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Vibrational control is an open loop stabilization technique via the application of highamplitude, high-frequency oscillatory inputs. The averaging theory has been the standard technique for designing vibrational control systems. However, it stipulates too high oscillation frequency that may not be practically feasible. Therefore, although vibrational control is very robust and elegant (stabilization without feedback), it is rarely used in practical applications. The only well-known example is the Kapitza pendulum; an inverted pendulum shose pivot is subject to vertical oscillation. the unstable equilibrium of the inverted pendulum gains asymptotic stability due to the high-frequency oscillation of the pivot. In this paper, we provide a new vibrational control system from Nature; flapping flight dynamics. Flapping flight is a rich dynamical system as a representative model will typically be nonlinear, time-varying, multi-body, multi-time-scale dynamical system. Over the last two decades, using direct averaging, there has been consensus in the flapping flight dynamics community that insects are unstable at the hovering equilibrium due to the lack of pitch stiffness. In this work, we perform higher-order averaging of the time-periodic dynamics of flapping flight to show a vibrational control mechanism due to the oscillation of the driving aerodynamic forces. We also experimentally demonstrate such a phenomenon on a flapping apparatus that has two degrees of freedom: forward translation and pitching motion. It is found that the time-periodic dynamics of the flapping micro-air-vehicle is naturally (without feedback) stabilized beyond a certain threshold. Moreover, if the averaged aerodynamic thrust force is produced by a propeller revolving at a constant speed while maintaining the wings stationary at their mean positions, no stabilization is observed. Hence, it is concluded that the observed stabilization in the flapping system at high frequencies is due to the oscillation of the driving aerodynamic force and, as such, flapping flight indeed enjoys vibrational stabilization.
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This content will become publicly available on November 17, 2026
How Optimal is Extremum Seeking Control for Hovering in Flapping Insects/MAVs?
The problem of hovering in flapping insects/hummingbirds, and potential bio-mimicry by micro aerial vehicles (MAVs), have been studied for decades by scientists and engineers. Said communities often study hovering in flapping systems as either an open-loop or closed-loop system to analyze stability and/or propose control designs. Recently, a fundamentally novel result has been achieved in the literature of the hovering problem. That is, hovering in flapping insects/hummingbirds can be characterized/mimicked as a stable, model-free, real-time extremum seeking control (ESC) feedback system. In this paper we aim at two contributions: (i) provide a novel open-loop, optimal control characterization of hovering; and (ii) compare the performance of closed-loop, real-time ESC in hovering vs. the provided open-loop, non-real-time optimal control in hovering.
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- PAR ID:
- 10676261
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- IFAC-PapersOnLine
- Volume:
- 59
- Issue:
- 19
- ISSN:
- 2405-8963
- Page Range / eLocation ID:
- 644 to 649
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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