The influence of saccades on yaw gaze stabilization in fly flight

In a way analogous to human vision, the fruit fly D. melanogaster and many other flying insects generate smooth and saccadic movements to stabilize and shift their gaze in flight, respectively. It has been hypothesized that this combination of continuous and discrete movements benefits both flight stability and performance, particularly at high frequencies or speeds. Here we develop a hybrid control system model to explore the effects of saccades on the yaw stabilization reflex of D. melanogaster. Inspired from experimental data, the model includes a first order plant, a Proportional-Integral (PI) continuous controller, and a saccadic reset system that fires based on the integrated error of the continuous controller. We explore the gain, delay and switching threshold parameter space to quantify the optimum regions for yaw stability and performance. We show that the addition of saccades to a continuous controller provides benefits to both stability and performance across a range of frequencies. Our model suggests that Drosophila operates near its optimal switching threshold for its experimental gain set. We also show that based on experimental data, D. melanogaster operates in a region that trades off performance and stability. This trade-off increases flight robustness to compensate for internal perturbations such as wing damage.