Geometric control of a flapping plate

Control of flapping micro-air-vehicles (MAVs) is challenging because the system models are nonlinear and time-varying. Moreover, as internally actuated multi-body systems, flapping MAVs are inherently underactuated. With stringent weight and size constraints, the actuator mechanization must be as simple as possible, introducing a further challenge for control design. Geometric control and averaging theory can be used to design control laws for underactuated nonlinear systems. In this work, we consider control design for a flapping plate with three degrees of freedom and two actuators. The averaging theorem and geometric control methods are used to stabilize and control the system. The simple example demonstrates an algorithmic approach that could be used within a multi-disciplinary design optimization framework for the design of biomimetic vehicles and their gaits.