PID Feedback and Heading Control in Pairwise Insect Flight Dynamics

Social interaction plays a crucial role in maintaining optimal performance within cooperative systems. Observations of natural swarms indicate that the number of neighbors in an individual's neighborhood is usually limited, and neighborhood sizes vary across species. Pairwise interactions and pursuit of individual targets are common features in animal group behaviors in foraging, mating, and flocking. However, the exact strategies of target interception or pairwise flight by flying insects remain largely unknown. In this paper, the leader-follower feedback rule and relative heading angles are investigated on 1000 groups of honeybees consisting of 3-10 bees while flying towards a moving entrance. A proportional-integral-derivative (PID) controller is used to model the follower trajectories from those of the leader. The proportional gains are found invariant for the dataset, but the integral gains show a large variation. Moreover, the study also identifies that the relative heading angles and speed variability of the followers are essential factors in executing pairwise flights.