Dyadic interactions, feedback rule changes, and deliberative decisions underlie honeybee inflight group coordination

<p dir="ltr">Understanding the interaction architectures that individual insects implement in group flight contributes to mathematics, biology, and robotics, including enabling dynamic aerial swarming. This study analyzes 1,000 trajectories of flying honeybees in crowded conditions approaching a stimulus and finds a dominant flight coordination architecture of ``dyadic" interactions and a new three-zone decision-making process. The experiment measures individual insect positions via an optical tracking system recording honeybees returning to a robotically-actuated hive entrance. Neighborhood analysis through three methods (cross-correlation, distance threshold, and average distance threshold) reveals the dominant interaction is dyadic, consisting of transient leader-follower behaviors embedded in the larger collective. The followers' update rules are then tested against three regulation candidates (optic flow, relative velocity, and ``optical expansion rate") to minimize root mean square error. The results show that in each dyad, the follower proceeds through a three-stage process involving a change to feedback rules that is separated by an intermediate unregulated period. An insect initially maintains a consistent (less than 8\% variation) optical expansion rate until the inter-agent distance closes to 10 cm. The regulation candidates then undergo large variations during an observation/decision zone lasting an average of 1.04 seconds. 79\% of agents entering the decision zone then re-engage to track the same initial leader while 21\% disengage. Upon re-engagement, the follower regulates inter-agent relative velocity, consistent with a closed-loop feedback proportional-integral (PI) controller regulating velocity tracking error. Proportional gain showed low variability across individuals, while derivative gain was found negligible and integral gain varied by individual. These findings highlight an alternative swarm architecture incorporating individual decision-making, feedback regulation target changes, and the presence of three interaction timescales.</p>