Hawkmoths use wingstroke-to-wingstroke frequency modulation for aerial recovery to vortex ring perturbations

Centimetre-scale fliers must contend with the high power requirements of
flapping flight. Insects have elastic elements in their thoraxes which may
reduce the inertial costs of their flapping wings. Matching wingbeat
frequency to a mechanical resonance can be energetically favourable, but
also poses control challenges. Many insects use frequency modulation on
long timescales, but wingstroke-to-wingstroke modulation of wingbeat
frequencies in a resonant spring-wing system is potentially costly because
muscles must work against the elastic flight system. Nonetheless, rapid
frequency and amplitude modulation may be a useful control modality. The
hawkmoth Manduca sexta has an elastic thorax capable of storing and
returning significant energy. However, its nervous system also has the
potential to modulate the driving frequency of flapping because its flight
muscles are synchronous. We tested whether hovering hawkmoths rapidly
alter frequency during perturbations with vortex rings. We observed both
frequency modulation (32% around mean) and amplitude modulation (37%)
occurring over several wingstrokes. Instantaneous phase analysis of wing
kinematics revealed that more than 85% of perturbation responses required
active changes in neurogenic driving frequency. Unlike their robotic
counterparts that abdicate frequency modulation for energy efficiency,
synchronous insects use wingstroke-to-wingstroke frequency modulation
despite the power demands required for deviating from resonance.