Flight control in the hawkmoth Manduca sexta: the inverse problem of hovering.

The inverse problem of hovering flight, that is, the range of wing movements appropriate for sustained flight at a fixed position and orientation, was examined by developing a simulation of the hawkmoth Manduca sexta. Inverse problems arise when one is seeking the parameters that are required to achieve a specified model outcome. In contrast, forward problems explore the outcomes given a specified set of input parameters. The simulation was coupled to a microgenetic algorithm that found specific sequences of wing and body motions, encoded by ten independent kinematic parameters, capable of generating the fixed body position and orientation characteristic of hovering flight. Additionally, we explored the consequences of restricting the number of free kinematic parameters and used this information to assess the importance to flight control of individual parameters and various combinations of them. Output from the simulated moth was compared to kinematic recordings of hovering flight in real hawkmoths; the real and simulated moths performed similarly with respect to their range of variation in position and orientation. The simulated moth also used average wingbeat kinematics (amplitude, stroke plane orientation, etc) similar to those of the real moths. However, many different subsets of the available kinematic were sufficient for hovering flight and available kinematic data from real moths does not include sufficient detail to assess which, if any, of these was consistent with the real moth. This general result, the multiplicity of possible hovering kinematics, shows that the means by which Manduca sexta actually maintains position and orientation may have considerable freedom and therefore may be influenced by many other factors beyond the physical and aerodynamic requirements of hovering flight.