Tsevi Beatus’s research while affiliated with Hebrew University of Jerusalem and other places

In systems control, the dynamics of a system are governed by modulating its inputs to achieve a desired outcome. For example, to control the thrust of a quad-copter propeller the controller modulates its rotation rate, relying on a straightforward mapping between the input rotation rate and the resulting thrust. This mapping can be inverted to determine the rotation rate needed to generate a desired thrust. However, in complex systems, such as flapping-wing robots where intricate fluid motions are involved, mapping inputs (wing kinematics) to outcomes (aerodynamic forces) is nontrivial and inverting this mapping for real-time control is computationally impractical. Here, we report a machine-learning solution for the inverse mapping of a flapping-wing system based on data from an experimental system we have developed. Our model learns the input wing motion required to generate a desired aerodynamic force outcome. We used a sequence-to-sequence model tailored for time-series data and augmented it with a novel adaptive-spectrum layer that implements representation learning in the frequency domain. To train our model, we developed a flapping wing system that simultaneously measures the wing's aerodynamic force and its 3D motion using high-speed cameras. We demonstrate the performance of our system on an additional open-source dataset of a flapping wing in a different flow regime. Results show superior performance compared with more complex state-of-the-art transformer-based models, with 11% improvement on the test datasets median loss. Moreover, our model shows superior inference time, making it practical for onboard robotic control. Our open-source data and framework may improve modeling and real-time control of systems governed by complex dynamics, from biomimetic robots to biomedical devices.

Thermal soaring, a technique used by birds and gliders to utilize updrafts of hot air, is an appealing model-problem for studying motion control and how it is learned by animals and engineered autonomous systems. Thermal soaring has rich dynamics and nontrivial constraints, yet it uses few control parameters and is becoming experimentally accessible. Following recent developments in applying reinforcement learning methods for training deep neural-network (deep-RL) models to soar autonomously both in simulation and real gliders, here we develop a simulation-based deep-RL system to study the learning process of thermal soaring. We find that this process has learning bottlenecks, we define a new efficiency metric and use it to characterize learning robustness, we compare the learned policy to data from soaring vultures, and find that the neurons of the trained network divide into function clusters that evolve during learning. These results pose thermal soaring as a rich yet tractable model-problem for the learning of motion control.

Understanding the mechanisms of insect flight requires high quality data of free-flight kinematics, e.g., for comparative studies or genetic screens. While recent improvements in high-speed videography allow us to acquire large amounts of free-flight data, a significant bottleneck is automatically extracting accurate body and wing kinematics. Here, we present an experimental system and a hull reconstruction-reprojection algorithm for measuring the flight kinematics of fruit flies. The experimental system can automatically record hundreds of flight events per day. Our algorithm resolves a significant portion of the occlusions in this system by a reconstruction-reprojection scheme that integrates information from all cameras. Wing and body kinematics, including wing deformation, are then extracted from the hulls of the wing boundaries and body. This model-free method is fully automatic, accurate and open-source, and can be readily adjusted for different camera configurations or insect species.

Thermal soaring, a technique used by birds and gliders to utilize updrafts of hot air, presents an attractive model for developing biomimetic autonomous and unmanned aerial vehicles (UAVs) capable of long-endurance flight. Previous studies have employed machine- and deep-learning models to control gliding UAVs in simplified environments without horizontal winds. The resulting neural network models operate as ‘black boxes’, with little insight into their navigation policy or the structure of the problem. Here, we present a deep reinforcement-learning framework for autonomous glider control in a simulated environment with thermal updrafts and challenging horizontal winds. Compared with vulture flight data, the resulting autonomous agent spontaneously adopted a vulture-like soaring technique that successfully and robustly exploited thermal updrafts under horizontal winds up to 5 m/sec. This system enabled us to reveal the underlying structure of the thermal soaring problem, which consists of two critical bottlenecks that should be solved sequentially: achieving stable flight and flying near the thermal center. Additionally, the agent’s neural network divides into functional clusters that correlate with distinct behavioral modes during thermal searching and soaring. Our findings may contribute to the development of biomimetic UAVs with vulture-like efficiency and to understanding the structure and bottlenecks of other motion-based problems.

In many insect species, the thoracic exoskeletal structure plays a crucial role in enabling flight. In the dipteran indirect flight mechanism, thoracic cuticle acts as a transmission link between the flight muscles and the wings, and is thought to act as an elastic modulator: improving flight motor efficiency thorough linear or nonlinear resonance. But peering closely into the drivetrain of tiny insects is experimentally difficult, and the nature of this elastic modulation is unclear. Here, we present a new inverse-problem methodology to surmount this difficulty. In a data synthesis process, we integrate literature-reported rigid-wing aerodynamic and musculoskeletal data into a planar oscillator model for the fruit fly Drosophila melanogaster, and use this integrated data to identify several surprising properties of the fly’s thorax. We find that fruit flies likely have an energetic need for motor resonance: absolute power savings due to motor elasticity range from 0%–30% across literature-reported datasets, averaging 16%. However, in all cases, the intrinsic high effective stiffness of the active asynchronous flight muscles accounts for all elastic energy storage required by the wingbeat. The D. melanogaster flight motor should be considered as a system in which the wings are resonant with the elastic effects of the motor’s asynchronous musculature, and not with the elastic effects of the thoracic exoskeleton. We discover also that D. melanogaster wingbeat kinematics show subtle adaptions that ensure that wingbeat load requirements match muscular forcing. Together, these newly-identified properties suggest a novel conceptual model of the fruit fly’s flight motor: a structure that is resonant due to muscular elasticity, and is thereby intensely concerned with ensuring that the primary flight muscles are operating efficiently. Our inverse-problem methodology sheds new light on the complex behaviour of these tiny flight motors, and provides avenues for further studies in a range of other insect species.

