Moth resonant mechanics are tuned to wingbeat frequency and energetic demands.

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.

The Weis-Fogh number describes resonant performance tradeoffs in flapping insects.

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.

Multimodal Locomotion in a Soft Robot Through Hierarchical Actuation.

Soft and continuum robots present the opportunity for extremely large ranges of motion, which can enable dexterous, adaptive, and multimodal locomotion behaviors. However, as the number of degrees of freedom (DOF) of a robot increases, the number of actuators should also increase to achieve the full actuation potential. This presents a dilemma in mobile soft robot design: physical space and power requirements restrict the number and type of actuators available and may ultimately limit the movement capabilities of soft robots with high-DOF appendages. Restrictions on actuation of continuum appendages ultimately may limit the various movement capabilities of soft robots. In this work, we demonstrate multimodal behaviors in an underwater robot called "Hexapus." A hierarchical actuation design for multiappendage soft robots is presented in which a single high-power motor actuates all appendages for locomotion, while smaller low-power motors augment the shape of each appendage. The flexible appendages are designed to be capable of hyperextension for thrust, and flexion for grasping with a peak pullout force of 32 N. For propulsion, we incorporate an elastic membrane connected across the base of each tentacle, which is stretched slowly by the high-power motor and released rapidly through a slip-gear mechanism. Through this actuation arrangement, Hexapus is capable of underwater locomotion with low cost of transport (COT = 1.44 at 16.5 mm/s) while swimming and a variety of multimodal locomotion behaviors, including swimming, turning, grasping, and crawling, which we demonstrate in experiment.

Bridging two insect flight modes in evolution, physiology and robophysics.

Since taking flight, insects have undergone repeated evolutionary transitions between two seemingly distinct flight modes1-3. Some insects neurally activate their muscles synchronously with each wingstroke. However, many insects have achieved wingbeat frequencies beyond the speed limit of typical neuromuscular systems by evolving flight muscles that are asynchronous with neural activation and activate in response to mechanical stretch2-8. These modes reflect the two fundamental ways of generating rhythmic movement: time-periodic forcing versus emergent oscillations from self-excitation8-10. How repeated evolutionary transitions have occurred and what governs the switching between these distinct modes remain unknown. Here we find that, despite widespread asynchronous actuation in insects across the phylogeny3,6, asynchrony probably evolved only once at the order level, with many reversions to the ancestral, synchronous mode. A synchronous moth species, evolved from an asynchronous ancestor, still preserves the stretch-activated muscle physiology. Numerical and robophysical analyses of a unified biophysical framework reveal that rather than a dichotomy, these two modes are two regimes of the same dynamics. Insects can transition between flight modes across a bridge in physiological parameter space. Finally, we integrate these two actuation modes into an insect-scale robot11-13 that enables transitions between modes and unlocks a new self-excited wingstroke strategy for engineered flight. Together, this framework accounts for repeated transitions in insect flight evolution and shows how flight modes can flip with changes in physiological parameters.

Structural damping renders the hawkmoth exoskeleton mechanically insensitive to non-sinusoidal deformations.

Muscles act through elastic and dissipative elements to mediate movement, which can introduce dissipation and filtering which are important for energetics and control. The high power requirements of flapping flight can be reduced by an insect's exoskeleton, which acts as a spring with frequency-independent material properties under purely sinusoidal deformation. However, this purely sinusoidal dynamic regime does not encompass the asymmetric wing strokes of many insects or non-periodic deformations induced by external perturbations. As such, it remains unknown whether a frequency-independent model applies broadly and what implications it has for control. We used a vibration testing system to measure the mechanical properties of isolated Manduca sexta thoraces under symmetric, asymmetric and band-limited white noise deformations. The asymmetric and white noise conditions represent two types of generalized, multi-frequency deformations that may be encountered during steady-state and perturbed flight. Power savings and dissipation were indistinguishable between symmetric and asymmetric conditions, demonstrating that no additional energy is required to deform the thorax non-sinusoidally. Under white noise conditions, stiffness and damping were invariant with frequency, suggesting that the thorax has no frequency-dependent filtering properties. A simple flat frequency response function fits our measured frequency response. This work demonstrates the potential of materials with frequency-independent damping to simplify motor control by eliminating any velocity-dependent filtering that viscoelastic elements usually impose between muscle and wing.

