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.

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.

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.

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.

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.

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.

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.

Wings as impellers: honey bees co-opt flight system to induce nest ventilation and disperse pheromones.

Honey bees (Apis mellifera) are remarkable fliers that regularly carry heavy loads of nectar and pollen, supported by a flight system - the wings, thorax and flight muscles - that one might assume is optimized for aerial locomotion. However, honey bees also use this system to perform other crucial tasks that are unrelated to flight. When ventilating the nest, bees grip the surface of the comb or nest entrance and fan their wings to drive airflow through the nest, and a similar wing-fanning behavior is used to disperse volatile pheromones from the Nasonov gland. In order to understand how the physical demands of these impeller-like behaviors differ from those of flight, we quantified the flapping kinematics and compared the frequency, amplitude and stroke plane angle during these non-flight behaviors with values reported for hovering honey bees. We also used a particle-based flow visualization technique to determine the direction and speed of airflow generated by a bee performing Nasonov scenting behavior. We found that ventilatory fanning behavior is kinematically distinct from both flight and scenting behavior. Both impeller-like behaviors drive flow parallel to the surface to which the bees are clinging, at typical speeds of just under 1 m s-1 We observed that the wings of fanning and scenting bees frequently contact the ground during the ventral stroke reversal, which may lead to wing wear. Finally, we observed that bees performing Nasonov scenting behavior sometimes display 'clap-and-fling' motions, in which the wings contact each other during the dorsal stroke reversal and fling apart at the start of the downstroke. We conclude that the wings and flight motor of honey bees comprise a multifunctional system, which may be subject to competing selective pressures because of its frequent use as both a propeller and an impeller.

Climbing, falling, and jamming during ant locomotion in confined environments.

Locomotion emerges from effective interactions of an individual with its environment. Principles of biological terrestrial locomotion have been discovered on unconfined vertical and horizontal substrates. However, a diversity of organisms construct, inhabit, and move within confined spaces. Such animals are faced with locomotor challenges including limited limb range of motion, crowding, and visual sensory deprivation. Little is known about how these organisms accomplish their locomotor tasks, and such environments challenge human-made devices. To gain insight into how animals move within confined spaces, we study the locomotion of the fire ant Solenopsis invicta, which constructs subterranean tunnel networks (nests). Laboratory experiments reveal that ants construct tunnels with diameter, D, comparable to body length, L = 3.5 ± 0.5 mm. Ants can move rapidly (> 9 bodylengths per s) within these environments; their tunnels allow for effective limb, body, and antennae interaction with walls, which facilitate rapid slip-recovery during ascending and descending climbs. To examine the limits of slip-recovery in artificial tunnels, we perform perturbations consisting of rapid downward accelerations of the tunnels, which induce falls. Below a critical tunnel diameter, Ds = 1.31 ± 0.02 L, falls are always arrested through rapid interaction of appendages and antennae with tunnel walls to jam the falls. Ds is comparable to the size of incipient nest tunnels (D = 1.06 ± 0.23 L), supporting our hypothesis that fire ants construct environments that simplify their control task when moving through the nest, likely without need for rapid nervous system intervention.

Collective Flow Enhancement by Tandem Flapping Wings.

We examine the fluid-mechanical interactions that occur between arrays of flapping wings when operating in close proximity at a moderate Reynolds number (Re≈100-1000). Pairs of flapping wings are oscillated sinusoidally at frequency f, amplitude θ_{M}, phase offset ϕ, and wing separation distance D^{*}, and outflow speed v^{*} is measured. At a fixed separation distance, v^{*} is sensitive to both f and ϕ, and we observe both constructive and destructive interference in airspeed. v^{*} is maximized at an optimum phase offset, ϕ_{max}, which varies with wing separation distance, D^{*}. We propose a model of collective flow interactions between flapping wings based on vortex advection, which reproduces our experimental data.

Behavioral and mechanical determinants of collective subsurface nest excavation.

