Periodic Proprioceptive Stimuli Learning and Internal Model Development for Avian-inspired Flapping-wing Flight State Estimation

TL;DR

The paper tackles online state estimation for avian-inspired flapping-wing aerial vehicles (FWAVs) plagued by high-frequency, flapping-induced oscillations. It introduces a divide-and-conquer framework that first learns and removes oscillatory components via Periodic Gaussian Process Learning and a phase-aware pipeline, then uses a cycle-averaged internal model to predict slow-varying dynamics in a forward slow-varying internal model built on averaging theory. The approach combines real-time periodic pattern learning with an internal-model-based EKF, yielding oscillation-free measurements that significantly improve attitude and state estimates, validated on a 1.7 m FWAV with low-cost MARG sensors under windy conditions. The results demonstrate improved accuracy and smoothness of attitude estimation and enable reconstruction of the full oscillatory state, advancing robust autonomous FWAV operation in complex environments.

Abstract

This paper presents a novel learning-based approach for online state estimation in flapping wing aerial vehicles (FWAVs). Leveraging low-cost Magnetic, Angular Rate, and Gravity (MARG) sensors, the proposed method effectively mitigates the adverse effects of flapping-induced oscillations that challenge conventional estimation techniques. By employing a divide-and-conquer strategy grounded in cycle-averaged aerodynamics, the framework decouples the slow-varying components from the high-frequency oscillatory components, thereby preserving critical transient behaviors while delivering an smooth internal state representation. The complete oscillatory state of FWAV can be reconstructed based on above two components, leading to substantial improvements in accurate state prediction. Experimental validations on an avian-inspired FWAV demonstrate that the estimator enhances accuracy and smoothness, even under complex aerodynamic disturbances. These encouraging results highlight the potential of learning algorithms to overcome issues of flapping-wing induced oscillation dynamics.

Figures (11)

• Figure 1: The FWAV in motion: The periodic motion of the flapping wings results in a non-negligible periodic pitch motion in the FWAV.
• Figure 2: Polar plots illustrating periodic-GPR learning utilizing data that encompass four cycles. The unprocessed sensor data preserved for the purpose of periodic-GPR learning are depicted as gray lines. The mean values are illustrated with darker colors, while the areas corresponding to the two standard deviations are shaded in lighter tones.
• Figure 3: Spectrograms over time generated by sliding-window Cooley-Tukey FFT alogorithm with real flight data. The signals of acceleration and angular velocity are employed for frequency estimation due to their superior update rates compared to all other available signals.
• Figure 4: Framework for implementing periodic Gaussian process learning in the estimation of internal attitude states.
• Figure 5: The longitudinal reference framework of the FWAV along with forces exerted upon it. The longitudinal inertia frame is denoted by $X_{I}$-$Z_{I}$, whereas the longitudinal body-fixed frame is represented by $X_{B}$-$Z_{B}$. Assuming the FWAV can execute banked turns without any lateral slip, we define a vertical frame, $X_V$–$Z_V$, based individually on its yaw rotation. The wind frame, $X_W$–$Z_W$, is defined based on the translational velocity. The deflection angles of the ruddervators on the inverted-V tail are anticipated to cause minimal variation in lift on the tail surfaces.