Detailed reference viewed: 8 (3 ULg)Clustering behaviors in networks of integrate-and-fire oscillators Mauroy, Alexandre ; Sepulchre, Rodolphe 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 ▲] Detailed reference viewed: 48 (16 ULg)Global synchronization on the circle Sarlette, Alain ; ; 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 ▲] Detailed reference viewed: 145 (7 ULg)Robotics and neuroscience: A rhythmic interaction ; ; Sepulchre, Rodolphe 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 ▲] Detailed reference viewed: 16 (3 ULg)Stabilization of Planar Collective Motion With Limited Communication Sepulchre, Rodolphe ; ; 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 ▲] Detailed reference viewed: 32 (1 ULg)Geometric framework for coordination on Lie groups Sarlette, Alain ; Bonnabel, Silvère ; Sepulchre, Rodolphe Conference (2008, March) Detailed reference viewed: 35 (11 ULg)Control of Bimanual Rhythmic Movements: Trading Efficiency for Robustness Depending on the Context ; ; 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 ▲] Detailed reference viewed: 13 (2 ULg)Clustering behaviours in networks of integrate-and-fire oscillators Mauroy, Alexandre ; Sepulchre, Rodolphe Poster (2008) Detailed reference viewed: 2 (0 ULg)Synchronization and clustering behaviors in networks of integrate-and-fire oscillators Mauroy, Alexandre ; Sepulchre, Rodolphe Poster (2008) Detailed reference viewed: 4 (0 ULg)Dynamical phenomena in pulse-coupled networks of firing integrators Mauroy, Alexandre ; Sepulchre, Rodolphe Conference (2008) Detailed reference viewed: 1 (0 ULg)Continuous-time susbspace flows related to the symmetric eigenvalue problem ; Sepulchre, Rodolphe ; 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 ▲] Detailed reference viewed: 24 (7 ULg)STABILIZATION OF THREE-DIMENSIONAL COLLECTIVE MOTION ; ; Sepulchre, Rodolphe 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 ▲] Detailed reference viewed: 15 (1 ULg)Spatial Models of Bistability in Biological Collectives ; ; Sepulchre, Rodolphe 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 ▲] Detailed reference viewed: 7 (0 ULg)Autonomous rigid body attitude synchronization Sarlette, Alain ; Sepulchre, Rodolphe ; in Proceedings of the 46th IEEE Conference on Decision and Control (2007, December) This paper studies some extensions to the decentralized attitude synchronization of identical rigid bodies. Considering fully actuated Euler equations, the communication links between the rigid bodies are ... [more ▼] This paper studies some extensions to the decentralized attitude synchronization of identical rigid bodies. Considering fully actuated Euler equations, the communication links between the rigid bodies are limited and the available information is restricted to relative orientations and angular velocities. In particular, no leader nor external reference dictates the swarm's behavior. The control laws are derived using two classical approaches of nonlinear control - tracking and energy shaping. This leads to a comparison of two corresponding methods which are currently considered for distributed synchronization - consensus and stabilization of mechanical systems with symmetries. [less ▲] Detailed reference viewed: 37 (9 ULg)Consensus under general convexity ; Sepulchre, Rodolphe in Proceedings of the 46th IEEE Conference on Decision and Control (2007, December) A method is proposed to characterize contraction of a set through orthogonal projections. For discrete-time multi-agent systems, quantitative estimates of convergence (to a consensus) rate are provided by ... [more ▼] A method is proposed to characterize contraction of a set through orthogonal projections. For discrete-time multi-agent systems, quantitative estimates of convergence (to a consensus) rate are provided by means of contracting convex sets. Required convexity for the sets that should include the values that the transition maps of agents take is considered in a more general sense than that of Euclidean geometry. [less ▲] Detailed reference viewed: 20 (0 ULg)Stabilization of Collective Motion in Three Dimensions : A Consensus Approach ; ; Sepulchre, Rodolphe in Proceedings of 46th IEEE Conference on Decision and Control (2007, December) 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 rst 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 ▲] Detailed reference viewed: 16 (0 ULg)Alternating Spatial Patterns for Coordinated Group Motion ; ; et al in Proceedings of the 46th IEEE Conference on Decision and Control (2007, December) Abstract—Motivated by recent observations of fish schools, we study coordinated group motion for individuals with oscillatory speed. Neighbors that have speed oscillations with common frequency, amplitude ... [more ▼] Abstract—Motivated by recent observations of fish schools, we study coordinated group motion for individuals with oscillatory speed. Neighbors that have speed oscillations with common frequency, amplitude and average but different phases, move together in alternating spatial patterns, taking turns being towards the front, sides and back of the group. We propose a model and control laws to investigate the connections between these spatial dynamics, communication when sensing is range or direction limited, and convergence of coordinated group motions. [less ▲] Detailed reference viewed: 13 (1 ULg)A Hybrid Systems Approach to Trajectory Tracking Control for Juggling Systems ; ; Sepulchre, Rodolphe in Proceedings of the 46th IEEE Conference on Decision and Control (2007, December) From a hybrid systems point of view, we provide a modeling framework and a trajectory tracking control design methodology for juggling systems. We present the main ideas and concepts in a one degree-of ... [more ▼] From a hybrid systems point of view, we provide a modeling framework and a trajectory tracking control design methodology for juggling systems. We present the main ideas and concepts in a one degree-of-freedom juggler, which consists of a ball bouncing on an actuated robot. We design a hybrid control strategy that, with only information of the ball’s state at impacts, controls the ball to track a reference rhythmic pattern with arbitrary precision. We extend this hybrid control strategy to the case of juggling multiple balls with different rhythmic patterns. Simulation results for juggling of one and three balls with a single actuated robot are presented. [less ▲] Detailed reference viewed: 17 (0 ULg) |
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