Though still in relative infancy, the field of flapping flight has potential to have a far-reaching impact on human life. Nature presents a myriad of examples of successful uses of this locomotion. Human efforts in flapping flight have seen substantial improvement in recent times. Wing kinematics are a key aspect of this study. This study summarizes previous wing trajectory generators and presents a new trajectory generation method built upon previous methods. This includes a novel means of commanding unequal half-stroke durations subject to robotic trajectory continuity requirements. Additionally, previous optimization methods are improved upon. Experimental optimization is performed using the new trajectory generation method and a more traditional means. Methods for quantifying and compensating for sensor time-dependence are also discussed. Results show that the Polar Fourier Series trajectory generator advanced rapidly through the optimization process, especially during the initial phase of experimentation. The Modified Berman and Wang trajectory generator moved through the design space more slowly due to the increased number of kinematic parameters. When optimizing lift only, the trajectory generators produced similar results and kinematic forms. The findings suggest that the objective statement should be modified to reward efficiency while maintaining a certain amount of lift. It is expected that the difference between the capabilities of the two trajectory generators will become more apparent under such conditions.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





trajectory generation, Box-Behnken design of experiment, objective function, wing kinematics, flapping flight, time history, micro-aerial vehicles, MAVs, flapping mechanism, response surface optimization