Collective construction of topologically complex structures is one of the triumphs of social behavior. For example, many ant species construct underground nests composed of networks of tunnels and chambers. Excavation by these 'superorganisms' depends on the biomechanics of substrate manipulation, the interaction of individuals, and media stability and cohesiveness. To discover principles of robust social excavation, we used X-ray computed tomography to monitor the growth in three dimensions of nests built by groups of fire ants (Solenopsis invicta) in laboratory substrates composed of silica particles, manipulating two substrate properties: particle size and gravimetric moisture content. Ants were capable of nest construction in all substrates tested other than completely dry or fully saturated; for a given particle size, nest volume was relatively insensitive to moisture content. Tunnels were deepest at intermediate moisture content and the maximum tunnel depth correlated with measured yield force on small rod-shaped intruders (a proxy for cohesive strength). This implies that increased cohesive strength allowed creation of tunnels that were resistant to perturbation but did not decrease individual excavation ability. Ants used two distinct behaviors to create pellets composed of wetted particles, depending on substrate composition. However, despite the ability to create larger stable pellets in more cohesive substrates, pellet sizes were similar across all conditions. We posit that this pellet size balances the individual's load-carrying ability with the need to carry this pellet through confined crowded tunnels. We conclude that effective excavation of similarly shaped nests can occur in a diversity of substrates through sophisticated digging behaviors by individuals which accommodate both differing substrate properties and the need to work within the collective.

Glass-like dynamics in confined and congested ant traffic.

The collective movement of animal groups often occurs in confined spaces. As animal groups are challenged to move at high density, their mobility dynamics may resemble the flow of densely packed non-living soft materials such as colloids, grains, or polymers. However, unlike inert soft-materials, self-propelled collective living systems often display social interactions whose influence on collective mobility are only now being explored. In this paper, we study the mobility of bi-directional traffic flow in a social insect (the fire ant Solenopsis invicta) as we vary the diameter of confining foraging tunnels. In all tunnel diameters, we observe the emergence of spatially heterogeneous regions of fast and slow traffic that are induced through two phenomena: physical obstruction, arising from the inability of individual ants to interpenetrate, and time-delay resulting from social interaction in which ants stop to briefly antennate. Density correlation functions reveal that the relaxation dynamics of high density traffic fluctuations scale linearly with fluctuation size and are sensitive to tunnel diameter. We separate the roles of physical obstruction and social interactions in traffic flow using cellular automata based simulation. Social interaction between ants is modeled as a dwell time (Tint) over which interacting ants remain stationary in the tunnel. Investigation over a range of densities and Tint reveals that the slowing dynamics of collective motion in social living systems are consistent with dynamics near a fragile glass transition in inert soft-matter systems. In particular, flow is relatively insensitive to density until a critical density is reached. As social interaction affinity is increased (increasing Tint) traffic dynamics change and resemble a strong glass transition. Thus, social interactions play an important role in the mobility of collective living systems at high density. Our experiments and model demonstrate that the concepts of soft-matter physics aid understanding of the mobility of collective living systems, and motivate further inquiry into the dynamics of densely confined social living systems.

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.

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.

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.

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.

Entangled granular media.

We study the geometrically induced cohesion of ensembles of granular "u particles" that mechanically entangle through particle interpenetration. We vary the length-to-width ratio l/w of the u particles and form them into freestanding vertical columns. In a laboratory experiment, we monitor the response of the columns to sinusoidal vibration (with peak acceleration Γ). Column collapse occurs in a characteristic time τ which follows the relation τ∝exp(Γ/Δ). Δ resembles an activation energy and is maximal at intermediate l/w. A simulation reveals that optimal strength results from competition between packing and entanglement.

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.

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.

Drag induced lift in granular media.

Laboratory experiments and numerical simulation reveal that a submerged intruder dragged horizontally at a constant velocity within a granular medium experiences a lift force whose sign and magnitude depend on the intruder shape. Comparing the stress on a flat plate at varied inclination angle with the local surface stress on the intruders at regions with the same orientation demonstrates that intruder lift forces are well approximated as the sum of contributions from flat-plate elements. The plate stress is deduced from the force balance on the flowing media near the plate.