Understanding the uncontrolled passive dynamics of flying insects is important for evaluating the constraints under which the insect flight control system operates and for developing biomimetic robots. Passive dynamics is typically analyzed using computational fluid dynamics (CFD) methods, relying on the separation of the linearized hovering dynamics into longitudinal and lateral parts. While the longitudinal dynamics are relatively understood across several insect models, our current understanding of the lateral dynamics is lacking, with a nontrivial dependence on wing–wing interaction and on the details of wing kinematics. Particularly, the passive stability of the fruit fly, D. melanogaster, which is a central model in insect flight research, has so far been analyzed using simplified quasi-steady aerodynamics and synthetic wing kinematics. Here, we perform a CFD-based lateral stability analysis of a hovering fruit fly, using accurately measured wing kinematics, and considering wing–wing interaction. Lateral dynamics are unstable due to an oscillating–diverging mode with a doubling time of 17 wingbeats. These dynamics are determined by wing–wing interaction and the wing elevation kinematics. Finally, we show that the fly's roll controller, with its one wingbeat latency, is consistent with the lateral instability. This work highlights the importance of accurate wing kinematics and wing–wing interactions in stability analyses and forms a link between such passive instability and the insects' controller.

Insect flight is a complex interdisciplinary phenomenon. Understanding its multiple aspects, such as flight control, sensory integration, physiology and genetics, often requires the analysis of large amounts of free flight kinematic data. Yet, one of the main bottlenecks in this field is automatically and accurately extracting such data from multi-view videos. Here, we present a model-based method for the pose estimation of free-flying fruit flies from multi-view high-speed videos. To obtain a faithful representation of the fly with minimum free parameters, our method uses a 3D model that includes two new aspects of wing deformation: a non-fixed wing hinge and a twisting wing surface. The method is demonstrated for free and perturbed flight. Our method does not use prior assumptions on the kinematics apart from the continuity of the wing pitch angle. Hence, this method can be readily adjusted for other insect species.

Structural resonance involves the absorption of inertial loads by a tuned structural elasticity: a process playing a key role in a wide range of biological and technological systems, including many biological and bio-inspired locomotion systems. Conventional linear and nonlinear resonant states typically exist at specific discrete frequencies and specific symmetric waveforms. This discreteness can be an obstacle to resonant control modulation: deviating from these states, by modulating waveform asymmetry or drive frequency, generally leads to losses in system efficiency. Here, we demonstrate a new strategy for achieving these modulations at no loss of energetic efficiency. Leveraging fundamental advances in nonlinear dynamics, we characterise a new form of structural resonance: band-type resonance, describing a continuous band of energetically optimal resonant states existing around conventional discrete resonant states. These states are a counterexample to the common supposition that deviation from a linear (or nonlinear) resonant frequency necessarily involves a loss of efficiency. We demonstrate how band-type resonant states can be generated via a spectral shaping approach: with small modifications to the system kinematic and load waveforms, we construct sets of frequency- and asymmetry-modulated resonant states that show equal energetic optimality to their conventional discrete analogues. The existence of these non-discrete resonant states in a huge range of oscillators—linear and nonlinear, in many different physical contexts—is a new dynamical systems phenomenon. It has implications not only for biological and bio-inspired locomotion systems but for a constellation of forced oscillator systems across physics, engineering, and biology.

Linear and nonlinear resonant states can be restrictive: they exist at particular discrete states in frequency and/or elasticity, under particular (e.g., simple-harmonic) waveforms. In forced oscillators, this restrictiveness is an obstacle to system design and control modulation: altering the system elasticity, or modulating the response, would both appear to necessarily incur a penalty to efficiency. In this work, we describe an approach for bypassing this obstacle. Using novel work-loop techniques, we prove and illustrate how certain classes of resonant optimisation problem lead to non-unique solutions. In a structural optimisation context, several categories of energetically-optimal elasticity are non-unique. In an optimal control context, several categories of energetically-optimal frequency are non-unique. For these classes of non-unique optimum, we can derive simple bounds defining the optimal region. These novel theoretical results have practical implications for the design and control of a range of biomimetic propulsion systems, including flapping-wing micro-air-vehicles: using these results, we can generate efficient forms of wingbeat modulation for flight control.

Linear and nonlinear resonant states can be restrictive: they exist at particular discrete states in frequency and/or elasticity, under particular (e.g., simple-harmonic) waveforms. In forced oscillators, this restrictiveness is an obstacle to system design and control modulation: altering the system elasticity, or modulating the response, would both appear to necessarily incur a penalty to efficiency. In this work, we describe an approach for bypassing this obstacle. Using novel work-loop techniques, we prove and illustrate how certain classes of resonant optimisation problem lead to non-unique solutions. In a structural optimisation context, several categories of energetically-optimal elasticity are non-unique. In an optimal control context, several categories of energetically-optimal frequency are non-unique. For these classes of non-unique optimum, we can derive simple bounds defining the optimal region. These novel theoretical results have practical implications for the design and control of a range of biomimetic propulsion systems, including flapping-wing micro-air-vehicles: using these results, we can generate efficient forms of wingbeat modulation for flight control.