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Analysis and synthesis of collective motion: from geometry to dynamics

dc.contributor.advisorKrishnaprasad, Perinkulam Sen_US
dc.contributor.authorMischiati, Matteoen_US
dc.description.abstractThe subject of this dissertation is collective motion, the coordinated motion of two or more individuals, in three-dimensional space. Inspired by the problems of understanding collective motion in nature and designing artificial collectives that can produce complex behaviors, we introduce mathematical methods for the analysis of collective motion data, and biologically-inspired algorithms for generating collective motion in engineered systems. We explore two complementary approaches to the analysis and synthesis of collective motion. The first "top-down" approach consists in exploiting the geometry of n-body systems to identify certain elementary components of collective motion. A main contribution of this thesis is to reveal a new geometrical structure (fiber bundle) of the translation-reduced configuration space and a corresponding classification of collective motions alternative to the classical one based on reduction to shape space. We derive a mathematical framework for decomposing arbitrary collective motions into elementary components, which can help identify the main modes of an observed collective phenomenon. We synthesize vector fields that implement some of the most interesting elementary collective motions, and suggest, whenever feasible, decentralized implementations. The second "bottom-up" approach consists in starting from known biologically-plausible individual control laws and exploring how they can be used to generate collective behaviors. This approach is illustrated using the motion camouflage proportional guidance law as a building block. We show that rich and coordinated motion patterns can be obtained when two individuals are engaged in mutual pursuit with this control law. An extension of these dynamics yields coordinated motion for a collective of n individuals.en_US
dc.titleAnalysis and synthesis of collective motion: from geometry to dynamicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.contributor.departmentElectrical Engineeringen_US
dc.subject.pqcontrolledElectrical engineeringen_US
dc.subject.pquncontrolleddemocratic motionen_US
dc.subject.pquncontrolleddistributed controlen_US
dc.subject.pquncontrolledenergy decompositionen_US
dc.subject.pquncontrolledinertia tensoren_US
dc.subject.pquncontrolledmotion camouflageen_US

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