Going against the flow: bumblebees prefer to fly upwind and display more variable kinematics when flying downwind.

Foraging insects fly over long distances through complex aerial environments, and many can maintain constant ground speeds in wind, allowing them to gauge flight distance. Although insects encounter winds from all directions in the wild, most lab-based studies have employed still air or headwinds (i.e. upwind flight); additionally, insects are typically compelled to fly in a single, fixed environment, so we know little about their preferences for different flight conditions. We used automated video collection and analysis methods and a two-choice flight tunnel paradigm to examine thousands of foraging flights performed by hundreds of bumblebees flying upwind and downwind. In contrast to the preference for flying with a tailwind (i.e. downwind) displayed by migrating insects, we found that bees prefer to fly upwind. Bees maintained constant ground speeds when flying upwind or downwind in flow velocities from 0 to 2 m s-1 by adjusting their body angle, pitching down to raise their air speed above flow velocity when flying upwind, and pitching up to slow down to negative air speeds (flying backwards relative to the flow) when flying downwind. Bees flying downwind displayed higher variability in body angle, air speed and ground speed. Taken together, bees' preference for upwind flight and their increased kinematic variability when flying downwind suggest that tailwinds may impose a significant, underexplored flight challenge to bees. Our study demonstrates the types of questions that can be addressed with newer approaches to biomechanics research; by allowing bees to choose the conditions they prefer to traverse and automating filming and analysis to examine massive amounts of data, we were able to identify significant patterns emerging from variable locomotory behaviors, and gain valuable insight into the biomechanics of flight in natural environments.

A virtuous cycle between invertebrate and robotics research: perspective on a decade of Living Machines research.

Many invertebrates are ideal model systems on which to base robot design principles due to their success in solving seemingly complex tasks across domains while possessing smaller nervous systems than vertebrates. Three areas are particularly relevant for robot designers: Research on flying and crawling invertebrates has inspired new materials and geometries from which robot bodies (their morphologies) can be constructed, enabling a new generation of softer, smaller, and lighter robots. Research on walking insects has informed the design of new systems for controlling robot bodies (their motion control) and adapting their motion to their environment without costly computational methods. And research combining wet and computational neuroscience with robotic validation methods has revealed the structure and function of core circuits in the insect brain responsible for the navigation and swarming capabilities (their mental faculties) displayed by foraging insects. The last decade has seen significant progress in the application of principles extracted from invertebrates, as well as the application of biomimetic robots to model and better understand how animals function. This Perspectives paper on the past 10 years of the Living Machines conference outlines some of the most exciting recent advances in each of these fields before outlining lessons gleaned and the outlook for the next decade of invertebrate robotic research.

Walking is like slithering: A unifying, data-driven view of locomotion.

Legged movement is ubiquitous in nature and of increasing interest for robotics. Most legged animals routinely encounter foot slipping, yet detailed modeling of multiple contacts with slipping exceeds current simulation capacity. Here we present a principle that unifies multilegged walking (including that involving slipping) with slithering and Stokesian (low Reynolds number) swimming. We generated data-driven principally kinematic models of locomotion for walking in low-slip animals (Argentine ant, 4.7% slip ratio of slipping to total motion) and for high-slip robotic systems (BigANT hexapod, slip ratio 12 to 22%; Multipod robots ranging from 6 to 12 legs, slip ratio 40 to 100%). We found that principally kinematic models could explain much of the variability in body velocity and turning rate using body shape and could predict walking behaviors outside the training data. Most remarkably, walking was principally kinematic irrespective of leg number, foot slipping, and turning rate. We find that grounded walking, with or without slipping, is governed by principally kinematic equations of motion, functionally similar to frictional swimming and slithering. Geometric mechanics thus leads to a unified model for swimming, slithering, and walking. Such commonality may shed light on the evolutionary origins of animal locomotion control and offer new approaches for robotic locomotion and motion planning.

Soft Molds with Micro-Machined Internal Skeletons Improve Robustness of Flapping-Wing Robots.

