Flow structure decides whether a robot searching for odour should follow the wind

Junlong Shen; Shunsuke Shigaki

cs.ROOct 14, 2026

Flow structure decides whether a robot searching for odour should follow the wind

Authors: Junlong Shen, Shunsuke Shigaki

Organizations: Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada. · Principles of Informatics Research Division, National Institute of Informatics, Tokyo, Japan.

Abstract

Robots searching for odour usually surge upwind on contact, steering by the wind sensed now. In simulated reversing wind this rule collapses, favouring controllers that hold an earlier heading. We show that on our benchmark the collapse came from the simulated anemometer. Reading the nominal wind, wind-following controllers reached the source in at most 3.5% of episodes. Reading the odour-carrying flow, the best reached 90%, ahead of a held heading. The winner then depends on the flow. A held heading won in smooth fields that reverse quickly and lost in a stochastic field. A controller-free measure of the sensed wind ranked a moth-inspired follower's success. On a quadruped in a reversing fan arena, wind-following controllers were pushed away from the source, while a heading held from a source-facing start was not. Benchmarks should state which wind their sensor reads and test more than one flow structure.

Figures & tables

Figure 1: Whether holding a heading beats following the wind depends on the flow and on the sensed wind. a , Success of the held heading (WindReacquire) minus that of each of two wind-following controllers, in percentage points, paired within one block of 400 simulated episodes per condition. Rows vary the spatial irregularity of pompy’s flow field and columns how quickly it follows a reversal, with a sensor that reads the carrying flow. Below, env-A, a uniformly advected puff model, and pompy read by a nominal-wind anemometer. ns, not resolved after Holm adjustment over the 16 grid contrasts. Cells come from their own seed blocks, so a condition that also appears in Table 1 can differ by a few points. b , Success against cue drift, the mean over all ticks of the source-ward component of sensed upwind, counted at odour detections and zero otherwise, measured with no controller. Squares, the moth model; circles, the held heading. Curve, fit to the ten filled squares; crosses, predictions sealed before the four open squares were run.

Figure 2: Wind-following collapses when its sensor reads a wind other than the carrying flow, and loses to a held heading in smooth fast reversals. a , Primary benchmark on pompy with an anemometer reading the nominal wind (open) or the flow at the robot (filled); 400 paired episodes per controller. b , Success against the field’s lag behind a reversal of its forcing, varied through pompy’s diffusivity. c , The fastest-relaxing field with pompy’s boundary noise on (stochastic) and off (smooth), and env-A, each with a sensor that reads the carrying flow. d , Rig-matched replica from the robot’s start, gas detected on every tick; 200 paired episodes per controller. Bars, Wilson 95% intervals.

plume	anemometer	flow lag	WR-G	surge-cast	moth model	infotaxis
pompy	nominal	3.6 s	65.5	3.5	2.5	59.25
pompy	local	3.6 s	58.25	82.5	90.25	58.75
pompy, $k=320$	nominal	0.2 s	–	–	53.25	–
pompy, $k=320$	local	0.2 s	68.75	86.75	88.0	59.5
pompy, smooth	local	3.6 s	50.75	72.75	35.5	–
pompy, smooth, $k=320$	local	0.2 s	70.75	46.25	49.0	–

Table 1: Wind-following succeeds or fails with the sensed wind and the flow; the held heading varies less.

Panel of Figure 3 — Figure 3: The wind at a detection can point away from the source because of the path the odour took. a , With the current wind equal to the emission-time wind, the stored heading differs from upwind by the sensing error $\eta$ , and the source bearing differs from emission-time upwind by the plume residual $\psi$ . Angles exaggerated. b , With uniform advection along two directions less than $\pi/2$ apart, the net transport stays inside their cone, so either upwind heading points to the source’s side. Sign errors in this regime measure departures from uniform advection and perfect sensing (Fig. 4 ).

