Interception by two predatory fly species is explained by a proportional navigation feedback controller

When aiming to capture a fast-moving target, animals can follow it until they catch up, or try to intercept it. In principle, interception is the more complicated strategy, but also more energy efficient. To study whether simple feedback controllers can explain interception behaviours by animals with miniature brains, we have reconstructed and studied the predatory flights of the robber fly <i>Holcocephala fusca</i> and killer fly <i>Coenosia attenuata</i> Although both species catch other aerial arthropods out of the air, <i>Holcocephala</i> contrasts prey against the open sky, while <i>Coenosia</i> hunts against clutter and at much closer range. Thus, their solutions to this target catching task may differ significantly. We reconstructed in three dimensions the flight trajectories of these two species and those of the presented targets they were attempting to intercept. We then tested their recorded performances against simulations. We found that both species intercept targets on near time-optimal courses. To investigate the guidance laws that could underlie this behaviour, we tested three alternative control systems (pure pursuit, deviated pursuit and proportional navigation). Only proportional navigation explains the timing and magnitude of fly steering responses, but with differing gain constants and delays for each fly species. <i>Holcocephala</i> uses a dimensionless navigational constant of <i>N</i> ≈ 3 with a time delay of ≈28 ms to intercept targets over a comparatively long range. This constant is optimal, as it minimizes the control effort required to hit the target. In contrast, <i>Coenosia</i> uses a constant of <i>N</i> ≈ 1.5 with a time delay of ≈18 ms, this setting may allow <i>Coenosia</i> to cope with the extremely high line-of-sight rotation rates, which are due to close target proximity, and thus prevent overcompensation of steering. This is the first clear evidence of interception supported by proportional navigation in insects. This work also demonstrates how by setting different gains and delays, the same simple feedback controller can yield the necessary performance in two different environments.