Mobile millimeter and centimeter scale robots often use smart composite manufacturing (SCM) for the construction of body components and mechanisms. The fabrication of SCM mechanisms requires laser machining and laminating flexible, adhesive, and structural materials into small-scale hinges, transmissions, and, ultimately, wings or legs. However, a fundamental limitation of SCM components is the plastic deformation and failure of flexures. In this work, we demonstrate that encasing SCM components in a soft silicone mold dramatically improves the durability of SCM flexure hinges and provides robustness to SCM components. We demonstrate this advance in the design of a flapping-wing robot that uses an underactuated compliant transmission fabricated with an inner SCM skeleton and exterior silicone mold. The transmission design is optimized to achieve desired wingstroke requirements and to allow for independent motion of each wing. We validate these design choices in bench-top tests, measuring transmission compliance, kinematics, and fatigue. We integrate the transmission with laminate wings and two types of actuation, demonstrating elastic energy exchange and limited lift-off capabilities. Lastly, we tested collision mitigation through flapping-wing experiments that obstructed the motion of a wing. These experiments demonstrate that an underactuated compliant transmission can provide resilience and robustness to flapping-wing robots.

Lateral contact yields longitudinal cohesion in active undulatory systems.

Many animals and robots move using undulatory motion of their bodies. When the bodies are in close proximity undulatory motion can lead to novel collective behavior such as gait synchronization, spatial reconfiguration, and clustering. Here we study the role of contact interactions between model undulatory swimmers: three-link robots in experiment and multilink swimmers in simulation. The undulatory gait of each swimmer is generated through a time-dependent sinusoidal-like waveform which has a fixed phase offset, ϕ. By varying the phase relationship between neighboring swimmers we seek to study how contact forces and planar configurations are governed by the phase difference between neighboring swimmers. We find that undulatory actuation in close proximity drives neighboring swimmers into planar equilibrium configurations that depend on the actuation phase difference. We propose a model for stable planar configurations of nearest-neighbor undulatory swimmers which we call the gait compatibility condition, which is the set of planar and phase configurations in which no collisions occur. Robotic experiments with two, three, and four swimmers exhibit good agreement with the compatibility model. To study the contact forces and the time-averaged equilibrium between undulatory systems we perform simulations. To probe the interaction potential between undulatory swimmers we apply a small force to each swimmer longitudinally to separate them from the compatible configuration and we measure their steady-state displacement. These studies reveal that undulatory swimmers in close proximity exhibit attractive longitudinal interaction forces that drive the swimmers from incompatible to compatible configurations. This system of undulatory swimmers provides new insight into active-matter systems which move through body undulation. In addition to the importance of velocity and orientation coherence in active-matter swarms, we demonstrate that undulatory phase coherence is also important for generating stable, cohesive group configurations.

The hawkmoth wingbeat is not at resonance.

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.

Anisotropic compliance of robot legs improves recovery from swing-phase collisions.

Uneven terrain in natural environments challenges legged locomotion by inducing instability and causing limb collisions. During the swing phase, the limb releases from the ground and arcs forward to target a secure next foothold. In natural environments leg-obstacle collisions may occur during the swing phase which can result in instability, and may require contact sensing and trajectory re-planning if a collision occurs. However, collision detection and response often requires computationally- and temporally-expensive control strategies. Inspired by low stiffness limbs that can pass past obstacles in small insects and running birds, we investigated a passive method for overcoming swing-collisions. We implemented virtual compliance control in a robot leg that allowed us to systematically vary the limb stiffness and ultimately its response to collisions with obstacles in the environment. In addition to applying a standard positional control during swing motion, we developed two virtual compliance methods: (1) an isotropic compliance for which perturbations in thexandydirections generated the same stiffness response, and (2) a vertical anisotropic compliance in which a decrease of the upwardyvertical limb stiffness enabled the leg to move upwards more freely. The virtual compliance methods slightly increased variability along the limb's planned pathway, but the anisotropic compliance control improved the successful negotiation of step obstacles by over 70% compared to isotropic compliance and positional control methods. We confirmed these findings in simulation and using a self-propelling bipedal robot walking along a linear rail over bumpy terrain. While the importance of limb compliance for stance interactions have been known, our results highlight how limb compliance in the swing-phase can enhance walking performance in naturalistic environments.

