Moth-inspired navigation algorithm in a turbulent odor plume from a pulsating source

Some female moths attract male moths by emitting series of pulses of pheromone filaments propagating downwind. The turbulent nature of the wind creates a complex flow environment, and causes the filaments to propagate in the form of patches with varying concentration distributions. Inspired by moth navigation capabilities, we propose a navigation strategy that enables a flier to locate a pulsating odor source in a windy environment using a single threshold-based detection sensor. The strategy is constructed based on the physical properties of the turbulent flow carrying discrete puffs of odor and does not involve learning, memory, complex decision making or statistical methods. We suggest that in turbulent plumes from a pulsating point source, an instantaneously measurable quantity referred as a "puff crossing time", improves the success rate as compared to the navigation strategy based on "internal counter" that does not use this information. Using computer simulations of fliers navigating in turbulent plumes of the pulsating point source for varying flow parameters: turbulent intensities, plume meandering and wind gusts, we obtained trajectories qualitatively resembling male moths flights towards the pheromone sources. We quantified the probability of a successful navigation as well as the flight parameters such as the time spent searching and the total flight time, with respect to different turbulent intensities, meandering or gusts. The concepts learned using this model may help to design odor-based navigation of miniature airborne autonomous vehicles

Effect of meandering and gusts on search success for different values of meandering or gusts shown in the legend.

<p>Graphs shown the average values.</p

Probability of success as a function of increasing turbulent intensity for three different radii around the pheromone source.

<p>Error bars demonstrate the standard deviation of 1000 simulation runs for random initial positions and simulated turbulent flow fields.</p

Typical velocity field and puff locations.

<p>Arrows—instantaneous two dimensional velocity field <b>U</b>(<i>x</i>, <i>y</i>); circles—puff locations (symbols size is arbitrary and not related to the puff size). Velocity field is a sum of the wind velocity and random, turbulent fluctuations, defined by turbulent intensity.</p

Success rate for a navigation strategy with an internal counter for different values of the counter.

<p>The point at zero is the success rate of a proposed navigation strategy with dynamically counter equal to <i>t</i>_<i>c</i>.</p

Typical paths of a navigator for different turbulent intensities and representative sets of flier coordinates (<i>x</i>_<i>m</i>, <i>y</i>_<i>m</i>), <i>α</i>_<i>s</i> ∈ (30° − 120°).

<p>(a) low 5% turbulence intensity; (b) 15% intermediate turbulence intensity; (c) 30% high turbulence intensity. (d) A typical flight path with symbols showing the detection points of puffs and their identification number.</p

Flow chart of the search navigation algorithm.

<p>Flow chart of the search navigation algorithm.</p

Probability density function of lateral deviation (defined as a sum of all lateral deviations from a straight line between the first and last trajectory points, normalized by the length of the straight line) for different values of turbulent intensity shown in the legend.

<p>Insets shown the average values and the standard deviations of the distributions as a function of turbulent intensity.</p

A sketch of a series of discrete puffs, released at a constant pulsing rate, and the trajectories of a male moth (view from above).

<p>A female moth is denoted as a small circle in the origin. The lowest detectable concentration of each puff is marked by a dashed contour line. A dash-dotted envelope denotes the limits of an average long term concentration distribution of a virtual plume. This figure manifests the major feature of the patchy plume—the size of patches of pheromone, the distance between them and the width of an isoline of the long time averaged concentration (i.e. “virtual plume”) grow proportionally in any given turbulent flow. The cross symbol × denotes schematically the turning point where the new casting search starts. The lateral spread of the search is equivalent to the size of the last patch, marked by two small circles on the moth path line.</p

Summary of simulation results (average 〈<i>x</i>〉 and standard deviation <i>S</i>_<i>x</i>) for the three levels of turbulent intensity: trajectory length, time of flight, lateral deviations, number of search cycles and number of counter-turns.

<p>The 0.05 (low) turbulence intensity pertains to field or wind tunnel conditions, 0.15 to a typical value in open field atmospheric boundary layer, and the 0.3 (high) turbulent intensity pertains to the air conditions in dense canopy layers, for example, in forests.</p