The design of stable trim conditions for forward flight and for hover has been achieved. In forward flight, an ornithopter
is configured like a conventional airplane or large bird. Its fuselage is essentially horizontal and the wings heave in a
vertical plane. In hover, however, the body pitches vertically so that the wing stroke in the horizontal plane. Thrust
directed downward, the vehicle remains aloft while the downdraft envelops the tail to provide enough flow for vehicle
control and stabilization. To connect these trajectories dynamically is the goal. The naïve approach-to choose two stable
trajectories and switch between them-has been accomplished. A new approach is to establish an open-loop trajectory through a trajectory optimization algorithm-optimized for shortest altitude drop, shortest stopping distance, or lowest energy consumption.
The quasi-steady aerodynamics model is coupled to a dynamic model of ornithopter flight. Previously, the combined model has been used to calculate forward flight trajectories, each a limit cycle in the vehicle's states. The limit cycle results from the periodic wing beat, producing a periodic force while on the cycle's trajectory. This was accomplished using a multiple shooting algorithm and numerical integration in MATLAB. An analysis of hover, a crucial element to vertical takeoff and landing in adverse conditions, follows. A method to calculate plausible wing flapping motions and control surface deflections for hover is developed, employing the above flight dynamics model. Once a hovering limit cycle trajectory is found, it can be linearized in discrete time and analyzed for stability (by calculating the trajectory's Floquet multipliers a type of discrete-time eigenvalue) are calculated. The dynamic mode shapes are discussed.
The quasi-steady aerodynamics model and the vehicle dynamics model of ornithopter flight are explained, and numerical
methods are described to capture limit cycle behavior in ornithopter flight. The Floquet method is used to determine
stability in forward flight, and a linear discrete-time state-space model is developed. This is used to calculate stabilizing
and disturbance-rejecting controllers.