Flowfield estimation in the wake of a pitching and heaving airfoil

Biological systems have shown great abilities for navigating dense and uncertain environments with variable winds or currents. These animals have unique sensors that allow them to detect the local flowfield and adjust their motor controls accordingly. One approach to leveraging biological sensing capabilities for engineered systems is to understand the sensing from a theoretical perspective. In this paper, flowfield observability and estimation is addressed in the framework of detecting vortices in the flow around a flapping airfoil. An unsteady potential flow model is developed, and the flowfield is measured using velocity sensors placed on the surface of the airfoil. The observability characteristics are identified using two methods, which reveal that for a set of surface velocity sensors, nonzero pitch and heave controls are required to achieve full state observability of airfoil velocities, angle-of-attack, and vortex locations and strengths. These interesting results indicate that wing flapping increases environment observability for animals with wing-mounted velocity sensors. The observability results are demonstrated in simulation with an unscented Kalman filter to estimate a discrete number of vortices in the wake of the flapping foil. Although the filter assumes only a small number of vortices to be estimated, the UKF is able to capture the structure of the wake vorticity.