Figure 4: Irregular transport produces wrong-side headings that uniform advection does not. Sign-error rate of the frozen variant’s stored heading against the separation

\sigma

of the two wind directions. Below

\pi/2

, uniform advection with perfect sensing predicts none (dashed). Both plume models use matched episode indices and the same sensing model; with reversal off their rates are equal. Counts and rank tests in Supplementary Table S6.

contrast	bench	effect (pp)	$p$
re-acquisition (gate on)	primary	+46.5	$4.3\!\times\!10^{-21}$
re-acquisition (gate off)	primary	+44.0	$2.8\!\times\!10^{-20}$
conflict rule (re-acq. on)	primary	+3.0	0.526
conflict rule (re-acq. off)	primary	+0.5	1
re-acquisition (gate on)	narrow	+34.0	$5.0\!\times\!10^{-15}$
re-acquisition (gate off)	narrow	+36.0	$1.5\!\times\!10^{-16}$

Table 2: Re-acquisition dominates the primary-benchmark factorial. The conflict rule has no resolved benefit in this comparison.

Figure 5: In a reversing fan arena, wind-following controllers and infotaxis are pushed away from the source, and a held heading is not. a , The Go1 and its sensors; inset, CAD model of the gas-sensor mast. b , The arena from the overhead scoring camera, with a fan bank at each end (operator blurred). c , Tracks of the fifteen reversing-wind runs; dotted circle, reach radius. d , Range to the source; grey lines, wind reversals. e , Settled distance per run (means in Table 3 ).

	steady wind		reversing wind, 20 s
controller	settled (closest)	reached	settled (closest)	reached	reversals
WindReacquire	0.31 (0.21)	3/3	0.31 (0.25)	3/3	2/2/2
surge-cast	0.33 (0.26)	3/3	1.90 (1.17)	0/3	3/3/1
moth model [ 15 ]	0.39 (0.35)	3/3	1.69 (0.87)	0/3	4/3/2
reliability-modulated	0.33 (0.26)	3/3	1.62 (1.23)	0/3	3/3/4
infotaxis [ 23 ]	0.21 (0.06)	3/3	1.05 (0.68)	0/3	4/4/4

Table 3: Only the reversal separates the controllers on the robot. Five controllers, two wind conditions, three runs each, scored by the overhead camera.

benchmark constant	symbol	value
wind speed	$U$	$160\text{\,}\mathrm{mm}\text{\,}{\mathrm{s}}^{-1}$
anemometer lag	$\tau_{w}$	$0.10\text{\,}\mathrm{s}$
anemometer noise (s.d.)	$s_{w}$	$5.0\text{\,}\mathrm{\SIUnitSymbolDegree}$
heading drift	$\dot{h}_{d}$	$4\text{\,}\mathrm{\SIUnitSymbolDegree}\text{\,}{\mathrm{s}}^{-1}$
episode cap	$T_{\max}$	$300\text{\,}\mathrm{s}$
success radius (distance to source)	$r_{g}$	$50\text{\,}\mathrm{mm}$

Table 4: Benchmark constants.

symbol	quantity	value
$\delta$	control timestep	$1/30\text{\,}\mathrm{s}$
$\beta$	reliability EWMA rate	$0.08$
$w_{1}$	single-antenna weight in the coincidence signal	$0.40$
$\theta_{r}$	detection gate half-angle	$120\text{\,}\mathrm{\SIUnitSymbolDegree}$
$r^{\pm}$	reliability switch thresholds (hysteresis)	$0.16$ $\pm$ $0.06$
$\gamma$	conflict-gate threshold	$90\text{\,}\mathrm{\SIUnitSymbolDegree}$

Table 5: Complete parameter set of WindReacquire.

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The German Tank Problem & Navigating by Scent

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A robot searching for the source of an odor must eventually answer a deceptively hard question: have I arrived? Near the source, concentration gradients flatten, turbulence makes the signal intermittent, and a small robot often lacks the positional accuracy to map the plume. Here, we describe a lightweight remedy inspired by a World War II statistics conundrum: the German tank problem. To approximate enemy armament production, Allied analysts developed an estimator based on serial numbers from captured tanks. Analogously, we use the same procedure over sampled chemical sensor readings from a robot to create estimates for the peak concentration of an odor plume, and therefore the odor's source. Treating each sensor reading as an observation, our unbiased estimator needs only a running maximum and a sample counter. An exact confidence bound turns both numbers into a principled rule that the robot or UAV can use to determine whether to keep searching for the plume source or land. We derive the estimator and its bound, demonstrate its sample efficiency, and examine its robustness even when its assumptions fail. Finally, we summarize the estimator's role as the termination criterion for olfactory navigation.

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