Mathematical modelling of turning delays in swarm robotics

Jake P. Taylor-King, Benjamin Franz, Christian A. Yates, Radek Erban

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We investigate the effect of turning delays on the behaviour of groups of differential wheeled robots andshow that the group-level behaviour can be described by a transport equation with a suitably incorporateddelay. The results of our mathematical analysis are supported by numerical simulations and experimentswith E-Puck robots. The experimental quantity we compare to our revised model is the mean time forrobots to find the target area in an unknown environment. The transport equation with delay better predicts the mean time to find the target than the standard transport equation without delay.
Original languageEnglish
Pages (from-to)1454-1474
Number of pages21
JournalIMA Journal of Applied Mathematics
Issue number5
Early online date31 Mar 2015
Publication statusPublished - Oct 2015


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