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Title:
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CONTRACTION THEORY AS METHOD FOR THE ANALYSIS AND DESIGN OF THE STABILITY OF COLLECTIVE BEHAVIOR IN CROWDS |
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Author(s):
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Albert Mukovskiy, Jean-Jacques Slotine, Martin A. Giese |
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ISBN:
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978-972-8939-22-9 |
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Editors:
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Yingcai Xiao, Tomaz Amon and Piet Kommers |
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Year:
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2010 |
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Edition:
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Single |
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Keywords:
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Computer animation, coordination, crowd animation, stability |
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Type:
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Full Paper |
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First Page:
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47 |
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Last Page:
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56 |
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Language:
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English |
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Cover:
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Full Contents:
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click to dowload 
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Paper Abstract:
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The modeling of the collective behavior of many characters is an important problem in crowd animation. Such behaviors can be described by solutions of large-scale nonlinear dynamical systems, which are built from many interacting components. The design of the stability properties of such complex multi-component systems has been rarely studied in computer animation. We present an approach for the solution of this problem that is based on Contraction Theory, a framework for the analysis of the stability of complex nonlinear dynamical systems. Based on learning-based realtime capable architecture for the animation of crowds, we demonstrate the application of this novel approach for stability design. We derive conditions guaranteeing the global asymptotic stability of the formation of coordinated navigation behavior of crowds. In addition, we demonstrate that the same approach permits to derive bounds that guarantee the minimal convergence rates of the formation of order in navigating crowds. |
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