Rapid frequency modulation in a resonant system: aerial perturbation recovery in hawkmoths.

Centimetre-scale fliers must contend with the high power requirements of flapping flight. Insects have elastic elements in their thoraxes which may reduce the inertial costs of their flapping wings. Matching wingbeat frequency to a mechanical resonance can be energetically favourable, but also poses control challenges. Many insects use frequency modulation on long timescales, but wingstroke-to-wingstroke modulation of wingbeat frequencies in a resonant spring-wing system is potentially costly because muscles must work against the elastic flight system. Nonetheless, rapid frequency and amplitude modulation may be a useful control modality. The hawkmoth Manduca sexta has an elastic thorax capable of storing and returning significant energy. However, its nervous system also has the potential to modulate the driving frequency of flapping because its flight muscles are synchronous. We tested whether hovering hawkmoths rapidly alter frequency during perturbations with vortex rings. We observed both frequency modulation (32% around mean) and amplitude modulation (37%) occurring over several wingstrokes. Instantaneous phase analysis of wing kinematics revealed that more than 85% of perturbation responses required active changes in neurogenic driving frequency. Unlike their robotic counterparts that abdicate frequency modulation for energy efficiency, synchronous insects use wingstroke-to-wingstroke frequency modulation despite the power demands required for deviating from resonance.

Dimensional analysis of spring-wing systems reveals performance metrics for resonant flapping-wing flight.

Flapping-wing insects, birds and robots are thought to offset the high power cost of oscillatory wing motion by using elastic elements for energy storage and return. Insects possess highly resilient elastic regions in their flight anatomy that may enable high dynamic efficiency. However, recent experiments highlight losses due to damping in the insect thorax that could reduce the benefit of those elastic elements. We performed experiments on, and simulations of, a dynamically scaled robophysical flapping model with an elastic element and biologically relevant structural damping to elucidate the roles of body mechanics, aerodynamics and actuation in spring-wing energetics. We measured oscillatory flapping-wing dynamics and energetics subject to a range of actuation parameters, system inertia and spring elasticity. To generalize these results, we derive the non-dimensional spring-wing equation of motion and present variables that describe the resonance properties of flapping systems: N, a measure of the relative influence of inertia and aerodynamics, and [Formula: see text], the reduced stiffness. We show that internal damping scales with N, revealing that dynamic efficiency monotonically decreases with increasing N. Based on these results, we introduce a general framework for understanding the roles of internal damping, aerodynamic and inertial forces, and elastic structures within all spring-wing systems.

Rapid two-anchor crawling from a milliscale prismatic-push-pull (3P) robot.

Many crawling organisms such as caterpillars and worms use a method of movement in which two or more anchor points alternately push and pull the body forward at a constant frequency. In this paper we present a milliscale push-pull robot which is capable of operating across a wide range of actuation frequencies thus enabling us to expand our understanding of two-anchor locomotion beyond the low-speed regime. We designed and fabricated a milliscale robot which uses anisotropic friction at two oscillating contact points to propel itself forward in a push-pull fashion. In experiments we varied the oscillation frequency,f, over a wide range (10-250 Hz) and observe a non-linear relationship between robot speed over this full frequency range. At low frequency (f< 100 Hz) forward speed increased linearly with frequency. However, at an intermediate push-pull frequency (f> 100 Hz) speed was relatively constant with increasing frequency. Lastly, at higher frequency (f> 170 Hz) the linear speed-frequency relationship returned. The speed-frequency relationship at low actuation frequencies is consistent with previously described two-anchor models and experiments in biology and robotics, however the higher frequency behavior is inconsistent with two-anchor frictional behavior. To understand the locomotion behavior of our system we first develop a deterministic two-anchor model in which contact forces are determined exactly from static or dynamic friction. Our experiments deviate from the model predictions, and through 3D kinematics measurements we confirm that ground contact is intermittent in robot locomotion at higher frequencies. By including probabilistic foot slipping behavior in the two-anchor friction model we are able to describe the three-regimes of robot locomotion.

Impact of slope on dynamics of running and climbing.

