Predicting fruit fly's sensing rate with insect flight simulations

Hummingbirds use wing inertial effects to improve manoeuvrability

Hummingbirds outperform other birds in terms of aerial agility at low flight speeds. To reveal the key mechanisms that enable such unparalleled agility, we reconstructed body and wing motion of hummingbird escape manoeuvres from high-speed videos; then, we performed computational fluid dynamics modelling and flight mechanics analysis, in which the time-dependent forces within each wingbeat were resolved. We found that the birds may use the inertia of their wings to achieve peak body rotational acceleration around wing reversal when the aerodynamic forces were small. The aerodynamic forces instead counteracted the reversed inertial forces at a different wingbeat phase, thereby stabilizing the body from inertial oscillations, or they could become dominant and provide additional rotational acceleration. Our results suggest such an inertial steering mechanism was present for all four hummingbird species considered, and it was used by the birds for both pitch-up and roll accelerations. The combined inertial steering and aerodynamic mechanisms made it possible for the hummingbirds to generate instantaneous body acceleration at any phase of a wingbeat, and this feature is probably the key to understanding the unique dexterity distinguishing hummingbirds from other small-size flyers that solely rely on aerodynamics for manoeuvering.

Neuromuscular embodiment of feedback control elements in Drosophila flight

While insects such as Drosophila are flying, aerodynamic instabilities require that they make millisecond time scale adjustments to their wing motion to stay aloft and on course. These stabilization reflexes can be modeled as a proportional-integral (PI) controller; however, it is unclear how such control might be instantiated in insects at the level of muscles and neurons. Here, we show that the b1 and b2 motor units-prominent components of the fly's steering muscle system-modulate specific elements of the PI controller: the angular displacement (integral) and angular velocity (proportional), respectively. Moreover, these effects are observed only during the stabilization of pitch. Our results provide evidence for an organizational principle in which each muscle contributes to a specific functional role in flight control, a finding that highlights the power of using top-down behavioral modeling to guide bottom-up cellular manipulation studies.

Recovery mechanisms in the dragonfly righting reflex

Insects have evolved sophisticated reflexes to right themselves in mid-air. Their recovery mechanisms involve complex interactions among the physical senses, muscles, body, and wings, and they must obey the laws of flight. We sought to understand the key mechanisms involved in dragonfly righting reflexes and to develop physics-based models for understanding the control strategies of flight maneuvers. Using kinematic analyses, physical modeling, and three-dimensional flight simulations, we found that a dragonfly uses left-right wing pitch asymmetry to roll its body 180 degrees to recover from falling upside down in ~200 milliseconds. Experiments of dragonflies with blocked vision further revealed that this rolling maneuver is initiated by their ocelli and compound eyes. These results suggest a pathway from the dragonfly's visual system to the muscles regulating wing pitch that underly the recovery. The methods developed here offer quantitative tools for inferring insects' internal actions from their acrobatics, and are applicable to a broad class of natural and robotic flying systems.

The two-body problem: Proprioception and motor control across the metamorphic divide

Like a rocket being propelled into space, evolution has engineered flies to launch into adulthood via multiple stages. Flies develop and deploy two distinct bodies, linked by the transformative process of metamorphosis. The fly larva is a soft hydraulic tube that can crawl to find food and avoid predators. The adult fly has a stiff exoskeleton with articulated limbs that enable long-distance navigation and rich social interactions. Because the larval and adult forms are so distinct in structure, they require distinct strategies for sensing and moving the body. The metamorphic divide thus presents an opportunity for comparative analysis of neural circuits. Here, we review recent progress toward understanding the neural mechanisms of proprioception and motor control in larval and adult Drosophila. We highlight commonalities that point toward general principles of sensorimotor control and differences that may reflect unique constraints imposed by biomechanics. Finally, we discuss emerging opportunities for comparative analysis of neural circuit architecture in the fly and other animal species.

Dynamic stability in hovering flight of insects with different sizes

Previous works on the flight dynamic stability of insects have focused on relatively large insects. Here, the longitudinal flight dynamic stability of two hovering miniature insects was computed. With the stability properties of the miniature insects from the present work and those of large insects from previous works, we studied the effects of insect size on the stability properties in the full range of insect sizes. The following results were obtained. Although the insects considered have a 30 000-fold difference in mass, their modal structure of flight stability is the same: an unstable oscillatory mode, a stable fast subsidence mode, and a stable slow subsidence mode; because of the unstable mode, the flight is unstable. An approximate analytical expression on the growth rate of the unstable mode as a function of insect mass (m) was derived. It shows that the time to double the initial values of disturbances (t_{d}) is proportional to the 0.17 power of the insect mass (m). That is, as m becomes smaller, t_{d} decreases (i.e., the instability becomes faster). This means that miniature insects need a faster nervous system to control the instability than larger insects. For example, the response time (represented by t_{d}) of a miniature insect, the gall midge (m≈0.05mg), needs to be faster by about 7 times than that of a larger insect, the hawk moth (m≈1600mg).

