First Experimental Demonstration of Natural Hovering Extremum Seeking: A New Paradigm in Flapping Flight Physics

TL;DR

This letter reports the first experimental demonstration of the recently emerged new paradigm in flapping flight physics called (Natural Hovering Extremum Seeking (NH-ES), and shows that the flapping body gains altitude and stabilizes hovering about the light source autonomously needing only sensor measurements of light intensity.

Abstract

In this letter, we report the first experimental demonstration of the recently emerged new paradigm in flapping flight physics called (Natural Hovering Extremum Seeking (NH-ES)) [doi.org/10.1103/4dm4-kc4g], which theorized that hovering flight physics observed in nature by flapping insects and hummingbirds can be generated via a model-free, real-time, computationally basic, sensory-based feedback mechanism that only needs the built-in natural oscillations of the flapping wing as its propulsive input. We run experiments, including moth-like, light source-seeking, on a flapping-wing body in a total model-free setting that is agnostic to morphological parameters and body/aerodynamic models, and show that the flapping body gains altitude and stabilizes hovering about the light source autonomously needing only sensor measurements of light intensity.

Figures (7)

• Figure 1: Model-free Natural Hovering Extremum Seeking (NH-ES) control architecture. The system dynamics $f(\cdot)$ and the objective function $J(\cdot)$ are treated as black boxes. The control input $u$ is composed of an adaptive component $\hat{u}$ and an oscillatory term naturally generated by wing flapping while $k$ is the learning parameter.
• Figure 2: Experimental setup for the flapping-wing body. The system is to perform vertical motion and relies exclusively on intrinsic flapping-induced oscillations and scalar sensory feedback. (#1): Motion-capturing system (MCS). (#2): Light source. (#3): Constraint line with relaxed tension. (#4): External power supply. (#5): Flapping-wing body.
• Figure 3: Natural perturbations in body-based sensory measurements induced by wing flapping. With a constant motor input (PWM $=38{,}000$) and fixed position relative to the light source, light-intensity measurements exhibit oscillations/perturbations arising solely from flapping-wing motion, confirming that intrinsic wing oscillations cause perturbation in sensory measurements, which is required by NH-ES to adjust flapping wing motion (propulsion) towards stabilization.
• Figure 4: Experimental validation of NH-ES for a known objective function (NH-ES parameters: $\omega=100$, $k=0.003$, $a=0.7$, $c=1.095$). The flapping-wing body autonomously ascends and converges to a stable hovering state about desired altitude using only scalar feedback of altitude and intrinsic flapping-induced oscillations, without any model-based control, injected perturbations, or information about morphological parameters or body/aerodynamic models.
• Figure 5: Completely model-free, moth-like source seeking in an unknown light field with a fixed source (NH-ES parameters: $\omega=120$, $k=0.5$, $a=0.7$, $c=1.1$, high-pass filter gain $h=0.2$). The flapping-wing body ascends toward increasing light intensity and converges beneath the light source, where it naturally transitions into stable hovering. The control mechanism does not have any access to morphological parameter, light source position or distribution model/estimate, or bode/aerodynamic models.