Abstract
We investigate the effect of turning delays on the behaviour of groups of differential wheeled robots and show that the group-level behaviour can be described by a transport equation with a suitably incorporated delay. The results of our mathematical analysis are supported by numerical simulations and experiments with E-Puck robots. The experimental quantity we compare with our revised model is the mean time for robots 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.
Highlights
Much theory has been developed for the coordination and control of distributed autonomous agents, where collections of robots are acting in environments in which only short-range communication is possible (Reif and Wang, 1999)
We will investigate an implementation of searching algorithms, similar to those used by flagellated bacteria, in a robotic system
We have studied an implementation of a run-and-tumble searching strategy in a robotic system
Summary
Much theory has been developed for the coordination and control of distributed autonomous agents, where collections of robots are acting in environments in which only short-range communication is possible (Reif and Wang, 1999). We will investigate an implementation of searching algorithms, similar to those used by flagellated bacteria, in a robotic system Many flagellated bacteria such as Escherichia coli (E. coli) use a run-and-tumble searching strategy in which movement consists of more-or-less straight runs interrupted by brief tumbles (Berg, 1983). When their motors rotate counter-clockwise the flagella form a bundle that propels the cell forward with a roughly constant speed; when one or more flagellar motors rotate clockwise the bundle flies apart and the cell ‘tumbles’ (Kim et al, 2003). We extend the classical model (1.1) through the introduction of a resting state r(t, x, v, η) that formally defines the number of particles currently “tumbling” (turning) towards their new chosen velocity v and remaining turning time η.
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