By combining biological studies and modeling work, the dynamics of running on horizontal terrain and climbing pure vertical surfaces have been distilled down to simple reduced order models. These models have inspired distinct control and design considerations for robots operating in each terrain. However, while the extremes are understood, the intermediate regions of moderate slopes have yet to be fully explored. In this paper, we examine how cockroaches vary their behavior as slope is changed from horizontal to vertical, with special care to examine individual leg forces when possible. The results are then compared with a lateral leg spring based (LLS, horizontal running) and Full-Goldman based (FG, vertical running) models. Overall, from the experimental data, there appears to be a continuous shift in the dynamics as slope varies, which is confirmed by similar behaviors exhibited by the LLS and FG models. Finally, by examining the stability and efficiency of the models, it is shown that there are stability limits related to the amount of energy added by the front versus rear legs. This corresponds to the shift in leg usage demonstrated by the biological experiments and may have significant implications for the design and control of multi-modal robotic systems.

Indirect actuation reduces flight power requirements in Manduca sexta via elastic energy exchange.

In many insects, wing movements are generated indirectly via exoskeletal deformations. Measurements of inertial and aerodynamic power suggest that elastic recovery of energy between wingstrokes might reduce power requirements of flight. We tested three questions. (1) Can the thorax itself provide significant energy return? (2) Does a simple damped elastic model describe the bulk mechanical behaviour? (3) Are different regions of the thorax specialized for elastic energy exchange? We measured deformation mechanics of the hawkmoth Manduca sexta thorax by recording the force required to sinusoidally deform the thorax over a wide frequency range. Elastic energy storage in the thorax is sufficient to minimize power requirements. However, we find that a structural (frequency-independent) damping model, not a viscoelastic model, best describes the thorax's mechanical properties. We next performed complementary experiments on a structurally damped homogeneous hemisphere. In contrast to the hemispherical shell, we find that mechanical coupling between different regions of the thorax improves energy exchange performance and that local mechanical properties depend on global strain patterns. Specifically, the scutum region provides energy recovery with low dissipation, while the majority of energy loss occurred in the wing hinge region, highlighting the specificity of thorax regions for flight energetics.

Author Correction: Spatial fidelity of workers predicts collective response to disturbance in a social insect.

The original version of the Article contained incorrect citation information in reference 67. The reference should read "Russell, A. L., Morrison, S. J., Moschonas, E. H. & Papaj, D. R. Patterns of pollen and nectar foraging specialization by bumblebees over multiple timescales using RFID. Sci. Rep. 7, 1-13 (2017)." This error has now been corrected in the PDF and HTML versions of the Article.

Spatial fidelity of workers predicts collective response to disturbance in a social insect.

Individuals in social insect colonies cooperate to perform collective work. While colonies often respond to changing environmental conditions by flexibly reallocating workers to different tasks, the factors determining which workers switch and why are not well understood. Here, we use an automated tracking system to continuously monitor nest behavior and foraging activity of uniquely identified workers from entire bumble bee (Bombus impatiens) colonies foraging in a natural outdoor environment. We show that most foraging is performed by a small number of workers and that the intensity and distribution of foraging is actively regulated at the colony level in response to forager removal. By analyzing worker nest behavior before and after forager removal, we show that spatial fidelity of workers within the nest generates uneven interaction with relevant localized information sources, and predicts which workers initiate foraging after disturbance. Our results highlight the importance of spatial fidelity for structuring information flow and regulating collective behavior in social insect colonies.

Robotics-inspired biology.

For centuries, designers and engineers have looked to biology for inspiration. Biologically inspired robots are just one example of the application of knowledge of the natural world to engineering problems. However, recent work by biologists and interdisciplinary teams have flipped this approach, using robots and physical models to set the course for experiments on biological systems and to generate new hypotheses for biological research. We call this approach robotics-inspired biology; it involves performing experiments on robotic systems aimed at the discovery of new biological phenomena or generation of new hypotheses about how organisms function that can then be tested on living organisms. This new and exciting direction has emerged from the extensive use of physical models by biologists and is already making significant advances in the areas of biomechanics, locomotion, neuromechanics and sensorimotor control. Here, we provide an introduction and overview of robotics-inspired biology, describe two case studies and suggest several directions for the future of this exciting new research area.