Effect and correction of control delay in longitudinal dynamics of insect hovering flight

Sensor-to-actuator delay is inevitable in any complex control system, be it one for a free-flying insect or a mimicking insectlike robotic flyer. In this work, we analyze the effects of control delay (latency) on the hovering performance of a model insect flyer, as exemplified by the hummingbird hawkmoth Re∼3000, and determine how control coefficients or gains may be modified to ameliorate the adverse effects of latency. The analyses are based on a simplified or reduced dynamic model of the hovering flyer. The longitudinal dynamics of the hovering flyer comprises the coupled forward (backward) and vertical translations and pitch rotation of the flyer, with kinematical wing actions being governed by proportional-differential (PD) closed-loop control. Keeping to the same PD control coefficients as a stable reference zero-delay case, the flight system becomes overly responsive at a small control delay, eventually diverging when delay approaches around one wing cycle. Stable hovering may be regained for control delay of up to several wingbeats by suitably reducing or softening the PD control coefficients. The results of the analyses are validated by a series of time-based simulations using the simplified dynamic model and a high-fidelity three-dimensional computational fluid dynamics with fluid structure-body interaction model of the hovering flyer. The simulations also show that noncyclic asymptotic oscillations about the mean equilibrium hovering state are enhanced with larger control delay. The analyses and simulations have helped us to gain a better understanding of the effects of control latency in insect free flight, which may be relevant for the design of mimetic insect flyers.

Multimodal integration across spatiotemporal scales to guide invertebrate locomotion

Locomotion is a hallmark of organisms that has enabled adaptive radiation to an extraordinarily diverse class of ecological niches, and allows animals to move across vast distances. Sampling from multiple sensory modalities enables animals to acquire rich information to guide locomotion. Locomotion without sensory feedback is haphazard, therefore sensory and motor systems have evolved complex interactions to generate adaptive behavior. Notably, sensory-guided locomotion acts over broad spatial and temporal scales to permit goal-seeking behavior, whether to localize food by tracking an attractive odor plume or to search for a potential mate. How does the brain integrate multimodal stimuli over different temporal and spatial scales to effectively control behavior? In this review, we classify locomotion into three ordinally ranked hierarchical layers that act over distinct spatiotemporal scales: stabilization, motor primitives, and higher-order tasks, respectively. We discuss how these layers present unique challenges and opportunities for sensorimotor integration. We focus on recent advances in invertebrate locomotion due to their accessible neural and mechanical signals from the whole brain, limbs and sensors. Throughout, we emphasize neural-level description of computations for multimodal integration in genetic model systems, including the fruit fly, Drosophila melanogaster, and the yellow fever mosquito, Aedes aegypti. We identify that summation (e.g. gating) and weighting-which are inherent computations of spiking neurons-underlie multimodal integration across spatial and temporal scales, therefore suggesting collective strategies to guide locomotion.

Bumblebees land remarkably well in red-blue greenhouse LED light conditions

Red-blue emitting LEDs have recently been introduced in greenhouses to optimise plant growth. However, this spectrum may negatively affect the performance of bumblebees used for pollination, because the visual system of bumblebees is more sensitive to green light than to red-blue light. We used high-speed stereoscopic videography to three-dimensionally track and compare landing manoeuvres of Bombus terrestris bumblebees in red-blue light and in regular, broad-spectrum white light. In both conditions, the landing approaches were interspersed by one or several hover phases, followed by leg extension and touchdown. The time between leg extension and touchdown was 25% (0.05 s) longer in red-blue light than in white light, caused by a more tortuous flight path in red-blue light. However, the total landing duration, specified as the time between the first hover phase and touchdown, did not differ between the light conditions. This suggests that the negative effects of red-blue light on the landing manoeuvre are confined to the final phase of the landing.This article has an associated First Person interview with the first author of the paper.

Sensory processing by motoneurons: a numerical model for low-level flight control in flies

Rhythmic locomotor behaviour in animals requires exact timing of muscle activation within the locomotor cycle. In rapidly oscillating motor systems, conventional control strategies may be affected by neural delays, making these strategies inappropriate for precise timing control. In flies, wing control thus requires sensory processing within the peripheral nervous system, circumventing the central brain. The underlying mechanism, with which flies integrate graded depolarization of visual interneurons and spiking proprioceptive feedback for precise muscle activation, is under debate. Based on physiological parameters, we developed a numerical model of spike initiation in flight muscles of a blowfly. The simulated Hodgkin–Huxley neuron reproduces multiple experimental findings and explains on the cellular level how vision might control wing kinematics. Sensory processing by single motoneurons appears to be sufficient for control of muscle power during flight in flies and potentially other flying insects, reducing computational load on the central brain during body posture reflexes and manoeuvring flight.

