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Interacting particles with Lévy strategies: limits of transport equations for swarm robotic systems Estrada Rodríguez, Gissell Gimperlein, Heiko Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. TP-EDP - Grup de Teoria de Funcions i Equacions en Derivades Parcials Àrees temàtiques de la UPC::Matemàtiques i estadística Harmonic functions Fractional Laplacian Lévy processes Anomalous diffusion Velocity jump model Léevy walk Swarm robotics Transportequation Fractional Laplacian Laplace, Transformacions de Funcions harmòniques Lévy, Processos de Lévy robotic systems combine superdiffusive random movement with emergent col-lective behavior from local communication and alignment in order to find rare targets or track objects.In this article we derive macroscopic fractional PDE descriptions from the movement strategies of theindividual robots. Starting from a kinetic equation which describes the movement of robots based onalignment, collisions, and occasional long distance runs according to a L\'evy distribution, we obtaina system of evolution equations for the fractional diffusion for long times. We show that the systemallows efficient parameter studies for a search problem, addressing basic questions like the optimalnumber of robots needed to cover an area in a certain time. For shorter times, in the hyperboliclimit of the kinetic equation, the PDE model is dominated by alignment, irrespective of the longrange movement. This is in agreement with previous results in swarming of self-propelled particles.The article indicates the novel and quantitative modeling opportunities which swarm robotic systemsprovide for the study of both emergent collective behavior and anomalous diffusion on the respectivetime scales Peer Reviewed Postprint (published version) 2020-01 Article Estrada, G.; Gimperlein, H. Interacting particles with Lévy strategies: limits of transport equations for swarm robotic systems. "SIAM journal on applied mathematics", 2020, vol. 80, núm. 1, p. 476-498. 0036-1399 https://arxiv.org/abs/1807.10124 https://hdl.handle.net/2117/376921 10.1137/18M1205327 eng https://epubs.siam.org/doi/10.1137/18M1205327 http://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access Attribution-NonCommercial-NoDerivatives 4.0 International 23 p. application/pdf Society for Industrial and Applied Mathematics (SIAM)