Collective olfactory search in a turbulent environment

Finding the source of an odor dispersed by a turbulent flow is a vital task for many organisms. When many individuals concurrently perform the same olfactory search task, sharing information about other members' decisions can potentially boost the performance. But how much of this information is actually exploitable for the collective task? Here we show, in a model of a swarm of agents inspired by moth behavior, that there is an optimal way to blend the private information about odor and wind detections with the public information about other agents' heading direction. Our results suggest an efficient multiagent olfactory search algorithm that could prove useful in robotics, e.g., in the identification of sources of harmful volatile compounds.

Figure 1

Collective olfactory search. (a) Odor particles (blue dots) are emitted by the source S and dispersed by the turbulent flow. Agents (red) are initially placed far from S in a packed configuration. (b) Perception of an agent (red). Detected odor particles by the agent are shown as darker blue dots and agent's neighbors in green. Arrows indicate the instantaneous moving direction of agents. We set $L_x=250R_d, R_b=25R_d, R_a=5R_d, R_d=0.2,b=2.5.$ (c) Trajectory of an isolated agent performing the cast-and-surge program (see text). Blue crosses mark the detection of odor particles.

Figure 2

Collective olfactory search in a stochastic flow. (a) Average search time $T$ for the first agent that reaches the target normalized to the straight-path time, $T_s=L_x/v_0$. The inset enlarges the region close to the minimum. (b) Fraction of agents within a region of size $R_b$ around the source at the first agent arrival time. (c, d) Average order parameter for mutual $\psi$ and wind alignment $M$. Error bars denote the upper and lower standard deviation with respect to the mean. Statistics is over ${10}^3$ episodes. The parameters are $\lambda =1, N=100, J=1, \eta =0.1, v_0=0.5, \mathrm{\Delta }t=1, L_x=50$.

Figure 3

Collective olfactory search in a turbulent flow. (a) Search time $T$ for the first agent reaching the target normalized by the shortest-path time $T_s$. (b) Zoom of panel (a) in the region close to the minimum. (c, d) Average order parameter for mutual $\psi$ and wind alignment $M$. Right panels: four different times $t$ of the search process with the optimal trust parameter $\beta =0.8$, velocity field (gray arrows), agents (red arrows), odor particles (blue dots), and the source (large blue circle).

Figure 4

(a) A short trajectory of an agent navigating according to the cast-and-surge algorithm with $\lambda \to 0$. (b) A complete sample trajectory. The black circle is the location of the source (S), while the blue $\times$'s correspond to the points where it detected an odor particle within its olfactory range.

Figure 5

Energy spectrum obtained by direct numerical simulations of Eq. (B3) with ${256}^2$ grid points. Hyperviscous dissipation of order 8 has been used with viscosity ${\nu }_8=1.3\times {10}^{-29}$, Ekman friction coefficient $\alpha =0.02$, and time step $dt={10}^{-3}$. The large scale of the flow is about half of the simulation box.

Figure 6

Collective olfactory search with various emission rates $J$, other parameters as in Tables 1 and 2: (black circles) $J=1$, (red triangles) $J=0.2$, (green stars) $J=0.1$, (blue crosses symbols) $J=0.05$. (a) Average search time $T_1$ normalized to $T_s=L_x/v_0$. The inset shows the ratio of average time taken by agents with only private information ($T_1^{\beta =0}$) to the average time taken by agents with optimal integration of private and public information ($T_1^{\beta ={\beta }^{*}}$). (b) Fraction of agents within a region of size $R_b$ around the source at the arrival time of the first agent reaching the target. (c) Average alignment against the mean wind $M$. (d) Average order parameter $\psi$. For all data, the error bars denote the upper and lower standard deviation with respect to the mean value. Statistics is over ${10}^3$ episodes.

Figure 7

Collective olfactory search for different values of the number of agents $N$, other parameters as in Tables 1 and 2: (red triangles) $N=50$, (black circles) $N=100$, (green stars) $N=150$, (blue crosses symbols) $N=200$. Panel description as in Fig. 6.

Figure 8

Collective olfactory search for different values of the agent-agent interaction range, other parameters as in Tables 1 and 2: (black circles) $R_a=1.0$, (green stars) $R_a=0.85$, (red triangles) $R_a=0.70$. Panel description as in Fig. 6.

Figure 9

Collective olfactory search with different agents' speeds, $v_0$, other parameters as in Tables 1 and 2: (black circles) $v_0=0.50$, (red triangles) $v_0=0.25$, (green stars) $v_0=0.125$. Panel description as in Fig. 6.

Figure 10

Collective olfactory search with various intensities of fluctuations in the model flow, other parameters as in Tables 1 and 2: (black circles) $u_{\mathrm{rms}}=0.4242U$, (red triangles) $u_{\mathrm{rms}}=0.6363U$, (green stars) $u_{\mathrm{rms}}=0.8484U$. Panel description as in Fig. 6.