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Insects show diverse flight kinematics and morphologies reflecting their evolutionary histories and ecological adaptations. Many silk moths use low wingbeat frequencies and large wings to fly and display body oscillations. Their bodies pitch and bob periodically, synchronized with their wingbeat cycle. Similar oscillations in butterflies improve weight support and forward thrust while reducing flight power requirements. However, how instantaneous body and wing kinematics interact for these beneficial aerodynamic and power consequences is not well understood. We hypothesized that body oscillations affect aerodynamic power requirements by influencing wing rotation relative to the airflow. Using three-dimensional forward flight video recordings of four silk moth species and a quasi-steady blade-element aerodynamic model, we analysed the aerodynamic effects of body and wing kinematics. We find that the body pitch and wing sweep angles maintain a narrow range of phase differences, which enhances the angle of attack variation between each half-stroke due to increased wing rotation relative to the airflow. This redirects the aerodynamic force to increase the upward and forward components during the downstroke and upstroke, respectively, thus lowering overall drag without compromising weight support and forward thrust. Reducing energy expenditure is beneficial because many adult silk moths do not feed and rely on limited energy budgets. 

Abstract Powering small-scale flapping flight is challenging, yet insects sustain exceptionally fast wingbeats with ease. Since insects act as tiny biomechanical resonators, tuning their wingbeat frequency to the resonant frequency of their springy thorax and wings could make them more efficient fliers. But operating at resonance poses control problems and potentially constrains wingbeat frequencies within and across species. Resonance may be particularly limiting for the many orders of insects that power flight with specialized muscles that activate in response to mechanical stretch. Here, we test whether insects operate at their resonant frequency. First, we extensively characterize bumblebees and find that they surprisingly flap well above their resonant frequency via interactions between stretch-activation and mechanical resonance. Modeling and robophysical experiments then show that resonance is actually a lower bound for rapid wingbeats in most insects because muscles only pull, not push. Supra-resonance emerges as a general principle of high-frequency flight across five orders of insects from moths to flies. 

ABSTRACT Flying insects solve a daunting control problem of generating a patterned and precise motor program to stay airborne and generate agile maneuvers. In this motor program, each muscle encodes information about movement in precise spike timing down to the millisecond scale. Whereas individual muscles share information about movement, we do not know whether they have separable effects on an animal's motion, or whether muscles functionally interact such that the effects of any muscle's timing depend heavily on the state of the entire musculature. To answer these questions, we performed spike-resolution electromyography and electrical stimulation in the hawkmoth Manduca sexta during tethered flapping. We specifically explored how flight power muscles contribute to pitch control. Combining correlational study of visually induced turns with causal manipulation of spike timing, we discovered likely coordination patterns for pitch turns, and investigated whether these patterns can drive pitch control. We observed significant timing change of the main downstroke muscles, the dorsolongitudinal muscles (DLMs), associated with pitch turns. Causally inducing this timing change in the DLMs with electrical stimulation produced a consistent, mechanically relevant feature in pitch torque, establishing that power muscles in M. sexta have a control role in pitch. Because changes were evoked in only the DLMs, however, these pitch torque features left large unexplained variation. We found this unexplained variation indicates significant functional overlap in pitch control such that precise timing of one power muscle does not produce a precise turn, demonstrating the importance of coordination across the entire motor program for flight. 

Flying insects are thought to achieve energy-efficient flapping flight by storing and releasing elastic energy in their muscles, tendons, and thorax. However, ‘spring-wing’ flight systems consisting of elastic elements coupled to nonlinear, unsteady aerodynamic forces present possible challenges to generating stable and responsive wing motion. The energetic efficiency from resonance in insect flight is tied to the Weis-Fogh number (N), which is the ratio of peak inertial force to aerodynamic force. In this paper, we present experiments and modeling to study how resonance efficiency (which increases withN) influences the control responsiveness and perturbation resistance of flapping wingbeats. In our first experiments, we provide a step change in the input forcing amplitude to a series-elastic spring-wing system and observe the response time of the wing amplitude increase. In our second experiments we provide an external fluid flow directed at the flapping wing and study the perturbed steady-state wing motion. We evaluate both experiments across Weis-Fogh numbers from 1 < N < 10. The results indicate that spring-wing systems designed for maximum energetic efficiency also experience trade-offs in agility and stability as the Weis-Fogh number increases. Our results demonstrate that energetic efficiency and wing maneuverability are in conflict in resonant spring-wing systems, suggesting that mechanical resonance presents tradeoffs in insect flight control and stability. 

Legged animals still outperform many terrestrial robots due to the complex interplay of various component subsystems. Centralization is a potential integrated design axis to help improve the performance of legged robots in variable terrain environments. Centralization arises from the coupling of multiple limbs and joints through mechanics or feedback control. Strong couplings contribute to a whole-body coordinated response (centralized) and weak couplings result in localized responses (decentralized). Rarely are both mechanical and neural couplings considered together in designing centralization. In this study, we use an empirical information theory-based approach to evaluate the emergent centralization of a hexapod robot. We independently vary the mechanical and neural coupling through adjustable joint stiffness and variable coupling of leg controllers, respectively. We found an increase in centralization as neural coupling increased. Changes in mechanical coupling did not significantly affect centralization during walking, but did change the total information processing of the neuromechanical control architecture. Information-based centralization increased with robotic performance in terms of cost of transport and speed, implying that this may be a useful metric in robotic design. 

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 frequencydependent 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. 

Synopsis Dimensionless numbers have long been used in comparative biomechanics to quantify competing scaling relationships and connect morphology to animal performance. While common in aerodynamics, few relate the biomechanics of the organism to the forces produced on the environment during flight. We discuss the Weis-Fogh number, N, as a dimensionless number specific to flapping flight, which describes the resonant properties of an insect and resulting tradeoffs between energetics and control. Originally defined by Torkel Weis-Fogh in his seminal 1973 paper, N measures the ratio of peak inertial to aerodynamic torque generated by an insect over a wingbeat. In this perspectives piece, we define N for comparative biologists and describe its interpretations as a ratio of torques and as the width of an insect’s resonance curve. We then discuss the range of N realized by insects and explain the fundamental tradeoffs between an insect’s aerodynamic efficiency, stability, and responsiveness that arise as a consequence of variation in N, both across and within species. N is therefore an especially useful quantity for comparative approaches to the role of mechanics and aerodynamics in insect flight. 

Animals are much better at running than robots. The difference in performance arises in the important dimensions of agility, range, and robustness. To understand the underlying causes for this performance gap, we compare natural and artificial technologies in the five subsystems critical for running: power, frame, actuation, sensing, and control. With few exceptions, engineering technologies meet or exceed the performance of their biological counterparts. We conclude that biology’s advantage over engineering arises from better integration of subsystems, and we identify four fundamental obstacles that roboticists must overcome. Toward this goal, we highlight promising research directions that have outsized potential to help future running robots achieve animal-level performance. 

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.