We present a data-driven optimization framework that aims to address online adaptation of the flight path shape for an airborne wind energy system (AWE) that follows a repetitive path to generate power. Specifically, Bayesian optimization, which is a data-driven algorithm for finding the optimum of an unknown objective function, is utilized to solve the waypoint adaptation. To form a computationally efficient optimization framework, we describe each figure-$8$ flight via a compact set of parameters, termed as basis parameters. We model the underlying objective function by a Gaussian Process (GP). Bayesian optimization utilizes the predictive uncertainty information from the GP to determine the best subsequent basis parameters. Once a path is generated using Bayesian optimization, a path following mechanism is used to track the generated figure-$8$ flight. The proposed framework is validated on a simplified $2$-dimensional model that mimics the key behaviors of a $3$-dimensional AWE system. We demonstrate the capability of the proposed framework in a simulation environment for a simplified $2$-dimensional AWE system model.
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