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

Abstract

Systematic descriptions of the underlying interaction rules that insects use to support group and swarm flight has the potential to contribute to mathematics, biology, and robotics, including aerial swarming under sensory and computational limitations. This study analyzes 1,000 trajectories of flying honeybees in crowded conditions approaching a moving stimulus and finds how during this stimulus, honeybees coordinate flight through pairwise interactions involving a novel three-zone decision-making process. The experimental setup consists of 3-D position reconstructions via a high speed camera system recording honeybee foragers returning to a hive entrance actuated to move robotically. The analysis consists of neighborhood identification through three methods (cross-correlation, distance threshold, and average distance threshold), which reveals the dominant interaction is pairwise. The individual leader-follower pair interactions are then tested against three regulation candidates: optic flow, relative velocity, and optical expansion rate, based on minimizing root mean square error. The results show that each follower demonstrates a three stage process involving a feedback rule change, linked by an intermediate observation/decision phase. During the initial ``lock'' phase, an insect maintains a consistent optical expansion rate until inter-agent distance closes to 10 cm. The regulation candidates then undergo large variations during a relatively long observation/decision zone, with 1.04 seconds being the average time in the decision zone. 79% of the paired insect entries into the decision zone result in subsequent re-engagement to track the same initial leader, while 21% result in disengagement from the group behavior. Visual regulation candidate comparison in the third stage indicates that upon re-engagement, the follower relative velocity is regulated to provide consistent velocity matching between agents. The third stage's velocity tracking is consistent with a closed-loop feedback proportional-integral (PI) controller regulating velocity tracking error. Across the insect population studied, the proportional gain remained showed minimal variability over individuals, a derivative gain was considered and found negligible, and the integral gain varied by individual. Collectively, these findings underscore the existence of an alternative swarm architecture, highlighting individual decision-making capabilities, feedback regulation target changes, and the presence of reactive, deliberative, and moderate (PI control) timescale interaction rules contained within aerial groups.