A task-level model for optomotor yaw regulation in drosophila melanogaster: A frequency-domain system identification approach

Fruit flies adeptly coordinate flight maneuvers to seek, avoid, or otherwise interact with salient objects in their environment. In the laboratory, tethered flies modulate yaw torque to steer towards a dark vertical visual stimulus. This stripe-fixation behavior is robust and repeatable, making it a powerful paradigm for the study of optomotor control in flies. In this work, we study stripe fixation through a series of closed-loop perturbation experiments; flies are observed stabilizing moving stripes oscillating over a range of frequencies. A system identification analysis of input-output data furnishes a frequency response function (FRF), a nonparametric description of the behavior. We parameterize this FRF description to hypothesize a Proportional-Integral-Derivative (PID) control model for the fixation behavior. Lastly, we revisit previous work in which discrepancies in open- and closed-loop performance in stripe fixation were used to support the reafference principle.We demonstrate that our hypothesized PID model (with a modest biologically plausible nonlinearity) provides a more parsimonious explanation for these previously reported discrepancies.