How to efficiently mimic the wing shape and kinematics pattern of an able hovering living flier is always a concern of researchers from the flapping wing micro aerial vehicles community. In this work, the separate or combined optimizations of wing geometry or/and wing kinematic parameters are systematically performed to minimize the energy of hovering flight, firstly on the basis of analytically extended quasi-steady aerodynamic model by using hybrid genetic algorithm. Before the elaboration of the optimization problem, the parametrization description of dynamically scaled wing with non-dimensional conformal feature of insect-scale rigid wing is firstly proposed. The optimization results show that the combined optimization of wing geometry and kinematic parameters can obtain lower flapping frequency, larger wing geometry parameters and lower power density in comparison with those from other cases of optimization. Moreover, the flapping angle for the optimization involving wing kinematic parameters manifests harmonic shape profile and the pitch angle possesses round trapezoidal profile with certain faster time scale of pitch reversal. The combined optimization framework provides a novel method for the conceptual design of fundamental parameters of biomimetic flapping wing micro aerial vehicle.
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