Fig. 8. Results from an under-actuated hovering simulation with two free parameters over a 15 s time span. (A) The location and orientation of the moth through time with a stick-figure shown for every 5.6 wingbeats. The simulation does not control X-axis position as precisely as in fully actuated cases. (B) Variation in the two free parameters, the wing sweep angle phase and the wing rotation angle amplitude, through time. The eight parameters not shown were fixed at their average values (taken from the set of hovering trials with all parameters free. The Y-axis scale for both variables reflects the limits imposed by the model. (C) Variation in the simulated moth's three degrees of freedom when restricted to two free kinematic parameters. There was a correlation between the pitch and X-velocity.