Macroscopic analysis of robot foraging behaviour

Dartel, Michel van; Postma, Eric; Herik, H.J. van den; Croon, Guido de

doi:10.1080/09540090412331314876

Cited by 17 publications

(19 citation statements)

References 13 publications

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“…In particular, Lévy statistics, among others models [1], have been successfully used to describe the emergence of optimal search strategies in natural systems at different length scales, from molecular entities [4,5], to swimming and swarming microorganisms [6][7][8], to crawling eukaryotic cells [9], to different species of foraging animals [10][11][12][13][14][15][16], to human motion patterns [17][18][19], although in the field of movement ecology there is some controversy on how universal Lévy searches are [20][21][22][23][24][25]. Lévy statistics have also found applications in science and engineering, e.g., for defining the optimal search strategy for robots [26] and for describing anomalous diffusion and navigation on networks [27,28].…”

Section: Introductionmentioning

confidence: 99%

The topography of the environment alters the optimal search strategy for active particles

Volpe

2017

Proc. Natl. Acad. Sci. U.S.A.

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In environments with scarce resources, adopting the right search strategy can make the difference between succeeding and failing, even between life and death. At different scales, this applies to molecular encounters in the cell cytoplasm, to animals looking for food or mates in natural landscapes, to rescuers during search and rescue operations in disaster zones, and to genetic computer algorithms exploring parameter spaces. When looking for sparse targets in a homogeneous environment, a combination of ballistic and diffusive steps is considered optimal; in particular, more ballistic Lévy flights with exponent [Formula: see text] are generally believed to optimize the search process. However, most search spaces present complex topographies. What is the best search strategy in these more realistic scenarios? Here, we show that the topography of the environment significantly alters the optimal search strategy toward less ballistic and more Brownian strategies. We consider an active particle performing a blind cruise search for nonregenerating sparse targets in a 2D space with steps drawn from a Lévy distribution with the exponent varying from [Formula: see text] to [Formula: see text] (Brownian). We show that, when boundaries, barriers, and obstacles are present, the optimal search strategy depends on the topography of the environment, with [Formula: see text] assuming intermediate values in the whole range under consideration. We interpret these findings using simple scaling arguments and discuss their robustness to varying searcher's size. Our results are relevant for search problems at different length scales from animal and human foraging to microswimmers' taxis to biochemical rates of reaction.

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Section: Introductionmentioning

confidence: 99%

The topography of the environment alters the optimal search strategy for active particles

Volpe

2017

Proc. Natl. Acad. Sci. U.S.A.

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“…Interesting findings were reported from robotics, where one of the important questions is how robots should search for hidden targets. From simulations it was concluded that the most successful robots performed motion consistent with LF foraging [38].…”

Section: Introductionmentioning

confidence: 99%

Space-fractional Fokker–Planck equation and optimization of random search processes in the presence of an external bias

2014

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We study the efficiency of random search processes based on Lévy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the bias of the searcher based on prior experience. While Lévy flights turn out to be efficient search processes when relative to the starting point the target is upstream, in the downstream scenario regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Lévy flights, due to which Lévy flights typically overshoot a point or small interval. Extending our recent work on biased LF search [V. V. Palyulin, A. V. Chechkin, and R. Metzler, Proc. Natl. Acad. Sci. USA, 111, 2931 (2014).] we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favors Lévy flights over regular Brownian search. Contrary to the common belief that Lévy flights with a Lévy index α = 1 (i.e., Cauchy flights) are optimal for sparse targets, we find that the optimal value for α may range in the entire interval (1, 2) and include Brownian motion as the overall most efficient search strategy.

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“…Also for microscopic creatures LF search may be found; for instance, for the movement of Escherichia coli owing to the power-law statistics underlying their flagella rotation switching (21,22). In engineering the optimal search behavior of robots was identified to follow LF behavior (23). However, in several cases the reports of LFs are debated.…”

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confidence: 99%

Lévy flights do not always optimize random blind search for sparse targets

Palyulin

Chechkin

Metzler

2014

Proc. Natl. Acad. Sci. U.S.A.

191

213

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It is generally believed that random search processes based on scalefree, Lévy stable jump length distributions (Lévy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Lévy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Lévy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Lévy flights with a critical exponent α = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal α may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy.search optimization | stochastic processes | Lévy foraging hypothesis H ow do you find the proverbial needle in the haystack or an enemy submarine in the vast expanse of the sea? Scientists have studied the dynamics and optimization of search processes for decades, their interests ranging from military tasks such as locating enemy vessels or mines in the ocean and search strategies of animals for food to diffusion control of molecular processes in biological cells (1-4). Without prior knowledge about the location of the target, a searcher randomly explores the search space. However, as already argued by Shlesinger and Klafter (5), instead of performing a Brownian walk a better search strategy for sparse targets is that of a Lévy flight (LF): The agent moves randomly with a power-law distribution λðxÞ ' jxj −1−α of relocation lengths. Owing to their scale-free, fractal character, LFs combine local exploration with decorrelating, long-range excursions. These effect a reduced oversampling compared with Brownian search (i.e., the forager is less likely to return to previously visited sites). In the field of movement ecology (6), such random jump-like search processes are often referred to as "blind search" using saltatory motion, which is typical for predators hunting at spatial scales that exceed their sensory range (7-10). Such blind search, inter alia, was observed for fully aquatic marine vertebrate predators including plankton-feeding basking sharks (Cetorhinus maximus) (11), jellyfish predators, leatherback turtles (Dermochelys coriacea) (12), and southern elephant seals (13). This is the kind of search motion we investigate here.How commonly are LFs actually observed in nature? Apart from the flight of the albatross (14, 15), power-law relocation...

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Macroscopic analysis of robot foraging behaviour

Cited by 17 publications

References 13 publications

The topography of the environment alters the optimal search strategy for active particles

The topography of the environment alters the optimal search strategy for active particles

Space-fractional Fokker–Planck equation and optimization of random search processes in the presence of an external bias

Lévy flights do not always optimize random blind search for sparse targets

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