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102
Learning from demonstration and adaptation of biped locomotion
 Robotics and Autonomous Systems
, 2004
"... Abstract — In this paper, we report on our research for learning biped locomotion from human demonstration. Our ultimate goal is to establish a design principle of a controller in order to achieve natural humanlike locomotion. We suggest dynamical movement primitives as a CPG of a biped robot, an a ..."
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Cited by 82 (7 self)
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Abstract — In this paper, we report on our research for learning biped locomotion from human demonstration. Our ultimate goal is to establish a design principle of a controller in order to achieve natural humanlike locomotion. We suggest dynamical movement primitives as a CPG of a biped robot, an approach we have previously proposed for learning and encoding complex human movements. Demonstrated trajectories are learned through the movement primitives by locally weighted regression, and the frequency of the learned trajectories is adjusted automatically by a novel frequency adaptation algorithm based on phase resetting and entrainment of oscillators. Numerical simulations demonstrate the effectiveness of the proposed locomotion controller. I.
On partial contraction analysis for coupled nonlinear oscillators
 technical Report, Nonlinear Systems Laboratory, MIT
, 2003
"... We describe a simple but general method to analyze networks of coupled identical nonlinear oscillators, and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized)results on synchroni ..."
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Cited by 61 (33 self)
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We describe a simple but general method to analyze networks of coupled identical nonlinear oscillators, and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized)results on synchronization, antisynchronization and oscillatordeath. The method can be applied to coupled networks of various structures and arbitrary size. For oscillators with positivedefinite diffusion coupling, it can be shown that synchronization always occur globally for strong enough coupling strengths, and an explicit upper bound on the corresponding threshold can be computed through eigenvalue analysis. The discussion also extends to the case when network structure varies abruptly and asynchronously, as in “flocks ” of oscillators or dynamic elements.
Visualizing Poincaré Maps Together With the Underlying Flow
 In International Workshop on Visualization and Mathematics'97 Proceedings
, 1997
"... We present a set of advanced techniques for the visualization of 2D Poincar'e maps. Since 2D Poincar'e maps are a mathematical abstraction of periodic or quasiperiodic 3D flows, we propose to embed the 2D visualization with standard 3D techniques to improve the understanding of the Poincar'e map ..."
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Cited by 22 (3 self)
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We present a set of advanced techniques for the visualization of 2D Poincar'e maps. Since 2D Poincar'e maps are a mathematical abstraction of periodic or quasiperiodic 3D flows, we propose to embed the 2D visualization with standard 3D techniques to improve the understanding of the Poincar'e maps. Methods to enhance the representation of the relation x $ P (x), e.g., the use of spot noise, are presented as well as techniques to visualize the repeated application of P , e.g., the approximation of P as a warp function. It is shown that animation can be very useful to further improve the visualization. For example, the animation of the construction of Poincar'e map P is inherently a proper visualization. During the paper we present a set of examples which demonstrate the usefulness of our techniques. Keywords: visualization, dynamical systems, Poincar'e maps 1 Introduction Poincar'e sections are an important tool for the investigation of dynamical systems in theory as well a...
Neural circuit dynamics underlying accumulation of timevarying evidence during perceptual decision making
, 2007
"... perceptual decision making ..."
Thorough Insights By Enhanced Visualization Of Flow Topology
 In 9th Int. Symposium on Flow Visualization, CDROM
, 2000
"... The investigation of flow data can be eased by the visualization of topological information about the flow. Especially, when empirical models or numerical results from flow simulation are investigated, often the first step of analysis is to search structural elements, like fixed points, separatric ..."
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Cited by 9 (2 self)
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The investigation of flow data can be eased by the visualization of topological information about the flow. Especially, when empirical models or numerical results from flow simulation are investigated, often the first step of analysis is to search structural elements, like fixed points, separatrices, etc. The work presented in this paper focuses on the visualization of 3D dynamical systems (comparable to flow data) on the basis of results which are obtained by automatic analysis of the flow topology. Fixed points are determined and the Jacobian matrix of the flow is investigated at these points of phase space to obtain the associated stable and/or unstable invariant sets. Furthermore, this paper presents how Poincar maps are used to visualize structural information about cyclic flow data together with direct visualization cues like stream lines or stream surfaces. 1 INTRODUCTION AND MOTIVATION Flow visualization has been a challenging task for quite a long time already and ma...
The computation and sensitivity of double eigenvalues
, 1999
"... This paper explores the problem left open by Wilkinson of computing the distance of a given diagonalizable matrix to the nearest nondiagonalizable matrix. Algorithms for finding the nearest nondiagonalizable matrix to a given diagonalizable matrix are presented and analyzed. It will be shown tha ..."
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Cited by 8 (1 self)
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This paper explores the problem left open by Wilkinson of computing the distance of a given diagonalizable matrix to the nearest nondiagonalizable matrix. Algorithms for finding the nearest nondiagonalizable matrix to a given diagonalizable matrix are presented and analyzed. It will be shown that this problem reduces to finding the critical points of the spectral portrait (the graph of the pseudospectrum) and that critical points are illconditioned if and only iff the corresponding nearby nondiagonalizable matrix problem is illconditioned.
DynSys3D: A workbench for developing advanced visualization techniques in the field of threedimensional dynamical systems
"... This work describes DynSys3D, a framework for testing and implementing visualization techniques in the area of threedimensional dynamical systems. DynSys3D has been designed to meet requirements which allow a fast and modular investigation of dynamical systems. Such requirements are, e.g., extendab ..."
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Cited by 7 (6 self)
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This work describes DynSys3D, a framework for testing and implementing visualization techniques in the area of threedimensional dynamical systems. DynSys3D has been designed to meet requirements which allow a fast and modular investigation of dynamical systems. Such requirements are, e.g., extendability, interactivity, and symmetry. Some visualization examples realized with DynSys3D illustrate the exibility of the system.
Ten Problems in Experimental Mathematics
, 2006
"... Challenge ” of Nick Trefethen, beautifully described in [12] (see also [13]). Indeed, these ten numeric challenge problems are also listed in [15, pp. 22–26], where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent in [15] was to present ..."
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Cited by 7 (6 self)
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Challenge ” of Nick Trefethen, beautifully described in [12] (see also [13]). Indeed, these ten numeric challenge problems are also listed in [15, pp. 22–26], where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent in [15] was to present ten problems that are characteristic of the sorts of problems
Contraction analysis of synchronization in networks of nonlinearly coupled oscillators
"... Nonlinear contraction theory allows surprisingly simple analysis of synchronisation phenomena in distributed networks of coupled nonlinear elements. The key idea is the construction of a virtual contracting system whose particular solutions include the individual subsystems ’ states. We also study t ..."
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Cited by 6 (0 self)
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Nonlinear contraction theory allows surprisingly simple analysis of synchronisation phenomena in distributed networks of coupled nonlinear elements. The key idea is the construction of a virtual contracting system whose particular solutions include the individual subsystems ’ states. We also study the role, in both nature and system design, of coexisting “power” leaders, to which the networks synchronize, and “knowledge” leaders, to whose parameters the networks adapt. Also described are applications to large scale computation using neural oscillators, and to timedelayed teleoperation between synchronized groups. Similarly, contraction theory can be systematically and simply extended to address classical questions in hybrid nonlinear systems. The key idea is to view the formal definition of a virtual displacement, a concept central to the theory, as describing the state transition of a differential system. This yields in turn a compositional contraction analysis of switching and resetting phenomena. Applications to hybrid nonlinear oscillators are also discussed.