Global and Local Optimization of Flapping Kinematics

In this work, optimization methodologies of the kinematics of flapping wings in forward and hover flights are considered. Particularly, local and global optimization algorithms are combined with the unsteady vortex lattice method (UVLM) to determine the most efficient kinematics. In the first problem, the kinematic optimization of a three-dimensional flapping wing in forward flight with active shape morphing is aimed at maximizing the propulsive efficiency under lift and thrust constraints. Results show that due to the quasi-concavity of the objective function associated with the flapping kinematics employed in forward flight, local gradient-based optimizers perform very well in terms of accuracy and computational cost. In the second problem, the objective is to identify the optimized kinematics of a twodimensional hovering wing that minimize the aerodynamic power under lift constraint. The results show that using a hybrid optimization algorithm (combination of local and global schemes) accelerates the convergence to optimal points and avoids being trapped at local minimum points. While the efficiency of using a local optimizer, a global optimizer, or a hybrid of the two depends on the nature of the problem and associated design space, it is determined that hybrid optimization is best suited for determining local minima.