Hovering efficiency comparison of rotary and flapping flight for rigid rectangular wings via dimensionless multi-objective optimization

In this work, a multi-objective optimization framework is developed for optimizing low Reynolds number ([Formula: see text]) hovering flight. This framework is then applied to compare the efficiency of rigid revolving and flapping wings with rectangular shape under varying [Formula: see text] and Rossby number ([Formula: see text], or aspect ratio). The proposed framework is capable of generating sets of optimal solutions and Pareto fronts for maximizing the lift coefficient and minimizing the power coefficient in dimensionless space, explicitly revealing the trade-off between lift generation and power consumption. The results indicate that revolving wings are more efficient when the required average lift coefficient [Formula: see text] is low (<1 for [Formula: see text] and  <1.6 for [Formula: see text]), while flapping wings are more efficient in achieving higher [Formula: see text]. With the dimensionless power loading as the single-objective performance measure to be maximized, rotary flight is more efficient than flapping wings for [Formula: see text] regardless of the amount of energy storage assumed in the flapping wing actuation mechanism, while flapping flight is more efficient for [Formula: see text]. It is observed that wings with low [Formula: see text] perform better when higher [Formula: see text] is needed, whereas higher [Formula: see text] cases are more efficient at [Formula: see text] regions. However, for the selected geometry and [Formula: see text], the efficiency is weakly dependent on [Formula: see text] when the dimensionless power loading is maximized.

Limitations of rotational manoeuvrability in insects and hummingbirds: evaluating the effects of neuro-biomechanical delays and muscle mechanical power

Flying animals ranging in size from fruit flies to hummingbirds are nimble fliers with remarkable rotational manoeuvrability. The degrees of manoeuvrability among these animals, however, are noticeably diverse and do not simply follow scaling rules of flight dynamics or muscle power capacity. As all manoeuvres emerge from the complex interactions of neural, physiological and biomechanical processes of an animal's flight control system, these processes give rise to multiple limiting factors that dictate the maximal manoeuvrability attainable by an animal. Here using functional models of an animal's flight control system, we investigate the effects of three such limiting factors, including neural and biomechanical (from limited flapping frequency) delays and muscle mechanical power, for two insect species and two hummingbird species, undergoing roll, pitch and yaw rotations. The results show that for animals with similar degree of manoeuvrability, for example, fruit flies and hummingbirds, the underlying limiting factors are different, as the manoeuvrability of fruit flies is only limited by neural delays and that of hummingbirds could be limited by all three factors. In addition, the manoeuvrability also appears to be the highest about the roll axis as it requires the least muscle mechanical power and can tolerate the largest neural delays.

Free flight odor tracking in Drosophila: Effect of wing chemosensors, sex and pheromonal gene regulation

The evolution of powered flight in insects had major consequences for global biodiversity and involved the acquisition of adaptive processes allowing individuals to disperse to new ecological niches. Flies use both vision and olfactory input from their antennae to guide their flight; chemosensors on fly wings have been described, but their function remains mysterious. We studied Drosophila flight in a wind tunnel. By genetically manipulating wing chemosensors, we show that these structures play an essential role in flight performance with a sex-specific effect. Pheromonal systems are also involved in Drosophila flight guidance: transgenic expression of the pheromone production and detection gene, desat1, produced low, rapid flight that was absent in control flies. Our study suggests that the sex-specific modulation of free-flight odor tracking depends on gene expression in various fly tissues including wings and pheromonal-related tissues.

A review on locomotion robophysics: the study of movement at the intersection of robotics, soft matter and dynamical systems

Discovery of fundamental principles which govern and limit effective locomotion (self-propulsion) is of intellectual interest and practical importance. Human technology has created robotic moving systems that excel in movement on and within environments of societal interest: paved roads, open air and water. However, such devices cannot yet robustly and efficiently navigate (as animals do) the enormous diversity of natural environments which might be of future interest for autonomous robots; examples include vertical surfaces like trees and cliffs, heterogeneous ground like desert rubble and brush, turbulent flows found near seashores, and deformable/flowable substrates like sand, mud and soil. In this review we argue for the creation of a physics of moving systems-a 'locomotion robophysics'-which we define as the pursuit of principles of self-generated motion. Robophysics can provide an important intellectual complement to the discipline of robotics, largely the domain of researchers from engineering and computer science. The essential idea is that we must complement the study of complex robots in complex situations with systematic study of simplified robotic devices in controlled laboratory settings and in simplified theoretical models. We must thus use the methods of physics to examine both locomotor successes and failures using parameter space exploration, systematic control, and techniques from dynamical systems. Using examples from our and others' research, we will discuss how such robophysical studies have begun to aid engineers in the creation of devices that have begun to achieve life-like locomotor abilities on and within complex environments, have inspired interesting physics questions in low dimensional dynamical systems, geometric mechanics and soft matter physics, and have been useful to develop models for biological locomotion in complex terrain. The rapidly decreasing cost of constructing robot models with easy access to significant computational power bodes well for scientists and engineers to engage in a discipline which can readily integrate experiment, theory and computation.

