A Novel Newton-Based Extremum Seeking Controller for Dynamic Soaring

Dynamic soaring is a remarkable flight strategy employed by soaring birds like albatrosses to harness energy from the atmospheric wind gradient. This strategy is so efficient that soaring birds can sustain flight for very long distances without almost flapping their wings. This phenomenon has intrigued researchers across multiple disciplines including biology, physics, and applied mathematics. For aerospace and control engineering researchers, mimicking dynamic soaring means new technologies that contribute to a more sustainable aviation industry. Significant work has been done in the literature to mimic dynamic soaring using optimal control frameworks. However, these approaches have limitations as they are non-real-time, model-dependent, and computationally expensive. Very recently, the authors of this paper introduced a novel autonomous, real-time, and model-free approach for mimicking dynamic soaring utilizing Extremum Seeking Control (ESC) methods. However, the ESC structures used in said emerging approach are sensitive to the curvature of the input-output map of the system. Therefore, in this paper, we propose a Newton-based ESC structure for dynamic soaring that is independent of the input-output map's curvature. This provides a twofold contribution: (1) further solidification that the dynamic soaring problem can be treated as a natural ESC system; and (2) a framework that captures dynamic soaring independent of the input-output map's curvature, which can be particularly useful in cases where the system model is unknown. We verify our real-time results via simulations and comparison with non-real-time powerful optimal control solvers.