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

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.

Finding an odor source in a turbulent flow requires effectively leveraging the history of olfactory observations into a robust navigation strategy. In this work, we use tabular Q-learning to train an olfactory search agent with a minimal memory of past observations: only a running clock since the last whiff. This agent learns an interpretable strategy to recover the plume which combines well-known behaviors observed in insects: surging, casting, and a return downwind. While achieving good performance on data from direct numerical simulations of turbulence, the agent is limited by an inability to adapt its strategy to the local intermittency level; we show that providing more flexibility improves robustness.

Locating and intercepting a moving target from possibly delayed, intermittent sensory signals is a paradigmatic problem in decision-making under uncertainty, and a fundamental challenge for, e.g., animals seeking prey or mates and autonomous robotic systems. Odor signals are intermittent, strongly mixed by turbulent-like transport, and typically lag behind the true target position, thereby complicating localization. Here, we formulate olfactory pursuit as a partially observable Markov decision process in which an agent maintains a joint belief over the target's position and velocity. Using a discrete run-and-tumble model, we compute quasi-optimal policies by numerically solving the Bellman equation and benchmark them against well-established information-theoretic strategies such as Infotaxis. We show that purely exploratory policies are near-optimal when the target frequently reorients, but fail dramatically when the target exhibits persistent motion. We thus introduce a computationally efficient hybrid policy that combines the information-gain drive of Infotaxis with a "greedy" value function derived from an associated fully observable control problem. Our heuristic achieves near-optimal performance across all persistence times and substantially outperforms purely exploratory approaches. Moreover, our proposal demonstrates strong robustness even in more complex search scenarios, including continuous run-and-tumble prey motion with moderate persistence time, model mismatch, and more accurate plume dynamics representation. Our results identify predictive inference of target motion as the key ingredient for effective olfactory pursuit and provide a general framework for search in information-poor, dynamically evolving environments.