A geometric control approach for optimum maneuverability of flapping wing MAVs near hover

Flapping wing micro-air vehicles are aerial robots that use biomimetic actuation for propulsion and control. Designing such a system requires an integrated system model describing the flight mechanics, propulsion, and control. Relative to conventional aircraft, the resulting model is nonlinear, high-dimensional, time-varying, and underactuated, making analysis and design challenging. Geometric control and averaging theory provide useful analysis tools for biomimetic locomotion systems that use high frequency, time-periodic inputs to generate control forces and moments. Recognizing the essential role of certain Lie bracket and symmetric product vector fields in the flight mechanics of a flapping wing micro-air vehicle, we develop analytical expressions for these vector fields in terms of system parameters. Using these expressions, we then pose and solve a design optimization problem aimed at maximizing vehicle maneuverability. The example illustrates a constructive technique for the design of biomimetic robots and their gaits.