The mechanics and control of pitching manoeuvres in a freely flying hawkmoth (Manduca sexta).

Insects produce a variety of exquisitely controlled manoeuvres during natural flight behaviour. Here we show how hawkmoths produce and control one such manoeuvre, an avoidance response consisting of rapid pitching up, rearward flight, pitching down (often past the original pitch angle), and then pitching up slowly to equilibrium. We triggered these manoeuvres via a sudden visual stimulus in front of free-flying hawkmoths (Manduca sexta) while recording the animals' body and wing movements via high-speed stereo videography. We then recreated the wing motions in a dynamically scaled model to: (1) associate wing kinematic changes with pitch torque production and (2) extract the open-loop dynamics of an uncontrolled moth. Next, we characterized the closed-loop manoeuvring dynamics from the observed flight behaviour assuming that hawkmoths use feedback control based on translational velocity, pitch angle and angular velocity, and then compared these with the open-loop dynamics to identify the control strategy used by the moth. Our analysis revealed that hawkmoths produce active pitch torque via changes in mean wing spanwise rotation angle. Additionally, body translations produce passive translational damping and pitch torque, both of which are linearly dependent on the translational velocity. Body rotations produce similar passive forces and torques, but of substantially smaller magnitudes. Our comparison of closed-loop and open-loop dynamics showed that hawkmoths rely largely on passive damping to reduce the body translation but use feedback control based on pitch angle and angular velocity to control their orientation. The resulting feedback control system remains stable with sensory delays of more than two wingbeats.