Flight mechanics and control of escape manoeuvres in hummingbirds II. Aerodynamic force production, flight control and performance limitations

The superior manoeuvrability of hummingbirds emerges from complex interactions of specialized neural and physiological processes with the unique flight dynamics of flapping wings. Escape manoeuvring is an ecologically relevant, natural behaviour of hummingbirds, from which we can gain understanding into the functional limits of vertebrate locomotor capacity. Here, we extend our kinematic analysis of escape manoeuvres from a companion paper to assess two potential limiting factors of manoeuvring performance of hummingbirds 1) muscle mechanical power output and 2) delays in the neural sensing and control system. We focused on the magnificent hummingbird, (Eugenes fulgens, 7.8g) and black-chinned hummingbird (Archilochus alexandri, 3.1 g), which represent large and small species, respectively. We first estimated the aerodynamic forces, moments and the mechanical power of escape manoeuvres using measured wing kinematics. Comparing active-manoeuvring and passive-damping aerodynamic moments, we found that pitch dynamics were lightly damped and dominated by effect of inertia while roll dynamics were highly damped. To achieve observed closed-loop performance, pitch manoeuvres required faster sensorimotor transduction, as hummingbirds can only tolerate half the delay allowed in roll manoeuvres. Accordingly, our results suggested that pitch control may require a more sophisticated control strategy, such as those based on prediction. For the magnificent hummingbird, we estimated escape manoeuvres required muscle mass-specific power 4.5 times that during hovering. Therefore, in addition to the limitation imposed by sensorimotor delays, muscle power could also limit the performance of escape manoeuvres.

Flight mechanics and control of escape manoeuvres in hummingbirds I. Flight kinematics

Hummingbirds are nature‘s masters of aerobatic manoeuvres. Previous research shows hummingbirds and insects converged evolutionarily upon similar aerodynamic mechanisms and kinematics in hovering. Herein, we use three-dimensional kinematic data to begin to test for similar convergence of kinematics used for escape flight and to explore the effects of body size upon manoeuvring. We studied four hummingbird species in North America including two large species (magnificent hummingbird, Eugenes fulgens, 7.8 g and blue-throated hummingbird, Lampornis clemenciae, 8.0 g) and two smaller species (broad-billed hummingbird, Cynanthus latirostris, 3.4 g and black-chinned hummingbirds Archilochus alexandri, 3.1 g). Starting from a steady hover, hummingbirds consistently manoeuvred away from perceived threats using a drastic escape response that featured body pitch and roll rotations coupled with a large linear acceleration. Hummingbirds changed their flapping frequency and wing trajectory in all three degrees-of-freedom on stroke-by-stroke basis, likely causing rapid and significant alteration of the magnitude and direction of aerodynamic forces. Thus it appears that the flight control of hummingbirds does not obey the “helicopter model” that is valid for similar escape manoeuvres in fruit flies. Except for broad-billed hummingbirds, the hummingbirds had faster reaction times than those reported for visual feedback control in insects. The two larger hummingbird species performed pitch rotations and global-yaw turns with considerably larger magnitude than the smaller species, but roll rates and cumulative roll angles were similar among the four species.

Pitch perfect: how fruit flies control their body pitch angle

Flapping insect flight is a complex and beautiful phenomenon that relies on fast, active control mechanisms to counter aerodynamic instability. To directly investigate how freely-flying D. melanogaster control their body pitch angle against such instability, we perturb them using impulsive mechanical torques and film their corrective maneuvers with high-speed video. Combining experimental observations and numerical simulation, we find that flies correct for pitch deflections of up to 40° in 29±8 ms by bilaterally modulating their wings' front-most stroke angle in a manner well-described by a linear proportional-integral (PI) controller. Flies initiate this corrective process only 10±2 ms after the perturbation onset, indicating that pitch stabilization involves a fast reflex response. Remarkably, flies can also correct for very large-amplitude pitch perturbations–greater than 150°–providing a regime in which to probe the limits of the linear-response framework. Together with previous studies regarding yaw and roll control, our results on pitch show that flies' stabilization of each of these body angles is consistent with PI control