Markovian robots: Minimal navigation strategies for active particles

Physical Review. E
Luis Gómez NavaFernando Peruani

Abstract

We explore minimal navigation strategies for active particles in complex, dynamical, external fields, introducing a class of autonomous, self-propelled particles which we call Markovian robots (MR). These machines are equipped with a navigation control system (NCS) that triggers random changes in the direction of self-propulsion of the robots. The internal state of the NCS is described by a Boolean variable that adopts two values. The temporal dynamics of this Boolean variable is dictated by a closed Markov chain-ensuring the absence of fixed points in the dynamics-with transition rates that may depend exclusively on the instantaneous, local value of the external field. Importantly, the NCS does not store past measurements of this value in continuous, internal variables. We show that despite the strong constraints, it is possible to conceive closed Markov chain motifs that lead to nontrivial motility behaviors of the MR in one, two, and three dimensions. By analytically reducing the complexity of the NCS dynamics, we obtain an effective description of the long-time motility behavior of the MR that allows us to identify the minimum requirements in the design of NCS motifs and transition rates to perform complex navigation tasks ...Continue Reading

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Citations

Jun 25, 2020·Soft Matter·Matteo PaoluzziM Cristina Marchetti
Jul 22, 2020·Physical Review. E·Ion SantraSanjib Sabhapandit
Apr 4, 2020·Physical Review Letters·Justus A KromerBenjamin M Friedrich
Aug 9, 2020·Science Advances·Zahra AlirezaeizanjaniCarsten Beta
Sep 17, 2020·Science Advances·Zahra AlirezaeizanjaniCarsten Beta

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