Geometric decompositions of collective motion.
| Autor: | Mischiati M; Institute for Systems Research, University of Maryland, College Park, MD 20742, USA.; Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA.; Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA 20147, USA., Krishnaprasad PS; Institute for Systems Research, University of Maryland, College Park, MD 20742, USA.; Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA. |
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| Jazyk: | angličtina |
| Zdroj: | Proceedings. Mathematical, physical, and engineering sciences [Proc Math Phys Eng Sci] 2017 Apr; Vol. 473 (2200), pp. 20160571. Date of Electronic Publication: 2017 Apr 26. |
| DOI: | 10.1098/rspa.2016.0571 |
| Abstrakt: | Collective motion in nature is a captivating phenomenon. Revealing the underlying mechanisms, which are of biological and theoretical interest, will require empirical data, modelling and analysis techniques. Here, we contribute a geometric viewpoint, yielding a novel method of analysing movement. Snapshots of collective motion are portrayed as tangent vectors on configuration space, with length determined by the total kinetic energy. Using the geometry of fibre bundles and connections, this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space. The resulting decomposition, when interleaved with classical shape space construction, is categorized into a family of kinematic modes-including rigid translations, rigid rotations, inertia tensor transformations, expansions and compressions. Snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy. Such quantitative measures can provide insight into the variation of the driving goals of a collective, as illustrated by applying these methods to a publicly available dataset of pigeon flocking. The geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots. Competing Interests: The authors declare no competing interests. |
| Databáze: | MEDLINE |
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