Response characteristics of visual altitude control system in Bombus terrestris.

Frequency response characteristics of bumblebees to vertical visual oscillations were measured and analyzed. We measured the vertical force of the bees at four oscillation frequencies (0.9, 1.8, 3.6 and 7.4 Hz), and summarized their response characteristics in terms of amplitude and phase differences. The amplitude was almost constant throughout the examined frequency domain, whereas the phase gradually lagged with increasing frequency. In order to view the relationship between the input (visual oscillation) and output (response of the bee) more clearly as a control system, we compared them in the same dimension; we calculated hypothetical positions of the tethered bees on the basis of the measured variation in the vertical force, and compared them with the visual stripe positions. The resultant gain and phase data were plotted on a Bode plot. A transfer function was identified from the Bode plot, revealing that the response characteristics of the measured system could be represented as a simple expression. The dynamic control characteristics of the bumblebees were analyzed on the basis of the frequency response data. First, we showed that the measured system possesses a substantial stability margin. This means that the control system has substantial damping characteristics, and was suitable for stable flight control. In addition, our results showed that the measured bumblebee system possesses superior steady state and quick-response characteristics in comparison with a human pilot-vehicle system. Such excellence in both the steady state and transient characteristics (i.e. damping and quick response characteristics) provide the evidence that bumblebees can effectively control their flight with stability and maneuverability.