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Flying insects have elastic materials within their exoskeletons that could reduce the energetic cost of flight if their wingbeat frequency is matched to a mechanical resonance frequency. Flapping at resonance may be essential across flying insects because of the power demands of small-scale flapping flight. However, building up large-amplitude resonant wingbeats over many wingstrokes may be detrimental for control if the total mechanical energy in the spring-wing system exceeds the per-cycle work capacity of the flight musculature. While the mechanics of the insect flight apparatus can behave as a resonant system, the question of whether insects flap their wings at their resonant frequency remains unanswered. Using previous measurements of body stiffness in the hawkmoth, Manduca sexta , we develop a mechanical model of spring-wing resonance with aerodynamic damping and characterize the hawkmoth's resonant frequency. We find that the hawkmoth's wingbeat frequency is approximately 80% above resonance and remains so when accounting for uncertainty in model parameters. In this regime, hawkmoths may still benefit from elastic energy exchange while enabling control of aerodynamic forces via frequency modulation. We conclude that, while insects use resonant mechanics, tuning wingbeats to a simple resonance peak is not a necessary feature for all centimetre-scale flapping flyers.
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Autonomous Actuation of Flapping Wing Robots Inspired by Asynchronous Insect Muscle
In most instances, flapping wing robots have emulated the “synchronous” actuation of insects in which the wingbeat timing is generated from a time-dependent, rhythmic signal. The internal dynamics of asynchronous insect flight muscle enable high-frequency, adaptive wingbeats with minimal direct neural control. In this paper, we investigate how the delayed stretch-activation (dSA) response of asynchronous insect flight muscle can be transformed into a feedback control law for flapping wing robots that results in stable limit cycle wingbeats. We first demonstrate - in theory and simulation - the mechanism by which asynchronous wingbeats self-excite. Then, we implement the feedback law on a dynamically-scaled robophysical model as well as on an insect-scale robotic flapping wing. Experiments on large- and small-scale robots demonstrate good agreement with the theory results and highlight how dSA parameters govern wingbeat amplitude and frequency. Lastly, we demonstrate that asynchronous actuation has several advantages over synchronous actuation schemes, including the ability to rapidly adapt or halt wingbeats in response to external loads or collisions through low-level feedback control.
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- Award ID(s):
- 2100858
- PAR ID:
- 10342646
- Date Published:
- Journal Name:
- 2022 IEEE International Conference on Robotics and Automation (ICRA)
- Page Range / eLocation ID:
- 2076 to 2083
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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In the last decade, roboticists have had significant success building centimeter-scale flapping wing micro aerial vehicles (FWMAVs) inspired by the flight of insects. Evidence suggests that insects store and release energy in the thoracic exoskeleton to improve energy efficiency by flapping at resonance. Insect-inspired micro flying robots have also leveraged resonance to improve efficiency, but they have discovered that operating at the resonant frequency leads to issues with flight control. This research seeks to investigate the roles that elasticity, aerodynamics, and muscle dynamics play in the emergent dynamics of flapping flight by studying elastic flapping spring-wing systems using dynamically-scaled robophysical models of springwings. Studying the dynamics of a robot with comparable features enables the validation of models from biology that are otherwise difficult to test in living insects, the generation of new hypotheses, and the development of novel FWMAV designs. In Chapter 1, the spring-wing system is characterized via a nonlinear spring-mass-damper model. A robophysical model validates that such systems gain energetic benefits from operating at resonance, but reveals that the benefit scales with an underappreciated dimensionless ratio of inertial to aerodynamic forces, the Weis-Fogh number. We show through dimensional analysis that any real system, living or robotic, must balance the mechanical advantage gained from operating at resonance with diminishing returns in efficiency. Chapter 2 further explores the impact of the Weis-Fogh number on flapping dynamics, showing that responsiveness to control inputs is reduced and resistance to environmental perturbations is increased as the dimensionless ratio increases. Together with calculations of Weis-Fogh number in insects, these studies illustrate tradeoffs that drive evolution of resonant flight in nature and guide development of future FWMAVs with elastic energy exchange. In the second half of the thesis, muscle dynamics are introduced in the form of a simplified model of self-excited asynchronous insect muscle. In Chapter 3, a form of velocity feedback, adapted from experiments on insect flight muscle, is developed and integrated with the springwing model, producing a system that generates steady flapping via limit-cycle oscillations despite the absence of periodic control inputs. The model is explored analytically, in simulation, and via implementation on the robotic spring-wing. Novel dynamic characteristics that enable adaptation to damage and passive response to wing collisions are described. Chapter 4 leverages the asynchronous feedback model as part of an interdisciplinary study of the evolution of asynchronous muscle. Phylogenetic analysis, direct measurement of insect muscle dynamics, and experiments on the robophysical system show that evolutionary transitions between periodicallyforced and self-excited insect muscle were likely made possible by a ”bridge” in the dynamic parameter space that could be traversed under specific conditions. The asynchronous spring-wing model provides new insight into the flight and evolution of some of the most agile insects in nature, and presents a novel adaptive control scheme for future FWMAVs.more » « less
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An insect’s wingbeat frequency is a critical determinant of its flight performance and varies by multiple orders of magnitude across Insecta. Despite potential energetic benefits for an insect that matches its wingbeat frequency to its resonant frequency, recent work has shown that moths may operate off their resonant peak. We hypothesized that across species, wingbeat frequency scales with resonance frequency to maintain favourable energetics, but with an offset in species that use frequency modulation as a means of flight control. The moth superfamily Bombycoidea is ideal for testing this hypothesis because their wingbeat frequencies vary across species by an order of magnitude, despite similar morphology and actuation. We used materials testing, high-speed videography and a model of resonant aerodynamics to determine how components of an insect’s flight apparatus (stiffness, wing inertia, muscle strain and aerodynamics) vary with wingbeat frequency. We find that the resonant frequency of a moth correlates with wingbeat frequency, but resonance curve shape (described by the Weis-Fogh number) and peak location vary within the clade in a way that corresponds to frequency-dependent biomechanical demands. Our results demonstrate that a suite of adaptations in muscle, exoskeleton and wing drive variation in resonant mechanics, reflecting potential constraints on matching wingbeat and resonant frequencies.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICRA46639.2022.9812028
